An adaptive control strategy for mechanical manipulators

This paper focuses on the study of an adaptive perturbation control which tracks a desired time-based trajectory as close as possible for all times over a wide range of manipulator motion and payloads. The proposed adaptive control is based on the linearized perturbation equations in the vicinity of a nominal trajectory. The controlled system is characterized by feedforward and feedback components which can be computed separately and simultaneously. The feedforward component computes the nominal torques from the Newton-Euler equations of motion to compensate all the interaction forces among the various joints. The feedback component consisting of recursive least-square identification and an optimal adaptive self-tuning control algorithm for the linearized system computes the perturbation torques which reduce the position and velocity errors of the manipulator along the nominal trajectory. A computer simulation study was conducted to evaluate the performance of the proposed adaptive control.     

Passivity based adaptive control for mechanical manipulators usingLS-type estimation

A novel adaptive controller for mechanical manipulators is presented. The convergence analysis is based on the passivity properties of the plant and those of the parameter estimation algorithm. Instead of using a gradient-type algorithm, as is currently the case in this sort of synthesis approach, a least-square-type estimation algorithm is proposed. The modified least squares (LS) algorithm is proved to be passive. The modification vanishes with time, and therefore the proposed parameter estimate converges to the LS estimate. The passivity properties of the mechanical manipulator and those of the proposed estimation algorithm are combined to conclude the stability of the control scheme     

Discrete-time modeling and control of robotic manipulators

A general approach is presented to derive discrete-time models of robotic manipulators. Such models are obtained by applying numerical discretization techniques directly to the problem of the minimization of the Lagrange action functional. Although these models are in implicit form, they own a dynamic structure that allows us to design discrete-time feedback linearizing control laws. The proposed models and control algorithms are validated by simulation with reference to a three link robot.     

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.     

Hybrid adaptive control for robot manipulators

A hybrid adaptive control scheme is proposed for robot manipulators. Unmodelled dynamics have been considered in the robot model. The standard RLS algorithm has been modified to take into account these unmodelled dynamics. Global stability of the system is ensured.     

Robust adaptive control for robot manipulators

A composite adaptive control law for robot manipulators in task space, which uses both the tracking error and the prediction error to drive parameter estimation, is developed in this paper. It is shown that global stability and convergence can be achieved for the adaptive control algorithm in the ideal case, and furthermore that the algorithm can be easily modified by using parameter projection to achieve robustness with respect to a class of unmodelled dynamics. In addition, the algorithm has the advantage that no requirement is needed for the inverse of the jacobian matrix or for the bounded inverse of the estimated inertia matrix. A simulation example is provided for performance demonstration.     

Robust adaptive controller design for flexible joint manipulators

In this paper the control problem for robot manipulators with flexible joints is considered. A reduced-order flexible joint model is constructed based on a singular perturbation formulation of the manipulator equations of motion. The concept of an integral manifold is utilized to construct the dynamics of a slow subsystem. A fast subsystem is constructed to represent the fast dynamics of the elastic forces at the joints. A composite control scheme is developed based on on-line identification of the manipulator parameters which takes into account the effect of certain unmodeled dynamics and parameter variations. Stability analysis of the resulting closed-loop full-order system is presented. Simulation results for a single link flexible joint manipulator are given to illustrate the applicability of the proposed algorithm.     

Discrete-time adaptive control for deterministic time-varying systems

There is currently considerable interest in the application of recently developed self-tuning control algorithms to real control problems. However, there exist few algorithms which will work for other than slow time-varying systems. A new algorithm which is able to successfully control unknown systems with quite rapidly varying parameters is presented. Several simulation results are also presented. A convergence proof in the linearly time-varying parameter case is given.     

Robust sliding composite adaptive control for mechanical manipulators with finite error convergence time

In this paper a new robust adaptive control scheme for mechanical manipulators is presented. The design basically consists of, on the one hand, a composite adaptive controller which implements a feedback law that compensates the modelled dynamics and, on the other hand, a nonlinear sliding mode control law that overcomes the unmodelled dynamics and noise. It is proved that the resulting closed-loop system is stable and that the trajectory-tracking error converges to zero in finite time. Moreover, an upper bound of this error convergence time is calculated. Finally, the design is evaluated by means of simulations.     

An adaptive control scheme for robot manipulators

An adaptive control scheme is developed for a robot manipulator to track a desired trajectory as closely as possible in spite of a wide range of manipulator motions and parameter uncertainties of links and payload.

The presented control scheme has two components: a nominal control and a variational control. The nominal control, generated from direct calculation of the manipulator dynamics along a desired trajectory, drives the manipulator to a neighbourhood of the trajectory. Then a new adaptive regulation scheme is devised based on the Lyapunov direct method, which generates the variational control that regulates the perturbation in the vicinity of the desired trajectory.     

Decentralized adaptive control of manipulators

This article presents two new adaptive schemes for motion control of robot manipulators. The first controller possesses a partially decentralized structure in which the control input for each task variable is computed based on information concerning only that variable and on two “scaling factors” that depend on the other task variables. The need for these scaling factors is eliminated in the second controller by exploiting the underlying topology of the robot configuration space, and this refinement permits the development of a completely decentralized adaptive control strategy. The proposed controllers are computationally efficient, do not require knowledge of either the mathematical model or the parameter values of the robot dynamics, and are shown to be globally stable in the presence of bounded disturbances. Furthermore, the control strategies are general and can be implemented for either position regulation or trajectory tracking in joint-space or task-space. Computer simulation results are given for a PUMA 762 manipulator, and these demonstrate that accurate and robust trajectory tracking is achievable using the proposed controllers. Experimental results are presented for a PUMA 560 manipulator and confirm that the proposed schemes provide simple and effective real-time controllers for accomplishing high-performance trajectory tracking. © 1994 John Wiley & Sons, Inc.     

Discrete-time robust backstepping adaptive control for nonlineartime-varying systems

This paper studies the problem of adaptive control for a class of nonlinear time-varying discrete-time systems with nonparametric uncertainties. The plant parameters considered here are not necessarily slowly time-varying in a uniform way. They are allowed to have a finite number of big jumps. By using the backstepping procedures with parameter projection update laws, a robust adaptive controller can be designed to achieve adaptive tracking of a reference signal for this class of systems. It is shown that the proposed controller can guarantee the global boundedness of the states of the whole adaptive system in the presence of parametric and nonparametric uncertainties. It can also ensure that the tracking error falls within a compact set whose size is proportional to the size of the uncertainties and disturbances. In the ideal case when there is no nonparametric uncertainties and time-varying parameters, perfect tracking can be achieved     

Design of a robust adaptive control law for robotic manipulators

In this article, a robust adaptive control scheme for robotic manipulators is designed based on the concept of performance index and Lyapunov's second method. Compensators are selected for a given feedback system by using a quadratic performance index. Then the stability of the system is proven based on Lyapunov's method, where a Lyapunov function and its time-derivative are derived from the selected compensators. In the process of stabilization, stability bounds are obtained for disturbances, control gains, adaptation gains, and desired trajectories, in the presence of feedback delay due to digital computation and first-order hold in the control loop. © 1994 John Wiley & Sons, Inc.     

Discrete-time adaptive control utilizing prior information

We present schemes for discrete-time adaptive control of a linear time-invariant system, which is partially known, along with an analysis of their convergence properties.     

Discrete-time minimal control synthesis adaptive algorithm

This article proposes a discrete-time Minimal Control Synthesis (MCS) algorithm for a class of single-input single-output discrete-time systems written in controllable canonical form. As it happens with the continuous-time MCS strategy, the algorithm arises from the family of hyperstability-based discrete-time model reference adaptive controllers introduced in (Landau, Y. (1979), Adaptive Control: The Model Reference Approach, New York: Marcel Dekker, Inc.) and is able to ensure tracking of the states of a given reference model with minimal knowledge about the plant. The control design shows robustness to parameter uncertainties, slow parameter variation and matched disturbances. Furthermore, it is proved that the proposed discrete-time MCS algorithm can be used to control discretised continuous-time plants with the same performance features. Contrary to previous discrete-time implementations of the continuous-time MCS algorithm, here a formal proof of asymptotic stability is given for generic n-dimensional plants in controllable canonical form. The theoretical approach is validated by means of simulation results.     

Fuzzy reinforcement learning control for compliance tasks ofrobotic manipulators

A fuzzy reinforcement learning (FRL) scheme which is based on the principles of sliding-mode control and fuzzy logic is proposed. The FRL uses only immediate reward. Sufficient conditions for the convergence of the FRL to the optimal task performance are studied. The validity of the method is tested through simulation examples of a robot which deburrs a metal surface.     

A discrete-time adaptive control scheme for robot manipulators

A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. The scheme utilizes feedback, feedforward, and auxiliary signals, obtained from joint angle measurement through simple expressions. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation. Simulations and experimental results are given to demonstrate the performance of the scheme.     

A fault-tolerant control algorithm having a decentralizedautonomous architecture for space hyper-redundant manipulators

Adaptation to partial failure is one of the most important requirements for space robotics, since space robots cannot be repaired after they have been launched. We propose a decentralized autonomous control algorithm for hyper-redundant manipulators that uses parallel processing with low-performance processors to achieve this adaptation. In this paper, a number of manipulator joints are locked at a certain angle in a computer simulation and the adaptability of the control algorithm to these failures is assessed. The control algorithm successfully continues its positioning task at a rate of more than 90%, even after half of its joints have failed. The control algorithm is also compared with behavior-based control architecture     

A global adaptive learning control for robotic manipulators

This paper addresses the problem of designing a global adaptive learning control for robotic manipulators with revolute joints and uncertain dynamics. The reference signals to be tracked are assumed to be smooth and periodic with known period. By developing in Fourier series expansion the input reference signals of every joint, an adaptive learning PD control is designed which ‘learns’ the input reference signals by identifying their Fourier coefficients: global asymptotic and local exponential stability of the tracking error dynamics are obtained when the Fourier series expansion of each input reference signal is finite, while arbitrary small tracking errors are achieved otherwise. The resulting control is not model based and depends only on the period of the reference signals and on some constant bounds on the robot dynamics.     

Nonlinear adaptive motion control for manipulators with compliantjoints

How to perform control and achieve stability of robotic manipulators with joint flexibility forms a problem of profound practical and theoretical interest. This paper is to investigate and to solve this problem without strict assumption on the joint stiffness. Here, an adaptive control scheme of a flexible-joint manipulator, which takes into account its full nonlinear dynamics, is presented. Without the knowledge of the system model, the developed control lams, requiring only the position and velocity information of the actuators and links, is capable of driving the link tracking errors asymptotically to zero, while maintaining the uniform boundedness of all signals in the closed-loop system. To demonstrate the effectiveness of the proposed control law, an example of a two-link flexible-joint manipulator is constructed and a number of computer simulations are performed which show quite satisfactory results.