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We present a method for providing statistical guarantees on runtime safetyand goal reachability for integrated planning and control of a class of systemswith unknown nonlinear stochastic underactuated dynamics. Specifically, given adynamics dataset, our method jointly learns a mean dynamics model, aspatially-varying disturbance bound that captures the effect of noise and modelmismatch, and a feedback controller based on contraction theory that stabilizesthe learned dynamics. We propose a sampling-based planner that uses the meandynamics model and simultaneously bounds the closed-loop tracking error via alearned disturbance bound. We employ techniques from Extreme Value Theory (EVT)to estimate, to a specified level of confidence, several constants whichcharacterize the learned components and govern the size of the tracking errorbound. This ensures plans are guaranteed to be safely tracked at runtime. Wevalidate that our guarantees translate to empirical safety in simulation on a10D quadrotor, and in the real world on a physical CrazyFlie quadrotor andClearpath Jackal robot, whereas baselines that ignore the model error andstochasticity are unsafe.

Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems