Animals rely on the elasticity of their tendons and muscles to execute robust and efficient locomotion patterns for a vast and continuous range of velocities. Replicating such capabilities in artificial systems is a long-lasting challenge in robotics. By taking advantage of a pitch dynamics decoupling spring potential, this work aims to provide design rules and a control strategy to generate dynamic, efficient locomotion patterns in quadrupeds moving in a sagittal plane. We rely on nonlinear modal theory, which provides the tools to characterize continuous families of efficient oscillations in nonlinear mechanical systems. We provide simulations of an elastic quadruped showing that the proposed solution can robustly excite efficient locomotion patterns under non-ideal conditions.

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Implementing dynamic legged locomotion entails stabilizing oscillatory behaviors in complex mechanical systems. Whenever possible, locomotion algorithms should also exploit the improved capabilities of elastic elements added to the structure to improve efficiency and robustness. This work aims to shed some light on implementing generic dynamic locomotion by stabilizing nonlinear modes. The nonlinear modal analysis extends the linear modal theory to nonlinear systems and thus characterizes the oscillations that a robot can execute as autonomous evolutions. We execute forward hopping motions with a single segmented elastic leg as the first step towards generic modal locomotion. We propose a locomotion algorithm that exploits the modes of an extension of the SLIP model. We develop this strategy to generalize to other robotic systems, and we extensively validate it with experiments on an elastically actuated segmented leg.@en

Eigenmanifolds are two-dimensional submanifolds of the state space, which generalize linear eigenspaces to nonlinear mechanical systems. Initializing a robot on an Eigenmanifold (or driving it there by control) yields hyper-efficient and regular oscillatory behaviors, called modal oscillations. This letter investigates the possibility of transitioning between two modal oscillations without ever leaving the Eigenmanifold. This is essential to generate control inputs that decrease or increase the amplitude of the nonlinear oscillations. First, we prove that this goal can be achieved using bounded inputs only for Eigenmanifolds with unidimensional projection in configuration space. Then, we show that by allowing for impulsive control actions, the problem can be solved for all Eigenmanifolds which self-intersect when projected in configuration space.

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