Stability of a contact task for a robotic arm modelled as a switched system

The task of stabilising an n-degree-of-freedom (dof) robot arm moving from free space to contact with a compliant surface is considered. A proportional derivative position controller with gravity compensation is used for the free motion and a parallel force/position controller for the contact task. The goal is to stabilise the robot in contact with the environment, exert a desired force and place the end-effector at a desired position. The robot is modelled as a switched system, and its stability is examined using hybrid stability theory by considering typical candidate Lyapunov functions for each of the two discrete system states. The stability analysis reveals that extra conditions involving control gains and control targets should be satisfied in order to guarantee asymptotic stability of the switched task in a Lyapunov sense. The system performance and robustness is illustrated by the simulation of a 3-dof planar robot.

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