Adaptive operational space control of redundant robot manipulators

The operation space formulation requires model certainty to completely decouple the null space and operational space dynamics. In this paper, we present an adaptive operational space control for redundant robots that does not require exact knowledge of the robot inertial parameters. The use of the inertia matrix as the weighting matrix in the generalized inverse of the Jacobian leads to nonlinearly parameterized task space dynamics. We show that the nonlinear parametrization can be expressed as ratios of linearly parameterized numerator and denominator terms. Based on this, we construct a control Lyapunov function to eliminate some of the denominator terms during control design, leaving behind a linearly parameterized form that can be easily compensated for. For uncertainties that cannot be transformed into linearly parameterized form, we consider them as time-varying uncertainties and dominate them based on the fact that they are bounded, without knowledge of the bounds. Asymptotic tracking performance of the end effector is achieved. Simulation results are shown to illustrate the control performance.