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Path Exploration in Unknown Environments Using Fokker-Planck Equation on Graph

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Abstract

This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by the Fokker-Planck equation and the intermittent diffusion process, the proposed method generates a tree connecting the initial and target configurations, and then finds a path on it using the available environmental information. The tree and path are updated iteratively when newly encountered obstacle information becomes available. The resulting method is a deterministic procedure proven to be complete, i.e., it is guaranteed to find a feasible path, when one exists, in a finite number of iterations. The method is scalable to high-dimensional problems. In addition, our method does not search the entire domain for the path, instead, the algorithm only explores a sub-region that can be described by the evolution of the Fokker-Planck equation on graph with a changing of diffusion coefficient intermittently. We demonstrate the performance of our algorithm via several numerical examples with different environments and dimensions, including high-dimensional cases.

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All source code can be accessed on https://github.com/haoyanzhai/path_planning.git

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Funding

The research is partially support by grants NSF DMS-1830225, DMS-1620345, and ONR N00014-18-1-2852.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Haoyan Zhai & Haomin Zhou

  2. Samueli School of Engineering, University of California, Irvine, Irvine, CA, 92697, USA

    Magnus Egerstedt

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  1. Haoyan Zhai
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  2. Magnus Egerstedt
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  3. Haomin Zhou
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Contributions

All authors (Haoyan Zhai, Magnus Egerstedt and Haomin Zhou) contributed to the study conception and design. Experiment design, analysis and theory proof were performed by Haoyan Zhai and Haomin Zhou. The first draft of the manuscript was written by Haoyan Zhai and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Haoyan Zhai.

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Zhai, H., Egerstedt, M. & Zhou, H. Path Exploration in Unknown Environments Using Fokker-Planck Equation on Graph. J Intell Robot Syst 104, 71 (2022). https://doi.org/10.1007/s10846-022-01598-0

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