Possible chaotic motions in a feedback controlled 2R robot

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. I n this paper, we explore the possibility of chaos in a system of differential equations which model a feedback controlled two link robot with rotary(R) joints. We 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. W e 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. W e discuss the di'culty of obtaining analytical results and describe numerical schemes t o test for chaos and to obtain ranges of gains and the mismatch which results in chaotic motions.