Analysis and control of a flexible joint robot

Dynamic equations for a flexible-joint robot are obtained. The robot is assumed to be an open kinematic chain with only revolute joints, modeled as linear torsional springs. The model equations consist of two coupled dynamic systems: slow dynamics of the rigid body and fast dynamics introduced by the joint flexibility. The model brings out the influence on the fast subsystem dynamics of the rigid body parameters and the robot geometry. It is shown that under certain assumptions there exists a decentralized velocity control law which asymptotically stabilizes the fast subsystem dynamics. In general, this control law is gain scheduled. For sufficiently small drive inertias there always exists a fixed decentralized control law that will asymptotically stabilize the fast dynamics, even for large drive ratios. For sufficiently large drive inertias it may not be possible to use a fixed decentralized 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