Non-Smooth Trajectory Optimization for Wheeled Balancing Robots with Contact Switches and Impacts

Recent years have seen a steady rise in the abilities of wheeled-legged balancing robots. Yet, their use is still severely restricted by the lack of efficient control algorithms for overcoming obstacles such as stairs. We take a considerable step towards closing this gap by presenting a fast trajectory optimizer for generating trajectories over a large class of challenging terrains. By limiting the underlying modeling to the planar, nonlinear rigid-body dynamics and subdividing the terrain into contact-phases, a tractable nonlinear programming problem is obtained. The model explicitly accounts for contact switches and impacts, traction limits, and actuation bounds. By introducing an arc-length-related parametrization, the trajectories are rendered inherently contact constraint-consistent. We apply our method to the specific case of the wheeled bipedal robot Ascento, for which we derive closed-form expressions of the dynamics equations, including the kinematic loops. To track the trajectories, we propose a simple LQR-based controller. The approach is validated in real-world experiments where we show the execution of trajectories for traversing steps, driving up ramps, jumping, standing up, and driving up entire stairways. To the authors' best knowledge, enabling the latter by means of trajectory optimization is a novelty for wheeled-legged robots.