Impact stabilizing controller for hydraulic actuators with friction: Theory and experiments

Stabilizing manipulators during the transition from free to constraint motion is an important issue in contact task control design. This paper documents the development, theoretical analysis and experimental evaluation of a Lyapunov-based control scheme to regulate the impacts of a hydraulic actuator that comes in contact with a nonmoving environment. Upon sensing a nonzero force, the controller positions the actuator at the location where the force was first sensed, exerting minimal force on the environment. The scheme does not require continuous measurement of force or velocity during the short period of impacts, making it very useful for practical cases. Furthermore, no knowledge of the impact dynamics, friction effects, servovalve dynamics, or hydraulic parameters is required for control action. Stability of the control scheme is verified via analytical analyses. Due to the discontinuous friction model and the discontinuous nature of the proposed control law, the control system is nonsmooth. The existence, continuation and uniqueness of Filippov's solution to the system are, therefore, investigated. The extension of LaSalle's invariance principle to nonsmooth systems is next employed to prove that all the solution trajectories converge to the equilibria. The controller is finally tested experimentally to verify its practicality and effectiveness in collisions with hard and soft environments and with various approach velocities.