Introducing elasticity in the mechanical design can endow robots with the ability of performing efficient and effective periodic motions. Yet, devising controllers that can take advantage of such elasticity is still an open challenge. This letter tackles an instance of this general problem, by proposing a control architecture for executing goal-oriented and efficient point-to-point periodic motions. This is achieved by (i) producing motor torques that excite intrinsic modal oscillations, and simultaneously (ii) adjusting parallel elasticity so to shape the natural modes. Analytical proofs of convergence are provided for the linear approximation. The performance and efficiency (in the sense of low energy expenditure) of the method in the nonlinear case are assessed with extensive simulations and experiments.@en

Robotic legs often lag behind the performance of their biological counterparts. The inherent passive dynamics of natural legs largely influences the locomotion and can be abstracted through the spring-loaded inverted pendulum (SLIP) model. This model is often approximated in physical robotic legs using a leg with minimal mass. Our work aims to embed the SLIP dynamics by using a nonlinear strict oscillatory mode into a segmented robotic leg with significant mass, to minimize the control required for achieving periodic motions. For the first time, we provide a realization of a nonlinear oscillatory mode in a robotic leg prototype. This is achieved by decoupling the polar task dynamics and fulfilling the resulting conditions with the physical leg design. Extensive experiments validate that the robotic leg effectively embodies the strict mode. The decoupled leg-length dynamic is exhibited in leg configurations corresponding to the stance and flight phases of the locomotion task, both for the passive system and when actuating the motors. We additionally show that the leg retains this behavior while performing jumping in place experiments. @en