Vibration control for a nonlinear three-dimensional flexible manipulator trajectory tracking

This paper proposes an innovative approach to the trajectory tracking in three-dimensional space and vibration control problems in the presence of a nonlinear three-dimensional flexible manipulator based on the partial differential equation model. Unlike two-dimensional plane, we select spherical coordinates to describe the position of the end point in three-dimensional space. This novel approach makes it possible to realise the trajectory tracking by controlling the two angles in spherical coordinates, meanwhile, a vibration control scheme is proposed to restrain vibrations. In addition, the existence and uniqueness of solutions are demonstrated. Finally, the performance of the desired trajectory tracking, the proposed vibration control scheme and their convergence properties are demonstrated by numerical simulations.     

Rule-based supervisory control of a two-link flexible manipulator

In this paper, we propose a two level hierarchical control strategy to achieve accurate end-point position of a planar two-link flexible manipulator. The upper level consists of a feedforward rule-based supervisory controller that incorporates fuzzy logic, whereas the lower level consists of conventional controllers that combine shaft position-endpoint acceleration feedback for disturbance rejection properties and shaping of the (joint) actuator inputs to minimize the energy transferred to the flexible modes during commanded movements. The effectiveness of this hierarchical control strategy is verified by experimental results for various movements of the links, in various configurations. In particular, we illustrate how the hierarchical intelligent control strategy performs better than conventional control techniques for endpoint position control in the presence of flexure effects.     

Nonlinear control with end-point acceleration feedback for a two-link flexible manipulator: Experimental results

Experimental results for end-point positioning of multi-link flexible manipulators through end-point acceleration feedback are presented in this article. The advocated controllers are implemented on a two-link flexible arm developed at the Control/Robotics Research Laboratory at Polytechnic University. The advocated approach in this article is based on a two-stage control design. The first stage is a nonlinear (1) feedback linearizing controller corresponding to the rigid body motion of the manipulator. Because this scheme does not utilize any feedback from the end-point motion, significant vibrations are induced at the end effector. To this effect, and to enhance the robustness of the closed-loop dynamics to parameter variations, the inner loop is augmented with an outer loop based on a linear output LQR design that utilizes an end-point acceleration feedback. The forearm of the manipulator is significantly more flexible as compared with the upper arm. Experimental and simulation results validate the fact that the end-effector performance is significantly better with the proposed (1) feedback linearizing control as compared with the linear independent joint PD control. In addition, the nonlinear control offers other advantages in terms of smaller and smoother actuator torques and reducing the effects of nonlinearities. Close conformation between simulation and experimental results validates the accuracy of the model.     

基于鲁棒滑模观测器的两关节柔性机械手控制

柔性机械手系统为非最小相位系统, 当控制有界时, 该特性阻碍其端点位移渐近跟踪期望轨迹. 本文首先重新定义柔性机械手系统的输出, 通过输入输出线性化, 将系统分解为输入输出子系统和零动态子系统; 然后提出一种用于观测柔性模态导数的鲁棒滑模观测器, 使状态估计达到预期的指标, 解决了柔性模态导数难以获得的问题; 设计积分滑模控制策略, 使输入输出子系统在有限时间收敛到零; 选择适当的控制器参数, 使零动态子系统在 平衡点附近渐近稳定, 从而保证整个系统的渐近稳定. 本文提出的方法设计过程简单, 易于实现. 仿真结果证明了设计的有效性.     

空间柔性机械臂高阶滑模干扰观测器轨迹跟踪

在空间漂浮状态时机械臂载体姿态均不受控的条件下,针对机械臂在关节空间内轨迹跟踪及振动抑制等问题,提出了一种基于空间机械臂改进高阶滑模干扰观测器控制策略。利用拉格朗日方程及动量守恒定律建立机械臂运动学数学模型,对误差估计值进行修正,设计干扰观测器,根据机械臂末端轨迹设计合理的高阶滑模面及滑模函数。针对设计的观测器进行模拟仿真实验,并改变理想轨迹,使其在复杂曲线中运行。仿真结果表明:高阶滑模干扰观测器可应用于更为复杂的工作空间中,并更有效、精确地实现了轨迹跟踪任务。     

Identification of a two-link flexible manipulator using adaptivetime delay neural networks

This paper deals with identification of a two-link flexible manipulator belonging to a class of multi-input, multi-output (MIMO) nonlinear systems, by using adaptive time delay neural networks (ATDNNs). Two neuro-dynamic identifiers are proposed. The capabilities of the proposed structures for representing the nonlinear input-output map of the flexible manipulator are shown analytically. Selection criteria for specifying the fixed structural parameters as well as the adaptation laws for updating the adjustable parameters of the networks are provided. During identification, the two-link flexible manipulator is under nonlinear control and the input-output data sets are generated for different desired trajectories. Simulation results reveal that the proposed neuro-dynamic structures are capable of successfully identifying a highly nonlinear system without any a priori information about the nonlinearities of the system and without any off-line training.     

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.     

机器人轨迹跟踪的间接自适应模糊控制

为把已有的模糊控制算法应用于多自由度机器人的实时控制中,将间接自适应模糊控制算法从单输入单输出(SISO)系统推广至多输入多输出(MIMO)系统,并给出了系统收敛的严格数学证明.另外对于n关节的机器人轨迹跟踪问题,设计了一种新型控制器能够保证系统的最终一致有界性(u.u.b.).通过对具有远程独立电机驱动的双连杆机械臂的仿真试验证明了该方案的可行性.     

Modelling the movement of a two-link manipulator

An algorithm for optimizing the control signal for simple movements of a two-link manipulator with four degrees of freedom is described. Based on the typical movement and functions of upper human extremities, the manipulator (so-called anthropomorphic manipulator) is composed of two links. The motion of the links is developed by four driving motors. The mathematic model is based of the Lagrange equations of the IInd king. The minimization of the time of movement with initial limitation of accuracy is obtained and the error of the final position is minimized without changing the time-optimal criterion. The relations connected with minimalization of both quality factors are considered. At the same time, the algorithm optimizes the torque distribution between the actuators which drive each link of manipulator. As well the manipulator as its activity are modelled on the digital computer. The results of the computer simulation of the algorithm, and the modelling of the time and accuracy optimal control, are presented.     

A coupled-sliding-surface approach for the robust trajectory control of a horizontal two-link rigid/flexible robot

This paper proposes a new robust trajectory control scheme for a two-link rigid/flexible robot. First, the energy dynamics of the flexible link is derived based on a distributed-parameter dynamic model (a partial differential equation). Second, a coupled sliding surface is defined based on the energy dynamics. Third, a new trajectory control scheme is designed based on the coupled sliding surface, and then extended to an adaptive scheme to cope with parametric uncertainties, where the Lyapunov stability theorem is used as a mathematical tool. The proposed control is a collocated control designed based on the distributed-parameter dynamic model and is free from the so-called spillover instability. Using only two joint actuators, the proposed control guarantees stability throughout the entire trajectory control and asymptotic stability at desired goal positions. Furthermore, the proposed control guarantees zero steady-state joint-tracking errors even in the presence of low-frequency disturbances due to unavoidable mechanical inaccuracies in application. The theoretical results have also been proven by control experiments.     

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.     

Precise trajectory control of a redundant flexible manipulator on a space platform

In this paper, we propose a trajectory control method for a redundant flexible space manipulator with slewing and deployable links on a space platform. This method consists manipulator tip position feedback with a transposed Jacobian matrix and local vibration control. We newly derive the Jacobian matrix for a flexible manipulator considering link deformation with the assumed modes method. Simulation results show the effectiveness of this method. We use dynamics consisting of an order N algorithm for N bodies, based on the non-recursive Lagrangian approach, to simulate the dynamics of an orbiting manipulator with an arbitrary number of slewing and deployable flexible links.     

改进RBFNN求机械臂轨迹跟踪的研究

为了使机械臂准确跟踪目标轨迹,达到控制精度高、实时性好的目的,提出一种改进的径向基函数（RBF）模糊神经网络算法。该算法采用模糊遗传算法在线调整神经模糊控制器的参数,对其参数进行改进和优化,同时采用最近邻聚类算法对控制器的模糊规则库进行更新。仿真结果表明,该算法与传统的神经网络算法相比具有较好的性能,学习速度快,跟踪精度高,并具有良好的控制性能和自学习能力。     

双连杆刚柔机械臂无残余振动位置控制

针对双连杆刚柔机械臂,提出一种基于轨迹规划的无残余振动位置控制方法,在将机械臂的末端执行器从任意初始位置移动到目标位置的同时,确保系统没有残余振动产生.首先,建立系统的动力学模型,并通过分析该模型得到系统的状态约束方程.其次,基于状态约束方程,运用双向轨迹规划方法规划一条系统前向轨迹和一条系统反向轨迹.然后,利用时间倒转方法及基于遗传算法的轨迹优化方法对两条轨迹进行拼合,得到一条从系统初始状态到目标状态的期望轨迹.最后,设计轨迹跟踪控制器使系统沿期望轨迹到达目标状态,实现系统的无残余振动位置控制目标.仿真结果验证了本文所提方法的有效性.     

基于参数不确定机械臂系统的自适应轨迹跟踪控制

针对机械臂系统惯性参数及运动学参数不能准确测量进而影响轨迹跟踪性能的问题,提出一种任务空间自适应轨迹跟踪控制方法,通过定义关节角速度参考误差,并将任务空间的轨迹跟踪误差及运动学参数误差反馈给控制器,以改善系统稳定性,设计电机参数传输矩阵及电机参数自适应率,以抵消电机发热引起参数漂移对跟踪性能影响,并给出了稳定性证明.实验结果表明,该方法能够较好地克服电机参数漂移对跟踪控制性能的影响.     

考虑重力影响的空间机械臂轨迹跟踪滑模控制

针对空间机械臂由地面装调到空间应用过程中重力环境发生变化的问题,使用滑模控制器对空间机械臂进行控制,通过将配置特殊的非线性结构-fal函数引入趋近律的设计中,提出一种新的基于趋近律的滑模控制方法,并基于李亚普诺夫理论证明了闭环系统的渐近稳定性。仿真结果表明该方法能够很好地完成不同重力环境下机械臂的轨迹跟踪控制任务,并具有较强的鲁棒性。     

On adaptive trajectory tracking of a robot manipulator usinginversion of its neural emulator

This paper is concerned with the design of a neuro-adaptive trajectory tracking controller. The paper presents a new control scheme based on inversion of a feedforward neural model of a robot arm. The proposed control scheme requires two modules. The first module consists of an appropriate feedforward neural model of forward dynamics of the robot arm that continuously accounts for the changes in the robot dynamics. The second module implements an efficient network inversion algorithm that computes the control action by inverting the neural model. In this paper, a new extended Kalman filter (EKF) based network inversion scheme is proposed. The scheme is evaluated through comparison with two other schemes of network inversion: gradient search in input space and Lyapunov function approach. Using these three inversion schemes the proposed controller was implemented for trajectory tracking control of a two-link manipulator. Simulation results in all cases confirm the efficacy of control input prediction using network inversion. Comparison of the inversion algorithms in terms of tracking accuracy showed the superior performance of the EKF based inversion scheme over others.     

Vibration control of a two-link flexible robot arm

Analysis and experimentation is described for a two-link apparatus in which both members are very flexible. Attention is focused on endpoint position control for point-to-point movements, assuming a fixed reference frame for the base, with two rotary joints. Each link is instrumented with acceleration sensing and is driven by a separate motor equipped with velocity and position sensing. The control perspective adopted is to implement a two-stage control strategy in which the vibration control problem for fine-motion endpoint positioning is considered separate from the gross-motion, large-angle slew problem. In the first stage the control law shapes the actuator inputsfor the large-angle movement in such a way that minimal energy is injected into the flexible modes, while in the second phase an endpoint acceleration feedback scheme is employed in independent joint controlfor vibration suppression at the link endpoints.     

Experiments on a floating underwater robot with a two-link manipulator

This article concerns experiments with a free-floating underwater robot with a two-dimensional, horizontal planar, two-link manipulator. Some dynamic models of underwater manipulators have been proposed, but only a few experiments have been carried out. Here, we derive a dynamic model for a free-floating underwater robot with a two-link manipulator, including the hydrodynamic forces, and validate the effectiveness of the model by simulation and experiment. We also show an experimental result using a resolved acceleration control method. These experimental results show the effectiveness the model and the control method. This work was presented in part at the 5th International Symposium on Artificial Life and Robotics, Oita, Japan, January 26–28, 2000