Experimental Control of a Two-Dof Flexible Robot Manipulator by Optimal and Sliding Methods

This paper presents an experimental study of a robust control scheme for flexible-link robotic manipulators. The design is based on a simple strategy for trajectory tracking which exploits the two-time scale nature of the flexible part and the rigid part of the dynamic equations of this kind of robotic arms: A slow subsystem associated with the rigid motion dynamics and a fast subsystem associated with the flexible link dynamics. Two experimental approaches are considered. In a first test an LQR optimal design strategy is used, while a second design is based on a sliding-mode scheme. Experimental results on a laboratory two-dof flexible manipulator show that this composite approach achieves good closed-loop tracking properties for both design philosophies, which compare favorably with conventional rigid robot control schemes.     

基于干扰观测器的机械臂广义模型预测轨迹跟踪控制

为实现对多自由度机械臂关节运动精确轨迹跟踪,提出一种基于非线性干扰观测器的广义模型预测轨迹跟踪控制方法。针对机械臂轨迹跟踪运动学子系统,采用广义预测控制（Generalized Predictive Control,GPC）方法设计期望的虚拟关节角速度。对于机械臂轨迹跟踪动力学子系统,考虑机械臂的参数不确定性和未知外界扰动,利用GPC方法设计关节力矩控制输入,基于非线性干扰观测器方法实时估计和补偿系统模型中的不确定性。在李雅普诺夫稳定性理论框架下证明了机械臂关节角位置和角速度的跟踪误差最终收敛于零的小邻域。数值仿真验证了所提出控制方法的有效性和优越性。     

A new approach to robust position/force control of flexible-joint robot manipulators

In this paper a new approach employing smooth robust compensators is proposed for the control of uncertain elastic-joint robot manipulators during contact tasks. It is assumed that the flexible-joint manipulators consist of two subsystems: the rigid subsystem and the flexible subsystem. The output of the flexible subsystem is assumed to be the input of the rigid subsystem. The control design is carried out in two steps. First, a desired input is designed for the rigid subsystem, which can robustly stabilize it. Second, a robust controller is designed to stabilize the flexible subsystem so that it generates the necessary torque designed for the rigid subsystem. By using this approach, the robot manipulator can exert a preset amount of force on the environment while tracking a desired trajectory with global asymptotic stability. Lyapunov's direct method is used here to prove the global asymptotic stability of the closed-loop system. The assumption of weak joint elasticity is relaxed and exact knowledge of joint stiffness is not required for the control design. Also, exact knowledge of robot kinematic and dynamic parameters and actuator parameters are not required. Unlike other approaches, this approach takes the environmental stick-slip friction as well as its dependency on normal contact force into consideration. It compensates for the adverse effects of the stick-slip friction. The proposed controller produces a smooth control action, and ensures smooth motion on the contact surface. The efficacy of the proposed controller is illustrated with the help of a numerical example of a two-link flexible-joint robot. © 1996 John Wiley & Sons, Inc.     

A Robust Tracking Controller for Electrically Driven Robot Manipulators: Stability Analysis and Experiment

 In this paper, a robust controller for electrically driven robotic systems is developed. The controller is designed in a backstepping manner. The main features of the controller are: 1) Control strategy is developed at the voltage level and can deal with both mechanical and electrical uncertainties. 2) The proposed control law removes the restriction of previous robust methods on the upper bound of system uncertainties. 3) It also benefits from global asymptotic stability in the Lyapunov sense. It is worth to mention that the proposed controller can be utilized for constrained and nonconstrained robotic systems. The effectiveness of the proposed controller is verified by simulations for a two link robot manipulator and a four-bar linkage. In addition to simulation results, experimental results on a two link serial manipulator are included to demonstrate the performance of the proposed controller in tracking a given trajectory.     

Motion Control of a Nonholonomic Mobile Manipulator in Task Space

In this paper, the motion control of a mobile manipulator subjected to nonholonomic constraints is investigated. The control objective is to design a computed‐torque controller based on the coupled dynamics of the mobile manipulator. The proposed controller achieves the capability of simultaneous tracking of a reference velocity for the mobile base and a reference trajectory for the end‐effector. The aforementioned reference velocity and trajectory are defined in the task space, such task setting imitates the actual working conditions of a mobile manipulator and thus makes the control problem practical. To solve this tracking problem, a steering velocity is firstly designed based on the first‐order kinematic model of the nonholonomic mobile base via dynamic feedback linearization. The main merit of the proposed steering velocity design is that it directly utilizes the reference velocity set in the task space without requiring the knowledge of a reference orientation. A torque controller is subsequently developed based on a proposed Lyapunov function which explicitly considers the coupled dynamics of the mobile manipulator to ensure the mobile base and end‐effector track the reference velocity and trajectory respectively. This proposed computed‐torque controller is able to realize asymptotic stability of both the base velocity tracking error and the end‐effector motion tracking error. Simulations are conducted to demonstrate the effectiveness of the proposed controller.     

考虑柔性关节的机械臂自适应运动控制策略研究

具有柔性关节的轻型机械臂因其自重轻、响应迅速、操作灵活等优点,取得了广泛应用;针对具有柔性关节的机械臂系统的关节空间轨迹跟踪控制系统动力学参数不精确的问题,提出一种结合滑模变结构设计的自适应控制器算法;通过自适应控制的思想对系统动力学参数进行在线辨识,并采用Lyapunov方法证明了闭环系统的稳定性;仿真结果表明,该控制策略保证了机械臂系统对期望轨迹的快速跟踪,具有良好的跟踪精度,系统具有稳定性。     

Hybrid control: A constrained motion perspective

Control of manipulators during execution of tasks that require the end-effector to come into contact with objects in its work environment represents an important class of control problem. Hybrid control, a concept which defines the architecture of a class of control laws has been proposed as a method with which to solve this control problem. One interpretation of the hybrid control method is within the framework of constrained motion control. Constrained motion occurs during contact by the manipulator end-effector with rigid objects in the workplace, hence the motion of the manipulator is kinematically constrained. Papers have appeared in the robotics control literature addressing hybrid control within the constrained motion context which do not explicitly use the constrained dynamic formulation that correctly describes the dynamic behaviour of the manipulator. This article serves to link results from constrained motion control and the existing literature on the hybrid control method. In this article a formulation of the constrained manipulator dynamics is presented in which the hybrid control design is most naturally carried out. This formulation of the manipulator dynamics, previously proposed in the robotics literature, is such that the generalized force and position coordinates to be controlled are mutually orthogonal. Hence, the hybrid selection matrices, a key element of the hybrid control design philosophy, are implicit in this coordinate representation. A hybrid control design methodology is then formulated based on this development. Two hybrid control laws are proposed. For each hybrid control law, the global asymptotic stability is readily established due to the natural coordinate representation. One of these hybrid control laws, a constrained motion control law already proposed in the literature, is given to illustrate the equivalence of the hybrid control design and certain existing constrained motion control methods. Finally, a concrete example of a three-degree-of-freedom robotic manipulator illustrates the hybrid design methodology proposed.     

On the learning control of a robot manipulator

This paper derives a learning control law to achieve trajectory following for a robot manipulator. The controller consists of two parts, a computed torque servo for the rigid body terms that can be modelled and a learning law for the unmodelled dynamics. An advantage of this method is that bounds can be assigned to the position and velocity tracking errors.     

Collaborative Multi-MSA Multi-Target Tracking and Surveillance: a Divide &; Conquer Method Using Region Allocation Trees

This work deals with the problem of the accurate task space control subject to finite-time convergence. Kinematic and dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, unbounded disturbances, i.e., such structures of the modelling functions that are generally not bounded by construction, are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous (chattering-free) robust controllers based on the estimation of a Jacobian transpose matrix, which seem to be effective in counteracting uncertain both kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a 2DOF robotic manipulator with two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.     

力矩输入有界的柔性关节机器人轨迹跟踪控制

为解决柔性关节机器人在关节驱动力矩输出受限情况下的轨迹跟踪控制问题,提出一种基于奇异摄动理论的有界控制器.首先,利用奇异摄动理论将柔性关节机器人动力学模型解耦成快、慢两个子系统.然后,引入一类平滑饱和函数和径向基函数神经网络非线性逼近手段,依据反步策略设计了针对慢子系统的有界控制器.在快子系统的有界控制器设计中,通过关节弹性力矩跟踪误差的滤波处理加速系统的收敛.同时,在快、慢子系统控制器中均采用模糊逻辑实现控制参数的在线动态自调整.此外,结合李雅普诺夫稳定理论给出了严格的系统稳定性证明.最后,通过仿真对比实验验证了所提出控制方法的有效性和优越性.     

State Space Constrained Iterative Learning Control for Robotic Manipulators

Real‐life work operations of industrial robotic manipulators are performed within a constrained state space. Such operations most often require accurate planning and tracking a desired trajectory, where all the characteristics of the dynamic model are taken into consideration. This paper presents a general method and an efficient computational procedure for path planning with respect to state space constraints. Given a dynamic model of a robotic manipulator, the proposed solution takes into consideration the influence of all imprecisely measured model parameters, making use of iterative learning control (ILC). A major advantage of this solution is that it resolves the well‐known problem of interrupting the learning procedure due to a high transient tracking error or when the desired trajectory is planned closely to the state space boundaries. The numerical procedure elaborated here computes the robot arm motion to accurately track a desired trajectory in a constrained state space taking into consideration all the dynamic characteristics that influence the motion. Simulation results with a typical industrial robot arm demonstrate the robustness of the numerical procedure. In particular, the results extend the applicability of ILC in robot motion control and provide a means for improving the overall trajectory tracking performance of most robotic systems.     

Unconstrained and constrained motion control of a planar two-link structurally flexible robotic manipulator

Unconstrained and constrained motion control of a planar two-link structurally-flexible robotic manipulator are considered in this study. The dynamic model is obtained by using the extended Hamilton's principle and the Galerkin criterion. A method is presented to obtain the linearized equations of motion in Cartesian space for use in designing the control system. The approach to solving the control problem is to use feedforward and feedback control torques. The feedforward torques maneuver the flexible manipulator along a nominal trajectory and the feedback torques minimize any deviations from the nominal trajectory. The feedforward and feedback torques are obtained by solving the inverse dynamics problem for the rigid manipulator and designing linear quadratic Gaussian with loop transfer recovery (LQG/LTR) compensators, respectively. The LQG/LTR design methodology is exploited to design a robust feedback control system that can handle modeling errors and sensor noise, and operate on Cartesian space trajectory errors. Computer simulated results are presented for an example planar, two-link, structurally flexible robotic manipulator. © 1994 John Wiley & Sons, Inc.     

Learning Control of Robot Manipulators in Task Space

Two important properties of industrial tasks performed by robot manipulators, namely, periodicity (i.e., repetitive nature) of the task and the need for the task to be performed by the end‐effector, motivated this work. Not being able to utilize the robot manipulator dynamics due to uncertainties complicated the control design. In a seemingly novel departure from the existing works in the literature, the tracking problem is formulated in the task space and the control input torque is aimed to decrease the task space tracking error directly without making use of inverse kinematics at the position level. A repetitive learning controller is designed which “learns” the overall uncertainties in the robot manipulator dynamics. The stability of the closed‐loop system and asymptotic end‐effector tracking of a periodic desired trajectory are guaranteed via Lyapunov based analysis methods. Experiments performed on an in‐house developed robot manipulator are presented to illustrate the performance and viability of the proposed controller.     

Trajectory control of a two DOF rigid–flexible space robot by a virtual space vehicle

Model based control schemes use inverse dynamics of the robot arm to produce the main torque component necessary for trajectory tracking. For a model-based controller one is required to know the model parameters accurately. This is a very difficult job especially if the manipulator is flexible. This paper presents a control scheme for trajectory control of the tip of a two arm rigid–flexible space robot, with the help of a virtual space vehicle. The flexible link is modeled as an Euler–Bernoulli beam. The developed controller uses the inertial parameters of the base of the space robot only. Bond graph modeling is used to model the dynamics of the system and to devise the control strategy. The efficacy of the controller is shown through simulated and animation results.     

Constrained motion control of flexible robot manipulators based on recurrent neural networks

In this paper, a neural network approach is presented for the motion control of constrained flexible manipulators, where both the contact force everted by the flexible manipulator and the position of the end-effector contacting with a surface are controlled. The dynamic equations for vibration of flexible link and constrained force are derived. The developed control, scheme can adaptively estimate the underlying dynamics of the manipulator using recurrent neural networks (RNNs). Based on the error dynamics of a feedback controller, a learning rule for updating the connection weights of the adaptive RNN model is obtained. Local stability properties of the control system are discussed. Simulation results are elaborated on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics, which show that the designed controller performs remarkably well.     

一类关于不确定性机器人的鲁棒控制策略

基于计算力矩结构,研究参数和结构不确定的机器人轨迹跟踪的鲁棒控制策略.其 特点是利用了机器人不确定动力学的集中包络函数,在该包络函数已知的情况下,设计的非 线性连续补偿控制律能够有效消除系统的不确定性影响,保证系统达到三种不同的稳定性结 果.另外,在该包络函数参数未知时,还没计了一个新颖的在线辨识器,可保证系统指数意义 下的渐近收敛或一致有界.     

Tracking trajectory in the workspace of rigid manipulators using distributed adaptive control strategy

This paper discusses the tracking trajectory in the workspace of rigid manipulators using distributed adaptive control strategy. This control strategy consists of two steps; first, the classical MIMO dynamical system is decomposed into a set of nonlinear interconnected subsystems. Each subsystem has one joint. Second, the distributed adaptive control strategy is introduced. This control strategy consists of controlling the last subsystem while assuming that the remaining subsystems are stable. Then, going backward to the second last subsystem, the same strategy is applied and so on until the first one. The system parameters are assumed to be unknown. An adaptive control is used to estimate these parameters. Indeed, the unknown parameters existing in the equation of motion of the last subsystem are first estimated and the control law is developed based on these estimated parameters. Then, going backward to the before last joint, the control law is developed using its own estimated parameters and the ones already estimated in the upper level subsystem. Asymptotical stability of the error dynamics is proved using Lyapunov approach. The developed algorithm is experimented on a 4 DOF hyper redundant articulated nimble adaptable trunk robot and compared with the classical computed torque approach. Good tracking in the workspace and joint space is obtained and effectiveness of the results is shown.     

Stability of hybrid position and force control for robotic manipulator with kinematics and dynamics uncertainties

Most research so far on hybrid position and force control laws of robotic manipulator has assumed that knowledge of kinematics is known exactly. In the presence of modeling errors, it is unknown whether the stability of the constrained robot system can still be ensured. In this paper, stability and setpoint control problems of constrained robot with kinematics and dynamics uncertainties are formulated and solved. We shall show that the manipulator end-effector's motion is asymptotically stable even in the presence of such uncertainties.     

Adaptive control of flexible link manipulators using a pseudolink dynamic model

This paper presents a novel adaptive control scheme for a lightweight manipulator arm governed by electric motors. The controller design is based on the dynamic model of the arm in a quasi-static approximation which consists of the transports subsystem and the motor equations corrected for the elastic compliance of the plant. A passivity property of the flexible electromechanical system is established and an adaptive motor controller is developed which contains the rigid manipulator controller as a part. The motor controller updates all unknown rigid manipulator parameters as well as elastic parameters and ensures global asymptotic stability of the tracking errors with all signals in the system remaining bounded. Projecting of parameter estimates is used in the update law to avoid possible singularities when generating control input. Simulation results for a single-link elastic arm confirm the validity and demonstrate advantages of the proposed method.     

Robust adaptive trajectory tracking independent of models for robotic manipulators

This article proposes a robust adaptive trajectory control scheme for robotic trajectory tracking under uncertainties. The control scheme is globally exponentially convergent without the knowledge of the robotic dynamics and is simple in structure with a small computation. It can make the trajectory error convergent to an arbitrary small region. Lyapunov approach is used to analyze the stability and the robustness of this control scheme. Experiments on a two‐link direct‐drive robotic manipulator verify the validity of the proposed control scheme. © 2001 John Wiley & Sons, Inc.