Generating Families of Optimally Actuated Gaits from a Legged System's Energetically Conservative Dynamics

We present a homotopic approach to generating energetically optimal gaits for legged robots that maps passive (i.e., unactuated) gaits of an energetically conservative model of the robot to a model with user-defined target dynamics with dissipation and actuation (i.e., the more "realistic" legged model). Our core contribution is advancing the state-of-the-art towards a turn-key approach where the seed values are known by design and do not rely on domain-specific knowledge to generate or randomly guess across a range of energetic cost functions and desired gait properties (e.g., walking speed, hopping height, etc.), which can limit the usefulness of the typical optimization-based approach. We demonstrate this methodology on a parallel elastic actuated planar monoped with five degrees of freedom. Our work also demonstrates an explicit connection between passive gaits and optimally actuated motions, which has long been an area of interest in the fields of robotics and biomechanics.