Resolving the problem of non-integrability of nullspace velocities for compliance control of redundant manipulators by using semi-definite Lyapunov functions

In this paper a compliance control law for kinematically redundant manipulators is proposed. The controller contains a Cartesian compliance part and a nullspace compliance part which are complemented by a power-conserving decoupling term. The approach deliberately avoids inertia shaping in order to obtain a control law which does not require the measurement of external forces and becomes less sensitive with respect to model uncertainties. While the controller formulation explicitly uses nullspace velocity coordinates, no integration of these velocities is required. Except for the kinematic singularities of the manipulator’s Jacobian matrix, no further algorithmic singularities are introduced. Asymptotic stability of the closed-loop system is shown by utilizing semi-definite Lyapunov functions. Finally, a short planar simulation study is presented which validates the effectiveness of the approach.