Hybrid Control Scheme for Robust Tracking of Two-Link Flexible Manipulator

The hybrid control scheme is proposed to stabilize the vibration of a two-link flexible manipulator while the robustness of Variable Structure Control (VSC) developed for rigid manipulators is maintained for controlling the joint angles. The VSC law alone, which is designed to accomplish only the asymptotic decoupled joint angle trajectory tracking, does not guarantee the stability of the flexible mode dynamics of the links. In order to actively suppress the flexible link vibrations, hybrid trajectories for the VSC are generated using the virtual control force concept, so that robust tracking control of the flexible-link manipulator can also be accomplished. Simulation results confirm that the proposed hybrid control scheme can achieve more robust tracking control of two-link flexible manipulator than the conventional control scheme in the presence of payload uncertainty.     

Hybrid Control Scheme for Robust Tracking of Two-Link Flexible Manipulator

A hybrid control scheme is proposed to stabilize the vibration of a two-link flexible manipulator while robustness of Variable Structure Control (VSC) developed for rigid manipulators is maintained for controlling the joint angles. The VSC law alone, which is designed to accomplish only the asymptotic decoupled joint angle trajectory tracking, does not guarantee the stability of the flexible mode dynamics of the links. In order to actively suppress the flexible link vibrations, hybrid trajectories for the VSC are generated using the virtual control force concept, so that robust tracking control of the flexible-link manipulator can also be accomplished. Simulation results confirm that the proposed hybrid control scheme can achieve more robust tracking control of two-link flexible manipulator than the conventional control scheme in the presence of payload uncertainty.     

Robust adaptive control for mobile manipulators

This paper addresses the trajectory tracking control of a nonholonomic wheeled mobile manipulator with parameter uncertainties and disturbances. The proposed algorithm adopts a robust adaptive control strategy where parametric uncertainties are compensated by adaptive update techniques and the disturbances are suppressed. A kinematic controller is first designed to make the robot follow a desired end-effector and platform trajectories in task space coordinates simultaneously. Then, an adaptive control scheme is proposed, which ensures that the trajectories are accurately tracked even in the presence of external disturbances and uncertainties. The system stability and the convergence of tracking errors to zero are rigorously proven using Lyapunov theory. Simulations results are given to illustrate the effectiveness of the proposed robust adaptive control law in comparison with a sliding mode controller.     

A nonlinear feedback controller for a single-link flexible manipulator based on a finite element model

In this article, a nonlinear dynamic model of a flexible manipulator is derived through finite element method associated with Lagrange approach. The flexible manipulator is modeled as an Euler-Bernoulli beam driven by a motor at its base and with a point mass tip payload. The generalized coordinates of the system are selected to be the displacements and rotations of the nodes on the considered flexible beam, and such that a state space model is obtained with all the state variables having physical meanings. Based on this model, an effective nonlinear feedback controller is developed to control the tip position. Furthermore, an efficient algorithm is developed to calculate the inverse of the system's inertia matrix for real-time implementation. Numerical simulation results are given to show the effectiveness of the controller and its robustness in handling payload variations. © 1997 John Wiley & Sons, Inc.     

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.     

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.     

Soft computing methods applied to the control of a flexible robot manipulator

The paper describes use of soft computing methods (fuzzy logic and neural network techniques) in the development of a hybrid fuzzy neural control (HFNC) scheme for a multi-link flexible manipulator. A manipulator with multiple flexible links is a multivariable system of considerable complexity due to the inter-link coupling effects that are present in both rigid and flexible motions. Modelling and controlling the dynamics of such manipulators is therefore difficult. The proposed HFNC scheme generates control actions combining contributions form both a fuzzy controller and a neural controller. The primary loop of the proposed HFNC contains a fuzzy controller and a neural network controller in the secondary loop to compensate for the coupling effects due to the rigid and flexible motion along with the inter-link coupling. It has been ascertained from the present investigation that the proposed soft-computing-based controller works effectively in the tracking control of such a multi-link flexible manipulator. The results are extendable to other multivariable systems of similar complexity.     

The control of flexible‐link robots manipulating large payloads: Theory and experiments

The control problem for flexible‐multilink robots carrying large payloads is revisited. A set of nonlinear approximate equations describing the payload‐dominated dynamics of the flexible plant is used in conjunction with the passivity property satisfied by a suitably defined modified input–output pair for the system, to derive a globally asymptotically stable controller together with its adaptive counterpart. Experimental results involving a specially designed 3‐degree‐of‐freedom planar arm with two flexible links, demonstrate their ability to combine end‐point tracking with simultaneous active suppression of the vibrations. © 2000 John Wiley & Sons, Inc.     

An Adaptive Controller for Two Cooperating Flexible Manipulators

The control problem for two serial flexible multilink robots which carry a common rigid payload is considered. An adaptive controller with feedback and feedforward elements is presented which can track a prescribed trajectory for the payload with simultaneous vibration suppression when the manipulated payload is sufficiently large. A free load‐sharing parameter appears in the passivity‐based control law which allows the torque requirement to be shared between the two arms in a largely arbitrary fashion. Simulation results using a complex model are given which demonstrate excellent tracking performance in the face of complete payload uncertainty. © 2003 Wiley Periodicals, Inc.     

Dynamic modelling, simulation and control of a manipulator with flexible links and joints

The paper presents a dynamic modelling technique for a manipulator with multiple flexible links and flexible joints, based on a combined Euler–Lagrange formulation and assumed modes method. The resulting generalised model is validated through computer simulations by considering a simplified case study of a two-link flexible manipulator with joint elasticity. Controlling such a manipulator is more complex than controlling one with rigid joints because only a single actuation signal can be applied at each joint and this has to control the flexure of both the joint itself and the link attached to it. To resolve the control complexities associated with such an under-actuated flexible link/flexible joint manipulator, a singularly perturbed model has been formulated and used to design a reduced-order controller. This is shown to stabilise the link and joint vibrations effectively while maintaining good tracking performance.     

Model reference adaptive impedance control in Cartesian coordinates for physical human–robot interaction

In this paper, a nonlinear model reference adaptive impedance controller is proposed and tested. The controller provides asymptotic tracking of a reference impedance model for the robot end-effector in Cartesian coordinates applicable to rehabilitation robotics or any other human–robot interactions such as haptic systems. The controller uses the parameters of a desired stable reference model which is the target impedance for the robot’s end-effector. It also considers uncertainties in the model parameters of the robot. The asymptotic tracking is proven using Lyapunov stability theorem. Moreover, the adaptation law is proposed in joint space for reducing the complexity of its calculations; however, the controller and the stability proof are all presented in Cartesian coordinates. Using simulations and experiments on a two DOFs robot, the effectiveness of the proposed controller is investigated.     

Neural network payload estimation for adaptive robot control

A concept is proposed for utilizing artificial neural networks to enhance the high-speed tracking accuracy of robotic manipulators. Tracking accuracy is a function of the controller's ability to compensate for disturbances produced by dynamical interactions between the links. A model-based control algorithm uses a nominal model of those dynamical interactions to reduce the disturbances. The problem is how to provide accurate dynamics information to the controller in the presence of payload uncertainty and modeling error. Neural network payload estimation uses a series of artificial neural networks to recognize the payload variation associated with a degradation in tracking performance. The network outputs are combined with a knowledge of nominal dynamics to produce a computationally efficient direct form of adaptive control. The concept is validated through experimentation and analysis on the first three links of a PUMA-560 manipulator. A multilayer perceptron architecture with two hidden layers is used. Integration of the principles of neural network pattern recognition and model-based control produces a tracking algorithm with enhanced robustness to incomplete dynamic information. Tracking efficacy and applicability to robust control algorithms are discussed.     

工业机器人在特殊位形下的瞬时运动

本文具体分析了工业机器人在特殊位形下的瞬时运动，以ＳＴＡＮＦＯＲＤ机器人为例，分析其在特殊位形下约束运动的性质及允许移动的方向和转动时轴线存在的子空间，得出反螺旋的螺距为零时，处地特殊位形的６种组合形成，并给出了每种特殊位形在参考价值 标的反螺旋及存在的运动螺旋的一般表达式和相应的运动图谱。     

受限机器人运动的自适应控制

本文基于[4]中对受限机器人运动方程的变换,给出了一种自适应控制方案,使得在系统某些参数未知的情况下,机器人末端操纵器的位置运动及其与刚性、无摩擦的工作环境之间的接触力渐近趋于期望值,本文中的仿真例子验证了给出的自适应控制方案的有效性。     

Direct adaptive control of a one-link flexible arm with tracking

A robust tracking controller for a one-link flexible arm based on a model reference adaptive control approach is proposed. In order to satisfy the model matching conditions, the reference model is chosen to be the optimally controlled linearized model of the system. The resulting controller overcomes the fundamental limitation in previously published research on direct adaptive control of flexible robots that required additional actuators solely to control the flexible degrees of freedom. The nominal trajectory is commanded by means of a tracking control. Simulation results for the prototype in the laboratory show improvements obtained with the outer adaptive feedback loop compared to a pure optimal regulator control. Robustness is tested by varying the payload mass.     

Adaptive inverse dynamics control of robots with uncertain kinematics and dynamics

It has been about two decades since the first globally convergent adaptive tracking controller was derived for robots with dynamic uncertainties. However, not until recently has the problem of concurrent adaptation to both the kinematic and dynamic uncertainties found its solution. This adaptive controller belongs to passivity-based control. Though passivity-based controllers have many attractive properties, in general, they are not able to guarantee the uniform performance of the robot over the entire workspace. Even in the ideal case of perfect knowledge of the manipulator parameters, the closed-loop system remains nonlinear and coupled. Thus the closed-loop tracking performance is difficult to quantify, while the inverse dynamics controllers can overcome these deficiencies. Therefore, in this work, we will develop a new adaptive Jacobian tracking controller based on the inverse manipulator dynamics. Using the Lyapunov approach, we have proved that the end-effector motion tracking errors converge asymptotically to zero. Simulation results are presented to show the performance of the proposed controller.     

On controlling robots with redundancy

Recently there has been considerable interest in increasing the applicability and utility of robots by developing manipulators which possess kinematic and/or actuator redundancy. This paper presents a unified approach to controlling these redundant robots. The proposed control system consists of two subsystems: an adaptive position controller which generates the Cartesian-space control force FR^m required to track the desired end-effector position trajectory, and an algorithm that maps this control input to a robot joint torque vector TRⁿ. The F → T map is constructed so that the robot redundancy (kinematic and/or actuator) is utilized to improve the performance of the robot. The control scheme does not require knowledge of the complex robot dynamic model or parameter values for the robot or the payload. As a result, the controller is very general and is computationally efficient for on-line implementation. Computer simulation results are given for a kinematically redundant robot, for a robot with actuator redundancy, and for a robot which possesses both kinematic and actuator redundancy. In each case the results demonstrate that accurate end-effector trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed scheme.     

A systematic formulation of dynamic equations for robot manipulators with elastic links

Although a variety of formulation schemes for the dynamic equations of robot manipulators with rigid links can be found in the literature, an efficient method of the formulation for robot manipulators with elastic links is not well known. Accordingly, this work presents the derivation of the equations of motion for application to mechanical manipulators with elastic links. The formulation is conducted analytically using Hamilton's principle. The resultant equations consist of the terms of inertial, Coriolis, centrifugal, gravitational, and exerted forces. They are expressed in terms of a set of independent generalized coordinates. In contrast to conventional variational approaches, the present method provides an efficient and systematic way for obtaining the compact symbolic equations of flexible manipulator systems. Two examples are presented to illustrate the proposed methodology. Firstly, a three-link flexible manipulator with three revolute joints is studied. A flexible manipulator consisting of a prismatic joint and a discrete mass is the second model.