Multi-Agent Motion Planning Using Burgers' Viscous Equation and Hopf-Cole Transformation, A Flatness-based implementation

Hugues Mounier 1 Etienne Servais 2 Brigitte d'Andréa-Novel 2
1 L2S - Laboratoire des signaux et systèmes
2 CAOR - Centre de Robotique
Abstract : In a previous work, we showed how the flatness of the heat equation with two controls at both ends of the domain could be used to generate solutions to create solutions to Burgers' equation. The created solutions were thought as a motion planner for a multi-agent systems of e.g. ground robots, UAVs. The trajectories of the different particles of the PDE are to be used as input for a feed-forward control. In this paper, we show a practical implementation of this method, oriented toward computational efficiency based on Particles Swarm Optimization. In a first section we introduce the flatness based mathematical framework of our planner. We present the implementation in a second part. We present examples of trajectories in a last section and study and discuss the performances and the properties of the generated trajectories before drawing conclusions and future use of the framework in real UAVs systems.
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Conference papers
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https://hal-centralesupelec.archives-ouvertes.fr/hal-02332412
Contributor : Delphine Le Piolet <>
Submitted on : Thursday, October 24, 2019 - 5:36:16 PM
Last modification on : Monday, January 13, 2020 - 1:17:14 AM

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  • HAL Id : hal-02332412, version 1

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Hugues Mounier, Etienne Servais, Brigitte d'Andréa-Novel. Multi-Agent Motion Planning Using Burgers' Viscous Equation and Hopf-Cole Transformation, A Flatness-based implementation. 4th International Conference on Systems and Control (ICSC), Apr 2015, Sousse, Tunisia. ⟨hal-02332412⟩

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