Trajectory Tracking Control of Unicycle Robots with Collision Avoidance and Connectivity Maintenance
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.
Keywords
Multi-objective control Collision avoidance Unicycle robotsPreview
Unable to display preview. Download preview PDF.
Notes
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.
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)MathSciNetCrossRefzbMATHGoogle 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)CrossRefGoogle 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)Google Scholar
- 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)MathSciNetCrossRefzbMATHGoogle Scholar
- 5.Egerstedt, M., Hu, X.: Formation constrained multi-agent control. IEEE T. Robotic. Autom. 17(6), 947–951 (2001)CrossRefGoogle Scholar
- 6.Arcak, M.: Passivity as a design tool for group coordination. IEEE T. Robotic. Autom. 52(8), 1380–1390 (2007)MathSciNetzbMATHGoogle 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)MathSciNetCrossRefzbMATHGoogle Scholar
- 8.Olfati-Saber, R.: Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE T. Automat. Contr. 51(3), 401–420 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
- 9.Olfati-Saber, R., Fax, J., Murray, R.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)CrossRefzbMATHGoogle 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)Google Scholar
- 12.Leitmann, G., Skowronski, J.M.: Avoidance control. J. Optimiz. Theory App. 23(4), 581–591 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
- 13.Getz, W.M., Leitmann, G.: Qualitative differential games with two targets. J. Math. Anal. Appl. 68, 421–430 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
- 14.Leitmann, G.: Guaranteed avoidance strategies. J. Optimiz. Theory App. 32(4), 569–576 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
- 15.Leitmann, G., Skowronski, J.M.: A note on avoidance control. Optim. Contr. Appl. Met. 4, 335–342 (1983)MathSciNetCrossRefzbMATHGoogle 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)CrossRefGoogle 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)Google Scholar
- 18.Fiedler, M.: Algebraic connectivity of graphs. Czechoslov. Math. J. 23(98), 298–305 (1973)MathSciNetzbMATHGoogle 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)Google Scholar
- 20.Zavlanos, M., Pappas, G.: Potential fields for maintaining connectivity of mobile networks. IEEE T. Robot. 23(4), 812–816 (2007)CrossRefGoogle Scholar
- 21.Zavlanos, M.M., Pappas, G.J.: Distributed connectivity control of mobile networks. IEEE T. Robot. 24 (6), 1416–1428 (2008)CrossRefGoogle 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)MathSciNetCrossRefzbMATHGoogle 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)MathSciNetCrossRefzbMATHGoogle 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)MathSciNetzbMATHGoogle 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)MathSciNetCrossRefzbMATHGoogle Scholar
- 26.Zavlanos, M., Egerstedt, M., Pappas, G.: Graph-theoretic connectivity control of mobile robot networks. Proc. IEEE 99, 1–16 (2011)CrossRefGoogle 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)Google Scholar
- 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)MathSciNetCrossRefzbMATHGoogle Scholar
- 30.Gazi, V., Passino, K.: Stability analysis of swarms. IEEE T. Automat. Contr. 48(4), 692–697 (2003)MathSciNetCrossRefzbMATHGoogle 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)Google Scholar
- 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)CrossRefGoogle Scholar
- 36.Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, Dordrecht (1988)CrossRefGoogle 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)Google Scholar
- 38.Dimarogonas, D., Kyriakopoulos, K.J.: On the rendezvous problem for multiple nonholonomic agents. IEEE Trans. Autom. Control 52(5), 916–922 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
- 39.Koditschek, D.E., Rimon, E.: Robot navigation functions on manifolds with boundary. Adv. Appl. Math. 11(4), 412–442 (1990)MathSciNetCrossRefzbMATHGoogle 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)Google Scholar