Underactuated robotics: A review <s> Practical difficulties <s> Underactuated mechanical systems are those possessing fewer actuators than degrees of freedom. Examples of such systems abound, including flexible joint and flexible link robots, space robots, mobile robots, and robot models that include actuator dynamics and rigid body dynamics together. Complex internal dynamics, nonholonomic behavior, and lack of feedback linearizability are often exhibited by such systems, making the class a rich one from a control standpoint. In this article the author studies a particular underactuated system known as the Acrobot: a two-degree-of-freedom planar robot with a single actuator. The author considers the so-called swing up control problem using the method of partial feedback linearization. The author gives conditions under which the response of either degree of freedom may be globally decoupled from the response of the other and linearized. This result can be used as a starting point to design swing up control algorithms. Analysis of the resulting zero dynamics as well as analysis of the energy of the system provides an understanding of the swing up algorithms. Simulation results are presented showing the swing up motion resulting from partial feedback linearization designs. > <s> BIB001 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this article, we look at the excellent effect of vertical force as regards the stabilization of the inverted pendulum (IP) and demonstrate how the fuzzy control design methodology can be used to construct a hybrid fuzzy control system that incorporates PD control into a Takagi–Sugeno fuzzy control structure for stabilizing the IP via a vertical force. By gaining an intuitive understanding of the dynamics of the IP, the IP state space is fuzzily divided into six regions. In each region, a PD controller is designed to satisfy the stability conditions obtained by Lyapunov’s direct and indirect methods. It shows that the proposed hybrid fuzzy control scheme provides a more flexible and intuitive way to stabilize the IP via a vertical force. © 2005 Wiley Periodicals, Inc. <s> BIB002 </s> Underactuated robotics: A review <s> Practical difficulties <s> Abstract In this paper we discuss some design methods for the control of a class of underactuated mechanical systems. This class of systems includes gymnastic robots, such as the Acrobot, as well the classical cart-pole system. The systems considered here are nonminimum phase which greatly complicates the control design issues. Our design techniques combine nonlinear partial feedback linearization with Lyapunov methods based on saturation functions, switching and energy shaping. <s> BIB003 </s> Underactuated robotics: A review <s> Practical difficulties <s> We consider tracking control of a surface vessel with only two control inputs. The surface vessel model has certain similarities with chained form systems, but cannot be transformed to chained form. In particular, the model has a drift vector field as opposed to the drift-free chained form systems. It is shown, however, that methods developed for tracking control of chained form systems, can be used for developing a tracking control law for the surface vessel. Through a coordinate transformation the model is put in a triangular-like form which makes it possible to use integrator backstepping to develop a tracking control law. The control law steers both the position variables and the course angle of the surface vessel, providing semi-global exponential stabilization of the desired trajectory. <s> BIB004 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper considers a stabilizing hybrid scheme to control a class of underactuated mechanical systems. The hybrid controller consists of a collection of state feedback controllers plus a discrete-event supervisor. When the continuous-state hits a switching boundary, a new controller is applied to the plant. Lyapunov theory is used to determine the switching boundaries and to guarantee the stability of the closed-loop hybrid system. This approach is applied to the well-known swing up and balancing control problem of the inverted pendulum. <s> BIB005 </s> Underactuated robotics: A review <s> Practical difficulties <s> From the Publisher: ::: This book gives a unified treatment of classical input output stability theory and recent developments in nonlinear robust and passivity-based control. The synthesis between these areas is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this vantage-ground. The connection between L - gain and passivity via scattering is detailed." "The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with modeling and control by interconnection. Feedback equivalence to a passive system and resulting stabilization strategies are discussed." "The potential of L[subscript 2] - gain techniques in nonlinear control is demonstrated, including a compact treatment of the nonlinear H[subscript [infinity]] optimal control problem. <s> BIB006 </s> Underactuated robotics: A review <s> Practical difficulties <s> The authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft. They employ the inverse optimal control approach which circumvents the task of solving a Hamilton-Jacobi equation and results in a controller optimal with respect to a meaningful cost functional. The inverse optimality approach requires the knowledge of a control Lyapunov function and a stabilizing control law of a particular form. For the spacecraft problem, they are both constructed using the method of integrator backstepping. The authors give a characterization of (nonlinear) stability margins achieved with the inverse optimal control law. <s> BIB007 </s> Underactuated robotics: A review <s> Practical difficulties <s> Transportation of massive loads using overhead cranes can excite undesirable payload swinging. These oscillations have to be damped before other payload manipulation is done. A fuzzy logic controller moves the overhead crane along a desired path while ensuring that the payload is swing-free at the end of the motion. The control action is divided between displacement and swing controllers to enable tuning the controllers. The fuzzy controller is used with a swing-damped bang-bang motion profile based on the natural frequency of the payload is used that ensures that large amplitudes are not excited. Examples, along with comparisons with a PD controller, are included. Experimental implementation of the proposed controller is presented. <s> BIB008 </s> Underactuated robotics: A review <s> Practical difficulties <s> A non-linear model for an overhead crane system is derived which takes into account a combination of a trolley and a pendulum. The overall mathematical model obtained is simulated using MATLAB-SIMULINK. Open-loop simulations run on cases depending on whether the air resistance is taken into account or not, and whether the angle of oscillation is small or large, indicate the validity of such model, hence reflecting similar trends in industries which are concerned with material handling equipment. A hand-crafted fuzzy controller, which includes two rule bases, one for position control, the other for sway-angle control, was designed and successfully implemented on the above simulated model. Preliminary results are very encouraging, and indicate the feasibility of such a two rule base control strategy. The results obtained are presented, analysed and discussed. <s> BIB009 </s> Underactuated robotics: A review <s> Practical difficulties <s> We introduce a method that provides a nonlinear noncollocated output for trajectory tracking of a flexible one-link robot. The link is modeled as a finite-order Lagrangian system obtained from truncated modal analysis. This noncollocated output is derived based on viewing a flexible link robot arm as an underactuated mechanical system and then applying an appropriate change of coordinates that transforms the system into a cascade nonlinear system with a minimum-phase zero dynamics. The output is the angle of rotation augmented with the (generalized) saturation of the weighted amplitudes of the deflection modes of the flexible link. <s> BIB010 </s> Underactuated robotics: A review <s> Practical difficulties <s> Abstract The theme for a switching-type fuzzy sliding mode controller for the cart–pole system is developed in this paper. The control strategy is to make a vertical pole straight up and regulate the position of cart simultaneously. This system is nonlinear, unstable and nonminimum phase in consideration of these two control purposes; the conventional control algorithms are difficult to solve such a problem because only one control input can be utilized. By taking the experience of balancing a pole by a finger, we divide the dynamic response of the cart–pole system into approaching and departure conditions. Then the cart can be directed to the desired location with a balanced pole by switching two types of fuzzy sliding mode controllers. The feasibility and robustness of the proposed algorithm are demonstrated by computer simulations and actual experimental results. <s> BIB011 </s> Underactuated robotics: A review <s> Practical difficulties <s> Bounded feedback control laws are designed for stabilization and tracking of underactuated spacecraft. The flat outputs of the system are computed and are used to generate reference trajectories for the tracking problem. <s> BIB012 </s> Underactuated robotics: A review <s> Practical difficulties <s> The paper considers the design of a nonlinear controller for the double inverted pendulum (DIP), a system consisting of two inverted pendulums mounted on a cart. The swingup controller bringing the pendulums from any initial position to the unstable up-up position is designed based on passivity properties and energy shaping. While the swingup controller drives the DIP into a region of attraction around the unstable up-up position, the balance controller designed on the basis of the linearized model stabilizes the DIP at the unstable equilibrium. The simulation results show the effectiveness of the proposed nonlinear design method for the DIP system. <s> BIB013 </s> Underactuated robotics: A review <s> Practical difficulties <s> Abstract To deal with the swinging up and balancing control for an under-actuated robot, Pendubot, a new fuzzy logical control method is proposed in this paper. Two separate fuzzy reasoning control laws are employed for the tasks of swinging up and balance control. The proposed control scheme is tested by both simulations and hardware experiments. Hardware experimental results show the applicability of the proposed scheme. <s> BIB014 </s> Underactuated robotics: A review <s> Practical difficulties <s> Abstract In this paper, a new fuzzy antiswing control scheme is proposed for a three-dimensional overhead crane. The proposed control consists of a position servo control and a fuzzy-logic control. The position servo control is used to control crane position and rope length, and the fuzzy-logic control is used to suppress load swing. The proposed control guarantees not only prompt suppression of load swing but also accurate control of crane position and rope length for simultaneous travel, traverse, and hoisting motions of the crane. Furthermore, the proposed control provides practical gain tuning criteria for easy application. The effectiveness of the proposed control is shown by experiments with a three-dimensional prototype overhead crane. <s> BIB015 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, a fuzzy disturbance observer (FDO) is developed and its application to the control of a nonlinear system under the internal and external disturbances is presented. To construct the FDO, two parameter tuning methods are proposed and shown to be useful in adjusting the parameters of the FDO. The first tuning method employs the disturbance observation error to guarantee that the FDO monitors the unknown disturbance. The next one enlarges the concept of error and introduces augmented error to guarantee that the FDO monitors the disturbance and the control objective is achieved. In addition, the relationships between the suggested FDO-based control and the conventional adaptive fuzzy controls reported in the previous literatures are discussed and it is shown in a rigorous manner that the disturbance observation error or the augmented error converges to a region of which size can be kept arbitrarily small. Finally, some examples and computer simulation results are presented to illustrate the effectiveness and the applicability of the FDO. <s> BIB016 </s> Underactuated robotics: A review <s> Practical difficulties <s> We propose a method of fuzzy rule extraction for switching partly stable controllers (PSCs) for online operations of underactuated manipulators. The fuzzy rule base of switching the PSCs is optimized using GA and the optimization is performed off-line. Design parameters of the fuzzy rules are encoded into chromosomes and shapes of the Gaussian functions are evolved to minimize the angular position errors. The angular position errors are used as the inputs to the Gaussian membership functions in the antecedent part and the one index of the PSCs is assigned in the consequent part of the fuzzy reasoning. Then, this trained rule base can be brought into the online operation of the underactuated manipulator. The effectiveness of the concept is illustrated by taking a 2-DOF RR planar manipulator and results show the effectiveness of the proposed control methodology. <s> BIB017 </s> Underactuated robotics: A review <s> Practical difficulties <s> Swing up and balance control are two interesting control problems for the Pendubot. Many studies have been conducted for swing up control of the Pendubot. A few results have been reported for feedback stabilization of the Pendubot. In this paper, we apply a new hybrid controller for feedback stabilization of the Pendubot. It is well-known that it is impossible to use smooth feedback to stabilize a class of underactuated mechanical systems around their equilibra, even locally. Various nonsmooth controllers have been presented for feedback stabilization of this type of system. However, most of the studies are either based on theoretical proofs or simulations. There is a strong need for experimental study. The Pendubot arises as a special test bed for this purpose. This experimental study has a particular interest for feedback stabilization of underactuated mechanical systems that are not feedback stabilizable using smooth control. <s> BIB018 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper studies the global tracking problem for an underactuated ship with only two propellers. Under sufficient conditions of persistent excitation, two constructive solutions are proposed by application of Lyapunov's direct method. Both solutions exploit the inherent cascade interconnected structure of the ship dynamics and generate explicit Lyapunov functions. A common feature of the second solution and the recent cascade approach of Lefeber (Tracking control of nonlinear mechanical systems, Ph.D. Thesis, University of Twente, 2000) is that global exponential tracking is achieved, but at the expense of transient performance. Extension to unmeasured thruster dynamics is also considered. Simulation results validate the proposed tracking methodology. <s> BIB019 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper introduces a new concept for designing a fuzzy logic based switching controller in order to control underactuated manipulators. The proposed controller employs elemental controllers, which are designed in advance. Parameters of both antecedent and consequent parts of a fuzzy indexer are optimized by using evolutionary computation, which is performed off-line. Design parameters of the fuzzy indexer are encoded into chromosomes, i.e., the shapes of the Gaussian membership functions and corresponding switching indices of the consequent part are evolved to minimize the angular position errors. Such parameters are trained for different initial configurations of the manipulator and the common rule base is extracted. Then, these trained fuzzy rules can be brought into the online operations of underactuated manipulators. 2-DOF underactuated manipulator is taken into consideration so as to illustrate the design procedure. Computer simulation results show that the new methodology is effective in designing controllers for underactuated robot manipulators. <s> BIB020 </s> Underactuated robotics: A review <s> Practical difficulties <s> This note develops a nonlinear output-feedback controller to force a nonminimum phase, underactuated vertical take-off and landing aircraft to globally asymptotically track a reference trajectory generated by a reference model. The control development is based on a global exponential observer, some global coordinate transformations, Lyapunov's direct method and an extension of the backstepping technique. Interestingly, the proposed methodology also yields new results for the previously studied problems of stabilization and output tracking or regulation. Numerical simulations illustrate the effectiveness of the proposed controller. <s> BIB021 </s> Underactuated robotics: A review <s> Practical difficulties <s> As an effective transportation tool, overhead crane is considered for transporting payloads effectively and safely. Two sliding mode controllers are designed for two control inputs of overhead crane system: one is proposed to control hoisting and lowering suspended payload, and the other is proposed to control both trolley positioning and payload swaying. Considering the second sliding mode controller is used to control two degrees of freedom (DOFs), a fuzzy tuning algorithm is proposed to dynamically adjust the coupling factor between the two DOFs to improve system performance. These two controllers guarantee that the payload track the predefined trajectory, are transported safely as fast and accurately as possible with minimum swing angle, and are placed at the appropriate position. Simulations are performed with these two proposed sliding mode controllers and the results show their effectiveness. <s> BIB022 </s> Underactuated robotics: A review <s> Practical difficulties <s> Discusses a modification of the Newton algorithm applied to nonholonomic motion planning with energy optimization. The energy optimization is performed either by optimizing motion in the null space of the Jacobian matrix derived from the nonholonomic system or coupling this motion with movement toward the goal. Resulting controls are smooth and easily generated by motors or thrusters. The two methods can be used, when kinematics are considered, to steer any driftless nonholonomic systems particular free-floating objects, underactuated manipulators, mobile robots (with trailers). Similarities and differences are also discussed in the Newton algorithm for holonomic and nonholonomic systems. <s> BIB023 </s> Underactuated robotics: A review <s> Practical difficulties <s> Ball and plate system is the extension of traditional ball and beam system. In this paper, a trajectory planning and tracking problem of ball and plate system is put forward to proof-test diverse control schemes. Firstly, we derive the mathematical model of the ball and plate system in detail. Then a hierarchical fuzzy control scheme is proposed to deal with this problem. Our scheme is composed of three levels. The lowest level is a TS type fuzzy tacking controller; the middle level is a fuzzy supervision controller that takes actions in extreme situations; and the top level is a fuzzy planning controller that determines the desired trajectory. In order to optimize the ball's moving trajectory, the genetic algorithm is introduced to adjust the output membership functions of the fuzzy planning controller. Simulation results have shown that the hierarchical fuzzy control scheme can control the ball from a point to another without hitting the obstacles and in the least time. <s> BIB024 </s> Underactuated robotics: A review <s> Practical difficulties <s> A novel concept for designing a fuzzy logic-based switching controller to control underactuated manipulators is presented. The proposed controller employs elemental controllers, which are designed in advance. Parameters of both antecedent and consequent parts of a fuzzy indexer are optimized by using evolutionary computation. Design parameters of the fuzzy indexer are encoded into chromosomes, i.e., the shapes of the Gaussian membership functions and corresponding switching laws of the consequent part are evolved to minimize the angular position errors. Then, these trained fuzzy rules can be brought into the online operation of underactuated manipulators. Simulation results show that the new methodology is effective in designing controllers for underactuated robot manipulators. <s> BIB025 </s> Underactuated robotics: A review <s> Practical difficulties <s> The overhead crane exhibits the double-pendulum dynamics because of the large-mass hook. The nonlinear dynamic model of the double-pendulum-type overhead crane is built using the Lagrangian method. Several properties of the system model such as the underactuated property, the passivity, and its two nature frequencies are analyzed. An adaptive sliding mode fuzzy control method is proposed for double-pendulum-type overhead crane. The method greatly reduces the rules of regular fuzzy logic controller and well utilizes some adaptive methods of sliding mode controller. Simulation results illustrate the complex system dynamics of the double-pendulum-type overhead crane and the proposed control algorithm. <s> BIB026 </s> Underactuated robotics: A review <s> Practical difficulties <s> An adaptive fuzzy sliding control scheme is proposed to control a passive robotic manipulator. The motivation for the design of the adaptive fuzzy sliding controller is to eliminate the chattering and the requirement of pre-knowledge on bounds of error associated with the conventional sliding control. The stability and convergence of the adaptive fuzzy sliding controller is proven both theoretically and practically by simulations. A three-link passive manipulator model with two unactuated joints is derived to be used in the simulations. Simulation results demonstrate that the proposed system is robust against structured and unstructured uncertainties. <s> BIB027 </s> Underactuated robotics: A review <s> Practical difficulties <s> A nonlinear-optimal control strategy is devised using Hamilton-Jacobi formulation for tracking attitude maneuvers of rigid- asymmetric spacecraft. The exact motion model employs kinematical representation by the modified Rodrigues parameters (MRP) for large principal rotations. For tracking a constant attitude trajectory, an infinite-horizon optimal control problem is posed, wherein nonlinear feedforward and feedback control torques minimize a performance index with a quadratic control cost and a fourth-order attitude and angular-velocity error cost. Closed-form solution is obtained employing a Lyapunov function of the same form as the error cost, and by solving the Hamilton-Jacobi equation. Numerical results are presented for a practical tracking case with arbitrarily large initial conditions and desired state. <s> BIB028 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper presents a general overview of the technological fields of mechatronic, robotic, components for automation and control. Five technical areas are considered: component and instruments, mechatronic, robotics, cost oriented automation and human-machine systems. The paper addresses their current key problems and the recent major accomplishments. At last the most promising forecasted development and applications are considered. <s> BIB029 </s> Underactuated robotics: A review <s> Practical difficulties <s> A composite sliding mode fuzzy control (CSMFC) approach is proposed for the underactuated double-pendulum-type overhead crane (DPTOC). The nonlinear dynamic model of DPTOC is built using Lagrangian method. The composite sliding mode function (CSMF) consists of three sliding mode functions that are used to decouple the complex DPTOC. In the CSMFC, CSMF works as the antecedent and control variable works as the consequent. The proposed control approach greatly reduces the complexity to design a controller for complex underactuated systems. The control system stability is analyzed for DPTOC through variable structure control theory. Simulation results illustrate the validity of proposed control algorithm. <s> BIB030 </s> Underactuated robotics: A review <s> Practical difficulties <s> A design method using hierarchical fuzzy sliding-mode (HFSM) decoupling control is proposed to achieve system stability and favorable decoupling performance for a class of nonlinear systems. In this approach, the nonlinear system is decoupled into several subsystems and the state response of each subsystem can be designed to be governed by a corresponding sliding surface. Then the whole system is controlled by a hierarchical sliding-mode controller. In this design, an adaptive law is derived based on the Lyapunov function to tune the coupling factor of the hierarchical sliding-mode controller so as to achieve favorable decoupling performance with guaranteed stability. The proposed design method is applied to investigate the decoupling control of a double inverted pendulum system. Simulations are performed and a comparison between the proposed HFSM decoupling control and a conventional fuzzy sliding-mode (FSM) decoupling control is presented to demonstrate the effectiveness of the proposed design method. <s> BIB031 </s> Underactuated robotics: A review <s> Practical difficulties <s> An adaptive sliding mode fuzzy control approach is proposed for a two-dimensional overhead crane. System linearization transforms the two-dimensional system to two independent systems: X-direction transport system and Y-direction transport system. Both the two systems are with the same dynamic model and include two subsystems: positioning subsystem and anti-swing subsystem. Combining SMC's robustness and FLC's independence of system model, a sliding mode fuzzy control approach is proposed for both X-direction transport and Y-direction transport. According to the influences on system dynamic performance, both the slope of sliding mode surface and the coordination between the two subsystems are automatically tuned by real time fuzzy inference respectively. The effectiveness of the proposed control approach is demonstrated by experiments with a two-dimensional prototype overhead crane. (c) 2005 Elsevier Ltd. All rights reserved. <s> BIB032 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, a new cascade fuzzy sliding-mode controller (CFSMC) for a class of uncertain underactuated systems is presented. Firstly, two states are chosen to construct the first-layer sliding-mode surface which can be considered as a general state variable. Then the first-level sliding surface and one of the left state variables are used to construct the second-layer sliding surface. This process continues till the last-level sliding surface is obtained. Considering there exists uncertainty in the system's model, fuzzy logic is used as an approximator to identify the uncertainty. Using Lyapunov law, we derive the sliding-mode control law and the related parameters adaptive law of fuzzy logic. The CFSMC can guarantee the stability of all the sliding surfaces, and the simulation results show the validity of this method. <s> BIB033 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper a new fuzzy PI+PD controller, which includes a Dynamic Switching Fuzzy System (DSFS), is applied to swing-up an underactuated mechanism: the pendubot. This mechanism consists of a double pendulum actuated only at the first joint. This new controller and its real-time application to the pendubot constitute our original contribution. <s> BIB034 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this brief, we address adaptive fuzzy control of the inverted-pendulum on a cart problem as an underactuated mechanical system. Many of the schemes presented in the adaptive fuzzy control literature tackle the problem as a second-order system based on feedback linearization. Such schemes render unstable zero dynamics for the cart-pole systems which hinders experimental implementation. The paradigm presented is also based on a feedback linearizing (FBL) scheme, yet it ensures system stabilization. A damping term and an adaptive fuzzy control term are added to guarantee asymptotic stability and to account for disturbances. Experimental results illustrate the success of the proposed controller in stabilization and cart-position tracking of a reference trajectory <s> BIB035 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper presents the fuzzy logic based method to control the trolley cranes. The information, including the position of trolley, load swing and the differences between the present and previous signals, are applied to derive the proper power to drive the trolley. An easy but effective switching algorithm is investigated to improve the control of trolley and suppress the load swing in this paper. This also helps to enhance the control power of the crane to depart from the deadzone. Finally, several experiments through the scaled trolley crane demonstrate the effectiveness of the scheme. <s> BIB036 </s> Underactuated robotics: A review <s> Practical difficulties <s> Since the dynamic characteristics of a nonlinear inverted-pendulum mechanism are highly nonlinear, it is difficult to design a suitable control system that realizes real time stabilization and accurate tracking control at all time. In this study, a robust fuzzy-neural-network (FNN) control system is implemented to control a dual-axis inverted-pendulum mechanism that is driven by permanent magnet (PM) synchronous motors. The energy conservation principle is adopted to build a mathematical model of the motor-mechanism-coupled system. Moreover, a robust FNN control system is developed for stabilizing and tracking control of the dual-axis inverted-pendulum system. In this control system, a FNN controller is used to learn an equivalent control law as in the traditional sliding-mode control, and a robust controller is designed to ensure the near total sliding motion through the entire state trajectory without a reaching phase. The salient advantages of this FNN-based control scheme are as follows. 1) It does not require a perfect knowledge of system uncertainties so that this brings a high level of autonomy to the overall system and make the use of this control scheme very attractive for real time applications. 2) All adaptive learning algorithms in this control system are derived in the sense of Lyapunov stability analysis, so that system-tracking stability can be guaranteed in the closed-loop system. 3) Not only the weight vector in the rule-to-output layer are adjusted on line but also the mean and the standard deviation of Gaussian functions in the membership function layer. This training scheme will increase the learning capability of the FNN. 4) An adaptive bound estimation algorithm is investigated to relax the requirement for the bound of uncertain term including the minimum reconstructed error, higher-order term in Taylor series, and network parameters approximation error. The effectiveness of the proposed control strategy can be verified by numerical simulation and experimental results. <s> BIB037 </s> Underactuated robotics: A review <s> Practical difficulties <s> This brief addresses the problem of controlling the planar position and orientation of an autonomous underactuated surface vessel. Under realistic assumptions, we show, first, that there exists a natural change of coordinates that transforms the whole dynamical system into a cascade nonlinear system, and, second, the control problem of the resulting system can be reduced to the stabilization of a third-order chained form. A time-invariant discontinuous feedback law is derived to guarantee global uniform asymptotic stabilization of the system to the desired configuration. The construction of such a controller is based on the backstepping design approach. A simulation example is included to demonstrate the effectiveness of the suggested approach <s> BIB038 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the system from an initial to a terminal state. We consider systems evolving on general manifolds. The class of nonholonomic systems we study in this paper includes, in particular, wheeled-type vehicles, which are important for many robotic locomotion systems. The two special aspects of this optimal control problem are the nonholonomic constraints and under-actuation. Nonholonomic constraints restrict the evolution of the system to a distribution on the manifold. The nonholonomic connection is used to express the constrained equations of motion. Furthermore, it is used to take variations of the cost functional. Many robotic systems are under-actuated since control inputs are usually applied through the robot's internal configuration space only. While we do not consider symmetries with respect to group actions in this paper, the fact that the system is under-actuated is taken into account in our problem formulation. This allows one to compute reaction forces due to any inputs applied in directions orthogonal to the constraint distribution. We illustrate our ideas by considering a simple example on a three-dimensional manifold. <s> BIB039 </s> Underactuated robotics: A review <s> Practical difficulties <s> Overhead cranes are common industrial structures that are used in many factories and harbors. They are usually operated manually or by some conventional control methods, such as the optimal and PLC-based methods. The theme of this paper is to provide an effective all-purpose adaptive fuzzy controller for the crane. This proposed method does not need the complex dynamic model of the crane system, but it uses trolley position and swing angle information instead to design the fuzzy controller. An adaptive algorithm is provided to tune the free parameters in the crane control system. The ways to speed the transportation and reduce the computational efforts are also given. Therefore, the designing procedure of the proposed controller will be very easy. External disturbance, such as the wind and the hit, which always deteriorates the control performance, is also discussed in this paper to verify the robustness of the proposed adaptive fuzzy algorithm. At last, several experimental results with different wire length and payload weight compare the feasibility and effectiveness of the proposed scheme with conventional methods <s> BIB040 </s> Underactuated robotics: A review <s> Practical difficulties <s> The research focuses on the issue of controlling a manipulator attached to a deployment, which typically exhibits compliance due to its mechanical nature. The problem is generalized as a motion control of a robotic manipulator attached to oscillatory bases. Due to the complexity of this problem, we decompose the control task into two subtasks and distribute them over two different levels. In the design of hierarchical fuzzy control structure, the lower level controllers take into account each subsystem ignoring the interactions among them, while the upper level controller handles subsystem interactions. The upper level coordinator to deal with the model reduction error and makes the supervisory decision to the lower level. Moreover, the supervisory fuzzy rule set is used to adjust the correction factors of the hierarchical fuzzy controller to achieve better performance. Consequently, it is shown that the proposed control model offers several implementation advantages such as less on-line computation time, reduced effect of overshoot and chattering, and a fast convergent rate in simulation. The results of this study can be feasible to various mechanical systems, such as mobile robot, gantry cranes, underwater robot, and other dynamic systems mounted on oscillatory bases. <s> BIB041 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper proposes fuzzy moving sliding surface (FMSS) approach to the hierarchical sliding mode control (HSMC) for a class of second-order under-actuated systems. The HSMC design is based on using separate first-level sliding surfaces for two subsystems that are combined in the second-level comprising a unique control input for both subsystems and therefore, it necessitates several design parameters to be obtained after a time-consuming trial-and-error procedure. In this study, we propose both the sliding surface coefficients and the coupling ratio between the sliding surfaces, which are used by the HSMC method, to be obtained by fuzzy logic control (FLC) method using FMSS approach. Computer simulation studies have shown that the proposed control approaches are able to determine necessary coefficients dynamically. <s> BIB042 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper presents results on the global structure of the time optimal trajectories of the planar pendulum on a cart. Relying on the geometric theory of time optimal synthesis, we provide a discontinuous feedback giving optimal solutions for any initial data. <s> BIB043 </s> Underactuated robotics: A review <s> Practical difficulties <s> The behavior of many mechanical systems, such as overhead cranes, can be predicted through intuitive observation of their motion under various forces. Mathematical modeling of an overhead crane shows that it is highly coupled. Nonetheless, it is surprisingly easy for an experienced crane operator to drive payloads to target positions with minimal cable swing. This observation naturally promotes the use of fuzzy logic to control overhead cranes. Traditionally, fuzzy logic controllers of overhead cranes were presented for specific crane system/motion parameters. This work presents a novel approach for automatically creating anti-swing fuzzy logic controllers for overhead cranes with hoisting. The model of the crane includes the distributed mass of the cable. The presented approach uses the inverse dynamics of the overhead crane and the desired motion parameters to determine the ranges of the variables of the controllers. The control action is distributed among three fuzzy logic controllers (FLCs): The trave... <s> BIB044 </s> Underactuated robotics: A review <s> Practical difficulties <s> Overhead cranes are typically operated manually or via conventional control methods, such as PD-, optimal- and PLC-based method. This study presents a novel method that accelerates transportation and minimizes the payload swing of the overhead cranes. Based on the inertia theorem, this method does not need a complex dynamic model for a crane system, but rather uses trolley position and swing angle data to design the proposed fuzzy projection controller. An enhanced fuzzy algorithm is also utilized to eliminate the deadzone problem. Last, the feasibility and effectiveness of the proposed scheme are compared with those of the conventional PD and nonlinear coupling methods. <s> BIB045 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper presents and analyzes a cascade direct adaptive fuzzy control (DAFC) scheme for a two-axis inverted-pendulum servomechanism. Because the dynamic characteristic of the two-axis inverted-pendulum servomechanism is a nonlinear unstable nonminimum-phase underactuated system, it is difficult to design a suitable control scheme that simultaneously realizes real-time stabilization and accurate tracking control, and it is not easy to directly apply conventional computed torque strategies to this underactuated system. Therefore, the cascade DAFC scheme including inner and outer control loops is investigated for the stabilizing and tracking control of a nonlinear two-axis inverted-pendulum servomechanism. The goal of the inner control loop is to design a DAFC law so that the stick angle vector can fit the stick angle command vector derived from the stick angle reference model. In the outer loop, the reference signal vector is designed via an adaptive path planner so that the cart position vector tracks the cart position command vector. Moreover, all adaptive algorithms in the cascade DAFC system are derived using the Lyapunov stability analysis, so that system stability can be guaranteed in the entire closed-loop system. Relying on this cascade structure, the stick angle and cart position tracking-error vectors will simultaneously converge to zero. Numerical simulations and experimental results are given to verify that the proposed cascade DAFC system can achieve favorable stabilizing and tracking performance and is robust with regard to system uncertainties. <s> BIB046 </s> Underactuated robotics: A review <s> Practical difficulties <s> Because the dynamic characteristic of a two-axis inverted-pendulum servomechanism is a nonlinear underactuated system, it is difficult to design a suitable control scheme that realizes real-time stabilization and accurate tracking control simultaneously. In general, the techniques developed for fully actuated systems cannot be used directly in underactuated systems. In this study, a cascade adaptive fuzzy sliding-mode control (AFSMC) scheme including inner and outer control loops is investigated for the stabilizing and tracking control of a nonlinear two-axis inverted-pendulum servomechanism. The aim of the inner control loop is to design an AFSMC law with fuzzy estimators so that the stick-angle vector can fit the stick-angle command vector derived from the stick-angle reference model. In the outer loop, the reference signal vector is designed via a fuzzy path-planning scheme so that the cart position vector tracks the cart-position command vector and the stick-angle tracking-error vector converges to zero simultaneously. All adaptive algorithms in the cascade AFSMC system are derived in the sense of Lyapunov stability analysis, so that system stability can be guaranteed in the entire closed-loop system. The effectiveness of the proposed control strategy is verified by numerical simulations and experimental results, and the superiority of the cascade AFSMC system is indicated in comparison with a cascade sliding-mode control system. <s> BIB047 </s> Underactuated robotics: A review <s> Practical difficulties <s> We present a global solution for an optimal feedback controller of the underactuated Heisenberg system or nonholonomic integrator. Employing a recently developed technique based on generating functions appearing in the Hamilton-Jacobi theory, we circumvent a singularity caused by under actuation to develop a nonlinear optimal feedback control in an implicitly analytical form. The systematic procedure to deal with under actuation indicates that generating functions should be effective tools for solving general underactuated optimal control problems. <s> BIB048 </s> Underactuated robotics: A review <s> Practical difficulties <s> Unlike statically stable wheeled mobile robots, dynamically stable mobile robots can have higher centers of gravity, smaller bases of support and can be tall and thin resembling the shape of an adult human. This paper concerns the ballbot mobile robot, which balances dynamically on a single spherical wheel. The ballbot is omni-directional and can also rotate about its vertical axis (yaw motion). It uses a triad of legs to remain statically stable when powered off. This paper presents the evolved design with a four-motor inverse mouse-ball drive, yaw drive, leg drive, control system, and results including dynamic balancing, station keeping, yaw motion while balancing, and automatic transition between statically stable and dynamically stable states. <s> BIB049 </s> Underactuated robotics: A review <s> Practical difficulties <s> The ballbot is a dynamically stable mobile robot that moves on a single spherical wheel and is capable of omnidirectional movement. The ballbot is an underactuated system with nonholonomic dynamic constraints. The authors propose an offline trajectory planning algorithm that provides a class of parametric trajectories to the unactuated joint in order to reach desired static configurations of the system with regard to the dynamic constraint. The parameters of the trajectories are obtained using optimization techniques. A feedback controller is proposed that ensures accurate trajectory tracking. The trajectory planning algorithm and tracking controller are validated experimentally. The authors also extend the offline trajectory planning algorithm to a generalized case of motion between non-static configurations. <s> BIB050 </s> Underactuated robotics: A review <s> Practical difficulties <s> This article proposes a simple but effective way to control 3D overhead crane. The proposed method uses PID control at the start for rapid transportation and fuzzy control with deadzone compensation when the crane is close to the goal for precise positioning and moving the load smoothly. Only the remaining distance and projection of swing angle are applied to design the fuzzy controller. No plant information of crane is necessary in this approach. Therefore, the proposed method greatly reduces the computational efforts. Several experiments illustrated the encouraging effectiveness of the proposed method through a scaled 3D crane model. The nonlinear disturbance, such as abrupt collision, is also taken into account to check the robustness of the proposed method. <s> BIB051 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, the stability analysis of the GA-based adaptive fuzzy sliding model controller for a nonlinear system is presented. First, an uncertain and nonlinear plant for the tracking of a reference trajectory is well approximated and described via the reference model and the fuzzy model involving fuzzy logic control rules. Next, the difficulty in designing a fuzzy sliding mode controller (FSMC) capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. The initial values of the consequent parameter vector are decided via the genetic algorithm. After this, a modified adaptive law can be adopted to find the best high-performance parameters for the fuzzy sliding model controller. The adaptive fuzzy sliding model controller is derived to simultaneously stabilize and control the system. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov's direct method. Finally, a numerical simulation is provided as an example to demonstrate the control methodology. <s> BIB052 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper investigates the tracking control of an electrically driven nonholonomic mobile robot with model uncertainties in the robot kinematics, the robot dynamics, and the wheel actuator dynamics. A robust adaptive controller is proposed with the utilization of adaptive control, backstepping and fuzzy logic techniques. The proposed control scheme employs the adaptive control approach to design an auxiliary wheel velocity controller to make the tracking error as small as possible in consideration of uncertainties in the kinematics of the robot, and makes use of the fuzzy logic systems to learn the behaviors of the unknown dynamics of the robot and the wheel actuators. The approximation errors and external disturbances can be efficiently counteracted by employing smooth robust compensators. A major advantage of the proposed method is that previous knowledge of the robot kinematics and the dynamics of the robot and wheel actuators is no longer necessary. This is because the controller learns both the robot kinematics and the robot and wheel actuator dynamics online. Most importantly, all signals in the closed-loop system can be guaranteed to be uniformly ultimately bounded. For the dynamic uncertainties of robot and actuator, the assumption of ldquolinearity in the unknown parametersrdquo and tedious analysis of determining the ldquoregression matricesrdquo in the standard adaptive robust controllers are no longer necessary. The performance of the proposed approach is demonstrated through a simulation example. <s> BIB053 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper presents a fuzzy-control method for the motion control of an acrobot. First, an explanation is given of the singularity that arises when a motion control law based on a Lyapunov function has an integrated control objective for energy and posture. Then, a fuzzy controller is designed that solves the singularity problem through regulation of a design parameter in the control law. Finally, an additional fuzzy controller is designed that improves the control performance through regulation of another design parameter in the control law. Simulation results demonstrate the effectiveness of this integrated fuzzy-control strategy. <s> BIB054 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, adaptive fuzzy logic control of dynamic balance and motion is investigated for wheeled inverted pendulums with parametric and functional uncertainties. The proposed adaptive fuzzy logic control based on physical properties of wheeled inverted pendulums makes use of a fuzzy logic engine and a systematic online adaptation mechanism to approximate the unknown dynamics. Based on Lyapunov synthesis, the fuzzy control ensures that the system outputs track the given bounded reference signals to within a small neighborhood of zero, and guarantees semi-global uniform boundedness of all closed-loop signals. The effectiveness of the proposed control is verified through extensive simulations. <s> BIB055 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper focuses on the design of a dynamic Petri recurrent fuzzy neural network (DPRFNN), and this network structure is applied to the path-tracking control of a nonholonomic mobile robot for verifying its validity. In the DPRFNN, the concept of a Petri net and the recurrent frame of internal-feedback loops are incorporated into a traditional FNN to alleviate the computation burden of parameter learning and to enhance the dynamic mapping of network ability. Moreover, the supervised gradient-descent method is used to develop the online-training algorithm for the DPRFNN control. In order to guarantee the convergence of path-tracking errors, analytical methods based on a discrete-type Lyapunov function are proposed to determine varied learning rates for DPRFNN. In addition, the effectiveness of the proposed DPRFNN control scheme under different moving paths is verified by experimental results, and its superiority is indicated in comparison with FNN, RFNN, Petri FNN, and PRFNN control systems. <s> BIB056 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper we propose a new fuzzy logic controller (FLC) for unicycle control. The FLC design integrates the linear quadratic regulator (LQR) and the gain-scheduling approach. By comparing FLC with the LQR designed around an operating point, the FLC coefficients can be easily tuned in a systematic way. The new FLC design aims at achieving three objectives: overcoming the difficulty in tuning the FLC coefficients, making full use of degrees of freedom in LQR design with weighting matrices, and applying gain scheduling to FLC by associating LQR weighting matrices with the variation of the operating point. The new FLC is applied to a unicycle that consists of a wheel and a saddle. Only one actuator is used to generate a torque on the wheel, and the saddle is treated as an inverse pendulum. We first study the dynamic characteristics of the unicycle, that is essentially an under-actuated mechanism, by applying input-output feedback linearization. It is shown that the zero dynamics of the unicycle is an unstable equilibrium, and full state feedback is indispensable. Next the FLC with full state feedback is designed such that the unicycle can reach any given position or setpoint while keeping the saddle stable. Through comprehensive simulation-based investigations, the effectiveness of the proposed FLC is validated, and the FLC shows superior performance than the LQR. <s> BIB057 </s> Underactuated robotics: A review <s> Practical difficulties <s> A surgical instrument is provided for use in endoscopic or laparoscopic procedures. The instrument includes a handle portion, an endoscopic portion extending from the handle portion, an articulating section pivotably connected to a distal end portion of the endoscopic portion, and a retractor assembly operatively associated with the articulating section. Structure is provided for manipulating the articulating section relative to the longitudinal axis of the endoscopic portion within an angular degree of rotation. An injection port may also be provided to deliver fluids through the endoscopic portion to the operative site. <s> BIB058 </s> Underactuated robotics: A review <s> Practical difficulties <s> An energy-compensated fuzzy swing-up and balance control is investigated for the planetary-gear-type inverted pendulum (PIP) in this paper. The proposed control scheme consists of a fuzzy swing-up controller (FSC), a fuzzy sliding balance controller (FSBC), and a fuzzy compensation mechanism. The PIP with the designed FSC can upswing the pendulum quickly and have the controlled system be stable in the sense of approaching the desired system energy. The pendulum of PIP system can be stably balanced at the upright position with the presented FSBC, where the chattering effect is significantly eliminated. With the proposed compensation mechanism, the overaccumulated upswing energy can be effectively compensated such that the influence of disturbance can be overcome. The simulation results are included to indicate the effectiveness of the provided controller. Moreover, based on an embedded control kernel, an experimental setup for the PIP control system is built up. It shows that the real-time experiment results empirically support the promising performance of desire. <s> BIB059 </s> Underactuated robotics: A review <s> Practical difficulties <s> Based on the previous studies, the dynamic balance of an electrical bicycle includes two control inputs: steering and pendulum torques, and three system outputs: steering, lean and pendulum angles. Two novel reference signals are first designed so that the uncontrolled mode is simultaneously included into these two control modes. Two scaling factors for each subsystem are first employed to normalize the sliding surface and its derivative. The so-called fuzzy decentralized sliding-mode under-actuated control (FDSMUC) is first designed. Because the uncertainties of a bicycle system, caused by different ground conditions, gusts of wind, and interactions among subsystems, are often huge, an extra compensation of learning uncertainty is plunged into FDSMUC to enhance system performance. We call it as “fuzzy decentralized sliding-mode adaptive under-actuated control” (FDSMAUC). To avoid the unnecessary transient response and then destroy the balance of the bicycle, the combination of FDSMUC and FDSMAUC with a transition (i.e., fuzzy decentralized sliding-mode robust adaptive under-actuated control, FDSMRAUC) is designed. Finally, the compared simulations for an electrical bicycle among the FDSMUC, FDSMAUC and FDSMRAUC validate the efficiency of the proposed method. <s> BIB060 </s> Underactuated robotics: A review <s> Practical difficulties <s> The purpose of this paper is to stabilize the running motion of an electrical bicycle. In order to do so, two strategies are employed in this paper. One is to control the bike's center of gravity (CG), and the other is to control the angle of the bike's steering handle. As in general, the control of the CG applies a pendulum. An additional factor is the lean angle with respect to the gravitational direction of the bicycle in motion. In this total, the proposed system produces three outputs that will affect the dynamic balance of an electrical bicycle: the bike's pendulum angle, lean angle, and steering angle. Based on the data of input-output, two scaling factors are first employed to normalize the sliding surface and its derivative. According to the concept of the if-then rule, an appropriate rule table for the ith subsystem is obtained. Then, the output scaling factor based on Lyapunov stability is determined. The purpose of using the proposed fuzzy sliding-mode underactuated control (FSMUAC) is to deal with the huge uncertainties of a bicycle system often caused by different ground conditions and gusts of wind. Finally, the simulations for the electrical bicycle in motion under ordinary PID control, modified proportional-derivative control, and FSMUAC are compared to judge the efficiency of our proposed control method. <s> BIB061 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper proposes an adaptive fuzzy sliding-mode controller for a class of underactuated systems. Here, the underactuated system is decoupled into two subsystems, and respectively define a sliding surface for each subsystem. The fuzzy models are applied to estimate the unknown functions of the controlled underactuated system. Then, we will propose the adaptive fuzzy sliding model controller to guarantee the tracking performance. Finally, computer simulations are given to demonstrate the tracking performance of the proposed control strategy. <s> BIB062 </s> Underactuated robotics: A review <s> Practical difficulties <s> A sliding mode control law is presented and experimentally implemented for setpoint control of an underactuated autonomous surface vessel. The control law is developed by defining a single sliding surface for orientation stabilization that determines the required yaw moment and three additional surfaces that determine the surge force. The trajectories are shown to converge to each of the surfaces in finite time and the sliding phase is shown to be asymptotically stable. Two setpoint control scenarios are simulated and then demonstrated experimentally. The experimental results show that the surface vessel converges to the desired setpoint with reasonable accuracy. <s> BIB063 </s> Underactuated robotics: A review <s> Practical difficulties <s> This article presents a robust fuzzy sliding mode controller. The methodology of sliding mode control provides an easy way to control under-actuated nonlinear systems with uncertainties. The structure of the sliding surface is designed as follows. First, decouple the entire system into second-order systems so that each subsystem has a separate control target expressed in terms of a sliding surface. Second, from the sliding surface of subsystems, organize the main sliding surface system. Third, generate a control input for the main sliding surface to make whole subsystems move toward their sliding surface. A fuzzy controller is used to obtain a smooth boundary layer to the sliding surface. Finally, the fuzzy sliding mode controller presented is used to control an under-actuated nonlinear system, and confirms the validity of the proposed approach and its robustness to uncertainties. <s> BIB064 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, an adaptive fuzzy switched swing-up and sliding controller (AFSSSC) is proposed for the swing-up and position controls of a double-pendulum-and-cart system. The proposed AFSSSC consists of a fuzzy switching controller (FSC), an adaptive fuzzy swing-up controller (FSUC), and an adaptive hybrid fuzzy sliding controller (HFSC). To simplify the design of the adaptive HFSC, the double-pendulum-and-cart system is reformulated as a double-pendulum and a cart subsystem with matched time-varying uncertainties. In addition, an adaptive mechanism is provided to learn the parameters of the output fuzzy sets for the adaptive HFSC. The FSC is designed to smoothly switch between the adaptive FSUC and the adaptive HFSC. Moreover, the sliding mode and the stability of the fuzzy sliding control systems are guaranteed. Simulation results are included to illustrate the effectiveness of the proposed AFSSSC. <s> BIB065 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper addresses a fuzzy aggregated hierarchical sliding mode control approach for a class of underactuated systems. By capturing the physical nature of the class, an aggregated hierarchical structure of the sliding surfaces is designed. The control law is deduced from the Lyapunov direct method. The stability of the inner sliding surfaces is proven. By fusing the priori knowledge about the class of systems, a fuzzy logic is designed to regulate the controller's gain. Finally, simulation results show the validity of the proposed approach through control problems of two typical underactuated systems. <s> BIB066 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper introduces the design and implementation of a two-wheel inverted pendulum (TWIP) system with a fuzzy control scheme and the system-on-a-programmable-chip (SoPC) technology. The control scheme includes three kinds of fuzzy controls which are the fuzzy balanced standing control (FBSC), the fuzzy traveling and position control (FTPC), and the fuzzy yaw steering control (FYSC). Based on the Takagi-Sugeno fuzzy model of the TWIP, the FBSC is a structure of a parallel distributed compensator solved by the linear matrix inequality approach. Based on the motion characteristic of the TWIP, the FTPC and the FYSC are designed with Mamdani architecture if-then rules. Furthermore, the fuzzy control scheme for the real TWIP is implemented into an SoPC development board with an embedded reduced-instruction-set-computer soft-core processor and user intellectual property modules. Both the computer simulations and practical experiments demonstrate the effectiveness of the proposed control scheme. <s> BIB067 </s> Underactuated robotics: A review <s> Practical difficulties <s> Abstract In contrast with fully controllable systems, a super articulated mechanical system (SAMS) is a controlled underactuated mechanical system in which the dimensions of the configuration space exceed the dimensions of the control input space. The control of the cart–seesaw system is especially difficult since it is an underactuated mechanism (three degrees of freedom and only two inputs). This research develops a balancing approach for a novel SAMS model, called the cart–seesaw system, using fuzzy logic and fuzzy coordinator compensation to drive the sliding carts and keep the seesaw angle close to zero in the equilibrium state. Experimental results indicate that utilizing the proposed control methodology significantly enhances the performance. Moreover, the presentation of the fuzzy balancing controller is not considerably affected by changes in the environmental parameters, which demonstrates the effectiveness of the fuzzy controller in minimizing the seesaw tilt angle in the time domain, although the system is caused by unpredicted loading variation. Moreover, the experimental results indicate the usefulness and robustness of the proposed fuzzy control methodology. Furthermore, the proposed software/hardware platform can be beneficial for standardizing laboratory equipment and developing amusement apparatus. <s> BIB068 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper mainly investigates the control for the ball and beam system. Combined with the conventional dynamic surface control, an adaptive fuzzy scheme is proposed for the equilibrium balance of the ball. First, with the proper defined tracking errors of state variables, an integrating of tracking errors is considered as the fuzzy input. The parameters of fuzzy controller can be optimized by using the proposed adaptive mechanism such that the control performance can be improved. For the proposed control scheme, the closed-loop stability is also analyzed by the Lyapunov theorem. Simulations are performed to evaluate the effectiveness of the proposed works. From simulation results, the proposed adaptive fuzzy dynamic surface control scheme can provide better tracking responses than the conventional dynamic surface control counterparts. <s> BIB069 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this study, adaptive fuzzy output feedback motion/force control is investigated for wheeled inverted pendulums with unmodelled dynamics, whose states and time derivatives of the output are unavailable. The proposed adaptive fuzzy output feedback control reconstructs the system states by using a high-gain observer, and makes use of bounds online adaptation mechanism to cancel the dynamics uncertainties. Based on Lyapunov synthesis, the proposed control ensures that the system outputs track the given bounded reference signals within a small neighbourhood of zero, and guarantees zero-dynamics stability. The effectiveness of the proposed control is verified through extensive simulations. <s> BIB070 </s> Underactuated robotics: A review <s> Practical difficulties <s> Double inverted pendulum on a cart (DIPC) is a highly nonlinear system. Due to its complex dynamics, it is widely used as a test-bed plant for the verification of newly designed controllers. In DIPC, two pendulums are kept upward by linear movements of cart. Because of this linear motions and frequent switching of velocity directions, another nonlinearity caused by friction becomes dominant around the equilibrium point. Friction introduces limit cycles to the system and results in a poor steady-state response. To eliminate these negative effects, the locally linear neuro-fuzzy (LLNF) approach is used to build an inverse model for friction compensation. This model is compared with multilayer perceptron network in order to demonstrate the better performance of LLNF. To stabilize DIPC, a common optimal controller is used, and despite its limited performance, experimental results show that the application of inverse modeling for friction compensation improves the steady-state response outstandingly. <s> BIB071 </s> Underactuated robotics: A review <s> Practical difficulties <s> A tracking control of a real inverted pendulum system is implemented in this paper via an adaptive self-constructing fuzzy neural network (ASCFNN) controller. The linear induction motor (LIM) has many excellent performances, such as the silence, high-speed operation and high-starting thrust force, fewer losses and size of motion devices. Therefore, the experiment is implemented by integrating the LIM and an inverted pendulum (IP) system. The ASCFNN controller is composed of an ASCFNN identifier, a computation controller and a robust controller. The ASCFNN identifier is used to estimate parameters of the real IP system and the computational controller is used to sum up the outputs of the ASCFNN identifier. In order to compensate the uncertainties of the system parameters and achieve robust stability of the considered system, the robust controller is adopted. Furthermore, the structure and parameter learning are designed in the ASCFNN identifier to achieve favorable approximation performance. The Mahalanobis distance (M-distance) method in the structure learning is also employed to determine if the fuzzy rules are generated/eliminated or not. Concurrently, the adaptive laws are derived based on the sense of Lyapunov so that the stability of the system can be guaranteed. Finally, the simulation and the actual experiment are implemented to verify the effectiveness of the proposed ASCFNN controller. <s> BIB072 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, we propose a hybrid design method for fuzzy logic controller (FLC), where the control objective for unicycle is to achieve velocity control of the wheel while keep the pendulum at the balanced position that is an unstable equilibrium. The hybrid design consists of three phases. First, FLC structure including the number of rules, membership function, inference, and parametric relations, are chosen based on heuristic knowledge about the unicycle. Then, based on a linearized model and linear feedback, the output parameters of FLC are determined quantitatively for the stabilization of the unicycle. Next, fine tuning of FLC output parameters are carried out using an iterative learning tuning (ILT) algorithm, where ILT iteratively minimizes an objective function that specifies the desired unicycle performance. The rationale of introducing the hybrid FLC design is to fully utilize available information, which is achieved by combining model-based and model-free designs, hence improve FLC performance. Through intensive simulations and comparisons, the effectiveness of the proposed hybrid FLC is validated. <s> BIB073 </s> Underactuated robotics: A review <s> Practical difficulties <s> Fast human walking includes a phase where the stance heel rises from the ground and the stance foot rotates about the stance toe. This phase where the biped becomes underactuated is not present during the walk of current humanoid robots. The objective of this study is to determine whether the introduction of this phase for a 3-D bipedal robot is useful to reduce the energy consumed in the walking. In order to study the efficiency of this new gait, two cyclic gaits are presented. The first cyclic motion is composed of successive single-support phases with a flat stance foot on the ground, and the stance foot does not rotate. The second cyclic motion is composed of single-support phases that include a subphase of rotation of the supporting foot about the toe. The single-support phases are separated by a double-support phase. For simplicity, this double-support phase is considered as instantaneous (passive impact). For these two gaits, optimal motions are designed by minimizing the torques cost. The given performances of actuators are taken into account. It is shown that, for a fast motion, a foot-rotation subphase is useful to reduce the cost criterion. These gaits are illustrated with simulation results. <s> BIB074 </s> Underactuated robotics: A review <s> Practical difficulties <s> We consider the optimal control of mechanical systems on Lie groups and develop numerical methods that exploit the structure of the state space and preserve the system motion invariants. Our approach is based on a coordinate-free variational discretization of the dynamics that leads to structure-preserving discrete equations of motion. We construct necessary conditions for optimal trajectories that correspond to discrete geodesics of a higher order system and develop numerical methods for their computation. The resulting algorithms are simple to implement and converge to a solution in very few iterations. A general software implementation is provided and applied to two example systems: an underactuated boat and a satellite with thrusters. <s> BIB075 </s> Underactuated robotics: A review <s> Practical difficulties <s> Abstract Time optimal control problems often admit as solution bang–bang controls but they present several drawbacks in real applications where additional degrees of regularity are desirable. In this paper, the rate limited time optimal swing up of an inverted pendulum is considered and necessary conditions that have to be satisfied by optimal trajectories in the presence of rate constraints are derived. A comparison between this approach and the results from the standard time optimal problem is reported. <s> BIB076 </s> Underactuated robotics: A review <s> Practical difficulties <s> A wheeled human-conveyance vehicle (WHCV) with a low-level microprocessor is realized in this paper. WHCVs are environmentally friendly short-range transportation vehicles. This paper proposes a simple Mamdani-like fuzzy controller for self-balancing WHCV control. System stability is guaranteed by establishing sufficient conditions based on the Lyapunov stability analysis. Finally, experimental results show that the proposed Mamdani-like fuzzy control strategy can control the WHCV. <s> BIB077 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, we propose synthesized design of a fuzzy logic controller (FLC) for control of an underactuated unicycle system. The FLC objective is velocity control of the wheel while keeping the pendulum upright, which is an unstable equilibrium. The synthesized design consists of three phases. First, the FLC structures including the number of rules, membership functions, inference and parametric relations are chosen based on heuristic knowledge about the unicycle. Second, on the basis of a linearized model and linear feedback, the FLC output parameters are determined quantitatively for stabilization of the unicycle. Third, the FLC output parameters are tuned using an iterative learning tuning (ILT) algorithm, which minimizes an objective function that specifies the desired unicycle performance. The rationale for the synthesized FLC design is full utilization of the available information, which is achieved by combining model-based and model-free designs, and hence improves the FLC performance. We minimize the number of FLC rules and fuzzy labels. Six rules are used for regulation or setpoint tasks, whereas 10 rules are used with extra integral control to eliminate steady-state errors induced by system uncertainties and disturbances. Only two fuzzy labels are adopted for each fuzzy variable. The ILT process consists of two phases, exploration for stabilization and exploitation for better performance. The effectiveness of the proposed FLC is validated using intensive simulations and comparisons. <s> BIB078 </s> Underactuated robotics: A review <s> Practical difficulties <s> Abstract This paper proposes a novel anti-swing control strategy for an overhead crane. The controller includes both position regulation and anti-swing control. Since the crane model is not exactly known, fuzzy rules are used to compensate friction, gravity as well as the coupling between position and anti-swing control. Ahigh-gain observer is introduced to estimate the joint velocities to realize PD control. Real-time experiments are presented comparing this new stable anti-swing PID control strategy with regular crane controllers. <s> BIB079 </s> Underactuated robotics: A review <s> Practical difficulties <s> Applying visual tracking technology to dynamic systems is important to many industrial applications. However, image sensing is difficult to implement in a fast dynamic plant without high-speed computational resources. This work presents a simple yet effective method of image processing to capture the dynamic movement of an overhead crane, enabling it to be controlled in real time. Visual tracking based on color histograms involves comparison of the color in a model image with the color in a sequence of images to track a dynamic object. The best match is identified using Bhattacharyya similarity measurement. Upon tracking, the sensing data are sent to an adaptive fuzzy sliding mode controller (AFSMC). The advantages of this approach include robustness and the model-free properties of the sliding mode and the fuzzy logic controllers; adaptable slopes of the sliding surface of AFSMC are also presented to improve control performance. <s> BIB080 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper mainly addresses the balance control of a ball and beam system, where a pair of decoupled fuzzy sliding-mode controllers (DFSMCs) are proposed. The DFSMC has the advantage of reducing the design complexity, in which the coupling dynamics of the state-error dynamics are considered as disturbance terms. Stability analysis of the ball and beam system with DFSMCs is also discussed in detail. To further improve the control performance, an improved ant colony optimization (ACO) is proposed to optimize the controller parameters. The proposed ACO algorithm has the enhanced capability of fuzzy pheromone updating and adaptive parameter tuning. The proposed ACO-optimized scheme is utilized to tune the parameters of the fuzzy sliding-mode controllers for a real ball-and-beam system. Compared to some conventional ACO algorithms, simulation and experimental results all indicate that the proposed scheme can provide better performance in the aspect of convergence rate and accuracy. <s> BIB081 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, the balance control of a ball and beam system is considered. Based on the T-S fuzzy modeling, the dynamic model of the ball and beam system is formulated as a strict feedback form with modeling errors. Then, an adaptive dynamic surface control (DSC) is utilized to achieve the goal of ball positioning subject to parameter uncertainties. The robust stability of the closed-loop system is preserved by using the Lyapunov theorem. In addition to simulation results, the proposed T-S fuzzy model-based adaptive dynamic surface controller is applied to a real ball and beam system for practical evaluations. Simulation and experimental results illustrate that the proposed control scheme has much better performance than that of conventional DSC. Furthermore, parameter uncertainties and external disturbance are considered to highlight the robustness of the proposed control scheme. <s> BIB082 </s> Underactuated robotics: A review <s> Practical difficulties <s> It is known that robotic manipulators are highly nonlinear systems, and an accurate mathematical model is difficult to obtain, thus making it difficult t@? analyze with conventional analytical methods. Here, a novel design of an adaptive neuro fuzzy inference system (ANFIS) for estimation contact forces of a new adaptive gripper is presented. Since the conventional analytical methods is a very challenging task, fuzzy logic based systems are considered as potential candidates for such an application. The main points of this paper are in explanation of kinetostatic analyzing of the new gripper structure using rigid body model with added compliance in every single joint. The experimental results can be used as training data for ANFIS network for estimation of gripping forces. An adaptive neuro-fuzzy network is used to approximate correlation between contact point locations and contact forces magnitudes. The simulation results presented in this paper show the effectiveness of the developed method. This system is capable to find any change in ratio of positions of the gripper contacts and magnitudes of the contact forces and thus indicates state of both finger phalanges. <s> BIB083 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, a new reduction approach is presented to simplify the type reduction procedure for an interval type-2 fuzzy sliding controller. An interval type-2 fuzzy set can be considered as a collection of a large number type-1 fuzzy set. The union and intersection of all type-1 fuzzy sets with the corresponding embedded membership functions being their membership functions are found. With the information represented by the union and intersection combined, a type-1 membership function is retrieved and an interval type-2 fuzzy set is reduced to be a type-1 fuzzy set. The proposed simplified type reduction approach is also applied to the design of a hybrid interval type-2 fuzzy sliding controller for a ball-and-beam system. Compared to Extended-Karnik-Mendel (EKM) type reduction method, the simulation results are included to show the effectiveness of the designed hybrid interval type-2 fuzzy sliding controllers using the simplified type reduction. <s> BIB084 </s> Underactuated robotics: A review <s> Practical difficulties <s> Motivated by the dynamic characteristics of underactuated mechanical systems with 2 degrees of freedom, a decoupling adaptive fuzzy sliding mode decoupling controller (DAFSMDC) is presented in this paper. By exploiting the universal approximation property of fuzzy logic systems and the sliding mode control method, this paper proposes a new decoupling strategy of the system into 2 second-order subsystems and introduces an adaptive control algorithm that guarantees the convergence of both subsystems. Since fuzzy systems are used to approximate an unknown ideal controller, the adjustable parameters of the used fuzzy systems are updated using a gradient descent algorithm that is designed to minimize the error between the unknown ideal controller and the fuzzy controller. Based on Lyapunov stability theory, proofs and conditions are then given to ensure the stability of the closed-loop system. Two examples are provided to illustrate the effectiveness and potential of the DAFSMDC technique for the stabilization of underactuated mechanical systems. <s> BIB085 </s> Underactuated robotics: A review <s> Practical difficulties <s> Stable hover flight control for small unmanned helicopter under light air turbulent environment is presented. Intelligent fuzzy logic is chosen because it is a nonlinear control technique based on expert knowledge and is capable of handling sensor created noise and contradictory inputs commonly encountered in flight control. The fuzzy nonlinear control utilizes these distinct qualities for attitude, height, and position control. These multiple controls are developed using two-loop control structure by first designing an inner-loop controller for attitude angles and height and then by establishing outer-loop controller for helicopter position. The nonlinear small unmanned helicopter model used comes from X-Plane simulator. A simulation platform consisting of MATLAB/Simulink and X-Plane© flight simulator was introduced to implement the proposed controls. The main objective of this research is to design computationally intelligent control laws for hovering and to test and analyze this autopilot for small unmanned helicopter model on X-Plane under ideal and mild turbulent condition. Proposed fuzzy flight controls are validated using an X-Plane helicopter model before being embedded on actual helicopter. To show the effectiveness of the proposed fuzzy control method and its ability to cope with the external uncertainties, results are compared with a classical PD controller. Simulated results show that two-loop fuzzy controllers have a good ability to establish stable hovering for a class of unmanned rotorcraft in the presence of light turbulent environment. <s> BIB086 </s> Underactuated robotics: A review <s> Practical difficulties <s> Using a combination of the cart-seesaw and the inverted pendulum system, this paper presents a novel laboratory apparatus called the cart-pendulum-seesaw (CPS) system. The proposed pneumatic CPS is a classic example of a super articulated mechanical system. The resulting system has two inputs: a force applied to the cart and another force applied to the loading cart which tries to balance the seesaw test-bed. With two inputs and four available for the measurement outputs, the unstable multi-input-multi-output system offers an interesting control challenge. This study breaks down the system into several tasks, one for pendulum swinging up and the other for seesaw balancing. The pendulum is first swung up; then, balancing the pendulum at the upright position with a fuzzy controller, the seesaw is balanced by another fuzzy controller. This study incorporates a fuzzy coordinator into the seesaw system to take control action in extreme situations. The experimental device is used to evaluate the efficiency of t... <s> BIB087 </s> Underactuated robotics: A review <s> Practical difficulties <s> Guaranteed stability fuzzy controller for stabilization the motion of an unmanned bicycle is proposed. First, a fuzzy control system capable of automatically balancing an unmanned bicycle through tracking desired roll angle is developed. Fuzzy logic controller membership functions are defined utilizing scaling factors. To guarantee the stability of the closed loop system, similar to previous approaches reported in the literature, fuzzy If–Then rules are constructed based on Lyapunov stability criterion. It is indicated that the proposed fuzzy controller violates Lyapunov stability criterion. The reason of such a violation is argued in detail. To cope with this shortcoming, some modifications are made to the control strategy to assure stability. Through these modifications, the modified fuzzy controller is developed which simultaneously balances the bicycle and guarantees stability while minimizing roll angle tracking error and its derivative. It is indicated that the improved fuzzy controller can adapt to a variety of initial conditions. Moreover, robustness of the controller against parameter variation is verified through its implementation on different bicycle designs (different sets of bicycle parameters). Simulation results confirm the efficacy of the proposed fuzzy controller in terms of settling time and overshoot in comparison with previous studies. Sensitivity analysis of the controller efficiency with respect to system parameters is also assessed. <s> BIB088 </s> Underactuated robotics: A review <s> Practical difficulties <s> Human being assistant transportation systems have received much attention in recent years. This study proposes a wheeled human transportation vehicle (WHTV). Two-wheeled vehicles have been known as powerful transporters for urban areas. Based on a low-level microprocessor, a WHTV is designed and implemented in this study. Moreover, a Mamdani-like output recurrent fuzzy controller (MLORFC) is used to control the WHTV in this study. As the MLORFC obtains system dynamics, it is better than the traditional Mamdani-type fuzzy controllers in terms of dynamic response. A necessary condition based on the Lyapunov stability analysis is established to guarantee the system stability. The recurrent weights are tuned on-line using the dynamic gradient descent method. The learning rates of the recurrent weights are automatically settled based on a Lyapunov analytical method to achieve the system error convergence. The experiment results in Section 4 show that the conveyance platform can stably move under the proposed control strategy. <s> BIB089 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, the interval type-2 fuzzy proportional–integral–derivative controller (IT2F-PID) is proposed for controlling an inverted pendulum on a cart system with an uncertain model. The proposed controller is designed using a new method of type-reduction that we have proposed, which is called the simplified type-reduction method. The proposed IT2F-PID controller is able to handle the effect of structure uncertainties due to the structure of the interval type-2 fuzzy logic system (IT2-FLS). The results of the proposed IT2F-PID controller using a new method of type-reduction are compared with the other proposed IT2F-PID controller using the uncertainty bound method and the type-1 fuzzy PID controller (T1F-PID). The simulation and practical results show that the performance of the proposed controller is significantly improved compared with the T1F-PID controller. <s> BIB090 </s> Underactuated robotics: A review <s> Practical difficulties <s> The ballbot is a human-sized dynamically stable mobile robot that balances on a single ball. Unlike statically stable mobile robots, the ballbot is tall and narrow with a high center of gravity and a small footprint. Moreover, its dynamic stability enables it to be physically interactive. These characteristics make it better suited to navigate and interact in cluttered human environments. This paper presents the evolved hardware design of the ballbot with a four-wheel inverse mouse-ball drive to actuate the ball, and a yaw drive mechanism that enables unlimited rotation about its vertical axis. The ballbot also has a triad of legs that provide static stability when powered down. This paper presents a detailed description of the ballbot's control architecture, and it presents several experimental results that demonstrate its balancing and locomotion capabilities. This paper also presents a trajectory planning algorithm that plans for body lean motions, which, when tracked, result in the desired rest-to-rest motions of the robot. Finally, the paper illustrates some interesting human-robot physical interaction behaviors that can be achieved as a result of the ballbot's dynamic stability. <s> BIB091 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper is concerned with the robust tracking control of an electrically driven free-floating space manipulator with internal parameter uncertainty and external disturbance. An adaptive disturbance-observer-based output feedback control is employed to provide a solution to the control problem, wherein the parameters are tuned online by using fuzzy logic systems to compensate for equivalent disturbance, and the stability condition of the closed-loop system is also derived. The suggested method does not require exact prior knowledge of the system and needs a few parameters to tune. The simulation results of a two-link electrically driven space manipulator show the effectiveness and applicability of the proposed control scheme. <s> BIB092 </s> Underactuated robotics: A review <s> Practical difficulties <s> The development of universal grippers able to pick up unfamiliar objects of widely varying shapes and surfaces is a very challenging task. Passively compliant underactuated mechanisms are one way to obtain the gripper which could accommodate to any irregular and sensitive grasping objects. The purpose of the underactuation is to use the power of one actuator to drive the open and close motion of the gripper. The fully compliant mechanism has multiple degrees of freedom and can be considered as an underactuated mechanism. This paper presents a new design of the adaptive underactuated compliant gripper with distributed compliance. The optimal topology of the gripper structure was obtained by iterative finite element method (FEM) optimization procedure. The main points of this paper are in explanation of a new sensing capability of the gripper for grasping and lifting up the gripping objects. Since the sensor stress depends on weight of the grasping object it is appropriate to establish a prediction model for estimation of the grasping object weight in relation to sensor stress. A soft computing based prediction model was developed. In this study an adaptive neuro-fuzzy inference system (ANFIS) was used as soft computing methodology to conduct prediction of the grasping objects weight. The training and checking data for the ANFIS network were obtained by FEM simulations. <s> BIB093 </s> Underactuated robotics: A review <s> Practical difficulties <s> The main purpose of this paper is to determine what joints are most strained in the proposed underactuated finger by adaptive neuro-fuzzy methodology. For this, kinetostatic analysis of the finger structure is established with added torsional springs in every single joint. Since the finger’s grasping forces depend on torsional spring stiffness in the joints, it is preferable to determine which joints have the most influence on grasping forces. Hence, the finger joints experiencing the most strain during the grasping process should be determined. It is desirable to select and analyze a subset of joints that are truly relevant or the most influential to finger grasping forces in order to build a finger model with optimal grasping features. This procedure is called variable selection. In this study, variable selection is modeled using the adaptive neuro-fuzzy inference system (ANFIS). Variable selection using the ANFIS network is performed to determine how the springs implemented in the finger joints affect the output grasping forces. This intelligent algorithm is applied using the Matlab environment and the performance is analyzed. The simulation results presented in this paper show the effectiveness of the developed method. <s> BIB094 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper mainly researches the swing-up control of Pendubot. Comparing with the uppermost unstable equilibrium position, it is more difficult to make the Pendubot swing up to the unstable nonequilibrium position. In order to complete the control target, the energy-based controller incorporated with fuzzy neural network compensation (ECFNNC) is designed in this paper. In addition, numerical simulations and experimental results of the Pendubot actuated by a dc servo motor are given in this paper. By comparing the results with other algorithms, it is found that the ECFNNC proposed in this paper has better performance under the same conditions. <s> BIB095 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper presents an efficient method to capture the dynamic movement of a three-dimensional (3-D) overhead crane, enabling it to be controlled by visual feedback in real time with two cheap handy cameras. Two tracking areas and one positioning block in each frame are used to search image features and determine the useful vision information. The depth information of 3-D crane system in images can be also obtained by a tag on the dynamic plant. The presented visual tracking method involves comparison of the lightest or darkest points in the tracking or positioning area of a dynamic object and then computes the necessary trolley position and load swing in 3-D space. Upon tracking, the sensing data are sent to an adaptive fuzzy sliding-mode controller (AFSMC) to derive control power for the crane system. Accordingly, the merits of this AFSMC approach, including robustness of the sliding-mode control and the model-free property of the fuzzy logic for the 3-D crane system, are confirmed. Experimental results verify the improvement of the proposed methodology. <s> BIB096 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper proposes an adaptive sliding-mode antisway control law for uncertain overhead cranes with high-speed hoisting motion. Since the sway dynamics are disturbed by the trolley acceleration and hoisting velocity, antisway control law is designed based on the sliding mode control by defining a sliding surface in such a way that the trolley acceleration contributes to the sway dynamics as nonlinear damping in sliding mode. In addition, this nonlinear damping is designed such that it dominates the inherent damping coupled with the hoisting velocity so that the asymptotic stability of the sway dynamics can be achieved. To cope with system uncertainties such as system parameter variations, unknown actuator nonlinearities, unmodeled dynamics, and external disturbances, we design a fuzzy uncertainty observer and incorporate it into the sliding-mode antisway control law. Via the stability analysis and computer simulations, we show that the proposed control law guarantees the robust antisway performance of overhead cranes, regardless of hoisting velocity, even in the presence of system uncertainties. <s> BIB097 </s> Underactuated robotics: A review <s> Practical difficulties <s> The trajectory tracking of uncertain underactuated nonlinear dynamic systems is tackled by an adaptive fuzzy hierarchical sliding-mode control (AFHSMC). First, one of the subsystems is assigned as the first layer sliding surface. Next, a second layer sliding surface from the first layer sliding surface and the sliding surface of another subsystem is constructed. In this paper, the nth layer is supposed to be the top layer (or hierarchical layer) for including the sliding surfaces of all subsystems. Because two nonlinear system functions and the time-varying external disturbance of each subsystem are supposed to be unknown, different online fuzzy models are employed to approximate these nonlinear system functions and the upper bounded functions of external disturbances. Moreover, the upper bound of uncertainties caused by these fuzzy modeling errors is estimated online. Based on these learning fuzzy models and the estimated upper bound of these modeling errors, an AFHSMC is developed. The stability analysis and tracking performance of the closed-loop system are verified by Lyapunov stability theory. Finally, two simulation examples including different amplitudes of external disturbance and comparison with hierarchical sliding-mode control confirm the effectiveness and robustness of the proposed control. <s> BIB098 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper presents the design of an optimized Interval Type 2 Fuzzy Proportional Derivative Controller (IT2F-PDC) in cascade form for Rotary Inverted Pendulum (RIP) system. The parameters of the IT2F-PDC are optimised by using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The goal is to balance the pendulum in upright unstable equilibrium position. The IT2F-PDC which is the extended version of conventional type 1 fuzzy logic controller, improves the control strategy by using the advantage ::: of its footprint of uncertainty for the fuzzy membership ::: function. The performance characteristics considered for the controller are steady state error, settling time, rise time, maximum overshoot, and control energy. Experimental and simulation results indicated that the effectiveness and robustness of the proposed GA- and PSO-based controllers on the RIP with respect to load disturbances, parameter variation, and noise effects have been improved over state-of-the-art method. However, the comparative results for simulation and experiment based on cascade IT2F-PDC indicate that GA-based IT2F-PDC has lower steady state error while PSO-based IT2F-PDC has lower overshoot, settling time, and control energy, but both have almost the same rise time. The proposed control strategy can be regarded as a promising strategy for controlling different unstable and nonlinear systems. <s> BIB099 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, the control problem of underactuated systems with mismatched and matched uncertainties is addressed. Adaptive fuzzy backstepping controller is proposed to solve the problem, ensuring the robustness against uncertainties and disturbances. Taking a general class of underactuated robotic systems into account, the nonlinear dynamical equations are first transformed to the so-called cascade form and then, an adaptive-based controller is constructed using the capability of fuzzy logic to tackle the perturbations. From the analytic point of view, the closed loop stability is ensured using the Lyapunov stability theorem. To demonstrate the effectiveness of the method, the proposed controller has been applied to a two-wheeled self-balancing robot with three degrees of freedom, and also to a pendubot with two degrees of freedom. In order to highlight the superiority of the proposed algorithm, the performance is compared with that of an existing robust strategy. <s> BIB100 </s> Underactuated robotics: A review <s> Practical difficulties <s> Complex systems, such as the interconnected self-balancing vehicles system, are known to be highly nonlinear, under-actuated, and challenging to control. Their complexity is further increased by the presence of time delays and external disturbances. Therefore, all attempts to control the interconnected self-balancing vehicles system were based on accurate determination of its states. However, it is well known that modelling of interconnected self-balancing vehicles systems is not an easy task. In this paper, trajectory tracking of a series of two-wheeled self-balancing vehicles, named B2-train system, is addressed. The highly nonlinear under-actuated system is analyzed and a nonlinear dynamic model of the B2-train system is derived using the Lagrangian method. The adaptive fuzzy controller is designed to approximate the unknown system parameters under the constraint that only the system output is available for measurement. To address this the constraint, a nonlinear state observer is employed to estimate the states including time delays. The aim is to design a state observer-based adaptive fuzzy controller using variable structure (VS) technique and a time delayed compensator which ensures the robust asymptotic stability of the closed-loop system and guarantees an H∞ norm bound constraint on disturbance attenuation for all admissible uncertainties based on Lyapunov criterion. Finally, a time-delayed B2-train system with 2 vehicles is used to demonstrate the performance and robustness of the proposed control scheme. <s> BIB101 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, an intelligent tracking control system (ITCS) is proposed for an omnidirectional spherical mobile platform (ODSMP) control problem. This intelligent tracking control system combined with a dual Mamdani-type fuzzy control strategy and supervisory control technique is proposed for ODSMPs real-world control with unknown system external disturbances. Then, this platform can move to any direction with no constraint. Since the dynamic characteristic of the spherical platform is nonlinear and time varying, an intelligent control method with little system information is designed. The stability of ITCS, which is based on the Lyapunov stability theorem, can be ensured without any strict constraint and detailed system knowledge such that it can flexibly extend to other control problems. In the end, the efficiency of the intelligent tracking control system is verified by ODSMP real-world implementation. <s> BIB102 </s> Underactuated robotics: A review <s> Practical difficulties <s> Abstract To obtain adaptive finger passive underactuation can be used. Underactuation principle can be used to adapt shapes of the fingers for grasping objects. The fingers with underactuation do not require control algorithm. In this study a kinetostatic model of the underactuated finger mechanism was analyzed. The underactuation is achieved by adding the compliance in every finger joint. Since the contact forces of the finger depend on contact position of the finger and object, it is suitable to make a prediction model for the contact forces in function of contact positions of the finger and grasping objects. In this study prediction of the contact forces was established by a soft computing approach. Adaptive neuro-fuzzy inference system (ANFIS) was applied as the soft computing method to perform the prediction of the finger contact forces. <s> BIB103 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper proposes an obstacle avoidance method in the position stabilization of the wheeled mobile robots using interval type-2 fuzzy neural network (IT2FNN). Previously, we have proposed the unified strategies of obstacle avoidance and shooting method of the robot soccer system using type-1 fuzzy neural network (T1FNN). Even though the previous T1FNN method can achieve the required tasks, the performance of the previous T1FNN method is not satisfactory in the following sense. The previous T1FNN cannot reduce the influence of uncertainties effectively because it uses the crisp set as the membership values. In addition, it can result in the large oscillation behavior during the obstacle avoidance. Accordingly, we should design the IT2FNN method to improve the performance with smoother behavior as well as improved obstacle avoidance. The proposed IT2FNN method has the fuzzy neural network structure different from the T1FNN. Since the IT2FNN uses the fuzzy set instead of the crisp set as the membership values and it is robust against uncertainties, the performance of the robot behavior can be significantly improved especially in the presence of obstacles. Both simulation and experimental results using the actual wheeled mobile robot with the vision information are provided to show the validity and the advantages of the proposed method. <s> BIB104 </s> Underactuated robotics: A review <s> Practical difficulties <s> For quadrotor UAV is a kind of under-actuated system with multiple inputs and strong coupling, manual optimization of PID control parameter for the quadrotor aircraft is time-consuming, and it is difficult to achieve good control effect. Therefore, the fuzzy radial basis function (RBF) neural network PID control system for a quadrotor UAV based on particle swarm optimization (PSO) is designed to realize steady control of the system. In this control system, the control parameters of PID controller were adaptively adjusted by fuzzy RBF neural network, the control parameters of system were optimized by the hybrid learning methods integrating the offline particle swarm optimization (PSO) algorithm with the online Gradient Descent algorithm of local searching ability. The Matlab/Simulink simulation results show that the control system solve the problems of complex object control like the quadrotor UAV effectively, its parameter optimization algorithms can quickly converged and cannot be easily fallen to partial minimum, the control method has fast tracking ability, small overshoot, good decoupling ability, strong robust and adaptive ability, and it has better quality than the traditional PID coupling control method. <s> BIB105 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, a robust controller for a Six Degrees of Freedom (6 DOF) coaxial trirotor helicopter control is proposed in presence of defects in the system. A control strategy based on the coupling of the interval type-2 fuzzy logic control and sliding mode control technique are used to design a controller. The main purpose of this work is to eliminate the chattering phenomenon and guaranteeing the stability and the robustness of the system. In order to achieve this goal, interval type-2 fuzzy logic control has been used to generate the discontinuous control signal. The simulation results have shown that the proposed control strategy can greatly alleviate the chattering effect, and perform good reference tracking in presence of defects in the system. <s> BIB106 </s> Underactuated robotics: A review <s> Practical difficulties <s> The development of the control algorithms for under-actuated systems is important. Decoupled sliding mode control has been successfully employed to control under-actuated systems in a decoupling manner with the use of sliding mode control. However, in such a control scheme, the system functions must be known. If there are uncertainties in those functions, the control performance may not be satisfactory.In this paper, the direct adaptive fuzzy sliding mode control is employed to control a class of under-actuated uncertain systems which can be regarded as a combination of several subsystems with one same control input. By using the hierarchical sliding control approach, a sliding control law is derived so as to make every subsystem stabilized at the same time. But, since the system considered is assumed to be uncertain, the sliding control law cannot be readily facilitated. Therefore, in the study, based on Lyapunov stable theory a fuzzy compensator is proposed to approximate the uncertain part of the sliding control law. From those simulations, it can be concluded that the proposed compensator can indeed cope with system uncertainties. Besides, it can be found that the proposed compensator also provide good robustness properties. <s> BIB107 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper addresses the path following problem of an underactuated autonomous underwater vehicle (AUV) with the aim of dealing with parameter uncertainties and current disturbances. An adaptive robust control system was proposed by employing fuzzy logic, backstepping and sliding mode control theory. Fuzzy logic theory is adopted to approximate unknown system function, and the controller was designed by combining sliding mode control with backstepping thought. Firstly, the longitudinal speed was controlled, then the yaw angle was made as input of path following error to design the calm function and the change rate of path parameters. The controller stability was proved by Lyapunov stable theory. Simulation and outfield tests were conducted and the results showed that the controller is of excellent adaptability and robustness in the presence of parameter uncertainties and external disturbances. It is also shown to be able to avoid the chattering of AUV actuators. <s> BIB108 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, an Adaptive Fuzzy Backstepping Control (AFBC) approach with state observer is developed. This approach is used to overcome the problem of trajectory tracking for a Quadrotor Unmanned Aerial Vehicle (QUAV) under wind gust conditions and parametric uncertainties. An adaptive fuzzy controller is directly used to approximate an unknown nonlinear backstepping controller which is based on the exact model of the QUAV. Besides, a state observer is constructed to estimate the states. The stability analysis of the whole system is proved using Lyapunov direct method. Uniformly Ultimately Bounded (UUB) stability of all signals in the closed-loop system is ensured. The proposed control method guarantees the tracking of a desired trajectory, attenuates the effect of external disturbances such as wind gust, and solves the problem of unavailable states for measurement. Extended simulation studies are presented to highlight the efficiency of the proposed AFBC scheme. <s> BIB109 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this study, a supervisory control system with an adaptive Mamdani-type fuzzy controller (AMFC) is used to control an omnidirectional spherical mobile robot (ODSMR). The system combines an adaptive Mamdani-type fuzzy controller and a supervisory controller for ODSMRs with unknown external disturbances. Tracking is provided by a Mamdani-type fuzzy controller that approximates a theoretically exact control law, and a separate controller is used to cancel the residual of the approximation error. The control law is derived using Lyapunov stability theory to ensure the stability of the closed-loop system. Many external factors can cause the system to become unstable, so a supervisory controller is included. A decoupled control approach provides a simple method to achieve asymptotic stability for a fourth-order nonlinear system. The main concept of this approach is to decouple the system into two subsystems. Then, the primary subsystem combines the information provided by the secondary subsystem to generate a control that drives both subsystems to their desired states. This platform can move in any direction with no constraints. The efficiency of the proposed controller is verified with tests on an actual robot. The contributions of this study are: (1) the implementation of an ODSMR and (2) the application of the proposed AMFC with a supervisory control system to real-time control of the ODSMR. <s> BIB110 </s> Underactuated robotics: A review <s> Practical difficulties <s> The requirement for new flexible adaptive grippers is the ability to detect and recognize objects in their environments. It is known that robotic manipulators are highly nonlinear systems, and an accurate mathematical model is difficult to obtain, thus making it difficult make decision strategies using conventional techniques. Here, an adaptive neuro fuzzy inference system (ANFIS) for controlling input displacement and object recognition of a new adaptive compliant gripper is presented. The grasping function of the proposed adaptive multi-fingered gripper relies on the physical contact of the finger with an object. This design of the each finger has embedded sensors as part of its structure. The use of embedded sensors in a robot gripper gives the control system the ability to control input displacement of the gripper and to recognize particular shapes of the grasping objects. Fuzzy based controllers develop a control signal according to grasping object shape which yields on the firing of the rule base. The selection of the proper rule base depending on the situation can be achieved by using an ANFIS strategy, which becomes an integrated method of approach for the control purposes. In the designed ANFIS scheme, neural network techniques are used to select a proper rule base, which is achieved using the back propagation algorithm. The simulation results presented in this paper show the effectiveness of the developed method. <s> BIB111 </s> Underactuated robotics: A review <s> Practical difficulties <s> Quad rotor as an Unmanned Aerial Vehicle (UAV) has always drawn attention due to its widespread military and civilian applications during the recent decades. Despite the simplicity in design, the vehicle is inherently unstable. Hence, designing a proper controller to reach the stability purpose is of a great importance. In this paper fuzzy controllers have been proposed to control a quad rotor. Due to the high reliance of fuzzy controller's performance on the membership functions, the membership functions are optimized using particle swarm optimization and genetic algorithm. Finally, the results of the proposed methods are compared to verify their effectiveness on the fuzzy controllers. <s> BIB112 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper presents a novel Adaptive Fuzzy Sliding Mode Controller (AFSMC) for a model-scaled unmanned helicopter as real nonlinear plant. First, in order to efficient control law design, the nonlinear model of the helicopter is reformulated as an affine nonlinear system. To do this aim, a Dynamic Inverter (DI) is introduced as a bijective function. The proposed DI is used to interconnect the helicopter actuators' main inputs to the helicopter dynamic inputs. Then, AFSMC is designed to control it, and the asymptotic stability of the closed loop system is proved using Lyapunov stability theorem. To verify the merits of the proposed controller, it is compared with traditional sliding mode control system. Simulation results confirmed that the controller as a robust and stable control method has desired controlling performance and well cope with the undesirable chattering phenomenon. <s> BIB113 </s> Underactuated robotics: A review <s> Practical difficulties <s> The trajectory tracking of underactuated nonlinear system with two degrees of freedom is tackled by an adaptive fuzzy hierarchical sliding mode controller. The proposed control law solves the problem of coupling using a hierarchical structure of the sliding surfaces and chattering by adopting different reaching laws. The unknown system functions are approximated by fuzzy logic systems and free parameters can be updated online by adaptive laws based on Lyapunov theory. Two comparative studies are made in this paper. The first comparison is between three different expressions of reaching laws to compare their abilities to reduce the chattering phenomenon. The second comparison is made between the proposed adaptive fuzzy hierarchical sliding mode controller and two other control laws which keep the coupling in the underactuated system. The tracking performances of each control law are evaluated. Simulation examples including different amplitudes of external disturbances are made. <s> BIB114 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper addresses a three-dimensional (3D) path following control problem for underactuated autonomous underwater vehicle (AUV) subject to both internal and external uncertainties. A two-layered framework synthesizing the 3D guidance law and heuristic fuzzy control is proposed to achieve robust adaptive following along a predefined path. In the first layer, a 3D guidance controller for underactuated AUV is presented to guarantee the stability of path following in the kinematics stage. In the second layer, a heuristic adaptive fuzzy algorithm based on the guidance command and feedback linearization Proportional-Integral-Derivative (PID) controller is developed in the dynamics stage to account for the nonlinear dynamics and system uncertainties, including inaccuracy modelling parameters and time-varying environmental disturbances. Furthermore, the sensitivity analysis of the heuristic fuzzy controller is presented. Against most existing methods for 3D path following, the proposed robust fuzzy control scheme reduces the design and implementation costs of complicated dynamics controller, and relaxes the knowledge of the accuracy dynamics modelling and environmental disturbances. Finally, numerical simulation results validate the effectiveness of the proposed control framework and illustrate the outperformance of the proposed controller as well. HighlightsA two-layered framework synthesizing the guidance and control is proposed for 3D AUV path following.Robust and heuristic fuzzy path following algorithm is adopted to account for the system uncertainties.Proposed control scheme reduces the design and implementation cost with regard to most existing methods.Case study and quantitative comparison explicitly show the effectiveness of the proposed framework. <s> BIB115 </s> Underactuated robotics: A review <s> Practical difficulties <s> Abstract Fuzzy critic-based learning forms a reinforcement learning method based on dynamic programming. In this paper, an adaptive critic-based neuro-fuzzy system is presented for an unmanned bicycle. The only information available for the critic agent is the system feedback which is interpreted as the last action performed by the controller in the previous state. The signal produced by the critic agent is used along with the error back propagation to tune (online) conclusion parts of the fuzzy inference rules of the adaptive controller. Simulations and experiments are conducted to evaluate the performance of the proposed controller. The results demonstrate superior performance of the developed controller in terms of improved transient response, robustness to model uncertainty and fast online learning. <s> BIB116 </s> Underactuated robotics: A review <s> Practical difficulties <s> In this paper, a robust controller for a three degree of freedom helicopter control is proposed in presence of modeling error and disturbance. In this frame, interval type-2 fuzzy logic control approach (IT2FLC) and sliding mode control (SMC) techniques are used to design a controller named interval type-2 fuzzy sliding mode controller (IT2FSMC). Elevation, pitch and travel angles are considered measurable, whereas unmeasured states are estimated by using a nonlinear observer. The proposed control scheme can not only attenuate the chattering effect of the SMC, but also it reduces the rules number of the fuzzy controller. As for stability, it is exponentially guaranteed by using the Lyapunov criteria. The simulation results show that the IT2FSMC significantly alleviates the chattering effect and provides a good tracking performance, in the presence of modeling error and disturbance. They also illustrate that the IT2FSMC achieves the best tracking performance in comparison with the type-1 fuzzy logic controller, the IT2FLC and the type-1 fuzzy sliding mode controller. <s> BIB117 </s> Underactuated robotics: A review <s> Practical difficulties <s> This paper deals with the design of stabilizing controllers for a class of uncertain nonlinear systems with unknown constant input time delay. A new control method is introduced which merges an adaptive fuzzy sliding mode predictor with an adaptive fuzzy sliding mode controller to circumvent the effects of the unknown time delay, nonlinearities, and unknown plant dynamics. The proposed predictor and controller can be implemented in the real time without recursive and tedious calculations and only by using output-feedback. The uniform ultimate boundedness of the closed-loop system is also guaranteed. Simulation and experiment studies on a nonlinear benchmark problem reveal the effectiveness of the proposed method. <s> BIB118 </s> Underactuated robotics: A review <s> Practical difficulties <s> A hierarchically improved fuzzy dynamical sliding-model control (HIFDSMC) is presented to address the autonomous ground vehicle (AGV) path tracking problem. The proposed controller has two portions: one is the virtual desired input (VDI), and the second is the path tracking control (PTC). In addition to the equivalent control in VDI and PTC, an improved fuzzy dynamical sliding-mode control (IFDSMC) is designed to deal with the system uncertainties, e.g., different payloads. Contributions of this paper include the following four parts: 1) Based on the nominal system response, the fuzzy rules and scaling factors of the IFDSMCs in the VDI and PTC are easily chosen. In contrast, a conventional fuzzy logic control approach requires more trial-and-error tuning to obtain a satisfactory performance. 2) The proposed HIFDSMC possesses the tuning mechanism (the coefficients of two sliding surfaces, the scaling factors in indirect and direct modes, and the fine tuning in fuzzy table) such that the uncertainties are tackled without a larger computational burden. 3) The stability of the closed-loop system is verified by the Lyapunov stability with hierarchical concept. 4) Different payloads not at the mass center of the AGV (e.g., greater than 25% in the total weight of the AGV) are tackled by the IFDSMCs to obtain a satisfactory performance. Finally, the application to the assembly line of the AGV with different payloads to track the circular and piecewise straight-line paths by the proposed HIFDSMC is compared with the hierarchical fuzzy decentralized PTC. <s> BIB119
Industrial problems. Now, UR is widely used in aerospace and industrial exploration and manufacturing. Examples of such systems include ships, underwater vehicles, helicopters, aircraft, satellites, and space platforms. Despite the success of these cases in a well-structured environment, their complex uncertainty control technology environment is still immature. BIB029  Nevertheless, an expectation exists for superior applications of UR that need to operate autonomously in an unstructured and potentially dynamical changing environment.  Therefore, control technologies to meet the requirements are critical. High DOF composite UR problems. The benefits of UR could reduce weight, cost, and energy consumption while maintaining sufficient flexibility without losing access to the available configuration space. They are not damaged when striking objects and withstanding actuator failures better. As the DOF of UR increases, the reliability of the system decreases, which could lead to the practical problems in the control system. Fault-tolerant detection and control problems. Actuator failures may result in a reduction in the number of control inputs that convert a fully driven robotic system into a UR Model-free fuzzy control BIB008 BIB014 BIB009 BIB015 BIB086 BIB044 BIB087 BIB088 BIB089  BIB045 BIB077 Hybrid fuzzy control BIB024 BIB067 BIB068 BIB078 The integration of fuzzy control with other traditional control Fuzzy PID composite control BIB034 BIB002  BIB115 BIB090 BIB091 BIB049 BIB050 BIB051 BIB099 BIB079 Sliding mode variable structure control BIB052 Backstepping control BIB108 BIB100  BIB053 BIB109 Adaptive fuzzy control BIB082 BIB054 BIB040 BIB069 BIB092 BIB035 BIB016 BIB070 BIB055 BIB046 BIB101 Switching fuzzy control BIB036 BIB020 BIB025 Supervisory fuzzy control BIB110 BIB102 BIB041 Fuzzy systems improved by various artificial intelligence algorithms Neural fuzzy control BIB071 BIB083 BIB093 BIB103 BIB111 BIB094 BIB116 Fuzzy neural network control BIB104 BIB072 BIB037 BIB056 BIB095 Optimization methods for fuzzy control  BIB057 BIB112 BIB017 BIB105 BIB073 BIB058 BIB059  PFL Collocated PFL BIB001  BIB005 BIB003 BIB013   Non-collocated PFL  BIB063 BIB010 BIB018 BIB004 Energy-based methods BIB021 BIB006 BIB019 BIB038 SMC SMC with a model-free fuzzy system BIB060  BIB030 BIB026 BIB022  BIB080 BIB061 BIB096 BIB011 BIB031 BIB032 BIB064 BIB065 BIB084 BIB117 BIB106 BIB059 BIB081 Adaptive SMC with a direct or indirect fuzzy system BIB052 BIB079 BIB033 BIB027 BIB118 BIB085 BIB113 BIB107 BIB047 BIB097 BIB119 Hierarchical SMC BIB066 BIB042 BIB098 BIB031 BIB119 BIB062 BIB114 Optimal control BIB023  BIB074 BIB007 BIB012 BIB028  BIB039 BIB075 BIB043 BIB076 BIB048  PID: proportional-integral-derivative; PFL: partial feedback linearization; SMC: sliding mode control. system 351 or a robotic system with more control inputs to a robotic system with fewer control inputs. Sensor failures cause feedback signals to be delayed or lost, affecting the overall tracking performance of the system. Therefore, scientists and engineers in robot system design should consider both types of faults. It is highly recommended to use fault detection mechanisms.  Networked UR systems problems. Another practical problem is the network control of UR systems. Once introduced into the network, the communication between the actuators and the sensors may be interrupted, and the delay or loss of communication packets may result in poor control performance. Control of UR systems should be robust for network delays and require network control techniques (e.g. predictive control).