Adaptive Admittance Control of a Robot Manipulator Under Task Space Constraint

We present adaptive admittance control of a robotic manipulator, with uncertain dynamic parameters, operating in a constrained task space. To provide compliance to external forces, we generate a differentiable reference trajectory that remains in the constrained task space. Then, adaptive backstepping control, based on a time-varying asymmetric Barrier Lyapunov Function (BLF), is designed to achieve tracking of the reference trajectory while guaranteeing constraint satisfaction. The improved BLF-based control renders the entire constrained task space positively invariant. Despite transient perturbations by external forces and online parameter adaptation, practical tracking of the reference trajectory is achieved without transgression of the constrained task space. In the absence of interaction forces, asymptotic tracking of the desired trajectory is achieved.