Finite-Time Leaderless Consensus of Euler-Lagrange Agents without Velocity Measurements: The Bounded Input Case

Resumen: One of the basic synchronization strategies of multiple agents is the leaderless consensus where, independently of the initial conditions, the agents agree at a certain constant coordinate. In this paper, we propose a novel controller that is capable of solving the leaderless consensus problem in finite-time in networks of fully-actuated Euler-Lagrange (EL) systems without employing velocity measurements and with bounded inputs. The controller is another EL-system with its own dissipation of energy that is back-propagated to the plant and the plant-controller interconnection is the force of a nonlinear spring.

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Emmanuel Cruz-Zavala, , Emmanuel Nuño & Jaime A. Moreno. Finite-Time Leaderless Consensus of Euler-Lagrange Agents without Velocity Measurements: The Bounded Input Case. Memorias del Congreso Nacional de Control Automático, pp. 146-151, 2018.

Palabras clave

Finite-Time, Consensus, Robots

• Abdessameud, A. and Tayebi, A. (2013). On consensus algorithms design for double integrator dynamics. Automatica, 49(1), 253–260.
• Abdessameud, A., Tayebi, A., and Polushin, I.G. (2017). Leader-follower synchronization of Euler-Lagrange systems with time-varying leader trajectory and constrained discrete-time communication. IEEE Transactions on Automatic Control, 62(5), 2539–2545.
• Andrieu, V., Praly, L., and Astolfi, A. (2008). Homogeneous approximation, recursive observer design and output feedback. SIAM J. Control Optim., 47(4), 1814– 1850.
• Arteaga, M. and Kelly, R. (2004). Robot control without velocity measurements: New theory and experimental results. IEEE Transactions on Robotics and Automation, 20(2), 297–308.
• Bacciotti, A. and Rosier, L. (2005). Lyapunov functions and stability in control theory. Springer-Verlag, New York, 2nd edition.
• Bhat, S. and Bernstein, D. (2000). Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization, 38, 751–766.
• Bhat, S. and Bernstein, D. (2005). Geometric homogeneity with applications to finite-time stability. Mathematics of Control, Signals, and Systems, 17(2), 101–127.
• Cao, Y. and Ren, W. (2011). Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues. Springer-Verlag.
• Chung, S. and Slotine, J. (2009). Cooperative robot control and concurrent synchronization of Lagrangian systems. IEEE Trans. on Robotics, 25(3), 686–700.
• Cortés, J. (2006). Finite-time convergent gradient flows with applications to network consensus. Automatica, 42(11), 1993–2000.
• Cruz-Zavala, E., Moreno, J., and Nuño, E. (2018). Leaderless and leader-follower consensus of euler-lagrange agents: Finite-time convergence without velocity measurements. In IEEE Conference on Decision and Control (Submitted).
• Davila, J. and Pisano, A. (2016). Fixed-time consensus for a class of nonlinear uncertain multi-agent systems. In Proc. of the American Control Conference (ACC).
• Galicki, M. (2015). Finite-time control of robotic manipulators. Automatica, 51(1), 49–54.
• Ge, M.F., Guan, Z.H., Yang, C., Li, T., and Wang, Y.W. (2016). Time-varying formation tracking of multiple manipulators via distributed finite-time control. Neurocomputing, 202, 20–26.
• Hatanaka, T., Chopra, N., Fujita, M., and Spong, M. (2015). Passivity-Based Control and Estimation in Networked Robotics. Communications and Control Engineering. Springer.
• Hong, Y., Xu, Y., and Huang, J. (2002). Finite-time control for robot manipulators. Systems & Control Letters, 46, 243–253.
• Jadbabaie, A., Lin, J., and Morse, A. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6), 988–1001.
• Kelly, R., Santibáñez, V., and Loría, A. (2005). Control of Robot Manipulators in Joint Space. Springer-Verlag, London, U.K.
• Klotz, J., Obuz, S., Kan, Z., and Dixon, W. (2018). Synchronization of uncertain euler-lagrange systems with uncertain time-varying communication delays. IEEE Transactions on Cybernetics, 48(2), 807–817.
• Liu, Y., Zhao, Y., Shi, Z., and Wei, D. (2017). Specifiedtime containment control of multi-agent systems over directed topologies. IET Control Theory & Applications, 11(4), 576–585.
• Nuño, E. (2017). Consensus of Euler-Lagrange systems using only position measurements. IEEE Transactions on Control of Network Systems. DOI:10.1109/TCNS.2016.2620806.
• Nuño, E. and Ortega, R. (2018). Achieving consensus of Euler-Lagrange agents with interconnecting delays and without velocity measurements via passivity-based control. IEEE Transactions on Control Systems Technology, 26(1), 222–232.
• Nuño, E., Ortega, R., Basáñez, L., and Hill, D. (2011). Synchronization of networks of nonidentical EulerLagrange systems with uncertain parameters and communication delays. IEEE Transactions on Automatic Control, 56(4), 935–941.
• Olfati-Saber, R. and Murray, R. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533.
• Orlov, Y. (2005). Finite time stability and robust control synthesis of uncertain switched systems. SIAM Journal on Control and Optimization, 43(4), 1253–1271.
• Orlov, Y. (2009). Discontinuos Systems: Lyapunov analysis and robust synthesis under uncertainty conditions. Springer.
• Ren, W. (2008). On consensus algorithms for doubleintegrator dynamics. IEEE Transactions on Automatic Control, 53(6), 1503–1509.
• Ren, W. (2009). Distributed leaderless consensus algorithms for networked Euler-Lagrange systems. Int. Jour. of Control, 82(11), 2137–2149.
• Ren, W. (2010). Distributed cooperative attitude synchronization and tracking for multiple rigid bodies. IEEE Transactions on Control Systems Technology, 18(2), 383–392.
• Sepulchre, R. and Aeyels, D. (1996). Homogeneous Lyapunov functions and necessary conditions for stabilization. Math. Control. Signals Syst., 9, 34–58.
• Venkataraman, S. and Gulati, S. (1993). Terminal slider control of robot systems. Journal of Intelligent and Robotic Systems, 5, 31–55.
• Zavala-Río, A. and Fantoni, I. (2014). Global finitetime stability characterized through a local notion of homogeneity. IEEE Trans. Autom. Control, 59(2), 471– 477.
• Zavala-Río, A. and Zamora-G´omez, G. (2017). Local homogeneity-based global continuous control for mechanical systems with constrained inputs: finite-time and exponential stabilisation. International Journal of Control, 90(5), 1037–1051.
• Zhao, Y., Duan, Z., and Wen, G. (2015). Distributed finite-time tracking of multiple Euler-Lagrange systems without velocity measurements. International Journal of Robust and Nonlinear Control, 25(11), 1688–1703.