Control of serial and parallel robots: Analysis and implementation

Abstract

The research presented in this thesis is categorized into two areas. In the first part we address the issue of uniform boundedness of the elements of the equations of motion of serial robots, an important issue for the control of robots in this class. The second part is dedicated to the dynamic modeling and model based control of parallel robots. The field of serial robot control experienced tremendous growth over the past few decades resulting in a rigorous body of control results. An important assumption that is frequently made in establishing stability properties of these control laws is that the terms associated with the equations of motion of serial robots such as the inertia matrix, the Coriolis/centrifugal terms, and the Hessian of potential energy are uniformly bounded. This assumption however, is not valid for all serial robots. Since the stability conclusions of many control laws become local for robots that violate this assumption, it's important to be able to determine whether the terms in question are indeed uniformly bounded for a given robot. In the first part of this research we examine this issue and characterize the class of serial robots for which each of these terms are uniformly bounded. We also derive explicit uniform bounds for these terms which become important in control synthesis since the uniform bounds appear in the expressions of many control laws. The second part of this research is dedicated to parallel robots. Unlike in the case of serial robots, in parallel robots the independent generalized coordinates corresponding to the actuated joints do not uniquely determine the configuration of the robot. Therefore, an important issue that must be resolved in order to derive the dynamics of parallel robots is the existence of a transformation from the independent coordinates to a set of dependent coordinates that completely determine the robot configuration. The existence of such a transformation will enable the extension of most results in serial robots to parallel robots. In this research we characterize a region with specified boundaries where such a transformation exists and derive a numerical scheme for implementing the transformation in real time. Another contribution of this research is the design and construction of the Rice Planar Delta Robot which will serve as a test bed for results on parallel robots. This robot was used to experimentally verify the above result in a trajectory tracking experiment and a fast pick and place experiment