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Consensus for double-integrator dynamics with velocity constraints

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  • Control Theory
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Abstract

The problem of consensus for double-integrator dynamics with velocity constraints and a constant group reference velocity is addressed such that: (i) the control law of an agent does not depend on the local neighbors’ velocities or accelerations, but only on the neighbors’ positions and on the own agent velocity; (ii) the constraints are non-symmetric; (iii) the class of nonlinear functions used to account for the velocity constraints is more general than the ones that are normally considered in the literature. We propose a decentralized control strategy with the neighboring topology described by an undirected interaction graph that is connected. Mathematical guarantees of convergence without violating the constraints are given. A numerical experiment is provided to illustrate the effectiveness of our approach.

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Authors and Affiliations

  1. Computation Department, Centro Federal de Educação Tecnológica de Minas Gerais, Av. Amazonas, 7675 - Gameleira, 30510-000, Belo Horizonte, MG, Brazil

    Tales A. Jesus

  2. School of Engineering, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, Pampulha, 31270-901, Belo Horizonte, MG, Brazil

    Luciano C. A. Pimenta, Leonardo A. B. Tôrres & Eduardo M. A. M. Mendes

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  1. Tales A. Jesus
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  2. Luciano C. A. Pimenta
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  3. Leonardo A. B. Tôrres
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  4. Eduardo M. A. M. Mendes
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Correspondence to Tales A. Jesus.

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Tales A. Jesus received his B.S. degree in Control and Automation Engineering, and his M.Sc. and Ph.D. degrees in Electrical Engineering from the Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil, in 2006, 2008, and 2013, respectively. He is currently an Assistant Professor with the Computation Department at Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Belo Horizonte, Brazil. His research interests include mobile robotics, multiagent coordination, and nonlinear control theory.

Luciano C. A. Pimenta received his B.S., M.Sc., and Ph.D. degrees in Electrical Engineering from the Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil, in 2003, 2005, and 2009, respectively. From April 2007 to June 2008, he was a visiting Ph.D. student at the General Robotics, Automation, Sensing and Perception (GRASP) Laboratory at the University of Pennsylvania, Philadelphia, USA. He is currently an Assistant Professor with the Department of Electronic Engineering at UFMG. His research interests include robotics, multi-robot systems, and control theory.

Leonardo A. B. Tôrres received his B.Eng. in 1997, and his PhD degree in 2001, both in Electrical Engineering, from the Federal University of Minas Gerais (UFMG), Brazil, and in 2010- 2011 he was a visiting scholar at University of California Santa Barbara. In 2002, he joined the Department of Electronic Engineering, at UFMG. As Associate Professor, he has been working with control and synchronization of nonlinear dynamical systems, with applications to information transmission, uninterruptible power supplies, and robotic coordination.

Eduardo M. A. M. Mendes received his Ph.D. degree in Automatic Control and Systems Engineering from the University of Sheffield, Sheffield, U.K. in 1995. He was appointed to his current position of Associate Professor, Department of Electronic Engineering, UFMG, Brazil in 2002. His research interests include system identification for nonlinear systems, NARMAX methods, model validation, prediction, spectral analysis, chaos, control of nonlinear systems, signal processing and analysis of biomedical signals and images. He has authored over 100 research and scientific publications in various fields.

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Jesus, T.A., Pimenta, L.C.A., Tôrres, L.A.B. et al. Consensus for double-integrator dynamics with velocity constraints. Int. J. Control Autom. Syst. 12, 930–938 (2014). https://doi.org/10.1007/s12555-013-0309-0

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