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

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.

[1]  Jacquelien M. A. Scherpen,et al.  Equal distribution of satellite constellations on circular target orbits , 2014, Autom..

[2]  Chih-fen Chang,et al.  Qualitative Theory of Differential Equations , 1992 .

[3]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[4]  Arjan van der Schaft,et al.  Port-Hamiltonian Systems on Graphs , 2011, SIAM J. Control. Optim..

[5]  A. Bacciotti,et al.  Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions , 1999 .

[6]  Arjan van der Schaft,et al.  Port-Hamiltonian Systems Theory: An Introductory Overview , 2014, Found. Trends Syst. Control..

[7]  John T. Wen,et al.  Cooperative Control Design - A Systematic, Passivity-Based Approach , 2011, Communications and control engineering.

[8]  Jacquelien M.A. Scherpen,et al.  Port-Hamiltonian approach to deployment , 2012 .

[9]  van de N Nathan Wouw,et al.  Robust impulsive control of motion systems with uncertain friction , 2012 .

[10]  Romeo Ortega,et al.  Synchronization of Networks of Nonidentical Euler-Lagrange Systems With Uncertain Parameters and Communication Delays , 2011, IEEE Transactions on Automatic Control.

[11]  N. van de Wouw,et al.  Attractivity of Equilibrium Sets of Systems with Dry Friction , 2004 .

[12]  Toshiharu Sugie,et al.  Passivity based control of a class of Hamiltonian systems with nonholonomic constraints , 2012, Autom..

[13]  Murat Arcak,et al.  Passivity as a Design Tool for Group Coordination , 2007, IEEE Transactions on Automatic Control.

[14]  Wei Ren,et al.  Distributed leaderless consensus algorithms for networked Euler–Lagrange systems , 2009, Int. J. Control.

[15]  Claudio De Persis,et al.  Robust Self-Triggered Coordination With Ternary Controllers , 2012, IEEE Transactions on Automatic Control.

[16]  Romeo Ortega,et al.  Putting energy back in control , 2001 .

[17]  Claudio De Persis,et al.  Coordination of Passive Systems under Quantized Measurements , 2011, SIAM J. Control. Optim..

[18]  Claudio De Persis,et al.  Exact formation control with very coarse information , 2013, 2013 American Control Conference.

[19]  Carlos Canudas de Wit,et al.  A new model for control of systems with friction , 1995, IEEE Trans. Autom. Control..

[20]  Otomar Hájek,et al.  Discontinuous differential equations, II , 1979 .

[21]  Claudio De Persis,et al.  Formation control using binary information , 2015, Autom..

[22]  Stefano Stramigioli,et al.  Modeling and Control of Complex Physical Systems - The Port-Hamiltonian Approach , 2014 .

[23]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[24]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[25]  Claudio De Persis,et al.  Discontinuities and hysteresis in quantized average consensus , 2010, Autom..