Probabilistic Feasibility for Nonlinear Systems with Non-Gaussian Uncertainty using RRT

Abstract

For motion planning problems involving many or unbounded forms of uncertainty, it may not be possible to identify a path guaranteed to be feasible, requiring consideration of the trade-o between planner conservatism and the risk of infeasibility. Recent work developed the chance constrained rapidly-exploring random tree (CC-RRT) algorithm, a real-time planning algorithm which can e ciently compute risk at each timestep in order to guarantee probabilistic feasibility. However, the results in that paper require the dual assumptions of a linear system and Gaussian uncertainty, two assumptions which are often not applicable to many real-life path planning scenarios. This paper presents several extensions to the CC-RRT framework which allow these assumptions to be relaxed. For nonlinear systems subject to Gaussian process noise, state distributions can be approximated as Gaussian by considering a linearization of the dynamics at each timestep; simulation results demonstrate the e ective of this approach for both open-loop and closed-loop dynamics. For systems subject to non-Gaussian uncertainty, we propose a particle-based representation of the uncertainty, and thus the state distributions; as the number of particles increases, the particles approach the true uncertainty. A key aspect of this approach relative to previous work is the consideration of probabilistic bounds on constraint satisfaction, both at every timestep and over the duration of entire paths.