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Autonomous robots that are capable of operating safely in the presence ofimperfect model knowledge or external disturbances are vital in safety-criticalapplications. In this paper, we present a planner-agnostic framework to designand certify safe tubes around desired trajectories that the robot is alwaysguaranteed to remain inside of. By leveraging recent results in contractionanalysis and $\mathcal{L}_1$-adaptive control we synthesize an architecturethat induces safe tubes for nonlinear systems with state and time-varyinguncertainties. We demonstrate with a few illustrative examples how contractiontheory-based $\mathcal{L}_1$-adaptive control can be used in conjunction withtraditional motion planning algorithms to obtain provably safe trajectories.

Safe Feedback Motion Planning: A Contraction Theory and $\mathcal{L}_1$-Adaptive Control Based Approach