Trajectory tracking of mechanical systems with unilateral constraints : experimental results of a recently introduced hybrid PD feedback controller

The problem of tracking a time-varying reference trajectory of a mechanical system with unilateral position constraints is addressed in this paper. We present for the first time simulation and experimental results of a recently introduced trajectory tracking controller for hybrid systems with state jumps. The controller is applied to (locally) stabilize a time-varying trajectory of a 1-DOF robotic arm impacting and bouncing off an aluminum rod. The arm is modeled as a rigid link with viscous and Coulomb friction. The impact phenomenon is assumed to instantaneously reset the velocity in accordance with the classical Newton's law of restitution. Kinematic and dynamic identified parameter values are reported. The employed controller, hereafter called “hybrid PD controller with acceleration feedforward”, requires the real time detection on each impact in order to properly define the error signal. To this end, a force sensor and a triggering logic based on a force threshold are employed.