Arbitrarily shaped formations of mobile robots: artificial potential fields and coordinate transformation
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In this paper we describe a novel decentralized control strategy to realize formations of mobile robots. We first describe how to design artificial potential fields to obtain a formation with the shape of a regular polygon. We provide a formal proof of the asymptotic stability of the system, based on the definition of a proper Lyapunov function. We also prove that our control strategy is not affected by the problem of local minima. Then, we exploit a bijective coordinate transformation to deform the polygonal formation, thus obtaining a completely arbitrarily shaped formation. Simulations and experimental tests are provided to validate the control strategy.
KeywordsFormation control Artificial potential fields Arbitrarily shaped formations Coordinate transformation
- Bachmayer, R., & Leonard, N. E. (2002). Vehicle networks for gradient descent in a sampled environment. In Proceedings of the IEEE international conference on decision and control (pp. 112–117). Google Scholar
- Balch, T., & Hybinette, M. (2000). Social potentials for scalable multi-robot formations. In Proceedings of the IEEE international conference on robotics and automation (pp. 73–80). Google Scholar
- Bullo, F., Cortes, J., & Martinez, S. (2008). Distributed Control of Robotic Networks. http://coordinationbook.info.
- Hsieh, M. A., & Kumar, V. (2006). Pattern generation with multiple robots. In Proceedings of the IEEE international conference on robotics and automation (pp. 2442–2447). Google Scholar
- Leonard, N., & Fiorelli, E. (2001). Virtual leaders, artificial potentials and coordinated control of groups. In Proceedings of the IEEE conference on decision and control (pp. 2968–2973). Google Scholar
- Marcolino, L. S., & Chaimowicz, L. (2008). No robot left behind: Coordination to overcome local minima in swarm navigation. In Proceedings of the IEEE international conference on robotics and automation (pp. 1904–1909). Google Scholar
- Matarić, M. J., Koenig, N., & Feil-Seifer, D. (2007). Materials for enabling hands-on robotics and STEM education. In AAAI spring symposium on robots and robot venues: resources for AI education. Google Scholar
- Meserve, B. E. (1983). Fundamental concepts of geometry. New York: Dover. Google Scholar