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arXiv · 2011.12569

Learning Certified Control using Contraction Metric

Dawei Sun·Susmit Jha·Chuchu Fan
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Abstract

In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds on the tracking error. Such a controller is crucial in safe motion planning. We leverage the advanced theory in Control Contraction Metric and design a learning framework based on neural networks to co-synthesize the contraction metric and the controller for control-affine systems. We further provide methods to validate the convergence and bounded error guarantees. We demonstrate the performance of our method using a suite of challenging robotic models, including models with learned dynamics as neural networks. We compare our approach with leading methods using sum-of-squares programming, reinforcement learning, and model predictive control. Results show that our methods indeed can handle a broader class of systems with less tracking error and faster execution speed. Code is available at https://github.com/sundw2014/C3M.

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BibTeXRIS

Dawei Sun, Susmit Jha, Chuchu Fan. 2020-11-25. Learning Certified Control using Contraction Metric. https://arxiv.org/abs/2011.12569

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