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# Uncertain-aware Safe Exploratory Planning using Gaussian Process and Neural Control Contraction Metric

*Proceedings of the 3rd Conference on Learning for Dynamics and Control*, PMLR 144:728-741, 2021.

#### Abstract

Robots operating in unstructured, complex, and changing real-world environments should navigate and maintain safety while collecting data about its environment and updating its model dynamics. In this paper, we consider the problem of using a robot to explore an environment with an unknown, state-dependent disturbance to the dynamics and forbidden areas. The goal of the robot is to safely collect observations on the disturbance and construct an accurate estimate of the underlying function. We use Gaussian process to get an estimate of the disturbance from data with a high-confidence bound on the regression error. Furthermore, we use neural contraction metrics to derive a tracking controller and the corresponding high-confidence uncertainty tube around the nominal trajectory planned for the robot, based on the estimate of the disturbance. From the robustness of the Contraction Metric, error bound can be pre-computed and used by the motion planner such that the actual trajectory is guaranteed to be safe.