SOME RESULTS IN MODEL-BASED ADAPTIVE AND SLIDING OBSERVER AIDED CONTROLLER STRUCTURE FOR ROBOT MANIPULATORS

Abstract

Robots have played a dominant role in the trends towards automation over the past years. The rapid development of its applications require controller that satisfies demands regarding tracking, speed and accuracy. Although, robot manipulators have been used in industry for a number of years, their full capabilities reach far beyond their present-day applications. At present, industrial applications of robot manipulators are mainly restricted to simple tasks. In order to improve the performance and capabilities, the application of advanced control concepts to robot manipulators is a necessity. Two basic facts about the robot manipulator dynamics make the control problem a challenging one. Primarily, the dynamics are described by nonlinear, coupled second order differential equations. Secondly, the parameters of the model are partially unknown due to parametric variations disturbances and errors in modeling. Much of the recent research in robotic manipulator control has been directed towards the development of adaptive controller due to their effectiveness in high speed, high precision tasks and robustness to parametric uncertainty. The development of controller structure in the present research work is inspired by the adaptive control strategy as reported in [7],[17],[23],[64],[73],[84]. Broadly, three new adaptive controller structures are proposed for robot manipulators. The sliding observer aided controller structure for adaptive case is heavily influenced by the work of Canudas et. al. [10]. Two new sliding observer aided adaptive controller structures are proposed by modifications in the existing sliding observer [10]. Further, two variations of nonlinear sliding observer based controller structures, motivated by [8]-[85], are also proposed for robot manipulators.

The aim of these proposed schemes are to improve tracking performance of robot manipulators and to satisfy the stability criterion in the Lyapunov sense. Performance of these new controllers have been verified through simulation. The work done in this thesis is briefly summarized below: 1. The controller structure for adaptive case, presented by Whitcomb et. al. [84], is based on position and velocity vectors. Their control law is modified by incorporation of acceleration term in feedback loop. This is based on two assumptions. The first is that the joint acceleration is measurable [17]-[23] and relatively noise free, and the second is that the inverse of sum of acceleration gain and estimated inertia matrix remains bounded. Simulation results show significant improvement in tracking error and velocity error for two different types of desired trajectories having different initial estimated parameters. The closed-loop system is shown to be globally asymptotically stable in the Lyapunov sense and has better convergence. 2. To overcome the noisy velocity measurement problem, a globally convergent adaptive controller structure for robot manipulators is presented by Berghuis et. al. [7]. Their controller structure has been modified by inclusion of nonlinear compensator [64] and virtual reference trajectories (sliding surface) [73]. In our work, three new structures of adaptive controller, associated with distinct form of sliding surfaces, are proposed and studied with respect to their tracking improvements (case -1,2 and 3). In case-1, all three virtual reference trajectories are considered where as case -2 uses the desired velocity reference trajectory instead of velocity virtual reference trajectory with other form of sliding surface. The proposed controller structure for case-3 consists of nonlinear compensator and existing controller [7]. The asymptotic stability of the control algorithms are proved via the Lyapunov direct method. These proposed schemes improve tracking performance significantly, enhance robustness with respect to the noisy velocity measurement, especially in under- excited operations and also compensate the additional error (bounded by sliding surface and tracking error, [64]). In another approach a bounded form (norm based) of adaptive controllerstructure is proposed. This is based on the inverse dynamics mod'el of robot manipulator with a premise that if each parameter is known within some bounds the parameter adaptation can be prevented from going out of bounds and thus makes the system more robust. The stability of closed-loop system is investigated via the Lyapunov direct method. Simulation results, when compared with [7], clearly indicate drastic improvements in tracking performance. It is known that velocity measurements are usually associated with rather high level of noise [10]. Only joint position measurements are assumed to be available, which is in contrast to full state measurements (positions and velocities). In this situation, estimated joint velocity vector obtained from a sliding observer is fed back to adaptive controller structure [10]. The proposed sliding observer structure is an extension of this by including the desired acceleration vector and a new uncertainty term (associated with desired trajectory based robot model properties) to estimate the velocity vector for adaptively controlled robot manipulator. The combined scheme is analysed with the Filippov's solution concept and tracking error dynamics via the Lyapunov stability criterion. The proposed

scheme shows the significant reduction in tracking error, velocity error and observation error (velocity). The sliding observer scheme is further modified by including the tracking error and the observation error (position) in estimating velocity vector, to take into account the dynamic interaction between observer and controller dynamics. This means that the observer shall not only depend on the- observation errors and controller not only on the tracking difference. This combined scheme is considered as a global control system with their gains tuned in order to ensure asymptotic tracking of the desired reference. The adaptation law and design vector, account for uncertainties on parameter vector associated with desired trajectory based model properties of robot, are derived using the Lyapunov direct method. Simulation results clearly indicate the improvements in comparison to [10]. In nonlinear systems the controller and the observer, in general, cannot be independently designed since the separation principle does not apply as in case of linear systems. In controller-observer scheme for robot manipulators presented by Canudas et. al. [8], the nonlinear sliding observer structure uses only observation error (position) in estimating velocity vector in order to fed back to controller structure. In view of nonlinear nature of robot manipulator and dynamic interaction between controller and observer, the square of tracking error and signum function of velocity observation error [85] are included as extended terms in the existing nonlinear sliding observer structure [8]. The first term reduces the observation error (velocity) due to application of the Filippov's solution concept and second term acts as a forcing (switching) element to (v) get good estimate of velocity. The closed-loop analysis is performed which is based on reduced order manifold dynamics and tracking error dynamics using the Lyapunov stability to ensure asymptotic stability. It is observed, through simulation, that drastic reduction in velocity error and observation error (velocity) results, in comparison to [8]. Again, the sliding observer is further modified by incorporating the signsign term in previously proposed observer structure. The observer scheme is termed as Sign-Sign Algorithm (SSA). The existing controller structure [8] is extended by incorporation of disturbance torque (as function of the desired position trajectory) in order to achieve the improved tracking performance of combined controller-observer scheme. The proposed scheme is illustrated by a simple example. The stability of closed-loop analysis is performed in the Lyapunov sense. New model-based adaptive and sliding observer aided controller structures developed in this thesis are new solutions to many constraints, complexities and ambiguities involved in the control of robotic manipulators.