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.

本文提出了一种基于收缩反馈的运动规划方法，通过学习动力学的深度控制函数逼近，建立了在未知动力学系统中的安全交互方式， 包括控制器优化和轨迹跟踪， 并在高维度的动力学系统中进行了验证。

通过学习的压缩度量，对未知系统进行安全反馈运动规划中的模型误差传播