Optimal impedance force-tracking control design with impact formulation for interaction tasks

The letter presents a force-tracking impedance controller granting a free-overshoots contact force (mandatory performance for many critical interaction tasks such as polishing) for partially unknown interacting environments (such as leather or hard-fragile materials). As in many applications, the robot has to gently approach the target environment (whose position is usually not well-known), then execute the interaction task. Therefore, the algorithm has been designed to deal with both the free space approaching motion (phase a.) and the succeeding contact task (phase b.) without switching from different control logics. Control gains have to be properly calculated for each phase in order to achieve the target force tracking performance (i.e., free-overshoots contact force). In detail, phase a. control gains are optimized based on the impact collision model to minimize the force error during the following contact task, while phase b. control gains are analytically calculated based on the solution of the LQR optimal control problem. The analytical solution grants the continuous adaptation of the control gains during the contact phase on the estimated value of the environment stiffness (obtained through an on-line extended Kalman filter). A probing task has been carried out to validate the performance of the control with partially unknown contact environment properties. Results show the avoidance of force overshoots and instabilities.