Chapter 9 - A Circuit-Theoretic Analysis of Robot Dynamics and Control

Abstract

This chapter aims to solve the problem of making robot arms and mechanical hands acquire the ability to manipulate things smoothly and dexterously without using a complicated mathematical model of nonlinear dynamics pertaining to robot tasks. Such abilities are related to adaptive control, iterative learning, and impedance matching when robots manipulate soft and deformable objects or touch a rigid object with their soft fingers. These abilities can be realized in robots by devising corresponding control schemes on the basis of physical properties such as passivity and dissipativity inherent in the dynamics of robot tasks. The essential idea is to observe that a large class of robot dynamics can be expressed by a nonlinear position-dependent circuit and the impedance concept inherent in linear electric circuits can be extended to cope with such a nonlinear circuit via the passivity and dissipativity. As a by-product of this analysis, it is shown that iterative learning based on such physical properties can be interpreted as steady progress of impedance matching. In the process of this interpretation, the concept of impedance matching is generalized by means of passivity to cope with nonlinear dynamics in the case in which a mechanical hand whose finger ends are covered by soft material grasps rigid objects. It is finally claimed that robot control must be advanced in a direction from using full-model-based control (for example, the computed torque method) to simple control schemes without using models of dynamics or using at most approximate models, as seen in human motion when tasks are executed dexterously.