Chaos and nonlinear control of a nonholonomic free-joint manipulator

Nonholonomic system is now one of the major topics in robotics. In this paper, we discuss the nonlinear behavior of a two-joint planer manipulator with the second joint free for time-periodic inputs. First, we illustrate that when the amplitude remains small, the Poincare map of the system follows an ellipse-like closed path and it becomes chaotic with large amplitude. We then propose a control method to position the both joints via amplitude modulation of the position error. The effectiveness and robustness of the control method are verified by experiments