Motion Planning using Reactive Circular Fields

A 2D Analysis of Collision Avoidance and Goal Convergence

authored by: Marvin Becker, Johannes Köhler, Sami Haddadin, Matthias A. Müller
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.
Organisation(s): Institute of Automatic Control
External Organisation(s): ETH Zurich
Technical University of Munich (TUM)
Type: Article
Journal: IEEE Transactions on Automatic Control
Volume: 69
Pages: 1552-1567
No. of pages: 16
ISSN: 0018-9286
Publication date: 03.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Electrical and Electronic Engineering, Control and Systems Engineering, Computer Science Applications
Electronic version(s): https://doi.org/10.48550/arXiv.2210.16106 (Access: Open)
https://doi.org/10.1109/TAC.2023.3303168 (Access: Closed)

BibTeX

@article{44263a4df91e4a939da60647681879cd,
title = "Motion Planning using Reactive Circular Fields: A 2D Analysis of Collision Avoidance and Goal Convergence",
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",
author = "Marvin Becker and Johannes K{\"o}hler and Sami Haddadin and M{\"u}ller, {Matthias A.}",
note = "Funding information: This work was supported in part by the Region Hannover in the project roboterfabrik. ",
year = "2024",
month = mar,
doi = "10.48550/arXiv.2210.16106",
language = "English",
volume = "69",
pages = "1552--1567",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3",
}