Optimal control and design guidelines for soft jumping robots: Series elastic actuation and parallel elastic actuation in comparison

A properly designed elastic actuation can increase the jumping height that a legged robot can reach. In this paper we compare the two most popular conceptual soft actuator designs, parallel elastic (PEA) and series elastic (SEA), in the task of maximizing the jumping height. Such task is translated into an optimal control problem. For a simplified version of the problem an analytical solution is provided, while a problem with more realistic constraints (e.g. the linear torque-speed motor characteristic is taken into account) is stated as a convex optimization problem and numerically solved. The results show that: (i) given the power of the motor there exists an optimal constant stiffness that maximizes the performance for both the SEA and the PEA; (ii) the optimal stiffness depends on the task terminal time, the inertial parameters of the system and the reduction ratio of the motor; (iii) in the condition considered the SEA behaves better than the PEA.