Optimal control of manipulators with any number of passive joints

Abstract

This article discusses the problem of controlling robot manipulators with passive joints, when the number of passive joints is larger than the number of active joints. Assuming that brakes and position sensors are available at each passive joint, we investigate the following issues: (1) what is a sufficient condition for controllability of the passive joints via dynamic coupling with the active joints and how can we quantify the controllability at a given configuration; (2) what is the optimal control and locking sequence of the passive joints; and (3) how can we control both passive and active joints to an equilibrium point in joint space. We propose an optimal control method and demonstrate its validity with both simulation and experimental results. The work presented here is significant because it provides a better understanding and a guideline for utilizing manipulators with passive joints for energy efficiency and fault-tolerant design in applications such as space robotics, hyperredundant robots, and sport mechanics.