Nonlinear behavior and control of a nonholonomic free-joint manipulator

The nonlinear motion of underactuated mechanisms has drawn recent interests of researchers. The nonlinearity is often referred to as nonholonomy and related to many both theoretical and practical issues. In this paper, we rst analyze the nonlinear behavior of a two-joint planer manipulator with the second joint free from nonlinear dynamics point of view. We then discuss the simultaneous positioning of the both joints. We use a time-periodic input and propose an amplitude modulation of the feedback error. The analysis via the Poincar e map shows that the behavior becomes even chaotic with large amplitude. The e ectiveness and robustness of the proposed positioning control are veri ed by experiments.