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Trajectory Tracking Control of Unicycle Robots with Collision Avoidance and Connectivity Maintenance

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Abstract

In this paper, we focus on a multiple objective control problem for unicycle robots. By utilizing the gradients of collision avoidance and connectivity potential fields in designing reference orientations, we derive control laws for unicycle robots and show that they can track reference trajectories with bounded errors, which can be made arbitrarily small, while avoiding inter-agent collisions and ensuring that the communication among the agents is maintained. Additionally, we present experimental results where we illustrate the effectiveness of our proposed control laws by implementing them on a testbed with mobile robots.

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References

  1. Ren, W., Beard, R.: Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE T. Automat. Contr. 50(5), 655–661 (2005)

    Article  MathSciNet  Google Scholar 

  2. Desai, J., Ostrowski, J., Kumar, V.: Modeling and control of formations of nonholonomic mobile robots. IEEE T. Robotic. Autom. 17(6), 905–908 (2001)

    Article  Google Scholar 

  3. Fierro, R., Das, A., Kumar, V., Ostrowski, J.: Hybrid control of formations of robots. In: Proceedings of the IEEE ICRA, vol. 1, pp. 157–162. IEEE (2001)

  4. Lin, Z., Broucke, M., Francis, B.: Local control strategies for groups of mobile autonomous agents. IEEE T. Automat. Contr. 49(4), 622–629 (2004)

    Article  MathSciNet  Google Scholar 

  5. Egerstedt, M., Hu, X.: Formation constrained multi-agent control. IEEE T. Robotic. Autom. 17(6), 947–951 (2001)

    Article  Google Scholar 

  6. Arcak, M.: Passivity as a design tool for group coordination. IEEE T. Robotic. Autom. 52(8), 1380–1390 (2007)

    MathSciNet  MATH  Google Scholar 

  7. Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE T. Automat. Contr. 48(6), 988–1001 (2003)

    Article  MathSciNet  Google Scholar 

  8. Olfati-Saber, R.: Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE T. Automat. Contr. 51(3), 401–420 (2006)

    Article  MathSciNet  Google Scholar 

  9. Olfati-Saber, R., Fax, J., Murray, R.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)

    Article  Google Scholar 

  10. Cao, Y., Yu, W., Ren, W., Chen, G.: An overview of recent progress in the study of distributed multi-agent coordination. arXiv:1207.3231 (2012)

  11. Inalhan, G., Stipanović, D., Tomlin, C.: Decentralized optimization, with application to multiple aircraft coordination. In: Proceedings of the IEEE Conference on Decision and Control, Las Vegas (2002)

  12. Leitmann, G., Skowronski, J.M.: Avoidance control. J. Optimiz. Theory App. 23(4), 581–591 (1977)

    Article  MathSciNet  Google Scholar 

  13. Getz, W.M., Leitmann, G.: Qualitative differential games with two targets. J. Math. Anal. Appl. 68, 421–430 (1979)

    Article  MathSciNet  Google Scholar 

  14. Leitmann, G.: Guaranteed avoidance strategies. J. Optimiz. Theory App. 32(4), 569–576 (1980)

    Article  MathSciNet  Google Scholar 

  15. Leitmann, G., Skowronski, J.M.: A note on avoidance control. Optim. Contr. Appl. Met. 4, 335–342 (1983)

    Article  MathSciNet  Google Scholar 

  16. Stipanović, D., Hokayem, P., Spong, M., Šiljak, D.: Cooperative avoidance control for multi-agent systems. J. Dyn. Syst-T ASME 129, 699–707 (2007)

    Article  Google Scholar 

  17. Stipanović, D.M.: A survey and some new results in avoidance control. In: Rodellar, J., Reithmeier, E. (eds.) 15Th International Workshop on Dynamics and Control. CIMNE, Barcelona (2009)

  18. Fiedler, M.: Algebraic connectivity of graphs. Czechoslov. Math. J. 23(98), 298–305 (1973)

    MathSciNet  MATH  Google Scholar 

  19. De Gennaro, M., Jadbabaie, A.: Decentralized control of connectivity for multi-agent systems. In: Proceedings of the IEEE Conference on Decision and Control, pp. 3628–3633. IEEE (2006)

  20. Zavlanos, M., Pappas, G.: Potential fields for maintaining connectivity of mobile networks. IEEE T. Robot. 23(4), 812–816 (2007)

    Article  Google Scholar 

  21. Zavlanos, M.M., Pappas, G.J.: Distributed connectivity control of mobile networks. IEEE T. Robot. 24 (6), 1416–1428 (2008)

    Article  Google Scholar 

  22. Zavlanos, M., Tanner, H., Jadbabaie, A., Pappas, G.: Hybrid control for connectivity preserving flocking. IEEE T. Automat. Contr. 54(12), 2869–2875 (2009)

    Article  MathSciNet  Google Scholar 

  23. Yang, P., Freeman, R.A., Gordon, G.J., Lynch, K.M., Srinivasa, S.S., Sukthankar, R.: Decentralized estimation and control of graph connectivity for mobile sensor networks. Automatica 46(2), 390–396 (2010)

    Article  MathSciNet  Google Scholar 

  24. Kan, Z., Dani, A.P., Shea, J.M., Dixon, W.E.: Network connectivity preserving formation stabilization and obstacle avoidance via a decentralized controller. IEEE T. Robotic. Autom. 57(7), 1827–1832 (2012)

    MathSciNet  MATH  Google Scholar 

  25. Flores-Resendiz, J.F., Aranda-Bricaire, E., Gonzalez-Sierra, J., Santiaguillo-Salinas, J.: Finite-time formation control without collisions for multiagent systems with communication graphs composed of cyclic paths. Math. Probl. Eng. 2015, Article ID 948086 (2015)

    Article  MathSciNet  Google Scholar 

  26. Zavlanos, M., Egerstedt, M., Pappas, G.: Graph-theoretic connectivity control of mobile robot networks. Proc. IEEE 99, 1–16 (2011)

    Article  Google Scholar 

  27. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. IJRR 5(1), 90–98 (1986)

    Google Scholar 

  28. Leonard, N.E., Fiorelli, E.: Virtual leaders, artificial potentials and coordinated control of groups. In: Proceedings of the IEEE Conference on Decision and Control, pp. 2968–2973 (2001)

  29. Dimarogonas, D., Loizou, S., Kyriakopoulos, K., Zavlanos, M.: A feedback stabilization and collision avoidance scheme for multiple independent non-point agents. Automatica 42(2), 229–243 (2006)

    Article  MathSciNet  Google Scholar 

  30. Gazi, V., Passino, K.: Stability analysis of swarms. IEEE T. Automat. Contr. 48(4), 692–697 (2003)

    Article  MathSciNet  Google Scholar 

  31. Tanner, H., Kumar, A.: Formation stabilization of multiple agents using decentralized navigation functions. In: Robotics: science and systems, pp. 49–56. Citeseer (2005)

  32. Biggs, N.: Algebraic Graph Theory, vol. 67. Cambridge Univ Pr, Cambridge (1993)

    Google Scholar 

  33. Mastellone, S., Stipanović, D., Graunke, C., Intlekofer, K., Spong, M.: Formation control and collision avoidance for multi-agent non-holonomic systems: Theory and experiments. IJRR 27(1), 107–126 (2008)

    Google Scholar 

  34. Khalil, H.: Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River (2001)

    Google Scholar 

  35. Rodríguez-Seda, E.J., Tang, C., Spong, M.W., Stipanović, D.: Trajectory tracking with collision avoidance for nonholonomic vehicles with acceleration constraints and limited sensing. Int. J. Robot. Res. 33(12), 1569–1592 (2014)

    Article  Google Scholar 

  36. Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, Dordrecht (1988)

    Book  Google Scholar 

  37. Dimarogonas, D., Johansson, K.H.: Decentralized connectivity maintenance in mobile networks with bounded inputs. In: 2008. ICRA, 2008 IEEE International Conference on Robotics and Automation, pp. 1507–1512. IEEE (2008)

  38. Dimarogonas, D., Kyriakopoulos, K.J.: On the rendezvous problem for multiple nonholonomic agents. IEEE Trans. Autom. Control 52(5), 916–922 (2007)

    Article  MathSciNet  Google Scholar 

  39. Koditschek, D.E., Rimon, E.: Robot navigation functions on manifolds with boundary. Adv. Appl. Math. 11(4), 412–442 (1990)

    Article  MathSciNet  Google Scholar 

  40. Atınç, G., Stipanović, D., Voulgaris, P., Karkoub, M.: Collision-Free Trajectory tracking while preserving connectivity in unicycle Multi-Agent systems. In: Proceedings of ACC, pp. 5392–5397 (2013)

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Acknowledgment

The work presented here was made possible by NPRP grant# 5-071-2-026 from the Qatar National Research Fund. The findings achieved herein are solely the responsibility of the authors.

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Authors and Affiliations

  1. Mechanical Engineering Department, Texas A&M University at Qatar, Doha, Qatar

    Mansour Karkoub

  2. Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, IL, USA

    Gokhan Atınç, Dusan Stipanovic & Petros Voulgaris

  3. Mechanical Engineering Department, Texas A&M University, College Station, Texas, USA

    Andy Hwang

Authors
  1. Mansour Karkoub
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  2. Gokhan Atınç
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  3. Dusan Stipanovic
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  4. Petros Voulgaris
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  5. Andy Hwang
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Correspondence to Mansour Karkoub.

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Karkoub, M., Atınç, G., Stipanovic, D. et al. Trajectory Tracking Control of Unicycle Robots with Collision Avoidance and Connectivity Maintenance. J Intell Robot Syst 96, 331–343 (2019). https://doi.org/10.1007/s10846-019-00987-2

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  • DOI: https://doi.org/10.1007/s10846-019-00987-2

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