Adaptive Integral Manifold Control of Flexible Joint Robots with Configuration Invariant Inertia

In this paper we derive a new adaptive corrective control law for a class of flexible joint robot manipulators with configuration-invariant inertia matrices. The control law consists of a fast controller to damp the elastic oscillations of the joints and a slow (corrective) controller designed based on the theory of integral manifolds for singularly perturbed nonlinear systems. We derive the first parameter update law that takes into consideration joint flexibility. We present detailed stability analysis using the composite Lyapunov function method.