Characterization of Chaos in the Zero Dynamics of Kinematically Redundant Robots

Chaos is a ubiquitous and robust phenomenon that is now well documented in nonlinear dynamical systems. The recent explosion of research in the feedback linearization of nonlinear control problems has uncovered interesting internal behavior in partially linearizable system. The internal dynamics subject to the constraint that the output is zero is defined as the zero dynamics of the partially linearized system. We numerically investigate the basin of attraction of chaotic behavior on the zero dynamics submanifold. The theoretical ramifications of such studies could lead to new avenues in the global feedback stabilization of nonlinear systems when the zero dynamics converge to a compact but strange attractor.