Geometric Gait Optimization with a five-link wheeled snake

Geometric mechanics offers a powerful set of tools for understanding locomotion. In past work we used data-driven oscillator theory to design a sample efficient method for modeling geometric systems such as the Purcell swimmer. We extended this method to include the modeling of highly damped systems inhabiting the perturbed Stokes dynamical regime. Here, we present a case study on a physical five-link wheeled snake robot. Under each link, a pair of wheels were co-aligned to decrease friction in the direction along the link. We seeded the geometric gait optimizer with a zero displacement gait. After 9 iterations of 80 cycles, we produced a motion that achieved 45% body length per cycle translation motion, while optimizing over 84 parameters. Running the system at 0.5 Hz, this took 24 minutes. We noticed the final gait changes combinations of wheels that are contacting and not contacting the ground, a feature not observed in the first gait, suggesting that the optimizer successfully exploited hybrid features of the dynamics.