Optimal Control for Clutched-Elastic Robots: A Contact-Implicit Approach

Intrinsically elastic robots surpass their rigid counterparts in a range of different characteristics. By tem- porarily storing potential energy and subsequently converting it to kinetic energy, elastic robots are capable of highly dynamic motions even with limited motor power. However, the time- dependency of this energy storage and release mechanism remains one of the major challenges in controlling elastic robots. A possible remedy is the introduction of locking elements (i.e. clutches and brakes) in the drive train. This gives rise to a new class of robots, so-called clutched-elastic robots (CER), with which it is possible to precisely control the energy-transfer timing. A prevalent challenge in the realm of CERs is the automatic discovery of clutch sequences. Due to complexity, many methods still rely on pre-defined modes. In this paper, we introduce a novel contact-implicit scheme designed to optimize both control input and clutch sequence simultaneously. A penalty in the objective function ensures the prevention of unnecessary clutch transitions. We empirically demonstrate the effectiveness of our proposed method on a double pendulum equipped with two of our newly proposed clutch-based Bi- Stiffness Actuators (BSA).