Inverse cartesian trajectory control and stabilization of a three-axis flexible manipulator

This article treats the question of end point trajectory control of a flexible manipulator based on the nonlinear inversion technique. The manipulator has two rigid links and the third link is elastic. A parameterization of the Cartesian coordinates of a point close to the end effector position is suggested. Using these coordinates as output variables, an inverse feedback control law is derived for tracking reference Cartesian trajectories. The stability of the zero dynamics associated with the end point motion control is examined. It is shown that inverse control of the end point causes divergent oscillatory flexible modes. In addition, for regulating the end point to a fixed position, a linear stabilizer is designed to damp the elastic vibration. Simulation results are presented to show that in the closed-loop system, reference end point trajectories can be accurately followed in spite of the parameter uncertainty in the arm dynamic model. © 1994 John Wiley & Sons, Inc.     

Trajectory control of a non-linear one-link flexible arm

The trajectory-tracking control problem is considered for a one-link flexible arm described by a non-linear model. Two meaningful system outputs are chosen; namely, the joint angle and the angular position of a suitable point along the link. The common goal is to stiffen the behaviour of the flexible link with respect to the chosen output. Based on the input-output inversion algorithm, a state-feedback control law is designed that enables exact tracking of any smooth trajectory specified for the output. In the closed loop an unobservable dynamics naturally arises, related to the variables describing the arm's distributed flexibility. Joint-based design is shown to be always stable, whereas in the link-point design the closed-loop dynamics may become unstable depending on the location of the output along the link. Open- versus closed-loop strategies are developed and compared. Extensive simulation results are included.     

The path precompensation method for flexible arm robot

This paper constructed a closed loop path precompensation method for a flexible arm robot. A torque computation method taking care of the elastic arm deformation was first proposed and discussed. A concept of partial deformation compensation was subsequently proposed to improve the torque profiles and the trajectory fidelity. The advantage of this concept was first shown by examples of planar trajectory. After the construction of the closed-loop path precompensation method for a flexible arm, the torque method and partial deformation compensation were incorporated to track the spatial trajectory. Numerical simulations were given to show the usefulness of the proposed concept and method.     

Variable structure trajectory control of an elastic robotic arm

This article introduces a variable structure system scheme to control the end effector trajectory of a two-link flexible robotic arm. Because control of the actual tip position leads to unstable zero dynamics, control of points in the neighborhood of the tip is considered. An output is chosen as the sum of the joint angle and tip elastic deformation times a constant factor for each link. For the chosen output, a discontinuous output control law is derived based on the variable structure theory. The control law thus derived accomplishes the desired trajectory tracking of the output. A linear stabilizer is designed using the pole assignment technique for the final capture of the terminal state and stabilization of the elastic modes. Simulation results are presented to show that in the closed-loop system large maneuvers can be performed in the presence of payload uncertainty, thereby exhibiting the robustness of the 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。     

Stability and control aspects of flexible link robot manipulators during constrained motion tasks

The effect of robotic manipulator structural compliance on system stability and trajectory tracking performance and the compensation of this structural compliance has been the subject of a number of publications for the case of robotic manipulator noncontact task execution. The subject of this article is the examination of dynamics and stability issues of a robotic manipulator modeled with link structural flexibility during execution of a task that requires the robot tip to contact fixed rigid objects in the work environment. The dynamic behavior of a general n degree of freedom flexible link manipulator is investigated with a previously proposed nonlinear computed torque constrained motion control applied, computed based on the rigid link equations of motion. Through the use of techniques from the theory of singular perturbations, the analysis of the system stability is investigated by examining the stability of the “slow” and “fast” subsystem dynamics. The conditions under which the fast subsystem dynamics exhibit a stable response are examined. It is shown that if certain conditions are satisfied a control based on only the rigid link equations of motion will lead to asymptotic trajectory tracking of the desired generalized position and force trajectories during constrained motion. Experiments reported here have been carried out to investigate the performance of the nonlinear computed torque control law during constrained motion of the manipulator. While based only on the rigid link equations of motion, experimental results confirm that high-frequency structural link modes, exhibited in the response of the robot, are asymptotically stable and do not destabilize the slow subsystem dynamics, leading to asymptotic trajectory tracking of the overall system. © 1992 John Wiley & Sons, Inc.     

On trajectory tracking control for nonholonomic mobile manipulators with dynamic uncertainties and external torque disturbances

This paper studies the trajectory tracking control problem of mobile manipulators subject to nonholonomic constraints, operating in task space, with the presence of external torque disturbances and dynamic uncertainties. The proposed controls are robust to external torque disturbances and can overcome the effects of the unknown dynamic parameters. The stability of the closed-loop system and the asymptotic convergences of tracking errors are proved using Lyapunov synthesis. The proposed control strategies have been designed to drive the system motion converges to the desired manifold and, at the same time, guarantees the boundedness of all the closed-loop signals. Simulation results validate that the system trajectory converge to the desired one.     

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.     

Decentralized adaptive tracking control of robot manipulators

An asymptotically stable decentralized adaptive control scheme is presented to enable accurate trajectory tracking without requiring specific knowledge about the robot dynamics. The scheme is based on expressing the robot dynamics as the product of individual joint quantities, and bounds on certain robot parameters. Parameter adaptation laws are derived using the Lyapunov theory, and asymptotic stability of tracking errors, and boundedness of parameter estimates are established. The control system is shown to be robust to torque disturbances affecting the system and to a class of unmodeled dynamics. The structure of the controller and the performance of the closed-loop system are analyzed. Simulations results using the complete dynamic model of a six degree of freedom industrial robot are presented to demonstrate the excellent tracking performance of the proposed adaptive control scheme. © 1996 John Wiley & Sons, Inc.     

On the Feedforward Torques and Reference Trajectory for Flexible Two-Link Arm

A method for synthesizing the feedforward torques and reference trajectory for a flexible two-link planar manipulator is proposed. These torques and the trajectory are not far from being time-optimal. The control law for each drive torque consists of two parts: a commanded feedforward torque and a linear angular position and velocity feedback.Initially, we theoretically prove that so-called 'fluent control enables an individual link to reach the desired hub acceleration with little error and avoid unwanted large flexible vibrations. With this control, the dynamics of a flexible link is close to the dynamics of the associated rigid link.We begin the design of the feedforward torques and reference trajectory by computing the control torques for an arm with two rigid links which are near time-optimal control functions. These torques are discontinuous functions of time. The jumps in the control torques are not acceptable for an arm with flexible links because large elastic vibrations appear in the links. This conclusion follows from a theoretical study of individual links and also from experimentation with one-link and two-link flexible arms. Therefore, fluent control is considered here. Designing this fluent control, we transform the obtained discontinuous control into continuous functions of time, taking into account the elasticity of flexible links. During the experiments with flexible arms, these continuous functions are used as commanded feedforward torques. We also feed on-line these control torques to a mathematical model of the arm with two rigid links and compute the corresponding desired angular velocities and positions of the links as functions of time. Then we feed this reference trajectory to the linear feedback system (usual PD-controller) of the flexible arm. Designed control does not excite large elastic vibrations although, simultaneously, it is not far from being time-optimal. The designed control algorithm has been successfully implemented in the experiments.     

Output feedback stabilization of MIMO non-linear systems via dynamic sliding mode

Previous work on asymptotic stabilization of MIMO non-linear systems using dynamic sliding mode control to produce dynamic state feedback has been generalized to dynamic output feedback. All the states in the feedback controller are replaced with estimated states which come from a semi-high-gain observer. The bound on the observer gain is explicitly given, which depends on some previously chosen design parameters. If the given differential input–output (I–O) system is minimum phase and proper, local uniform asymptotic output feedback stabilization can be achieved. In addition, the restriction on the stability of the zero dynamics has been relaxed to weakly minimum phase and semi-global results are obtained under some mild conditions. The stability of the closed-loop system is based on some stability results of triangular systems when continuous or discontinuous controllers are adopted. Two pertinent examples are given to illustrate the design method. Copyright © 1999 John Wiley & Sons, Ltd.     

On tracking control of flexible robot arms

A controller for solving the tracking problem of flexible robot arms is presented. In order to achieve this goal, the desired trajectory for the link (flexible) coordinates is computed from the dynamic model of the robot arm and is guaranteed to be bounded, and the desired trajectory for the joint (rigid) coordinates can be assigned arbitrarily. The case of no internal damping is also considered, and a robust control technique is used to enhance the damping of the system     

基于扰动和摩擦补偿的柔性机械臂系统非奇异快速终端滑模控制

本文针对系统中存在的关节摩擦、动力学参数不确定性和外部负载干扰等因素引起的柔性机械臂系统控制性能下降的问题,提出了一种基于扰动和摩擦补偿的非奇异快速终端滑模控制方法(NFTSMC-DE-FC).首先,设计扰动估计器(DE)对系统未知动态参数和负载干扰进行估计.然后,针对扰动估计器不能精确估计的关节摩擦力矩进行辨识.最后,利用滑模控制技术设计非奇异快速终端滑模控制器,并将扰动估计值和摩擦力辨识值以前馈的方式进行补偿,实现对柔性机械臂系统给定参考轨迹跟踪的准确性以及对外界扰动的鲁棒性.值得注意的是,与传统只使用扰动估计器的方法相比,本文考虑到了摩擦力等非线性因素的影响,并利用辨识技术对摩擦力进行辨识,提高了控制精度.利用Lyapunov稳定性定理从理论上证明了所设计的控制器可以保证闭环系统的稳定性.实验结果表明,相较于非奇异快速终端滑模控制方法(NFTSMC)和基于扰动估计器的非奇异快速终端滑模控制方法(NFTSMC-DE),所提方法提高了柔性机械臂系统的轨迹跟踪性能.     

Global Convergence of a Decentralized Adaptive Fuzzy Control for the Motion of Robot Manipulators: Application to the Mitsubishi PA10-7CE as a Case of Study

In general terms, robot control consists in making a robot execute a commanded task. One of the most important cases is the trajectory tracking or motion control. In this paper, a control algorithm that uses adaptive fuzzy systems to approximate local portions of the robot manipulator dynamics is proposed in order to solve the trajectory tracking problem. This scheme is characterized by not requiring any knowledge of the dynamic model and, in contrast to some fuzzy adaptive controllers previously developed, the one proposed here is in a decentralized configuration, wherein each joint is considered as a subsystem and is independently controlled only through its local variables. Furthermore, a study that guarantees the stability and the boundedness of the solutions of the closed-loop system via Lyapunov theory is presented, including a functional analysis which proves for the first time that a decentralized adaptive fuzzy controller satisfies the motion control objective. The theoretical results exposed here are verified via experimentation by applying the designed algorithm to the Mitsubishi PA10-7CE robot arm and the outcomes are reported.     

Robot discrete adaptive control based on dynamic inversion using dynamical neural networks

A stable discrete time adaptive control approach using dynamic neural networks (DNNs) is developed in this paper for the trajectory tracking of a robotic manipulator with unknown nonlinear dynamics. By using dynamic inversion constructed by a DNN, the assumption under which the system state should be on a compact set can be removed. This assumption is usually required in neuro-adaptive control. The NN-based variable structure control is designed to guarantee the stability and improve the dynamic performance of the closed-loop system. The proposed control scheme ensures the global stability and desired tracking as well.     

Trajectory generation and control of a knee exoskeleton based on dynamic movement primitives for sit-to-stand assistance

This paper presents a novel control approach for a knee exoskeleton to assist individuals with lower extremity weakness during sit-to-stand motion. The proposed method consists of a trajectory generator and an impedance controller. The trajectory generator uses a library of sample trajectories as the training data and the initial joint angles as the input to predict the user’s intended sit-to-stand trajectory. Utilizing the dynamic movement primitives theory, the trajectory generator represents the predicted trajectory in a time-normalized and rather a flexible framework. The impedance controller is then employed to provide assistance by guiding the knee joint to move along the predicted trajectory. Moreover, the human-exoskeleton interaction force is used as the feedback for on-line adaptation of the trajectory speed. The proposed control strategy was tested on a healthy adult who wore the knee exoskeleton on his leg. The subject was asked to perform a number of sit-to-stand movements from different sitting positions. Next, the measured data and the inverse dynamic model of the human-exoskeleton system are used to calculate the knee power and torque profiles. The results reveal that average muscle activity decreases when the subject is assisted by the exoskeleton.     

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.     

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.     

SLIDING-MODE ADAPTIVE CONTROL FOR FLEXIBLE-LINK MANIPULATORS USING A COMPOSITE DESIGN

ABSTRACT

A robust adaptive control scheme for flexible link robotic manipulators is presented. The design is based on considering the flexible mechanical structure as a singular perturbed system, which allows us to assume the existence of slow (rigid) and fast (flexible) modes that separately can be controlled. The rigid dynamics are controlled by means of a robust sliding adaptive approach with well-established stability properties. The flexible dynamics can be controlled using H _∞ or optimal designs, which successfully handle the actual interaction between the slow and fast subsystems. This composite approach achieves good closed-loop tracking properties, both in simulation and experimental results on a laboratory-flexible arm.     

不确定性R¨ossler 系统的自适应鲁棒跟踪控制

研究具有外部不确定性R¨ossler 混沌系统的鲁棒跟踪控制问题. 基于动态面控制原理设计自适应鲁棒控制器, 给出了系统参数的自适应更新律, 使得被控闭环系统的各误差变量一致有界. 系统输出曲线渐近跟踪任意期望轨道, 且跟踪误差能被控制在任意小的范围内, 而无须知道系统的参数及外部不确定性的界限. 基于稳定理论给出了具体的稳定性分析, 并通过数值仿真验证了该方法的有效性及鲁棒性.