Robust Trajectory Optimization Over Uncertain Terrain With Stochastic Complementarity

Trajectory optimization with contact-rich behaviors has recently gained attention for generating diverse locomotion without pre-specified ground contact sequences. However, these approaches rely on precise models of robot dynamics and the terrain are susceptible to uncertainty. Recent works have attempted handle uncertainties in system model, but few investigated uncertainty dynamics. In this letter, we model stemming from design corresponding risk-sensitive objectives contact-implicit trajectory optimization. particular, parameterize distance friction coefficients using probability distributions propose a expected residual minimization cost approach. We evaluate our method three simple robotic examples, including legged hopping robot, benchmark one examples simulation against robust worst-case solution. show that produces contact-averse trajectories perturbations. Moreover, demonstrate resulting converge those generated by traditional, non-robust as becomes more certain. Our study marks an important step towards fully robust, approach suitable deploying robots real-world terrain.