Chaotic Behavior and Nonlinear Control of a Two-joint Planer Arm with a Free Joint. Control on Nonholonomic Mechanisms with Drift.

Abstract

The nonholonomic systems considered in robotics are mechanical systems with nonintegrable constraints. These systems have the property that the dimension of the reachable space is larger than the number of degree-of-freedom. A two-joint planar manipulator with the second joint free is one of such systems. Chaos, on the other hand, is another major topic in nonlinear dynamics and has the property that a dynamical system is sensitive in the initial conditions. The two phenomena have the same mathematical background from integrability point of view. In this paper, we study when and how the manipulator exhibits the chaotic behavior. We propose a control strategy for simultaneous positioning of the two joints, based on the analysis of nonlinear behavior. Its effectiveness is to be shown by experiments.