Motion Planning using Reactive Circular Fields: A 2D Analysis of Collision Avoidance and Goal Convergence

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  • ETH Zurich
  • Technical University of Munich (TUM)
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Original languageEnglish
Pages (from-to)1552-1567
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume69
Issue number3
Early online date8 Aug 2023
Publication statusPublished - Mar 2024

Abstract

Recently, many reactive trajectory planning approaches were suggested in the literature because of their inherent immediate adaption in the ever more demanding cluttered and unpredictable environments of robotic systems. However, typically those approaches are only locally reactive without considering global path planning and no guarantees for simultaneous collision avoidance and goal convergence can be given. In this article, we study a recently developed circular field (CF)-based motion planner that combines local reactive control with global trajectory generation by adapting an artificial magnetic field such that multiple trajectories around obstacles can be evaluated (cf., Becker et al., 2021). In particular, we provide a mathematically rigorous analysis of this planner for static environments in the horizontal plane to ensure safe motion of the controlled robot. Contrary to existing results, the derived collision avoidance analysis covers the entire CF motion planning algorithm including attractive forces for goal convergence and is not limited to a specific choice of the rotation field, i.e., our guarantees are not limited to a specific potentially suboptimal trajectory. Our Lyapunov-type collision avoidance analysis is based on the definition of an (equivalent) 2-D auxiliary system, which enables us to provide tight, if and only if conditions for the case of a collision with point obstacles. Furthermore, we show how this analysis naturally extends to multiple obstacles and we specify sufficient conditions for goal convergence. Finally, we provide challenging simulation scenarios with multiple nonconvex point cloud obstacles and demonstrate collision avoidance and goal convergence.

Keywords

    cs.RO, cs.SY, eess.SY, autonomous systems, collision-free motion planning, Force, robotics, Magnetic analysis, Autonomous robots, Convergence, Planning, Trajectory, Collision avoidance, Robots

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Cite this

Motion Planning using Reactive Circular Fields: A 2D Analysis of Collision Avoidance and Goal Convergence. / Becker, Marvin; Köhler, Johannes; Haddadin, Sami et al.
In: IEEE Transactions on Automatic Control, Vol. 69, No. 3, 03.2024, p. 1552-1567.

Research output: Contribution to journalArticleResearchpeer review

Becker M, Köhler J, Haddadin S, Müller MA. Motion Planning using Reactive Circular Fields: A 2D Analysis of Collision Avoidance and Goal Convergence. IEEE Transactions on Automatic Control. 2024 Mar;69(3):1552-1567. Epub 2023 Aug 8. doi: 10.48550/arXiv.2210.16106, 10.1109/TAC.2023.3303168
Becker, Marvin ; Köhler, Johannes ; Haddadin, Sami et al. / Motion Planning using Reactive Circular Fields : A 2D Analysis of Collision Avoidance and Goal Convergence. In: IEEE Transactions on Automatic Control. 2024 ; Vol. 69, No. 3. pp. 1552-1567.
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abstract = "Recently, many reactive trajectory planning approaches were suggested in the literature because of their inherent immediate adaption in the ever more demanding cluttered and unpredictable environments of robotic systems. However, typically those approaches are only locally reactive without considering global path planning and no guarantees for simultaneous collision avoidance and goal convergence can be given. In this article, we study a recently developed circular field (CF)-based motion planner that combines local reactive control with global trajectory generation by adapting an artificial magnetic field such that multiple trajectories around obstacles can be evaluated (cf., Becker et al., 2021). In particular, we provide a mathematically rigorous analysis of this planner for static environments in the horizontal plane to ensure safe motion of the controlled robot. Contrary to existing results, the derived collision avoidance analysis covers the entire CF motion planning algorithm including attractive forces for goal convergence and is not limited to a specific choice of the rotation field, i.e., our guarantees are not limited to a specific potentially suboptimal trajectory. Our Lyapunov-type collision avoidance analysis is based on the definition of an (equivalent) 2-D auxiliary system, which enables us to provide tight, if and only if conditions for the case of a collision with point obstacles. Furthermore, we show how this analysis naturally extends to multiple obstacles and we specify sufficient conditions for goal convergence. Finally, we provide challenging simulation scenarios with multiple nonconvex point cloud obstacles and demonstrate collision avoidance and goal convergence.",
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AU - Haddadin, Sami

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