We present a method for providing statistical guarantees on runtime safety and goal reachability for integrated planning and control of a class of systems with unknown nonlinear stochastic underactuated dynamics. Specifically, given a dynamics dataset, our method jointly learns a mean dynamics model, a spatially-varying disturbance bound that captures the effect of noise and model mismatch, and a feedback controller based on contraction theory that stabilizes the learned dynamics. We propose a sampling-based planner that uses the mean dynamics model and simultaneously bounds the closed-loop tracking error via a learned disturbance bound. We employ techniques from Extreme Value Theory (EVT) to estimate, to a specified level of confidence, several constants which characterize the learned components and govern the size of the tracking error bound. This ensures plans are guaranteed to be safely tracked at runtime. We validate that our guarantees translate to empirical safety in simulation on a 10D quadrotor, and in the real world on a physical CrazyFlie quadrotor and Clearpath Jackal robot, whereas baselines that ignore the model error and stochasticity are unsafe.

Robot navigation traditionally relies on building an explicit map that is used to plan collision-free trajectories to a desired target. In deformable, complex terrain, using geometric-based approaches can fail to find a path due to mischaracterizing deformable objects as rigid and impassable. Instead, we learn to predict an estimate of traversability of terrain regions and to prefer regions that are easier to navigate (e.g., short grass over small shrubs). Rather than predicting collisions, we instead regress on realized error compared to a canonical system model. We train with an on-policy approach, resulting in successful navigation policies using as little as 50 minutes of training data split across simulation and real world. Our learning-based navigation system is a sample efficient short-term planner that we demonstrate on a Clearpath Husky navigating through a variety of terrain including grassland and forest.

Safe and high-speed navigation is a key enabling capability for real world deployment of robotic systems. A significant limitation of existing approaches is the computational bottleneck associated with explicit mapping and the limited field of view (FOV) of existing sensor technologies. In this paper, we study algorithmic approaches that allow the robot to predict spaces extending beyond the sensor horizon for robust planning at high speeds. We accomplish this using a generative neural network trained from real-world data without requiring human annotated labels. Further, we extend our existing control algorithms to support leveraging the predicted spaces to improve collision-free planning and navigation at high speeds. Our experiments are conducted on a physical robot based on the MIT race car using an RGBD sensor where were able to demonstrate improved performance at 4 m/s compared to a controller not operating on predicted regions of the map.