Stabilization of the Fast Modes of a Flexible-Joint Robot

Abstract

In this work the robot is assumed to be an open kinematic chain with only revolute joints. Each joint is modeled as a linear torsional spring. The model equations consist of two coupled dy namic systems, one representing the usual rigid body or slow dynamics and the other the fast dynamics introduced by the joint flexibility. The model presented in this article is in aform that brings out the influence on the fast subsystem dynamics of the rigid body parameters and the robot geometry. The model clearly shows the effect that link and drive parameters have on the dynamics of the fast subsystem. It is shown that under certain assumptions there exists a decen tralized velocity control law that asymptotically stabilizes the fast subsystem dynamics. In general this control law is gain scheduled. For sufficiently small drive inertias there always exists a fixed de centralized control law that will asymptotically stabilize the fast dynamics. This is true even for large drive ratios. For sufficiently large drive inertias it may not be possible to use a fixed decentral ized control law. Under certain conditions a gain-scheduled velocity feedback law can be designed to give attractive pole damping factors. Some examples are given to illustrate these ideas.