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We present a framework that uses control Lyapunov functions (CLFs) to implement provably stable path-following controllers for autonomous mobile platforms. Our approach is based on learning a guaranteed CLF for path following by using recent approaches — combining machine learning with automated theorem proving — to train a neural network feedback law along with a CLF that guarantees stabilization for driving along low-curvature reference paths. We discuss how key properties of the CLF can be exploited to extend the range of the curvatures for which the stability guarantees remain valid. We then demonstrate that our approach yields a controller that obeys theoretical guarantees in simulation, but also performs well in practice. We show our method is both a verified method of control and better than a common MPC implementation in computation time. Additionally, we implement the controller on-board on a 18 -scale autonomous vehicle testing platform and present results for various robust path following scenarios.
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Lyapunov Neural Network with Region of Attraction Search
Deep learning methods have been widely used in robotic applications, making learning-enabled control design for complex nonlinear systems a promising direction. Although deep reinforcement learning methods have demonstrated impressive empirical performance, they lack the stability guarantees that are important in safety-critical situations. One way to provide these guarantees is to learn Lyapunov certificates alongside control policies. There are three related problems: 1) verify that a given Lyapunov function candidate satisfies the conditions for a given controller on a region, 2) find a valid Lyapunov function and controller on a given region, and 3) find a valid Lyapunov function and a controller such that the region of attraction is as large as possible. Previous work has shown that if the dynamics are piecewise linear, it is possible to solve problem 1) and 2) by solving a Mixed-Integer Linear Program (MILP). In this work, we build upon this method by proposing a Lyapunov neural network that considers monotonicity over half spaces in different directions. We 1) propose a specific choice of Lyapunov function architecture that ensures non-negativity and a unique global minimum by construction, and 2) show that this can be leveraged to find the controller and Lyapunov certificates faster and with a larger valid region by maximizing the size of a square inscribed in a given level set. We apply our method to a 2D inverted pendulum, unicycle path following, a 3-D feedback system, and a 4-D cart pole system, and demonstrate it can shorten the training time by half compared to the baseline, as well as find a larger ROA.
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- Award ID(s):
- 2409733
- PAR ID:
- 10628063
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- Proceedings of the American Control Conference
- ISSN:
- 2378-5861
- ISBN:
- 979-8-3503-8265-5
- Page Range / eLocation ID:
- 3403 to 3410
- Format(s):
- Medium: X
- Location:
- Toronto, ON, Canada
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC60939.2024.10644877
