Optimal configuration of series and parallel elasticity in a 2D Monoped

This paper uses optimal control to simultaneously optimize the motion and morphology of a realistic model of a 2D Monoped. In particular, we compare the energetics of four different actuator configurations: a parallel elastic actuator (PEA) in the hip and a series elastic actuator in the leg (SEA), series hip and parallel leg, series hip and series leg, and parallel hip and parallel leg. We use realistic models with mass in the legs and feet, damping in the springs, and detailed DC electric motor models. The comparison is carried out for the cost of transport of three energetic measures: positive motor work, electrical losses, and positive electrical work, and evaluated as a function of velocity. In our optimization we include motor parameters, stiffness, and spring pre-compression terms as free variables, ensuring that we compare the energetically optimal version of each configuration at each velocity. We show that for the positive motor work and the electrical losses costs of transport (COT), the parallel hip and series leg configuration is energetically optimal. For the electrical work, the optimal configuration is speed dependent, with series hip and parallel leg optimal at low speeds, and both series hip series leg and parallel hip series leg optimal at high speeds.