Realization of $r$ -Robust Formations in the Plane Using Control Barrier Functions

This letter presents control laws to drive groups of robots into formations with communication graphs that satisfy the <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-robustness property, which allows for consensus in the presence of malicious robots. Using results in <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>-robustness and control barrier functions, the presented control laws ensure such formations in finite time, using a reference adjacency matrix or only a desired number of neighboring robots. The results are illustrated through simulations.

[1]  Li Wang,et al.  Formally Correct Composition of Coordinated Behaviors Using Control Barrier Certificates , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[2]  Mehran Mesbahi,et al.  On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian , 2006, IEEE Transactions on Automatic Control.

[3]  Vijay Kumar,et al.  Design Guarantees for Resilient Robot Formations on Lattices , 2019, IEEE Robotics and Automation Letters.

[4]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[5]  Vijay Kumar,et al.  Connectivity management in mobile robot teams , 2008, 2008 IEEE International Conference on Robotics and Automation.

[6]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[7]  Shreyas Sundaram,et al.  Robustness of information diffusion algorithms to locally bounded adversaries , 2011, 2012 American Control Conference (ACC).

[8]  Vijay Kumar,et al.  Formations for Resilient Robot Teams , 2017, IEEE Robotics and Automation Letters.

[9]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[10]  Antonio Bicchi,et al.  Consensus Computation in Unreliable Networks: A System Theoretic Approach , 2010, IEEE Transactions on Automatic Control.

[11]  Shreyas Sundaram,et al.  A Notion of Robustness in Complex Networks , 2015, IEEE Transactions on Control of Network Systems.

[12]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[13]  Shreyas Sundaram,et al.  Robustness and Algebraic Connectivity of Random Interdependent Networks , 2015, ArXiv.

[14]  Shreyas Sundaram,et al.  Resilient Asymptotic Consensus in Robust Networks , 2013, IEEE Journal on Selected Areas in Communications.

[15]  Mario Vento,et al.  Thirty Years Of Graph Matching In Pattern Recognition , 2004, Int. J. Pattern Recognit. Artif. Intell..

[16]  G. Farin.  Curves and Surfaces for Cagd: A Practical Guide , 2001 .

[17]  Carey E. Priebe,et al.  Fast Approximate Quadratic Programming for Graph Matching , 2015, PloS one.

[18]  Aaron D. Ames,et al.  Safety Barrier Certificates for Collisions-Free Multirobot Systems , 2017, IEEE Transactions on Robotics.