Contact task stability and maintenance with a compliant surface using a switched one dof robot model

This work refers to the control of the contact of a simple one degree-of-freedom (dof) robot with a compliant surface using ideas from hybrid stability theory. The robot is modeled as a switched system. A position controller is used for the free motion and a force controller for the contact task. The goal is to stabilize the robot in contact with the environment and exert a desired force. The surface is modeled by an unknown, nonlinear elasticity function. By considering typical candidate Lyapunov functions for each of the two discrete system states, conditions on feedback gains are derived that guarantee Lyapunov asymptotic stability of the hybrid task. A sufficient condition that ensures that the robot will remain in contact with the surface is derived involving the system´s velocity at the time of contact