Discontinuous model-based adaptive control for robots executing free and constrained tasks

We propose a robot controller for stably executing all phases of contact tasks involving discontinuities due to the introduction or removal of contact forces. Systems executing such tasks are characterized by ambiguous right hand sides in the differential equations of motion. Consequently, our approach develops upon ideas from generalized dynamical systems (GDSs), an orthogonalization principle, the Hertz contact model, and model-based adaptive control. The result is an asymptotically stable controller that discontinuously switches among three possible configurations based on the contact situation. The method is used to tune the controller independently for both position and constrained motion as also for reducing contact forces during the process of making contact with the environment. The underlying theory is first described. Then the controller synthesis and proof of its asymptotic stability, based on Lyapunov´s method, are presented. The idea is illustrated with a simulation of a simple task