Passivity based distributed tracking control of networked Euler-Lagrange systems

Abstract In this paper we present three distributed control laws for the coordination of networked Euler-Lagrange (EL) systems. We first reformulate the passivity-based control design method in Arcak (2007) by considering that each edge is associated with an artificial spring system instead of the usual diffusive coupling among the communicating agents. With this configuration, the networked EL system possesses a "symmetric" feedback structure which together with the strict passivity of both agents’ and edges’ dynamics lead to a strictly passive network dynamics. Subsequently we present the networked version of two different passivity-based tracking controllers that are particular cases of our method. A numerical simulation is presented to show the performance of the proposed method.

[1]  Bayu Jayawardhana,et al.  Tracking Control of Fully-actuated port-Hamiltonian Mechanical Systems via Sliding Manifolds and Contraction Analysis , 2017 .

[2]  M. Areak,et al.  Passivity as a design tool for group coordination , 2006, 2006 American Control Conference.

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

[4]  Bayu Jayawardhana,et al.  Transverse Exponential Stability and Applications , 2016, IEEE Transactions on Automatic Control.

[5]  Arjan van der Schaft,et al.  Virtual Differential Passivity based Control for Tracking of Flexible-joints Robots , 2017, ArXiv.

[6]  Ming Cao,et al.  Taming inter-distance mismatches in formation-motion control for rigid formations of second-order agents , 2016, ArXiv.

[7]  Soon-Jo Chung,et al.  Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems , 2007, IEEE Transactions on Robotics.

[8]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[9]  Arjan van der Schaft,et al.  Tracking Control of Marine Craft in the port-Hamiltonian Framework: A Virtual Differential Passivity Approach , 2018, 2019 18th European Control Conference (ECC).

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

[11]  Mark W. Spong,et al.  Adaptive motion control of rigid robots: a tutorial , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[12]  Mark W. Spong,et al.  Passivity-Based Control of Multi-Agent Systems , 2006 .

[13]  Thor I. Fossen,et al.  Nonlinear vectorial backstepping design for global exponential tracking of marine vessels in the presence of actuator dynamics , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[14]  Alessandro Astolfi,et al.  Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems , 2001, IEEE Trans. Autom. Control..

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

[16]  Diana Bohm,et al.  L2 Gain And Passivity Techniques In Nonlinear Control , 2016 .

[17]  J. Slotine,et al.  On the Adaptive Control of Robot Manipulators , 1987 .

[18]  Romeo Ortega,et al.  Coordination of multi-agent Euler-Lagrange systems via energy-shaping: Networking improves robustness , 2013, Autom..

[19]  Romeo Ortega,et al.  Networking improves robustness in flexible-joint multi-robot systems with only joint position measurements , 2013, Eur. J. Control.

[20]  Mark W. Spong,et al.  Comments on "Adaptive manipulator control: a case study" by J. Slotine and W. Li , 1990 .

[21]  Thor I. Fossen,et al.  A Tutorial on Incremental Stability Analysis using Contraction Theory , 2010 .

[22]  Ming Cao,et al.  Taming Mismatches in Inter-agent Distances for the Formation-Motion Control of Second-Order Agents , 2016, IEEE Transactions on Automatic Control.

[23]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .