An Adaptive Gravity Compensation Controller for the Leaderless Consensus of Uncertain Euler-Lagrange Agents

Resumen: Consensus is the most basic synchronization behavior in multiagent systems. For networks of Euler-Lagrange (EL) agents different controllers have been proposed to achieve consensus, requiring in all cases, either the cancellation or the estimation of the gravity forces. In the latter case, it is necessary to estimate, not just the gravity forces, but the parameters of the whole dynamics. This requires the computation of a complicated regressor matrix, that grows in complexity as the degrees-of-freedom of the EL-agents increase. In this paper, we propose an adaptive controllers to solve the leaderless consensus problem by only estimating the gravitational term of the agents and hence without requiring the complete regressor matrix. To the best of our knowledge, this is the first work that achieves such an objective. The controller is a simple Proportional plus damping (P+d) scheme that does not require to exchange velocity information between the agents. Simulation results demonstrate the performance of the proposed controllers.

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Seyed-Mostafa Almodarresi, Emmanuel Nuño, Romeo Ortega, Marzieh Kamali & Farid Sheikholeslam. An Adaptive Gravity Compensation Controller for the Leaderless Consensus of Uncertain Euler-Lagrange Agents. Memorias del Congreso Nacional de Control Automático, pp. 564-569, 2019.

Palabras clave

Sistemas Multi-Agente, Robótica y Mecatrónica, Control de Sistemas No Lineales

• Abdessameud, A., Tayebi, A., and Polushin, I.G. (2012). Attitude synchronization of multiple rigid bodies with communication delays. IEEE Transactions on Automatic Control, 57(9), 2405–2411.
• Abdessameud, A., Tayebi, A., and Polushin, I. (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.
• Aldana, C.I., Romero, E., Nuño, E., and Basáñez, L. (2015). Pose consensus in networks of heterogeneous robots with variable time delays. International Journal of Robust and Nonlinear Control, 25(14), 2279–2298.
• Arcak, M. (2007). Passivity as a design tool for group coordination. IEEE Transactions on Automatic Control, 52(8), 1380–1390.
• Chen, F., Feng, G., Liu, L., and Ren, W. (2015a). Distributed average tracking of networked Euler-Lagrange systems. IEEE Transactions on Automatic Control, 60(2), 547–552.
• Chen, F., Feng, G., Liu, L., and Ren, W. (2015b). Distributed average tracking of networked euler-lagrange systems. IEEE Transactions on Automatic Control, 60(2), 547–552.
• Chopra, N. and Spong, M. (2005). On synchronization of networked passive systems with time delays and application to bilateral teleoperation. In Proc. of the IEEE/SICE Int. Conf. on Instrumentation, Control and Information Technology.
• Chung, S. and Slotine, J. (2009). Cooperative robot control and concurrent synchronization of Lagrangian systems. IEEE Trans. on Robotics, 25(3), 686–700.
• Gu, D.B. and Wang, Z. (2009). Leader-follower flocking: Algorithms and experiments. IEEE Transactions on Control Systems Technology, 17(5), 1211–1219.
• Hatanaka, T., Chopra, N., Fujita, M., and Spong, M. (2015). Passivity-Based Control and Estimation in Networked Robotics. Communications and Control Engineering. Springer.
• Hernández -Guzmán, V. and Orrante-Sakanassi, J. (2019). Model-independent consensus control of euler-lagrange agents with interconnecting delays. International Journal of Robust and Nonlinear Control, 29(12), 4069– 4096.
• Kelly, R. (1993). Comments on Adaptive PD Controller for Robot Manipulators’. IEEE Transactions on Robotics and Automation, 9(1), 117–119.
• Kelly, R., Santibáñez, V., and Loria, A. (2005). Control of robot manipulators in joint space. Springer-Verlag.
• Klotz, J., Kan, Z., Shea, J., Pasiliao, E., and Dixon, W. (2015). Asymptotic synchronization of a leaderfollower network of uncertain Euler-Lagrange systems. IEEE Transactions on Control of Network Systems, 2(2), 174–182.
• Krasovskii, N.N. (1963). Stability of motion. Translation of Russian edition, Moscow 1959. Stanford Univ. Press.
• Lee, D. and Spong, M.W. (2007). Stable flocking of multiple inertial agents on balanced graphs. IEEE Transactions on Automatic Control, 52(8), 1469–1475.
• Liu, Y., Min, H., Wang, S., Ma, L., and Liu, Z. (2014). Consensus for multiple heterogeneous Euler-Lagrange systems with time-delay and jointly connected topologies. Journal of the Franklin Institute, 351(6), 3351– 3363.
• Meng, Z., Dimarogonas, D., and Johansson, K. (2014). Leader-follower coordinated tracking of multiple heterogeneous lagrange systems using continuous control. IEEE Transactions on Robotics, 30(3), 739–745.
• 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., Basa˜nez, 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.
• Nuño, E., Ortega, R., Jayawardhana, B., and Basáñez, L. (2013a). Coordination of multi-agent Euler-Lagrange systems via energy-shaping: Networking improves robustness. Automatica, 49(10), 3065–3071.
• Nuño, E., Sarras, I., and Basáñez, L. (2013b). Consensus in networks of nonidentical Euler-Lagrange systems using P+d controllers. IEEE Transactions on Robotics, 26(6), 1503–1508.
• Nuño, E., Sarras, I., Loría, A., Maghenem, M., Cruz Zavala, E., and Panteley, E. (2018). Strict LyapunovKrasovski˘ı functionals for undirected networks of EulerLagrange systems with time-varying delays. Systems & Control Letters (In review).
• Ortega, R., Loria, A., Nicklasson, P., and Sira-Ramirez, H. (1998). Passivity-based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications. Springer.
• Qin, J., Zheng, W., and Gao, H. (2012). Coordination of multiple agents with double-integrator dynamics under generalized interaction topologies. IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics, 42(1), 44–57.
• Ren, W. (2009). Distributed leaderless consensus algorithms for networked Euler-Lagrange systems. Int. Jour. of Control, 82(11), 2137–2149. Ren, W. and Cao, Y. (2011). Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues. Springer-Verlag.
• Rodriguez-Angeles, A. and Nijmeijer, H. (2004). Mutual synchronization of robots via estimated state feedback: a cooperative approach. IEEE Transactions on Control Systems Technology, 12(4), 542–554.
• Spong, M., Hutchinson, S., and Vidyasagar, M. (2005). Robot Modeling and Control. Wiley.
• Takegaki, M. and Arimoto, S. (1981). A new feedback method for dynamic control of manipulators. Journal of Dynamic Systems, Measurement, and Control, 103(2), 119–125.
• Tomei, P. (1991). Adaptive PD controller for robot manipulators. IEEE Transactions on Robotics and Automation, 7(4), 565–570.
• Wang, H. (2014). Consensus of networked mechanical systems with communication delays: A unified framework. IEEE Transactions on Automatic Control, 59(6), 1571–1576.
• Wang, H. (2017). Dynamic feedback for consensus of networked lagrangian systems. arXiv preprint arXiv:1707.03657.
• Wang, X., Yu, C., and Lin, Z. (2012). A dual quaternion solution to attitude and position control for rigid-body coordination. IEEE Transactions on Robotics, 28(5), 1162–1170.
• Ye, M., Anderson, B., and Yu, C. (2017). Distributed model-independent consensus of Euler-Lagrange agents on directed networks. International Journal of Robust and Nonlinear Control, 27(14), 2428–2450.