Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems Article Swipe

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Glen Chou , Necmiye Özay , Dmitry Berenson ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2104.08695

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.

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Computer science Tracking error Upper and lower bounds Trajectory Probabilistic logic Control theory (sociology) Correctness Contraction (grammar) Controller (irrigation) Artificial intelligence Algorithm Mathematics Control (management) Mathematical analysis Internal medicine Physics Medicine Astronomy Biology Agronomy

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2104.08695
PDF: https://arxiv.org/pdf/2104.08695
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Cited By: 1
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2104.08695

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Title: Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems

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Language: en

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Publication year: 2021

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Publication date: 2021-04-18

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Authors: Glen Chou, Necmiye Özay, Dmitry Berenson

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Concepts: Computer science, Tracking error, Upper and lower bounds, Trajectory, Probabilistic logic, Control theory (sociology), Correctness, Contraction (grammar), Controller (irrigation), Artificial intelligence, Algorithm, Mathematics, Control (management), Mathematical analysis, Internal medicine, Physics, Medicine, Astronomy, Biology, Agronomy

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