Discrete-Time Formulation for Optimal Impact Control in Interaction Tasks

Lightweight manipulators are increasingly involved in industrial scenarios due to their intrinsic safety features allowing to share working space and to cooperate with humans/robots. In particular, interaction tasks are one of their main application. In fact, by imposing a compliant behavior (at software or hardware level) a target interaction can be tracked while ensuring safety during the whole task. Despite the wide range of control strategies developed to face the interaction control problem, the limited control frequency and the measurements noise (especially considering the estimation of end-effector wrenchs from joint side measurements/estimation) are the main limitation in order to achieve improved interaction tracking performance. This paper presents a discrete time formulation for impedance controlled tasks granting a free-overshoot contact force throughout the whole contact phase between the robot and a partially unknown environment, involving finite sampling and force measurements filtering. Moreover, since many applications require the manipulator to approach the not well-known positioned target environment, the proposed algorithm is capable to avoid any force overshoot during the initial contact phase, taking into account non-zero approaching velocities. The main control structure is used in both the free-motion and contact phases, without switching from different control laws, by properly optimizing the control gains solving the defined LQR optimal control problem. A probing task has been carried out in order to validate the control performance with particular attention to the smoothness of the response. Results show the avoidance of force overshoots and instabilities. Moreover, the method has been compared to a continuous time control algorithm, showing improved performance.