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.     

Vision-Based Task-Level Control of a Flexible-Link Manipulator

This paper discusses a vision-based approach to implement task-level control in flexible-link manipulators. The proposed approach emphasizes the advantage of using vision in the control of flexible manipulators. It is pointed out that taking advantage of the inherent robustness, implementation of an image-based visual servo can be regarded as a synthetic solution to precise task-level control of flexible manipulators. This approach is implemented in a three-dimensional flexible-link manipulator. The implementation makes good use of filters in decoupling task-level control and vibration suppression control. Moreover, we point out that although the robustness of the approach can help to overcome the difficulty in control resulting from the complex measurement of the link's elastic deformation, it lacks in capability of tip trajectory specification. This problem is analyzed in this research and it leads to the proposal for the integration of the image interpolation technique. This technique makes the proposed approach adequate for tasks involved with complex tip trajectories. For flexible-link manipulators, the proposed approach with the remedy is the first vision-based synthetic solution that attempts to make a flexible manipulator usable for a practical task.     

柔性臂漂浮基空间机器人建模与轨迹跟踪控制

利用拉格朗日法和假设模态方法建立了末端柔性的两臂漂浮基空间机器人的非线性动力学方程．通过坐标变换,推导出一种新的以可测关节角为变量的全局动态模型,并在此基础上运用基于模型的非线性解耦反馈控制方法得到关节相对转角与柔性臂的弹性变形部分解耦形式控制方程．最后,讨论了柔性臂漂浮基空间机器人的轨迹跟踪问题,并通过仿真实例计算,表明该模型转换及控制方法对于柔性臂漂浮基空间机器人末端轨迹跟踪控制的有效性．     

Impedance Control of Flexible Robot Arms with Parametric Uncertainties

This paper presents an adaptive impedance control strategy for flexible manipulators by using an end-effector trajectory control approach. The impedance control objective is converted into tracking a trajectory generated by a designed ideal impedance model. A manifold is designed to prescribe desirable performance of the system. An adaptive control scheme is derived in such that the motion of the system will converge and remain to the ideal manifold for the case of parametric uncertainties. Stability of the control system is analyzed. Simulations are carried out to demonstrate the effectiveness of the proposed control method.     

A composite adaptive control with flexible quantity feedback for flexible-link manipulators

This article presents a mixture of joint subsystem-based adaptive control and simple flexible quantity feedback for flexible-link manipulators. The complex full flexible-arm system is composed of two severely coupling subsystems called the joint subsystem and flexible subsystem. Linear parametrization is first used to design an adaptive law for identifying the unknown parameters of a flexible manipulator based only on the joint subsystem. Joint-angle trajectory tracking can thus be achieved using the derived stable nonlinear adaptive control with the estimates of unknown parameters. To stabilize the flexible subsystem, we can simply add the feedback of transversal acceleration or deflection at the end point and/or along the flexible beam. The suggested approach is much simpler than those based on the full dynamics model of a flexible arm in required computations. Computer simulations on a single-link and a two-link flexible arm are tested to illustrate the validity of the strategy for both trajectory tracking and active damping. © 1996 John Wiley & Sons, Inc.     

Tracking Controller Using Normalized Quasi-velocities

In this paper a tracking controller expressed in terms of the normalized quasi-velocities (NQV) for rigid manipulators is proposed. These quasi-velocities introduced by [Jain and Rodriguez, IEEE Trans. Robot. Autom., 11:571–584, 1995] are utilized here in order to reveal some useful features which are observable if we track a desired quasi-velocity trajectory. The presented controller in terms of NQV is exponentially convergent. Moreover, some geometrical interpretation of the normalized quasi-variables based on Riemannian geometry is given. It is shown that the controller can be helpful for evaluation and reduction of dynamical couplings existing in the system. As a result it is helpful at the design step of manipulators. The control strategy was tested in simulation on two 3 d.o.f. spatial manipulators.     

六自由度机械臂约束预测控制系统的设计

本文提出了一种基于约束预测控制的机械臂实时运动控制方法.该控制方法分为两层,分别设计了约束预测控制器和跟踪控制器.其中,约束预测控制器在考虑系统物理约束的条件下,在线为跟踪控制器生成参考轨迹;跟踪控制器采用最优反馈控制律,使机械臂沿参考轨迹运动.为了简化控制器的设计和在线求解,本文采用输入输出线性化的方式简化机械臂动力学模型.同时,为了克服扰动,在约束预测控制器中引入前馈策略,提出了带前馈一反馈控制结构的预测控制设计.因此,本文设计的控制器可以使机械臂在满足物理约束的条件下快速稳定地跟踪到目标位置.通过在PUMA560机理模型上进行仿真实验,验证了预测控制算法的可行性和有效性.     

柔性机械臂运动轨迹的鲁棒自适应控制

本文针对多连杆柔性机械臂的运动轨迹问题，讨论了动力学建模，控制系统结构设计以及鲁棒自适应控制法，运用假设模记方法得到了柔性机械臂动力学所似方程，通过对柔性机械臂动力学特性分析，建立了等价动力学模型，依此提出了一种鲁棒自适应控制算法，并给出仿真研究结果。     

Optimal Trajectory Planning for Flexible Link Manipulators with Large Deflection Using a New Displacements Approach

The main objective of the present paper is to determine the optimal trajectory of very flexible link manipulators in point-to-point motion using a new displacement approach. A new nonlinear finite element model for the dynamic analysis is employed to describe nonlinear modeling for three-dimensional flexible link manipulators, in which both the geometric elastic nonlinearity and the foreshortening effects are considered. In comparison to other large deformation formulations, the motion equations contain constant stiffness matrix because the terms arising from geometric elastic nonlinearity are moved from elastic forces to inertial, reactive and external forces, which are originally nonlinear. This makes the formulation particularly efficient in computational terms and numerically more stable than alternative geometrically nonlinear formulations based on lower-order terms. In this investigation, the computational method to solve the trajectory planning problem is based on the indirect solution of open-loop optimal control problem. The Pontryagin’s minimum principle is used to obtain the optimality conditions, which is lead to a standard form of a two-point boundary value problem. The proposed approach has been implemented and tested on a single-link very flexible arm and optimal paths with minimum effort and minimum vibration are obtained. The results illustrate the power and efficiency of the method to overcome the high nonlinearity nature of the problem.     

Dynamic modelling and adaptive robust tracking control of a space robot with two-link flexible manipulators under unknown disturbances

In this paper, both the closed-form dynamics and adaptive robust tracking control of a space robot with two-link flexible manipulators under unknown disturbances are developed. The dynamic model of the system is described with assumed modes approach and Lagrangian method. The flexible manipulators are represented as Euler–Bernoulli beams. Based on singular perturbation technique, the displacements/joint angles and flexible modes are modelled as slow and fast variables, respectively. A sliding mode control is designed for trajectories tracking of the slow subsystem under unknown but bounded disturbances, and an adaptive sliding mode control is derived for slow subsystem under unknown slowly time-varying disturbances. An optimal linear quadratic regulator method is proposed for the fast subsystem to damp out the vibrations of the flexible manipulators. Theoretical analysis validates the stability of the proposed composite controller. Numerical simulation results demonstrate the performance of the closed-loop flexible space robot system.     

Hierarchical control of end-point impedance and joint impedance forredundant manipulators

This paper proposes an impedance control method for redundant manipulators, which can control not only the end-point impedance using one of the conventional impedance control methods, but the joint impedance which has no effects on the end-point impedance. First, a sufficient condition for the joint impedance controller is derived. Then, the optimal controller for a given desired joint impedance is designed using the least squares method. Finally, computer simulations and experiments using a planar direct-drive robot are performed in order to confirm the validity of the proposed method     

An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators

In this article, we present an inverse dynamics control strategy to achieve small tracking errors for a class of multi-link structurally flexible manipulators. This is done by defining new outputs near the end points of the arms as well as by augmenting the control inputs by terms that ensure stable operation of the closed loop system under specific conditions. The controller is designed in a two-step process. First, a new output is defined such that the zero dynamics of the original system are stabilized. Next, to ensure stable asymptotic tracking, the control input is modified such that stable asymptotic tracking of the new output or approximate tracking of the actual output may be achieved. This is illustrated for the case of single- and two-link flexible manipulators. ©1997 John Wiley & Sons, Inc.     

Dynamic Modeling Based on Real-Time Deflection Measurement and Compensation Control for Flexible Multi-Link Manipulators

The problem of tip trajectory tracking control is considered in this paper for flexible multi-link manipulators. An integrated optical laser sensor system is utilized to measure the tip deformations of the flexible links. The Lagrangian assumed-mode method incorporating the measured linear displacements and angular deflections of flexible links is used to derive the dynamic model of the flexible manipulator. To reduce as far as possible the tip tracking/positioning errors caused by the link flexibility, an error compensation approach is proposed. The additional compensation amounts of joint variables are calculated kinematically in terms of the measured deformations, and are added to the nominal commands generated by the computed torque controller. The simulation results demonstrate the effectiveness of the proposed approach.     

Dynamic Analysis and Control Synthesis of Undesired Slippage of End-Effectors in a Cooperative Grasping

This paper addresses dynamic analysis and control synthesis of object grasping in a cooperative multirobot system with n-serial manipulators from an undesired slippage point of view. Two control approaches are presented in this article; a modified version of a conventional method in grasp synthesis and a new method based on a new modeling of system dynamics. A new formulation for frictional contact is used in dynamical modeling, where equality and inequality equations of the standard Coulomb friction model are all converted to a single second-order differential equation. A multiphase controller is utilized to control the object trajectory tracking as well as object slippage in the new control approach. Performance and robustness of both approaches are studied numerically. The results show superiority of the new method and its desirable and excellent performance.     

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.     

Adaptive neural controller for cooperative multiple robot manipulator system manipulating a single rigid object

In this article, an adaptive neural controller is developed for cooperative multiple robot manipulator system carrying and manipulating a common rigid object. In coordinated manipulation of a single object using multiple robot manipulators simultaneous control of the object motion and the internal force exerted by manipulators on the object is required. Firstly, an integrated dynamic model of the manipulators and the object is derived in terms of object position and orientation as the states of the derived model. Based on this model, a controller is proposed that achieves required trajectory tracking of the object as well as tracking of the desired internal forces arising in the system. A feedforward neural network is employed to learn the unknown dynamics of robot manipulators and the object. It is shown that the neural network can cope with the unknown nonlinearities through the adaptive learning process and requires no preliminary offline learning. The adaptive learning algorithm is derived from Lyapunov stability analysis so that both error convergence and tracking stability are guaranteed in the closed loop system. Finally, simulation studies and analysis are carried out for two three-link planar manipulators moving a circular disc on specified trajectory.     

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.     

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.