Safe Feedback Motion Planning: A Contraction Theory and ℒ1-Adaptive Control Based Approach

Autonomous robots that are capable of operating safely in the presence of imperfect model knowledge or external disturbances are vital in safety-critical applications. In this paper, we present a planner-agnostic framework to design and certify safe tubes around desired trajectories that the robot is always guaranteed to remain inside. By leveraging recent results in contraction analysis and ℒ
₁
-adaptive control we synthesize an architecture that induces safe tubes for nonlinear systems with state and time-varying uncertainties. We demonstrate with a few illustrative examples
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how contraction theory-based ℒ
₁
-adaptive control can be used in conjunction with traditional motion planning algorithms to obtain provably safe trajectories.