Underactuated robotics: A review <s> a. Model-based fuzzy control <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> BIB001 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <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> BIB002 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <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> BIB003 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <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> BIB004 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <s> This paper presents acrobatic control of an underactuated two-link robot called the pendubot. To achieve acrobatic control for the pendubot, we design a fuzzy controller for keeping first link swinging periodically while the second link maintains standing vertically. To facilitate the controller design, we represent the pendubot dynamics with a Takagi-Sugeno fuzzy model. We derive a linear matrix inequality (LMI) design condition to realize the acrobatic behavior. To accomplish the numerical feasibility design, we need to select carefully reference fuzzy model dynamics by taking into account some constraints. After selecting reference fuzzy model dynamics, an acrobatic controller is designed by solving the LMI condition. Simulation results show the utility of the proposed acrobatic control. <s> BIB005 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <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> BIB006 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <s> A new closed loop fuzzy motion control system including on-line Kalman's filter (KF) for the two dimensional motion of underactuated and underwater Remotely Operated Vehicle (ROV) is presented. Since the sway force is unactuated, new continuous and discrete time models are developed using a polar transformation. A new hierarchical control architecture is developed, where the high level fuzzy guidance controller generates the surge speed and the yaw rate needed to achieve the objective of planar motion, while the low level controller gives the thruster surge force and the yaw torque control signals. The Fuzzy controller ensures robustness with respect to uncertainties due to the marine environment, forward surge speed and saturation of the control signals. Also Lyapunov's stability of the motion errors is proved based on the properties of the fuzzy maps. If Inertial Measurement Unit data (IMU) is employed for the feedback directly, aleatory noises due to accelerometers and gyros damage the performances of the motion control. These noises denote a kind of non parametric uncertainty which perturbs the model of the ROV. Therefore a KF is inserted in the feedback of the control system to compensate for the above uncertainties and estimate the feedback signals with more precision. <s> BIB007 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <s> This paper presents a new direct discrete-time design methodology of a sampled-data observer-based output-feedback fuzzy controller for a class of nonlinear system that is exactly modeled in Takagi-Sugeno's form at least locally. A fundamental yet challenging issue in this direction is the unavailability of the exact discrete-time model of the nonlinear plant in a closed form. In contrast to the earlier works that are based on an approximate discrete-time model thus the stability obtained in the design step is not preserved in the implementation step, we employ an exact discrete-time fuzzy model in an integral form. Sufficient asymptotic stabilization conditions are investigated in the discrete-time Lyapunov sense. We then show that the resulting sampled-data controller indeed asymptotically stabilizes the nonlinear plant. An example is provided to illustrate the effectiveness of the proposed methodology. <s> BIB008 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <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> BIB009 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <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> BIB010 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <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> BIB011 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <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> BIB012 </s> Underactuated robotics: A review <s> a. Model-based fuzzy control <s> When modeling cranes, the hook and the suspended cargo are usually regarded roughly as one mass point for simplicity, i.e., the cargo swing is modeled as that of a single pendulum. However, in practice, when the hook mass is nonnegligible or the cargo has a large size, the crane always exhibits double-pendulum swing dynamics, which is much more complicated and makes most existing control methods unapplicable. In addition, all existing closed-loop controllers for (double-pendulum) cranes require full state feedback, while velocities are unavailable in most cases. Moreover, they need to linearize the nonlinear crane model and cannot respect the actuator's practical saturation constraint, which may probably lead to actuator saturation and badly degrade the control performance (even unstable). In response to these practical issues, we suggest a novel amplitude-saturated output feedback (OFB) control approach for underactuated crane systems exhibiting double-pendulum effects. We provide explicit Lyapunov-based analysis to rigorously prove that the equilibrium point of the closed-loop system is almost globally asymptotically stable, without any approximation to the original nonlinear dynamics. As far as we know, this paper presents the first closed-loop control method that can achieve control for an underactuated double-pendulum crane with merely OFB and theoretically-guaranteed saturated control efforts. Hardware experimental results demonstrate the superior performance of the proposed approach over existing methods and its strong robustness as well. <s> BIB013
The T-S fuzzy system is a special type of fuzzy logic system. Its fuzzy rules are different from the general fuzzy rule forms. The output of the T-S fuzzy system is still accurate without the blur canceller. The advantage is that the output could be represented by a linear combination of the input values. Therefore, the method of parameter estimation could be fully utilized to determine the parameters of the system. At the same time, the analytical method of the linear control system could be used to approximate the analysis and design of the fuzzy logic system. A disadvantage of this system is that the output portion of the rule does not have the form of a fuzzy linguistic value. Therefore, expert knowledge could not be fully utilized. The freedom of application of the various principles of fuzzy logic in this system is also limited. The research on T-S fuzzy system includes two aspects: T-S fuzzy system modeling and T-S fuzzy system control. Based on the T-S fuzzy model, Ma and Sun 154 studied the stability of nonlinear systems. And the effectiveness of the new method for nonlinear system output tracking and adjustment problems is proved by numerical simulation. Begovich et al.  combined the linear regulator theory with the T-S blur method. A method for realizing trajectory tracking of nonlinear systems is proposed. And the algorithm used for this tracking is described. Li et al. BIB005 designed a fuzzy controller for keeping the first link periodically oscillating while the second link remains vertically standing. Therefore, the stunt control of the Pendubot underactuated two-link robot is realized. Lee BIB008 presented a new direct discrete-time design methodology of a sampled-data observer-based output feedback (OFB) fuzzy controller for a class of nonlinear system that is exactly modeled in T-S's form at least locally. Xu et al.  presented a novel implementation of a T-S-type fuzzy logic controller (FLC) on a two-WMR, which consists of two wheels in parallel and an inverse pendulum. The controllability property for a class of T-S fuzzy models is analyzed, while a fully nonlinear stabilizer is designed in a practical way. b. Model-free fuzzy control Model-free fuzzy control is a heuristic method based on human experience and knowledge. Nalley and Trabia BIB001 designed a distributed FLC for each subsystem of the crane. Control is then distributed to multiple controllers. This makes it easier to identify fuzzy rules and collections. In order to improve the stability of UR, a new fuzzy logic control method for swing and balance control is proposed. Two independent fuzzy inference control laws are used for swing and balance control tasks. The fact shows the feasibility of fuzzy control methods in the application of nonlinear systems. BIB003 Based on the nonlinear model of crane, Mahfouf et al. BIB002 proposed an FLC with two rule bases for anti-sway control of bridge cranes. A novel amplitudesaturated OFB control method is used for underactuated crane systems with double pendulum effects. BIB013 Cho and Lee BIB004 designed a new fuzzy anti-swing control scheme for 3-D bridge cranes. The control scheme includes position servo control and fuzzy logic control. The robustness and effectiveness of the control are verified by experiments. It could be concluded that this control scheme has great potential for the anti-swing control of industrial 3-D bridge cranes. Based on the new continuous-and discrete-time models developed by polar coordinate transformation, Raimondi and Melluso BIB007 proposed a new fuzzy/Kalman closed-loop fuzzy motion control system for underactuated remotely operated vehicle. Khizer et al. BIB009 detailed the dynamics model of a small unmanned helicopter. Based on the nonlinear control technology of professional knowledge, the stable hover flight control of small unmanned helicopters in light air turbulence environment is proposed. Using a combination of expert knowledge and pilot-based experience, a stable inner-and outer-loop fuzzy control was designed. This control is used for attitude, altitude, and position. Based on the characteristics of the system and the desired motion, Trabia et al. BIB006 proposed a new method of inverse dynamics for adjusting the input and output variable ranges of three FLCs. The relative shape and distribution of the membership functions relative to each other remains fixed. The proposed method could be extended to other dynamic systems. It has the advantage of avoiding guessing the acceptable range of fuzzy variables. Based on the cart-seesaw and IP system, Lin et al. BIB010 proposed a new type of laboratory instrument called the cart-pendulumseesaw system. Unlike other model-based methods, the proposed fuzzy control method does not require accurate measurement of all state parameters. In addition, it is robust to parameter variations and other disturbances in the system. Based on the Lyapunov stability criterion, Hashemnia et al. proposed a stable fuzzy controller for stabilizing the motion of unmanned bicycles. BIB011 The Mamdani-like output recurrent fuzzy control strategy with a low-level microcontroller for the wheeled conveyance platform was presented in this study. A necessary condition based on the Lyapunov stability analysis is established to guarantee the system stability. BIB012 