Probabilistic modeling and optimal design of robotic manipulators

Abstract

A high performance, high speed robotic arm must be able to manipulate objects with a high degree of accuracy, repeatability and dexterity. As with any other physical system, there are a number of factors causing uncertainties in the behavior of a robotic manipulator. These factors include manufacturing and assembling tolerances, and errors in the joint actuators and controllers. In order to study the effect of these uncertainties on the robotic end-effector and to obtain a better insight into the manipulator behavior, the concepts of theory of probability are applied to the manipulator kinematics and dynamics. Based on these probabilistic models, kinematic and dynamic performance criteria are defined to provide a measure of the behavior of the robotic end-effector. Techniques are presented to compute these criteria. The effect of the tolerances on various manipulator parameters on these criteria is studied. A methodology is developed to assign the tolerances optimally, that maximizes these criteria subject to constraints on the manipulator cost. Results show that very significant and cost effective improvements can be achieved in the manipulator performance with the use of optimal tolerances. Another desirable property of a robotic arm is the degree of dexterity with which it can manipulate objects. This aspect of the manipulator performance is investigated, and new criteria are proposed to provide a measure of the kinematic, dynamic and force manipulating abilities. It is shown that optimization of these criteria can lead to significant improvements in the overall manipulating capabilities of a robotic arm. Numerical illustrations are presented throughout this dissertation using a two-link planar manipulator and the Stanford arm.