Possible chaotic motions in a feedback controlled 2R robot

Abstract

The equations describing the motion of a feedback controlled robot are known, to be non-linear. Several non-linear equations are known to exhibit chaos for certain ranges of parameters. In this paper, the authors explore the possibility of chaos in a system of differential equations which model a feedback controlled two link robot with rotary(R) joints. The authors examine a simple proportional and derivative controller and a model based controller for a 2R planar robot undergoing repetitive motions in a plane in the absence of gravity. The authors show that the differential equations describing such a system exhibits chaotic behavior for certain ranges of the proportional and derivative gains and for certain values of a parameter which quantifies the mismatch between the model and the actual system. The authors discuss the difficulty of obtaining analytical results and describe numerical schemes to test for chaos and to obtain ranges of gains and the mismatch which results in chaotic motions.