Simple Motions as Templates for Generating Gait Spaces of Robophysical Systems*

A stated goal of the field of robophysics is to understand the core dynamics of complicated robotic systems through simplified models (Aguilar et al., 2016).  In the context of legged locomotion, simple often means low-dimensional models whose gaits are used as reference trajectories for robots in the field.  An advantage of simple models is the ease with which a set of gaits can be generated.  In our work, we expand what simple can mean in terms of gait generation.  Our work attempts to mathematically describe the complete set of motions of a broad class of models using fundamental concepts from the fields of nonlinear dynamics and topology.  Our results show that many gaits of interest are continuously connected to each other in a properly defined trajectory space.  This transforms the problem of gait generation into finding the simplest gait in the connected set for generating the other gaits; we numerically compute the set using continuation methods.  This approach has generated a variety of gaits for a legged hopper using a hopping-in-place motion (Gan et al., 2018) and 2D and 3D biped walkers from a standing still position (Rosa and Lynch, 2021) as the simple gaits.  These results motivate the study of a model's gait space in simplifying the challenges of gait generation.