Trajectory Optimization for a Wheel-Legged System for Dynamic Maneuvers that Allow for Wheel Slip

Wheel-legged systems have the potential to combine the benefits of two heavily studied research areas: the speed and efficiency of locomotion on wheels with the versatility and agility to surmount various obstacles of legged systems. However, there have been limited results in dynamic locomotion taking advantage of both of these areas. In this paper, we present a trajectory optimization framework for a skating system on passive unactuated wheels, which has no means to locomote itself without exploiting tangential frictional forces. Research in planning for wheeled systems traditionally enforces non-slip (the velocity in the rolling direction is exactly equal to the wheel angular velocity multiplied by the wheel radius, without loss) and non-skid (no velocity perpendicular to the wheel roll direction) conditions, which may be violated in practice, especially over terrains with low coefficients of friction such as icy or slippery roads. By explicitly modeling friction, and specifically not enforcing these traditional non-slip and non-skid conditions, our framework naturally discovers dynamic maneuvers to avoid and/or exploit wheel slipping and skidding depending on the cost function. We illustrate several examples such as energy-efficient forward locomotion, skidding to a halt, and hybrid wheel-legged skating. A video showing these examples can be found at https://youtu.be/SV7Kw3vlRQI.