Underactuated robotics: A review <s> Control methods of UR <s> A method of controlling the position of a manipulator composed of active and passive joints is described. The active joints have actuators and position sensors. The passive joints have holding brakes instead of actuators. While the brakes are released, the passive joints are indirectly controlled by the motion of the active joints using the coupling characteristics of manipulator dynamics. While the brakes are engaged, the passive joints are fixed and the active joints are controlled. The position of the manipulator is controlled by combining these two control modes. The basic principle of the control method and the conditions that ensure the controllability of the passive joints are described. An algorithm for point-to-point control of the manipulator is presented. The feasibility of the method is demonstrated by simulations for a manipulator with two degrees of freedom. > <s> BIB001 </s> Underactuated robotics: A review <s> Control methods of UR <s> A method for controlling a manipulator with passive joints, which have no actuators, in operational space is presented. The equation of motion is described in terms of operational coordinates. The coordinates are separated into active and passive components. The acceleration of the active components can be arbitrarily adjusted by using the coupling characteristics of manipulator dynamics. This method is also extended to path tracking control of a manipulator with passive joints. A desired path is geometrically specified in operational space. The position of the manipulator is controlled to follow the path. In this method, a path coordinate system based on the path is defined in operational space. The path coordinates consist of a component parallel to the path and components normal to the path. The acceleration of the components normal to the path is controlled according to feedback based on tracking error by using the dynamic coupling among the components. This in turn keeps the manipulator on the path. The effectiveness of the method is verified by experiments using a two-degree-of-freedom manipulator with a passive joint. > <s> BIB002 </s> Underactuated robotics: A review <s> Control methods of UR <s> A mechanism and a control method of a two-link brachiation robot are described. The robot can generate motions by a heuristic method and locomotes with the trajectory and arm-direction feedback control. It controls the switching amplitude by a method based on parametric excitation. Experimental results of the swing and locomotion control of the robot using these methods are given. They enable the robot to catch its target and to continue locomotion from any initial states. > <s> BIB003 </s> Underactuated robotics: A review <s> Control methods of UR <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> BIB004 </s> Underactuated robotics: A review <s> Control methods of UR <s> Chain form systems have recently been introduced to model the kinematics of a class of nonholonomic mechanical systems. The first part of the study is centered on control design and analysis for nonlinear systems which can be converted to the chain form. Solutions to various control problems (open-loop steering, partial or complete state feedback stabilization) are either recalled, generalized, or developed. In particular, globally stabilizing time-varying feedbacks are derived, and a discussion of their convergence properties is provided. Application to the control of nonholonomic wheeled mobile robots is described in the second part of the study by considering the case of a car pulling trailers. > <s> BIB005 </s> Underactuated robotics: A review <s> Control methods of UR <s> In our previous work, we analyzed nonlinear behaviours of a 2DOF free-joint manipulator with a periodic input and developed a positioning of the both joints by modulating the amplitude of the input. The strategy was effective but very heuristic and cannot be applied to other systems. In this paper, we apply the averaging method to the system and derive its behaviour from the averaged system. We also discuss its feedback control and design a feedback stabilization to a desired manifold. Even though its concept is the same as in Suzuki et al. (1996), the control strategy is analytically constructed. The feedback control is designed by a Lyapunov function for the averaged system and it is also effective for the real system. <s> BIB006 </s> Underactuated robotics: A review <s> Control methods of UR <s> Considers the problem of controlling an underactuated manipulator with less actuators than passive joints. The control methodology consists of dividing the passive joints in several groups, and of controlling one group at a time via its dynamic coupling with the actuators. Among the many possible control sequences for a given robot, we choose the optimal one based on the dynamic programming method. The optimization is based on a control cost defined as the reciprocal of the coupling index, a measure of the dynamic coupling available between the active and the passive joints of the manipulator. The detailed theory, computational procedures, simulation results, and experimental results are presented. <s> BIB007 </s> Underactuated robotics: A review <s> Control methods of UR <s> We outline a general approach for the stabilization of robots with passive joints, an interesting example of mechanical systems that may not be controllable in the first approximation. The proposed method is based on a recently introduced iterative steering paradigm, which prescribes the repeated application of a contracting open-loop control law. In order to complete efficiently such a law, the dynamic equations of the robot are put in a suitable form, via partial feedback linearization and approximate nilpotentization. The design procedure is illustrated for a 2R robot moving in the horizontal plane with a single actuator at the base. Experimental results are presented for a laboratory prototype. <s> BIB008 </s> Underactuated robotics: A review <s> Control methods of UR <s> A manipulator with free joints is a class of under-actuated mechanisms. Control of such systems is one of major topics in robotics and control engineering. In this paper, we apply the averaging method to manipulators connected by free joints and describe their behaviors in response to periodic inputs. We analyze 2R and 3R free-joint manipulators and show that each system has invariant manifolds defined by an energy-like conserved quantity. We also develop a control method via feedback modulation of the input amplitude to reach a desired invariant manifold. The effectiveness of the method is verified by computer simulations. <s> BIB009 </s> Underactuated robotics: A review <s> Control methods of UR <s> The nonlinear motion of underactuated mechanisms has drawn recent interests of researchers. Underactuated mechanical systems are often subject to so-called nonholonomic constraints which are related to many both theoretical and practical issues. We first analyze the nonlinear behavior of a two-joint planar manipulator with the second joint free, from nonlinear dynamics point of view. We then discuss the simultaneous positioning of both joints. We use a time-periodic input and propose an amplitude modulation of the feedback error. The analysis via the Poincare map shows that the behavior becomes chaotic with large amplitude. The effectiveness of the proposed positioning control is verified by experiments. <s> BIB010 </s> Underactuated robotics: A review <s> Control methods of UR <s> Manipulators with free joints are typical underactuated mechanisms. The constraints are second-order nonholonomic and control of such systems is quite difficult. Many researches have been made on control of such systems without considering friction at free joints. In this paper, we analyze the behaviors of 2R underactuated manipulators with friction at free joints by the averaging method in response to a periodic input. We define an energy-like function from analyses of frictionless systems and utilize it to the system with friction for feedback stabilization onto an invariant elliptic manifold. We also propose a control method to stabilize it to a stable manifold for systems with friction. The effectiveness of the method is verified by experiments. <s> BIB011 </s> Underactuated robotics: A review <s> Control methods of UR <s> A particular class of underactuated systems is obtained by considering kinematically redundant manipulators for which all joints are passive and the only available inputs are forces/torques acting on the end-effector. Under the assumption that the degree of redundancy is provided by prismatic joints located at the base, we address the problem of steering the robot between two arbitrary equilibrium configurations. By performing a preliminary partial feedback linearization, the dynamic equations take a convenient triangular form, which is further simplified under additional hypotheses. We give sufficient conditions for controllability of this kind of mechanisms. With a PPR robot as a case study, an algorithm is proposed for computing end-effector commands that produce the desired reconfiguration in finite time. Simulation results and a discussion on possible generalizations are given. <s> BIB012 </s> Underactuated robotics: A review <s> Control methods of UR <s> Abstract A new fuzzy controller for stabilization control of inverted pendulum systems is presented based on the Single Input Rule Modules (SIRMs) dynamically connected fuzzy inference model. The fuzzy controller has four input items, each with a SIRM and a dynamic importance degree. The SIRMs and the dynamic importance degrees are designed such that pendulum angular control has priority over cart position control. It is made clear that the fuzzy controller performs the pendulum angular control and the cart position control in parallel, and switching between the two controls is realized by automatically tuning the dynamic importance degrees according to control situations. The simulation results show that the proposed fuzzy controller has a high generalization ability to stabilize completely a wide range of the inverted pendulum systems within 9.0 s for an initial angle up to 30.0°. <s> BIB013 </s> Underactuated robotics: A review <s> Control methods of UR <s> This paper focuses on adaptive control of strict-feedback nonlinear systems using multilayer neural networks (MNNs). By introducing a modified Lyapunov function, a smooth and singularity-free adaptive controller is firstly designed for a first-order plant. Then, an extension is made to high-order nonlinear systems using neural network approximation and adaptive backstepping techniques. The developed control scheme guarantees the uniform ultimate boundedness of the closed-loop adaptive systems. In addition, the relationship between the transient performance and the design parameters is explicitly given to guide the tuning of the controller. One important feature of the proposed NN controller is the highly structural property which makes it particularly suitable for parallel processing in actual implementation. Simulation studies are included to illustrate the effectiveness of the proposed approach. <s> BIB014 </s> Underactuated robotics: A review <s> Control methods of UR <s> A robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances. The controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique. For each auxiliary system, an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics, and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well. It is shown that the resulting closed-loop systems guarantee a satisfactory transient and asymptotic performance. A simulation example is also presented to illustrate the design procedure and controller performance. <s> BIB015 </s> Underactuated robotics: A review <s> Control methods of UR <s> Ball and beam system is one of a nonlinear and unstable control system, thus providing a challenge to the control engineers and researchers. There are a number of controllers which have been studied for years that can be used to stabilize the ball and beam system. This paper investigates the performance of few different control approaches that consist of conventional controller, modern controller and intelligent controller for a ball and beam system. It will involve the derivation of the mathematical modeling that includes the linearization of the model in order to be used with the linear controllers. The works followed with designing those controllers and simulating it in MATLAB. Each controller performance will be analyzed and compared which is based on common criteria’s of the step response. An appropriate graphic user interface (GUI) has been developed to view the animation of the ball and beam system. <s> BIB016 </s> Underactuated robotics: A review <s> Control methods of UR <s> In this paper, we revisit the energy-based swing-up control problem for a rotational pendulum. Different from the existing energy-based control solution, first, we present a necessary and sufficient condition for avoiding singular points in the control law and carry out a global motion analysis of the pendulum. Next, we remove the previous required constraint on the initial state of the pendulum and the control parameters for preventing the pendulum getting stuck at the downward equilibrium point by revealing that the point is saddle (hyperbolic and unstable). Specifically, we show that the Jacobian matrix evaluated at the point has two and two eigenvalues in the open leftand right-half planes, respectively. We prove that the pendulum will eventually be swung up into the basin of attraction of any locally stabilizing controller for all initial conditions with the exception of a set of Lebesgue measure zero. Finally, we validate the presented theoretical results via numerical simulation of two rotational pendulums. Our simulation results show that the swing-up control can be achieved quickly under the improved conditions on the control parameters. <s> BIB017 </s> Underactuated robotics: A review <s> Control methods of UR <s> To accelerate the convergence of a terminal sliding mode and avoid the singularity of the controller,an analysis for the cause of singularity in terminal sliding mode is presented in this paper.Based on Lie algebra,the nonsingular criterion is provided for the terminal sliding mode controller.Thereafter,two novel nonsingular fast terminal sliding modes are designed with convergence speed faster than that of a normal fast terminal sliding mode at any points.The formula of convergence time is derived.The new fast terminal sliding mode is combined with the dynamic sliding mode to eliminate chattering.Then,controllers are designed for the fast loop and slow loop of a near space vehicle.In order to improve the control effect,a nonlinear disturbance observer is used to approximate the compound disturbances.By means of the Lyapunov theorem,the system is proved to be stable.Finally,simulation is conducted. <s> BIB018 </s> Underactuated robotics: A review <s> Control methods of UR <s> The ball and beam system is a laboratory equipment with high nonlinearity in its dynamics. The aims of this research are to model the ball and beam system considering nonlinear factors and coupling effect and to design controllers to control the ball position. The LQR is designed considering two Degrees-of-Freedom and coupling dynamics. The parameters of the LQR are tuned using Genetic Algorithm (GA). Jacobian linearization method is used to linearize the system around operating-point. Due to the noise of the sensor in the experimental setup, a state observer is designed to observe the velocity of the ball. In order to compare the performance of the LQR and study the effect of simplifying assumptions, two control strategies are designed and implemented: Proportional Derivative Integral (PID) as non-model based control strategy, hybrid PID and Linear Quadratic Regulator (LQR) as combination of model based and non-model based control strategies. The experimental results of this research prove the model based control strategies outperforms the non-model based or hybrid controllers in a nonlinear and noisy ball and beam system. In addition, it is shown that the coupling dynamics cannot be eliminated as a simplifying assumption in designing the controller. <s> BIB019 </s> Underactuated robotics: A review <s> Control methods of UR <s> This paper presents an improved backstepping design (IBD) for the control of a new type of underactuated inverted pendulum. The characteristics and possible applications of the inverted pendulum are presented. Nonlinear models and a linearized model are given for a straightforward explanation of its dynamic features. The conventional backstepping design (CBD) is revisited for this plant. The IBD is then used to reduce the complexity of the design and to allow the specification of transient characteristics, to improve the system’s performance. Experimental studies are conducted to investigate the effectiveness of the proposed scheme. <s> BIB020 </s> Underactuated robotics: A review <s> Control methods of UR <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> BIB021 </s> Underactuated robotics: A review <s> Control methods of UR <s> Overhead power line inspection robots,which mainly adopt suspension arm mechanism,always perform less capabilities of attitude control and obstacle crossing.For the features of dual-arm mechanism based on the centroid adjustment,a novel structure of climbing mechanism is proposed.The climbing mechanism is analyzed and parameterized from the aspects of capability improvement of attitude control and slope climbing.Based on the kinematic model of climbing mechanism the scheme of attitude monitoring is proposed.The results of simulation based on ADAMS confirm that the climbing mechanism design is reasonable and can improve the capabilities of robot’s attitude control and obstacle crossing. <s> BIB022 </s> Underactuated robotics: A review <s> Control methods of UR <s> In this paper, a new fuzzy adaptive control approach is developed for a class of SISO uncertain pure-feedback nonlinear systems with immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions; and the filtered signals are introduced to circumvent algebraic loop systems encountered in the implementation of the controller, and a fuzzy state adaptive observer is designed to estimate the immeasurable states. By combining the adaptive backstepping technique, an adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach. <s> BIB023 </s> Underactuated robotics: A review <s> Control methods of UR <s> A boundary layer adaptive sliding-mode controller is developed for a class of multi-input and multi-output(MIMO) nonlinear uncertain systems based on the nonlinear disturbance observer(NDO). The developed adaptive slidingmode controller has been applied to the high-precision attitude control for near space vehicles. Considering the system uncertainty and the unknown upper bound of the external disturbance, we design the boundary layer adaptive sliding-mode control scheme for eliminating the chattering phenomenon appeared in the traditional sliding-mode control and making the tracking error to approach zero. The rigorous stability of the closed-loop system is proved by using the Lyapunov method.Finally, simulation results demonstrate that the proposed control scheme can achieve good control performances for the attitude control of the near space vehicle under the unknown disturbance and the system uncertainty. <s> BIB024 </s> Underactuated robotics: A review <s> Control methods of UR <s> A new type of tele-supervisory system is developed for power transmission line inspection robot.By real-time communicating with robot local controller and multi-thread technology,this system realizes robot attitude control and machine vision detection.By sending control commands and receiving data to the robot controller,robot artificial remote tele-operation is achieved,along with mixed programming of Lab VIEW and Matlab by using Matlab Script node for purpose of the calculation of centroid and multi-joint attitude.And by sharing databases between LabVIEW and Visual Prolog to call application functions of robot motion planning developed by the latter,robot autonomous attitude control is achieved.The results of experiments show that the system has strong real-time performance,good interactivity and acceptable reliability. <s> BIB025 </s> Underactuated robotics: A review <s> Control methods of UR <s> Combining sliding mode control method with radial basis function neural network (RBFNN), this paper proposes a robust adaptive control scheme based on backstepping design for re-entry attitude tracking control of near space hypersonic vehicle (NSHV) in the presence of parameter variations and external disturbances. In the attitude angle loop, a robust adaptive virtual control law is designed by using the adaptive method to estimate the unknown upper bound of the compound uncertainties. In the angular velocity loop, an adaptive sliding mode control law is designed to suppress the effect of parameter variations and external disturbances. The main benefit of the sliding mode control is robustness to parameter variations and external disturbances. To further improve the control performance, RBFNNs are introduced to approximate the compound uncertainties in the attitude angle loop and angular velocity loop, respectively. Based on Lyapunov stability theory, the tracking errors are shown to be asymptotically stable. Simulation results show that the proposed control system attains a satisfied control performance and is robust against parameter variations and external disturbances. <s> BIB026 </s> Underactuated robotics: A review <s> Control methods of UR <s> An adaptive backstepping-based non-singular terminal sliding mode (NTSM) control method is proposed for a class of uncertain nonlinear systems in the parameteric-strict feedback form. The adaptive control law is combined with the first n−1 steps of the backstepping method to estimate the unknown parameters of the system. In the nth step, an NTSM control strategy is utilized to drive the last state of the system to converge in a finite time. Furthermore, the derivate estimator is used to obtain the derivates of the states of the error system; the higher-order non-singular terminal sliding mode control (HONTSMC) law is designed to eliminate the chattering and make the system robust to both matched and unmatched uncertainties. Compared to the adaptive backstepping-based linear sliding mode control method (LSMC), the proposed method improves the convergence rate and the steady-state tracking accuracy of the system, and makes the control signal smoother. Finally, the compared simulation results are presented to validate the method. <s> BIB027 </s> Underactuated robotics: A review <s> Control methods of UR <s> In this paper, a composite adaptive fuzzy output-feedback control approach is proposed for a class of single-input and single-output strict-feedback nonlinear systems with unmeasured states and input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws are developed. It is proved that all the signals of the closed-loop system are bounded and the system output can follow the given bounded reference signal. A numerical example and simulation comparisons with previous control methods are provided to show the effectiveness of the proposed approach. <s> BIB028 </s> Underactuated robotics: A review <s> Control methods of UR <s> This paper presents a gain scheduling backstepping control (GSBC) for motion balance adjusting of a power-line inspection (PLI) robot, which is an underactuted mechanical system of two degrees of freedom with one control input. First, a dynamic model of the motion balance adjusting of the PLI robot is constructed. Second, this model is linearized at a nominal operating point to overcome the computation infeasibility of the conventional backstepping technique. Finally, to extend the operation area of the closed-loop system further from the nominal operating point, an equilibrium manifold linearization model (EML model) is developed using a scheduling variable, and then the GSBC scheme is designed based on the EML model. The robust stability of the closed-loop system is ensured by the Lyapunov theorem. Simulation results show that the GSBC gives much better performance than that of the backstepping control, these results illustrate the feasibility of the proposed control scheme. <s> BIB029 </s> Underactuated robotics: A review <s> Control methods of UR <s> This paper is concerned with the adaptive sliding mode control problem of uncertain nonlinear systems. Interval type-2 Takagi–Sugeno (T–S) fuzzy model is employed to represent uncertain nonlinear systems. The input matrices of the nonlinear systems are allowed to be different for the sliding mode controller design. The uncertain parameters are described by the lower and upper membership functions. An integral sliding mode surface is designed for analysis of sliding motion. Based on the sliding mode surface, a novel sliding mode controller is designed to guarantee that the closed-loop system is uniformly ultimately bounded. Some simulation results are given to illustrate the effectiveness of the presented control scheme. <s> BIB030 </s> Underactuated robotics: A review <s> Control methods of UR <s> The present paper deals with the control of a knee joint orthosis intended to be used for rehabilitation and assistive purposes. A model, integrating human shank and orthosis, is presented. To reduce the influence of the uncertainties in muscular torque modeling on the system control, a nonlinear observer is proposed to estimate the muscular torque developed by the wearer. Additionally, a robust terminal sliding mode control approach combined with the nonlinear observer is presented. To illustrate the effectiveness of the proposed control method, a comparison with two control methods, basic sliding mode and sliding mode with nonlinear observer, are also given. The asymptotic stability of the presented approaches and observer convergence are proved by means of a Lyapunov analysis. Furthermore, the proof of advantage of the robust terminal sliding mode control method with the nonlinear observer (improving the tracking precision and reducing the required time for eliminating external disturbances) is proposed as well. The experiment results show that the robust terminal sliding mode control approach combined with the nonlinear observer has a significant advantage with respect to the position tracking and robustness regarding the modeling identification errors and external disturbances. This paper deals with the control of a knee joint exoskeleton for rehabilitation purposes.An observer is proposed to estimate the muscular torque developed by the wearer.A robust terminal sliding mode control method combined with the observer is presented.Asymptotic stability is proved by means of a Lyapunov analysis.Experiment tests were conducted with three subjects. <s> BIB031 </s> Underactuated robotics: A review <s> Control methods of UR <s> In this paper, a novel adaptive sliding mode controller is designed for Takagi–Sugeno (T–S) fuzzy systems with actuator saturation and system uncertainty. By the delta operator approach, the discrete-time nonlinear system is described by a T–S fuzzy model with unmeasurable state. By singular value decomposition of system input matrix, a reduced-order system is obtained for the design of sliding mode surface. A new adaptive sliding mode controller based on system output is presented to guarantee that the closed-loop system is uniformly ultimately bounded. Four examples are provided to illustrate the effectiveness and applicability of the proposed control scheme. <s> BIB032 </s> Underactuated robotics: A review <s> Control methods of UR <s> In this paper, a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict-feedback nonlinear systems with unknown time-varying delays, unmeasured states, and input saturation. First, fuzzy logic systems are employed to approximate unknown nonlinear functions in the system. Next, a smooth function is used to approximate the input saturation and an adaptive fuzzy state observer is constructed to solve the problem of unmeasured states. Based on the designed adaptive fuzzy state observer, a serial-parallel estimation model is established. By applying adaptive fuzzy dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial–parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws is developed based on Lyapunov–Krasovskii functional. It is proved that all variables of the closed-loop system are bounded and the system outputs can follow the given bounded reference signals as close as possible. A simulation example is provided to further show the effectiveness of this novel control scheme. <s> BIB033 </s> Underactuated robotics: A review <s> Control methods of UR <s> INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises <s> BIB034 </s> Underactuated robotics: A review <s> Control methods of UR <s> An underactuated mechanical system with \(n~(n\ge 3)\) degree of freedoms (DOFs) is a complicated nonlinear system. This paper develops a new strategy to solve the nonlinear stabilizing control problem for this kind of mechanical systems. First, we introduce a coupled relationship between control torques. It changes the n-DOF underactuated system into a cascade-connected system, which has a 2-DOF driven subsystem and a \((n-2)\)-DOF stable driving subsystem. And then, we analyze the passivity of the driven subsystem and discuss how to design an passivity-based controller that stabilizes the driven subsystem at the origin. Finally, the stabilization of the n-DOF underactuated system is achieved by the triangle lemma. Our proposed strategy transforms the stabilization of the n-DOF underactuated system into that of the 2-DOF driven subsystem. This makes the structure of the control system simple and also makes the problem of stabilizing a multi-DOF underactuated system easy to handle. As an application of the strategy, we give detailed statements of using it to achieve the global stabilization of a 3-DOF underactuated mechanical system called spring-coupled horizontal three-link underactuated manipulator. Simulation results demonstrate its validity. <s> BIB035 </s> Underactuated robotics: A review <s> Control methods of UR <s> This paper presents an adaptive gain-scheduled backstepping control ( AGSBC ) scheme for the balance control of an underactuated mechanical power-line inspection ( PLI ) robotic system with two degrees of freedom and a single control input. First, a nonlinear dynamic model of the balance adjustment process of the PLI robot is constructed, and then the model is linearized at a nominal equilibrium point to overcome the computational infeasibility of the conventional backstepping technique. Second, to solve generalized stabilization control issue for underactuated systems with multiple equilibrium points, an equilibrium manifold linearized model is developed using a scheduling variable, and then a gain-scheduled backstepping control ( GSBC ) scheme for expanding the operational area of the controlled system is constructed. Finally, an adaptive mechanism is proposed to counteract the impact of external disturbances. The robust stability of the closed-loop system is ensured by Lyapunov theorem. Simulation results demonstrate the effectiveness and high performance of the proposed scheme compared with other control schemes. <s> BIB036
In the early 1990s, in the theory of nonlinear control, the control of underactuated systems once attracted widespread attention and study. So far, the control of underactuated systems has been studied mainly by point stabilization, trajectory tracking, and path tracking. The strong coupling and high nonlinearity of underactuated systems make their control more difficult. In the development of robotics for more than 30 years, almost all design methods that could be provided from classical to modern control theory have been tried on UR. On the basis of summarizing the predecessors, the researchers developed various control strategies to solve the control problem of UR. However, most of these control strategies are based on accurate mathematical models in mathematical theories, which make it difficult for most control theories and strategies to be used in UR systems. Usually, the control of the underactuated part of the underactuated mechanical system is realized by using motion coupling or dynamic coupling. BIB004 BIB001 BIB003 BIB034  BIB008 BIB011 BIB006 BIB009 BIB002 BIB012 BIB010 BIB005 Zhang et al. BIB035 presented a torque-coupled control strategy to solve the stabilization control problem for a class of n-DOF (n 3) underactuated mechanical systems. Examples of utilizing motion coupling are first-order nonholonomic systems, such as WMRs and smart robotic hands. The equations of these systems are drift-free with inputs entering linearly. A second type of system characterized by dynamic coupling is provided by many examples: crane systems, the classical cart-pole system, Acrobots, and manipulators with flexible elements. The second type of equation includes drift terms for gravity, centripetal, Coriolis, and/or elastic forces whose inputs are affine. Underactuation does not always mean uncontrollability. Whether or not it is controllable depends on the structure of the system under consideration. All previous examples are controllable. However, in the case of a planar manipulator with a free joint, BIB006 BIB001 demonstrated that the number of active joints should be equal to or greater than the number of passive joints to control the passive ones. A Cartesian space controller was also designed to achieve the desired set points for all joints. BIB002 Saito et al. BIB003 developed a two-link underactuated arm robot that could be moved along the crossbar with just one actuator. Bergerman and Xu 122 studied the variable structure control of a three-link manipulator with a passive joint in both joint and Cartesian space. Compared with systems using passive joints, it is very rare to control systems that have free joints. Working with a PFL and energy-based method, Spong 8 studied the vibration control problem of Acrobot. Recently, a scholastic work by Nakamura et al. BIB011 BIB006 BIB009 BIB010 investigated the application of periodic oscillations to control the manipulators with free joints. Oscillation control based on Poincaré mapping analysis also appears in the study by Suzuki et al. BIB009 De Luca et al. BIB008 proposed a constructive open-loop control strategy involving nilpotent approximations and iterative steps. Then, because fewer actuators reduce costs and weight, the control of the robot systems with an underactuation property is more attractive. There are many UR systems in practical applications, such as pendulum systems, BIB020 BIB017 BIB013 ball-and-beam systems, BIB021 BIB019 BIB016 and power line inspection robotic systems. BIB007 BIB029 BIB036 BIB025 BIB022 However, the controller designs of UR systems are more complex than fully actuated robot systems, especially UR systems could cause performance degradation when subjected to external disturbances. In recent years, controller design of uncertain UR systems has attracted widespread attention, and various control algorithms have been proposed, such as sliding mode control (SMC),  BIB030 BIB031 BIB018 BIB024 BIB032 backstepping control, BIB023 BIB026 BIB027 BIB015 BIB014 and robust control and adaptive control.  BIB028 BIB033 The control of UR would be discussed in the following two control methods: open-loop control and closed-loop control. The UR has the feature that the number of independent generalized coordinate change is less than the number of its generalized coordinates, that is, the number of DOF is less than the dimension of the spatial space. Then, from the perspective of control theory, the concern is how to control the shape or motion of the UR with less control input than the dimension of the UR's positional space for a controllable UR.