Formation control of a multi-agent system subject to Coulomb friction

Authors

Matin Jafarian, Ewoud Vos, Claudio De Persis, Arjan J. van der Schaft, Jacquelien M.A. Scherpen

Abstract

This paper considers the formation control problem for a network of point masses which are subject to Coulomb friction. A dynamical model including the planar discontinuous friction force is presented in the port-Hamiltonian framework. Moreover, continuous and discontinuous controllers are designed in order to achieve a desired prescribed formation. The main results are derived using tools from nonsmooth Lyapunov analysis. It is shown that the continuous static feedback controller fails to achieve the exact formation, while the discontinuous controller achieves the desired task exactly. Numerical simulations are provided to illustrate the effectiveness of the approach.

Keywords

Discontinuous dynamical systems; Nonsmooth analysis; Multi-agent systems; Port-Hamiltonian systems

Citation

• Journal: Automatica
• Year: 2015
• Volume: 61
• Issue:
• Pages: 253–262
• Publisher: Elsevier BV
• DOI: 10.1016/j.automatica.2015.08.021

BibTeX

@article{Jafarian_2015,
  title={{Formation control of a multi-agent system subject to Coulomb friction}},
  volume={61},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2015.08.021},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Jafarian, Matin and Vos, Ewoud and De Persis, Claudio and van der Schaft, Arjan J. and Scherpen, Jacquelien M.A.},
  year={2015},
  pages={253--262}
}

Download the bib file

References

• Arcak, M. Passivity as a Design Tool for Group Coordination. IEEE Transactions on Automatic Control vol. 52 1380–1390 (2007) – 10.1109/tac.2007.902733
• Bacciotti, A. & Ceragioli, F. Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions. ESAIM: Control, Optimisation and Calculus of Variations vol. 4 361–376 (1999) – 10.1051/cocv:1999113
• Bai, (2011)
• Bollobás, (1998)
• Ceragioli, F., De Persis, C. & Frasca, P. Discontinuities and hysteresis in quantized average consensus. Automatica vol. 47 1916–1928 (2011) – 10.1016/j.automatica.2011.06.020
• Cortés, J. Finite-time convergent gradient flows with applications to network consensus. Automatica vol. 42 1993–2000 (2006) – 10.1016/j.automatica.2006.06.015
• De Persis, C. & Frasca, P. Robust Self-Triggered Coordination With Ternary Controllers. IEEE Transactions on Automatic Control vol. 58 3024–3038 (2013) – 10.1109/tac.2013.2273302
• Persis, C. D. & Jayawardhana, B. Coordination of Passive Systems under Quantized Measurements. SIAM Journal on Control and Optimization vol. 50 3155–3177 (2012) – 10.1137/110844994
• Canudas de Wit, C., Olsson, H., Astrom, K. J. & Lischinsky, P. A new model for control of systems with friction. IEEE Transactions on Automatic Control vol. 40 419–425 (1995) – 10.1109/9.376053
• Duindam, (2009)
• Fujimoto, K., Sakai, S. & Sugie, T. Passivity based control of a class of Hamiltonian systems with nonholonomic constraints. Automatica vol. 48 3054–3063 (2012) – 10.1016/j.automatica.2012.08.032
• Godsil, (2001)
• Hájek, O. Discontinuous differential equations, I. Journal of Differential Equations vol. 32 149–170 (1979) – 10.1016/0022-0396(79)90056-1
• Jafarian, M. & De Persis, C. Exact formation control with very coarse information. 2013 American Control Conference 3026–3031 (2013) doi:10.1109/acc.2013.6580295 – 10.1109/acc.2013.6580295
• Jafarian, M. & De Persis, C. Formation control using binary information. Automatica vol. 53 125–135 (2015) – 10.1016/j.automatica.2014.12.016
• Nemytskii, (1960)
• Nuno, E., Ortega, R., Basanez, L. & Hill, D. Synchronization of Networks of Nonidentical Euler-Lagrange Systems With Uncertain Parameters and Communication Delays. IEEE Transactions on Automatic Control vol. 56 935–941 (2011) – 10.1109/tac.2010.2103415
• Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
• Ren, W. Distributed leaderless consensus algorithms for networked Euler–Lagrange systems. International Journal of Control vol. 82 2137–2149 (2009) – 10.1080/00207170902948027
• van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
• van der Schaft, A. J. & Maschke, B. M. Port-Hamiltonian Systems on Graphs. SIAM Journal on Control and Optimization vol. 51 906–937 (2013) – 10.1137/110840091
• van de Wouw, N. & Leine, R. I. Attractivity of Equilibrium Sets of Systems with Dry Friction. Nonlinear Dynamics vol. 35 19–39 (2004) – 10.1023/b:nody.0000017482.61599.86
• van de Wouw, N. & Leine, R. I. Robust impulsive control of motion systems with uncertain friction. International Journal of Robust and Nonlinear Control vol. 22 369–397 (2011) – 10.1002/rnc.1694
• Vos, E., Scherpen, J. M. A. & van der Schaft, A. J. Equal distribution of satellite constellations on circular target orbits. Automatica vol. 50 2641–2647 (2014) – 10.1016/j.automatica.2014.08.027