We present an approach for feedback motion planning of systems with unknown dynamics which provides guarantees on safety, reachability, and stability about the goal. Given a learned control-affine approximation of the true dynamics, we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model. Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists. This allows for a small bound on the tracking error when the trajectory is executed on the real system. Our method imposes a check for the existence of the feedback law as constraints in a samplingbased planner, which returns a feedback policy ensuring that under the true dynamics, the goal is reachable, the path is safe in execution, and the closed-loop system is invariant in a small set about the goal. We demonstrate our approach by planning using learned models of a 6D quadrotor and a 7DOF Kuka arm. We show that a baseline which plans using the same learned dynamics without considering the error bound or the existence of the feedback law can fail to stabilize around the plan and become unsafe.
Robot navigation traditionally relies on building an explicit map that is used to plan collisionfree 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 dynamics 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 learningbased navigation system is a sample efficient shortterm planner that we demonstrate on a Clearpath Husky navigating through a variety of terrain including grassland and forest.
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