Distance-coupling as an Approach to Position and Formation Control
Abstract: In this letter, we study the case of autonomous agents which are required to move to some new position based solely on the distance measured from predetermined reference points, or anchors. A novel approach, referred to as distance-coupling, is proposed for calculating the agent's position exclusively from differences between squared distance measurements. The key insight in our approach is that, in doing so, we cancel out the measurement's quadratic term and obtain a function of position which is linear. We apply this method to the homing problem and prove Lyapunov stability with and without anchor placement error; identifying bounds on the region of attraction when the anchors are linearly transformed from their desired positions. As an application of the method, we show how the policy can be implemented for distributed formation control on a set of autonomous agents, proving the existence of the set of equilibria.
- Michael S. Floater “Generalized barycentric coordinates and applications” Publisher: Cambridge University Press In Acta Numerica 24, 2015, pp. 161–214 DOI: 10.1017/S0962492914000129
- “Distributed Formation Control via Mixed Barycentric Coordinate and Distance-Based Approach” ISSN: 2378-5861 In 2019 American Control Conference (ACC), 2019, pp. 51–58 DOI: 10.23919/ACC.2019.8814890
- “A Barycentric Coordinate-Based Approach to Formation Control Under Directed and Switching Sensing Graphs” Conference Name: IEEE Transactions on Cybernetics In IEEE Transactions on Cybernetics 48.4, 2018, pp. 1202–1215 DOI: 10.1109/TCYB.2017.2684461
- Dimos V. Dimarogonas and Kostas J. Kyriakopoulos “A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems” In Automatica 44.10, 2008, pp. 2648–2654 DOI: 10.1016/j.automatica.2008.03.013
- Dimos V. Dimarogonas, Panagiotis Tsiotras and Kostas J. Kyriakopoulos “Leader–follower cooperative attitude control of multiple rigid bodies” In Systems & Control Letters 58.6, 2009, pp. 429–435 DOI: 10.1016/j.sysconle.2009.02.002
- Zhiyun Lin, B. Francis and M. Maggiore “Necessary and sufficient graphical conditions for formation control of unicycles” Conference Name: IEEE Transactions on Automatic Control In IEEE Transactions on Automatic Control 50.1, 2005, pp. 121–127 DOI: 10.1109/TAC.2004.841121
- Dimos V. Dimarogonas and Karl H. Johansson “On the stability of distance-based formation control” ISSN: 0191-2216 In 2008 47th IEEE Conference on Decision and Control, 2008, pp. 1200–1205 DOI: 10.1109/CDC.2008.4739215
- Yun Ho Choi and Doik Kim “Distance-Based Formation Control With Goal Assignment for Global Asymptotic Stability of Multi-Robot Systems” Conference Name: IEEE Robotics and Automation Letters In IEEE Robotics and Automation Letters 6.2, 2021, pp. 2020–2027 DOI: 10.1109/LRA.2021.3061071
- “Information patterns and Hedging Brockett’s theorem in controlling vehicle formations” In Proceedings of the 42nd IEEE, 2003 URL: https://ieeexplore.ieee.org/document/1272622
- “Distributed multi-vehicle coordinated control via local information exchange” _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/rnc.1147 In International Journal of Robust and Nonlinear Control 17.10-11, 2007, pp. 1002–1033 DOI: 10.1002/rnc.1147
- “Formation control for second-order nonlinear multi-agent systems with external disturbances via adaptive method” ISSN: 2688-0938 In 2022 China Automation Congress (CAC), 2022, pp. 5616–5620 DOI: 10.1109/CAC57257.2022.10055393
- “Distributed Formation Control of Multi-Agent Systems Using Complex Laplacian” In IEEE Transactions on Automatic Control 59.7, 2014, pp. 1765–1777 DOI: 10.1109/TAC.2014.2309031
- Kwang-Kyo Oh, Myoung-Chul Park and Hyo-Sung Ahn “A survey of multi-agent formation control” In Automatica 53, 2015, pp. 424–440 DOI: 10.1016/j.automatica.2014.10.022
- Hassan Khalil “Nonlinear Systems” Pearson, 2001 URL: https://www.pearson.com/en-us/subject-catalog/p/nonlinear-systems/P200000003306/9780130673893
- Mikkel B Stegmann and David Delgado Gomez “A Brief Introduction to Statistical Shape Analysis”
- W. Kabsch “A discussion of the solution for the best rotation to relate two sets of vectors” Number: 5 Publisher: International Union of Crystallography In Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography 34.5, 1978, pp. 827–828 DOI: 10.1107/S0567739478001680
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.