A comparison of series and parallel elasticity in a monoped hopper

In this paper we use optimal control on a geared electric DC motor to compare the energetic efficiency of a simulation of conceptual monoped hoppers with either parallel elastic actuation (PEA) or series elastic actuation (SEA). The energy is measured using three cost functions: positive actuator work, electrical losses, and positive electrical work. For PEA, the presence of the motor inertia in the collision losses leads to increased collision losses at large transmission ratios, which lead to energetically costly compensatory strategies where the SEA is at its most efficient. At small transmission ratios, the motor force increases for both cases, leading to increased thermal losses. In agreement with those theoretical predictions, our work shows that for positive actuator work and positive electrical work the optimal parameter choice for SEA is significantly more energetically efficient than the optimal choice for PEA. For electrical losses, a suitable choice of the transmission ratio can lead to negligible cost values for both actuator concepts.