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.United States. Air Force (USAF, grant FA9550-08-1-0086)United States. Air Force Office of Scientific Research (AFOSR, Grant FA9550-08-1-0086