Trajectory Optimization through Mixed-Integer Optimization of Contact Dynamics for Switching End Effector Locomotion

Abstract

Trajectory optimizers for legged robots typically assume a single end effector on each leg, often a foot or wheel, without switching to another. Robots employing point-modeled end effectors, compared to those with wheeled end effectors, often benefit in adaptability and maneuverability but at the cost of higher energy expenditure and lower speed. While current hardware supports switching between these two end-effector types, existing research has largely focused on maintaining stability during switching, with little attention to determining when each type is most effective. To our knowledge, this paper introduces the first framework that simultaneously optimizes both trajectories and end-effector contact dynamics through mixed-integer optimization. We validate our approach by solving and executing trajectories with a whole-body controller in Gazebo across a variety of terrains, including ramps and stepping stones. The results show that our framework not only handles diverse terrains but also exploits contact dynamics to reduce cost of transport and increase speed compared to foot-only locomotion.