Geometry of contact: contact planning for multi-legged robots via spin models

While gaits for bipedal and quadrupedal robots have been extensively studied, multi-legged locomotors with six or more legs have received comparatively less attention and are often limited to symmetric alternating tripod gaits. The complexity of the gait search space increases exponentially with each added leg, challenging our conventional intuitions developed from bipedal and quadrupedal templates. This study develops an analytic tool to explore the high-dimensional search space in multi-legged systems. Combining geometric mechanics theory, graph theory, spin model, and robophysical experiment, we study the locomotion of the general multi-legged locomotors with a focus on the contact planning and its coordination with internal shape changes. Using geometric mechanics analysis, we map the multi-legged contact planning design into a well-defined graph problem. Leveraging the symmetries in locomotion, we map the graph problem to special cases of spin models. This mapping facilitates the identification of global optima in polynomial time, enabling a systematic analysis of multi-legged robots grounded in physics principles. We verified our models using robophysical experiments on a 20-cm long hexapod robot: our analysis identified an agile asymmetric gait with speed of 0.62 ± 0.03 BL/cyc (body length per cycle), faster than a standard symmetric alternating tripod gait with 0.43 ± 0.02 BL/cyc.