  We present a method for contraction-based feedback motion planning of locally
incrementally exponentially stabilizable systems with unknown dynamics that
provides probabilistic safety and reachability guarantees. Given a dynamics
dataset, our method learns a deep control-affine approximation of the dynamics.
To find a trusted domain where this model can be used for planning, we obtain
an estimate of the Lipschitz constant of the model error, which is valid with a
given probability, in a region around the training data, providing a local,
spatially-varying model error bound. We derive a trajectory tracking error
bound for a contraction-based controller that is subjected to this model error,
and then learn a controller that optimizes this tracking bound. With a given
probability, we verify the correctness of the controller and tracking error
bound in the trusted domain. We then use the trajectory error bound together
with the trusted domain to guide a sampling-based planner to return
trajectories that can be robustly tracked in execution. We show results on a 4D
car, a 6D quadrotor, and a 22D deformable object manipulation task, showing our
method plans safely with learned models of high-dimensional underactuated
systems, while baselines that plan without considering the tracking error bound
or the trusted domain can fail to stabilize the system and become unsafe.
