Online Gait Optimization for Running in Resistive Media

In-field legged robots need gaits and behaviors that allow them to run over and through all types of terrain, including through fluidic media such as ponds, bogs, and sand dunes. This paper presents a method of rapidly generating legged running gaits, on-the-fly, for these resistive fluid-like terrains. To accelerate gait computation, we adapted a reduced-order dynamic model of legs in fluid fields for rapid optimization of energy-efficient motion plans. For the first time, we achieve online optimization for a legged model in resistive fluid-like media by formulating an optimal control problem with smooth and analytical cost functions and constraints. In numerical tests, we benchmark the computation times for our nonlinear optimization and validate that the optimized gaits follow a U-shaped speed versus cost curve commonly associated with energy optimal legged locomotion. We further present a proof-of-concept demonstration of optimized gaits on a planarized monopod robot hopping through a bed of fluidized granular material - a surrogate fluid-like substrate.