Achieving Consensus of Euler–Lagrange Agents With Interconnecting Delays and Without Velocity Measurements via Passivity-Based Control

Authors

Emmanuel Nuno, Romeo Ortega

Abstract

This paper deals with the problem of achieving consensus of multiple Euler–Lagrange (EL) systems using the energy shaping plus damping injection principles of passivity-based control. It proposes a novel decentralized controller that is capable of solving the leaderless and the leader–follower consensus problems in networks of fully actuated EL-systems with interconnecting time-varying delays and without employing velocity measurements. This paper also presents a comparative simulation study with different controllers and provides experimental evidence of the performance of the novel controller.

Citation

• Journal: IEEE Transactions on Control Systems Technology
• Year: 2018
• Volume: 26
• Issue: 1
• Pages: 222–232
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tcst.2017.2661822

BibTeX

@article{Nuno_2018,
  title={{Achieving Consensus of Euler–Lagrange Agents With Interconnecting Delays and Without Velocity Measurements via Passivity-Based Control}},
  volume={26},
  ISSN={1558-0865},
  DOI={10.1109/tcst.2017.2661822},
  number={1},
  journal={IEEE Transactions on Control Systems Technology},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Nuno, Emmanuel and Ortega, Romeo},
  year={2018},
  pages={222--232}
}

Download the bib file

References

• Arcak M (2007) Passivity as a Design Tool for Group Coordination. IEEE Trans Automat Contr 52(8):1380–1390. https://doi.org/10.1109/tac.2007.902733 – 10.1109/tac.2007.902733
• Nuño E, Ortega R, Jayawardhana B, Basañez L (2013) Networking improves robustness in flexible-joint multi-robot systems with only joint position measurements. European Journal of Control 19(6):469–476. https://doi.org/10.1016/j.ejcon.2013.09.005 – 10.1016/j.ejcon.2013.09.005
• Astolfi A, Ortega R, Venkatraman A (2010) A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints. Automatica 46(1):182–189. https://doi.org/10.1016/j.automatica.2009.10.027 – 10.1016/j.automatica.2009.10.027
• nuño, Consensus of Euler-Lagrange systems using only position measurements. IEEE Trans Control Netw Syst (0)
• nuño, Consensus in delayed robot networks using only position measurements. Proc Autom Control Nat Congr (2015)
• Zheng Y, Wang L (2012) Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements. Systems & Control Letters 61(8):871–878. https://doi.org/10.1016/j.sysconle.2012.05.009 – 10.1016/j.sysconle.2012.05.009
• Ortega R, Donaire A, Romero JG (2017) Passivity-Based Control of Mechanical Systems. In: Lecture Notes in Control and Information Sciences. Springer International Publishing, Cham, pp 167–199 – 10.1007/978-3-319-51298-3_7
• Duindam V, Macchelli A, Stramigioli S, Bruyninckx H (2009) Modeling and Control of Complex Physical Systems. Springer Berlin Heidelberg, Berlin, Heidelberg – 10.1007/978-3-642-03196-0
• Ortega R, Spong MW (1989) Adaptive motion control of rigid robots: A tutorial. Automatica 25(6):877–888. https://doi.org/10.1016/0005-1098(89)90054-x – 10.1016/0005-1098(89)90054-x
• Takegaki M, Arimoto S (1981) A New Feedback Method for Dynamic Control of Manipulators. Journal of Dynamic Systems, Measurement, and Control 103(2):119–125. https://doi.org/10.1115/1.3139651 – 10.1115/1.3139651
• Abdessameud A, Tayebi A, Polushin IG (2012) Attitude Synchronization of Multiple Rigid Bodies With Communication Delays. IEEE Trans Automat Contr 57(9):2405–2411. https://doi.org/10.1109/tac.2012.2188428 – 10.1109/tac.2012.2188428
• Ren W (2010) Distributed Cooperative Attitude Synchronization and Tracking for Multiple Rigid Bodies. IEEE Trans Contr Syst Technol 18(2):383–392. https://doi.org/10.1109/tcst.2009.2016428 – 10.1109/tcst.2009.2016428
• Abdessameud A, Tayebi A (2013) On consensus algorithms design for double integrator dynamics. Automatica 49(1):253–260. https://doi.org/10.1016/j.automatica.2012.08.044 – 10.1016/j.automatica.2012.08.044
• Olfati-Saber R, Murray RM (2004) Consensus Problems in Networks of Agents With Switching Topology and Time-Delays. IEEE Trans Automat Contr 49(9):1520–1533. https://doi.org/10.1109/tac.2004.834113 – 10.1109/tac.2004.834113
• Jadbabaie A, Jie Lin, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Automat Contr 48(6):988–1001. https://doi.org/10.1109/tac.2003.812781 – 10.1109/tac.2003.812781
• Wang H (2014) Consensus of Networked Mechanical Systems With Communication Delays: A Unified Framework. IEEE Trans Automat Contr 59(6):1571–1576. https://doi.org/10.1109/tac.2013.2293413 – 10.1109/tac.2013.2293413
• Abdessameud A, Polushin IG, Tayebi A (2014) Synchronization of Lagrangian Systems With Irregular Communication Delays. IEEE Trans Automat Contr 59(1):187–193. https://doi.org/10.1109/tac.2013.2270053 – 10.1109/tac.2013.2270053
• hatanaka, Passivity-Based Control and Estimation in Networked Robotics Communications and Control Engineering (2015)
• Arteaga MA, Kelly R (2004) Robot Control Without Velocity Measurements: New Theory and Experimental Results. IEEE Trans Robot Automat 20(2):297–308. https://doi.org/10.1109/tra.2003.820872 – 10.1109/tra.2003.820872
• Abdessameud A, Polushin IG, Tayebi A (2015) Synchronization of nonlinear systems with communication delays and intermittent information exchange. Automatica 59:1–8. https://doi.org/10.1016/j.automatica.2015.05.020 – 10.1016/j.automatica.2015.05.020
• Aldana CI, Nuño E, Basañez L, Romero E (2014) Operational space consensus of multiple heterogeneous robots without velocity measurements. Journal of the Franklin Institute 351(3):1517–1539. https://doi.org/10.1016/j.jfranklin.2013.11.012 – 10.1016/j.jfranklin.2013.11.012
• Namvar M (2009) A Class of Globally Convergent Velocity Observers for Robotic Manipulators. IEEE Trans Automat Contr 54(8):1956–1961. https://doi.org/10.1109/tac.2009.2023960 – 10.1109/tac.2009.2023960
• Salvo Rossi P, Romano G, Palmieri F, Iannello G (2006) Joint end-to-end loss-delay hidden Markov model for periodic UDP traffic over the Internet. IEEE Trans Signal Process 54(2):530–541. https://doi.org/10.1109/tsp.2005.861066 – 10.1109/tsp.2005.861066
• Avila-Becerril S, Espinosa-Pérez G, Panteley E, Ortega R (2015) Consensus control of flexible-joint robots. International Journal of Control 88(6):1201–1208. https://doi.org/10.1080/00207179.2014.1000379 – 10.1080/00207179.2014.1000379
• Nuño E, Valle D, Sarras I, Basañez L (2014) Leader–follower and leaderless consensus in networks of flexible-joint manipulators. European Journal of Control 20(5):249–258. https://doi.org/10.1016/j.ejcon.2014.07.003 – 10.1016/j.ejcon.2014.07.003
• Ortega R, Loría A, Nicklasson PJ, Sira-Ramírez H (1998) Passivity-based Control of Euler-Lagrange Systems. Springer London, London – 10.1007/978-1-4471-3603-3
• chopra, On synchronization of networked passive systems with time delays and application to bilateral teleoperation. Proc IEEE/SICE Int Conf Instrum Control Inf Technol (2005)
• Proskurnikov AV, Zhang F, Cao M, Scherpen JMA (2015) A general criterion for synchronization of incrementally dissipative nonlinearly coupled agents. In: 2015 European Control Conference (ECC). IEEE, pp 581–586 – 10.1109/ecc.2015.7330606
• Nuno E, Ortega R, Basanez L, Hill D (2011) Synchronization of Networks of Nonidentical Euler-Lagrange Systems With Uncertain Parameters and Communication Delays. IEEE Trans Automat Contr 56(4):935–941. https://doi.org/10.1109/tac.2010.2103415 – 10.1109/tac.2010.2103415
• Ren W (2009) Distributed leaderless consensus algorithms for networked Euler–Lagrange systems. International Journal of Control 82(11):2137–2149. https://doi.org/10.1080/00207170902948027 – 10.1080/00207170902948027
• Nuno E, Sarras I, Basanez L (2013) Consensus in Networks of Nonidentical Euler–Lagrange Systems Using P+d Controllers. IEEE Trans Robot 29(6):1503–1508. https://doi.org/10.1109/tro.2013.2279572 – 10.1109/tro.2013.2279572
• Nuño E, Ortega R, Jayawardhana B, Basañez L (2013) Coordination of multi-agent Euler–Lagrange systems via energy-shaping: Networking improves robustness. Automatica 49(10):3065–3071. https://doi.org/10.1016/j.automatica.2013.07.002 – 10.1016/j.automatica.2013.07.002
• Chung S-J, Slotine J-JE (2009) Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems. IEEE Trans Robot 25(3):686–700. https://doi.org/10.1109/tro.2009.2014125 – 10.1109/tro.2009.2014125
• Abdessameud A, Tayebi A, Polushin IG (2015) On the leader-follower synchronization of Euler-Lagrange systems. In: 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, pp 1054–1059 – 10.1109/cdc.2015.7402011
• Chen F, Feng G, Liu L, Ren W (2015) Distributed Average Tracking of Networked Euler-Lagrange Systems. IEEE Trans Automat Contr 60(2):547–552. https://doi.org/10.1109/tac.2014.2343111 – 10.1109/tac.2014.2343111
• Klotz JR, Kan Z, Shea JM, Pasiliao EL, Dixon WE (2015) Asymptotic Synchronization of a Leader-Follower Network of Uncertain Euler-Lagrange Systems. IEEE Trans Control Netw Syst 2(2):174–182. https://doi.org/10.1109/tcns.2014.2378875 – 10.1109/tcns.2014.2378875
• cao, Distributed Coordination of Multi-agent Networks Emergent Problems Models and Issues (2011)
• Meng Z, Ren W, Cao Y, You Z (2011) Leaderless and Leader-Following Consensus With Communication and Input Delays Under a Directed Network Topology. IEEE Trans Syst, Man, Cybern B 41(1):75–88. https://doi.org/10.1109/tsmcb.2010.2045891 – 10.1109/tsmcb.2010.2045891
• Yao Chen, Jinhu Lu, Xinghuo Yu, Hill DJ (2013) Multi-Agent Systems with Dynamical Topologies: Consensus and Applications. IEEE Circuits Syst Mag 13(3):21–34. https://doi.org/10.1109/mcas.2013.2271443 – 10.1109/mcas.2013.2271443
• Cao Y, Yu W, Ren W, Chen G (2013) An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination. IEEE Trans Ind Inf 9(1):427–438. https://doi.org/10.1109/tii.2012.2219061 – 10.1109/tii.2012.2219061
• Wei Ren, Haiyang Chao, Bourgeous W, Sorensen N, YangQuan Chen (2008) Experimental Validation of Consensus Algorithms for Multivehicle Cooperative Control. IEEE Trans Contr Syst Technol 16(4):745–752. https://doi.org/10.1109/tcst.2007.912239 – 10.1109/tcst.2007.912239
• Aldana CI, Romero E, Nuño E, Basañez L (2014) Pose consensus in networks of heterogeneous robots with variable time delays. Int J Robust Nonlinear Control 25(14):2279–2298. https://doi.org/10.1002/rnc.3200 – 10.1002/rnc.3200
• Pasumarthy R, Kao C-Y (2009) On stability of time delay Hamiltonian systems. In: 2009 American Control Conference. IEEE, pp 4909–4914 – 10.1109/acc.2009.5160619
• Meng Z, Dimarogonas DV, Johansson KH (2014) Leader–Follower Coordinated Tracking of Multiple Heterogeneous Lagrange Systems Using Continuous Control. IEEE Trans Robot 30(3):739–745. https://doi.org/10.1109/tro.2013.2294060 – 10.1109/tro.2013.2294060
• Nuno E, Ortega R, Barabanov N, Basanez L (2008) A Globally Stable PD Controller for Bilateral Teleoperators. IEEE Trans Robot 24(3):753–758. https://doi.org/10.1109/tro.2008.921565 – 10.1109/tro.2008.921565
• Nuño E, Basañez L, Ortega R, Spong MW (2009) Position Tracking for Non-linear Teleoperators with Variable Time Delay. The International Journal of Robotics Research 28(7):895–910. https://doi.org/10.1177/0278364908099461 – 10.1177/0278364908099461
• Schiffer J, Fridman E, Ortega R, Raisch J (2016) Stability of a class of delayed port-Hamiltonian systems with application to microgrids with distributed rotational and electronic generation. Automatica 74:71–79. https://doi.org/10.1016/j.automatica.2016.07.022 – 10.1016/j.automatica.2016.07.022
• Schiffer J, Fridman E, Ortega R (2015) Stability of a class of delayed port-Hamiltonian systems with application to droop-controlled microgrids. In: 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, pp 6391–6396 – 10.1109/cdc.2015.7403226
• Jafarian M, Vos E, De Persis C, van der Schaft AJ, Scherpen JMA (2015) Formation control of a multi-agent system subject to Coulomb friction. Automatica 61:253–262. https://doi.org/10.1016/j.automatica.2015.08.021 – 10.1016/j.automatica.2015.08.021
• zhang, Cooperative robust output regulation of heterogeneous Lur’e networks. Proc IEEE 54th Annu Conf Decision Control (CDC) (2015)
• Hong Y, Hu J, Gao L (2006) Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42(7):1177–1182. https://doi.org/10.1016/j.automatica.2006.02.013 – 10.1016/j.automatica.2006.02.013
• Ortega R, van der Schaft A, Castanos F, Astolfi A (2008) Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Trans Automat Contr 53(11):2527–2542. https://doi.org/10.1109/tac.2008.2006930 – 10.1109/tac.2008.2006930