A singular perturbation approach to stabilization of the internal dynamics of multilink flexible robots

Abstract

One of the main difficulties in controls design for multilink flexible arms is the instability of its internal dynamics. This paper presents a singular perturbation method to stabilize the internal dynamics and to achieve desired tracking performance. It is shown that by first applying partial feedback linearization and then inducing time-scale separation, a better time-scale separation can be obtained. The slow part of the control ensures tracking of the desired rigid trajectory and the fast part is then designed for stabilizing the internal dynamics. It is shown that the off-manifold error, the tracking error and its first and second-order derivatives are uniformly bounded by exponentially decaying terms plus a small constant term. It is also proved that the first-order derivative of the off-manifold error is uniformly bounded. One of the special features of the authors' approach is that the bounds for the tracking error, the off-manifold error, the initial off-manifold value, and the bound for stiffness which guarantees the convergence can be explicitly computed. The simulations show excellent path tracking and vibration rejection properties.