One of the hallmarks of the performance, versatility, and robustness of biological motor control is the ability to adapt the impedance of the overall biomechanical system to different task requirements and stochastic disturbances. A transfer of this principle to robotics is desirable, for instance to enable robots to work robustly and safely in everyday human environments. It is, however, not trivial to derive variable impedance controllers for practical high DOF robotic tasks. In this contribution, we ac- complish such gain scheduling with a reinforcement learning ap- proach algorithm, PI 2 (Policy Improvement with Path Integrals). PI 2 is a model-free, sampling based learning method derived from first principles of optimal control. The PI 2 algorithm requires no tuning of algorithmic parameters besides the exploration noise. The designer can thus fully focus on cost function design to specify the task. From the viewpoint of robotics, a particular useful property of PI 2 is that it can scale to problems of many DOFs, so that RL on real robotic systems becomes feasible. We sketch the PI 2 algorithm and its theoretical properties, and how it is applied to gain scheduling. We evaluate our approach by presenting results on two different simulated robotic systems, a 3-DOF Phantom Premium Robot and a 6-DOF Kuka Lightweight Robot. We investigate tasks where the optimal strategy requires both tuning of the impedance of the end-effector, and tuning of a reference trajectory. The results show that we can use path integral based RL not only for planning but also to derive variable gain feedback controllers in realistic scenarios. Thus, the power of variable impedance control is made available to a wide variety of robotic systems and practical applications. I. INTRODUCTION
['Jonas Buchli', 'Evangelos Theodorou', 'Freek Stulp', 'Stefan Schaal']
Variable Impedance Control A Reinforcement Learning Approach