Application of Learning Control Theory to Mechanisms: Part 1 — Inverse Kinematics and Parametric Error Compensation

Abstract

Abstract Fundamental concepts of learning control theory are applied to problems in mechanisms. The theory provides an integrated approach that can simplify the numerical solution of inverse kinematics of mechanisms as well as the practical problem of inverse kinematics in the presence of parametric errors. The procedure makes repeated use of forward kinematics that can be carried out analytically for off-line computation, or experimentally for on-line tuning of mechanisms, to arrive at the correct inverse kinematic solution. With repetitive learning, learning control theory will identify the appropriate input function to a mechanism so that its output will track a given desired output function. The learning process is based on the output error alone, without accurate or explicit knowledge of the physical system, so that the analytical algebraic inverse is avoided. This is achievable even in the presence of geometric nonlinearities as well as parametric errors in mechanisms modeling as long as measurements of the output relative to the given desired output function, are available. A general formalism is presented to explain the applicability of such repetitive learning to mechanism problems. Several examples will illustrate the important benefits of the learning approach using very simple learning rules.