  Intrinsically elastic robots surpass their rigid counterparts in a range of
different characteristics. By temporarily 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).
