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A General Solution to the Formation Control Problem Without Collisions for First-Order Multi-Agent Systems

Published online by Cambridge University Press:  22 August 2019

J. F. Flores-Resendiz Open the ORCID record for J. F. Flores-Resendiz [Opens in a new window]  and
E. Aranda-Bricaire
J. F. Flores-Resendiz*
Affiliation:
Universidad Autónoma de Baja California, Facultad de Ingeniería y Negocios Tecate, 21460 Tecate, Baja California, México
E. Aranda-Bricaire
Affiliation:
CINVESTAV, Electrical Engineering Department, Mechatronics Section, AP 14-740, 07000 México City, México
*
*Corresponding author. E-mail: [email protected]
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Summary

In this paper, a general solution to the formation control problem without collisions for first-order multi-agent systems is proposed. The case of an arbitrary number of mobile agents on a plane with saturated input velocity is analysed. Besides, conditions on the communication graph among agents are relaxed to the only requirement of containing a directed spanning tree. This general approach is an extended result from the simpler case of combinations of cyclic pursuit communication graphs. The proposed solution to this problem is designed in two steps. First, the asymptotic convergence in the absence of collisions is ensured. After this, the non-collision problem is faced by analysing the most general possible geometrical scenario which can lead to collision among agents. Discontinuous vector fields with unstable counterclockwise focus behaviour are applied by every agent in order to repel each other. Numerical simulations illustrate the performance of the proposed scheme.

Keywords

Multi-agent systemsFormation controlCollision avoidanceDiscontinuous vector field
Type
Articles
Information
Robotica , Volume 38 , Issue 6 , June 2020 , pp. 1123 - 1137
Copyright
© Cambridge University Press 2019

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References

Kim, T and Bang, H, “Decentralized Control of Multiple Unmanned Aircraft for Target Tracking and Obstacle Avoidance,” Proc. International Conference on Unmanned Aircraft Systems, ICUAS 2016, Arlington, USA (2016).CrossRefGoogle Scholar
Lin, Z, Broucke, M and Francis, B, “Local control strategies for groups of mobile autonomous agents,” IEEE Trans. Autom. Control 49(4), 622–629 (2004).CrossRefGoogle Scholar
Marshall, J, Broucke, M and Francis, B, “Formations of vehicles in cyclic pursuit,” IEEE Trans. Autom. Control 49(11), 1963–1974 (2004).CrossRefGoogle Scholar
Mousavi, M, Khaghani, M and Vossoughi, G, “Collision avoidance with obstacle in flocking for multi agent systems,” Proc. International Conference on Industrial Electronics, Control and Robotics, Phoenix, USA (2010).CrossRefGoogle Scholar
Barogh, S, Rosero, E and Werner, H, “Formation Control of Non-holonomic Agents with Collision avoidance,” Proc. American Control Conference 2015, Chicago, USA (2015)Google Scholar
Kostic, D, Adinandra, S, Caarls, J and Nijmeijer, H, “Collision-free Motion Coordination of Unicycle Multi-agent Systems,” Proc. American Control Conference 2010, Baltimore, USA (2010).CrossRefGoogle Scholar
Phan, D, Yang, J, Ratasich, D, Grosu, R, Smolka, S and Stoller, S, “Collision avoidance for mobile robots with limited sensing and limited information about the environment,” Proc. 6th International Conference, RV 2015, Vienna, Austria (2015) pp. 201–215.Google Scholar
Dimarogonas, D and Kyriakopoulos, K, “Distributed cooperative control and collision avoidance for multiple kinematic agents,” Proc. 45th IEEE Conference on Decision and Control, San Diego, CA, USA (2006).CrossRefGoogle Scholar
Do, K. D., “Formation control of mobile agents using local potential functions,” Proc. American Control Conference, Minneapolis, NM, USA (2006).CrossRefGoogle Scholar
Flores-Resendiz, J. F. and Aranda-Bricaire, E, “Cyclic pursuit formation control without collisions in multi-agent systems using discontinuous vector fields,” Proc. Congreso Latinoamericano de Control Automático, Cancún, México (2014).Google Scholar
Flores-Resendiz, J. F., Aranda-Bricaire, E, Gonzalez-Sierra, J and Santiaguillo-Salinas, J, “Finite-time formation control without collisions for multiagent systems with communication graphs composed of cyclic paths,” Math. Prob. Eng. 2015, Article ID 948086, 17 pages (2015). doi:10.1155/2015/948086.CrossRefGoogle Scholar
Hernández-Martínez, E. G. and Aranda-Bricaire, E, “Convergence and Collision Avoidance in Formation Control: A survey of the Artificial Potential Functions approach,” In: Multi-agent Systems- Modeling, Control, Programming, Simulations and Applications, INTECH, Austria (2011) pp. 105–126.Google Scholar
Hernández-Martínez, E. G. and Aranda-Bricaire, E, “Non-Collision Conditions in Multi-Agent Virtual Leader-Based Formation Control,” Int. J. Adv. Robot. Syst. INTECH 9(4) (2012).Google Scholar
Mastellone, S, Stipanovic, D, Graunke, C, Intlekofer, K and Spong, M, “Formation control and collision avoidance for multi-agent non-holonomic systems: Theory and experiments,” Int. J. Robot. Res. 27(1), 107–126 (2008).CrossRefGoogle Scholar
Mondal, A, Behera, L, Sahoo, S. R. and Shukla, A, “A novel multi-agent formation control law with collision avoidance,” IEEE/CAA J. Autom. Sinica 4(3), 558–568 (2017).CrossRefGoogle Scholar
Rodriguez-Seda, E, Tang, C, Spong, M and Stipanovic, D, “Trajectory tracking with collision avoidance for nonholonomic vehicles with acceleration constraints and limited sensing,” Int. J. Robot. Res. 33(12), 1569–1592 (2014).CrossRefGoogle Scholar
Hernández-Martínez, E. G. and Aranda-Bricaire, E, “Collision Avoidance in Formation Control Using Discontinuous Vector Fields,” Proc. 9th IFAC Symposium on Nonlinear Control Systems, Toulouse, France, September 4–6 (2013) pp. 797–802.Google Scholar
Lafferriere, G, Williams, A, Caughman, J and Veerman, J, “Decentralized control of vehicle formations,” Syst. Control Lett. 54, 899–910 (2005).CrossRefGoogle Scholar
Ren, W and Beard, R, “Distributed consensus in multi-vehicle cooperative control: theory and applications,” Communications and Control Engineering Series, Springer-Verlag (2008).Google Scholar
Hirsch, M. W. and Smale, S, “Differential Equations, Dynamical Systems and Linear Algebra,” Pure and Applied Mathematics Series (Academic Press, New York, 1974).Google Scholar
Perko, L, “Differential equations and dynamical systems,” Texts in Applied Mathematics (Springer-Verlag, New York, 2001).Google Scholar
Bhat, S. P. and Bernstein, D. S., “Finite-time stability of continuous autonomous systems,” SIAM J. Control Optim. 38(3), 751–766 (2000).CrossRefGoogle Scholar