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Efficient and scalable path-planning algorithms for curvature constrained motion in the Hamilton-Jacobi formulation

Published: 18 July 2024 Publication History

Abstract

We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic programming, and Hamilton-Jacobi-Bellman equations. We develop efficient and scalable algorithms for solutions of high dimensional Hamilton-Jacobi equations which can solve these types of path-planning problems efficiently, even in high dimensions, while maintaining the Hamilton-Jacobi formulation. Because our method is rooted in optimal control theory and has no black box components, it has solid interpretability, and thus averts the tradeoff between interpretability and efficiency for high-dimensional path-planning problems. We demonstrate our method with several examples.

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Information

Published In

cover image Journal of Computational Physics
Journal of Computational Physics  Volume 509, Issue C
Jul 2024
579 pages

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 18 July 2024

Author Tags

  1. Optimal path-planning
  2. Curvature constrained motion
  3. Hamilton-Jacobi equations
  4. Hopf-Lax formulas
  5. Dynamic programming

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