Robust sampling-based motion planning for autonomous vehicles in uncertain environments

While navigating, autonomous vehicles often must overcome significant uncertainty in their understanding of the world around them. Real-world environments may be cluttered and highly dynamic, with uncertainty in both the current state and future evolution of environmental constraints. The vehicle may also face uncertainty in its own motion. To provide safe navigation under such conditions, motion planning algorithms must be able to rapidly generate smooth, certifiably robust trajectories in real-time. The primary contribution of this thesis is the development of a real-time motion planning framework capable of generating feasible paths for autonomous vehicles in complex environments, with robustness guarantees under both internal and external uncertainty. By leveraging the trajectory-wise constraint checking of sampling-based algorithms, and in particular rapidly-exploring random trees (RRT), the proposed algorithms can efficiently evaluate and enforce complex robustness conditions. For linear systems under bounded uncertainty, a sampling-based motion planner is presented which iteratively tightens constraints in order to guarantee safety for all feasible uncertainty realizations. The proposed bounded-uncertainty RRT* (BURRT*) algorithm scales favorably with environment complexity. Additionally, by building upon RRT*, BU-RRT* is shown to be asymptotically optimal, enabling it to efficiently generate and optimize robust, dynamically feasible trajectories. For large and/or unbounded uncertainties, probabilistically feasible planning is provided through the proposed chance-constrained RRT (CC-RRT) algorithm. Paths generated by CC-RRT are guaranteed probabilistically feasible for linear systems under Gaussian uncertainty, with extensions considered for nonlinear dynamics, output models, and/or non-Gaussian uncertainty. Probabilistic constraint satisfaction is represented in terms of chance constraints, extending existing approaches by considering both internal and external uncertainty, subject to time-step-wise and path-wise feasibility constraints. An explicit bound on the total risk of constraint violation is developed which can be efficiently evaluated online for each trajectory. The proposed CC-RRT* algorithm extends this approach to provide asymptotic optimality guarantees; an admissible risk-based objective uses the risk bounds to incentivize risk-averse trajectories. Applications of this framework are shown for several motion planning domains, including parafoil terminal guidance and urban navigation, where the system is subject to challenging environmental and uncertainty characterizations. Hardware results demonstrate a mobile robot utilizing this framework to safely avoid dynamic obstacles.