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A formation maneuvering controller for multiple non-holonomic robotic vehicles

Published online by Cambridge University Press:  19 September 2018

Milad Khaledyan  and
Marcio de Queiroz Open the ORCID record for Marcio de Queiroz [Opens in a new window]
Milad Khaledyan
Affiliation:
Department of Mechanical and Industrial Engineering, Louisiana State University, Baton Rouge, LA 70803, USA. E-mail: [email protected]
Marcio de Queiroz*
Affiliation:
Department of Mechanical and Industrial Engineering, Louisiana State University, Baton Rouge, LA 70803, USA. E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
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Summary

In this paper, we present a new leader–follower type solution to the translational maneuvering problem for formations of multiple, non-holonomic wheeled mobile robots. The solution is based on the graph that models the coordination among the robots being a spanning tree. Our control law incorporates two types of position errors: individual tracking errors and coordination errors for leader–follower pairs in the spanning tree. The control ensures that the robots globally acquire a given planar formation while the formation as a whole globally tracks a desired trajectory, both with uniformly ultimately bounded errors. The control law is first designed at the kinematic level and then extended to the dynamic level. In the latter, we consider that parametric uncertainty exists in the equations of motion. These uncertainties are accounted for by employing an adaptive control scheme. The main contributions of this work are that the proposed control scheme minimizes the number of control links and global position measurements, and accounts for the uncertain vehicle dynamics. The proposed formation maneuvering controls are demonstrated experimentally and numerically.

Keywords

Multi-agent systemFormation controlNon-holonomic vehicleAdaptive control
Type
Articles
Information
Robotica , Volume 37 , Issue 1 , January 2019 , pp. 189 - 211
Copyright
Copyright © Cambridge University Press 2018 

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References

1. Baillieul, J. and Suri, A., “Information Patterns and Hedging Brockett's Theorem in Controlling Vehicle Formations,” Proceedings of the IEEE Conference on Decision Control, Maui, HI, USA (2003) pp. 556–563.Google Scholar
2. Borowska, J., Lacinska, L. and Rychlewska, J., “A system of linear recurrence equations for determinant of pentadiagonal matrix,” J. Appl. Math. Comp. Mech. 13 (2), 5–12 (2014).Google Scholar
3. Cai, Z., de Queiroz, M. S. and Dawson, D. M., “A sufficiently smooth projection operator,” IEEE Trans. Autom. Contr. 51 (1), 135–139 (2006).Google Scholar
4. Cai, X. and de Queiroz, M., “Multi-Agent Formation Maneuvering and Target Interception with Double-Integrator Model,” Proceedings of the American Control Conference, Portland, OR (2014) pp. 287–292.Google Scholar
5. Cai, X. and de Queiroz, M., “Rigidity-based stabilization of multi-agent formations,” ASME J. Dyn. Syst., Measur., Contr. 136 (1), Paper 014502 (2014).Google Scholar
6. Cai, X. and de Queiroz, M., “Formation maneuvering and target interception for multi-agent systems via rigid graphs,” Asian J. Contr. 17 (4), 1174–1186 (2015).Google Scholar
7. Cai, X. and de Queiroz, M., “Adaptive rigidity-based formation control for multi-robotic vehicles with dynamics,” IEEE Trans. Contr. Syst. Tech. 23 (1), 389–396 (2015).Google Scholar
8. Cao, Y., Stuart, D., Ren, W. and Meng, Z., “Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: Algorithms and experiments,” IEEE Trans. Contr. Syst. Tech. 19 (4), 929–938 (2011).Google Scholar
9. Carona, R., Aguiar, A. P. and Gaspar, J., “Control of Unicycle Type Robots Tracking, Path Following and Point Stabilization,” Proceedings of the International Conference IV Electronics Telecommunication, Lisbon, Portugal (2008) pp. 180–185.Google Scholar
10. Chen, G. and Lewis, F. L., “Distributed adaptive tracking control for synchronization of unknown networked lagrangian systems,” IEEE Trans. Syst. Man Cybern. - Part B 41 (3), 805–816 (2011).Google Scholar
11. Chung, S.-J. and Slotine, J.-J., “Cooperative robot control and concurrent synchronization of Lagrangian systems,” IEEE Trans. Rob. 25 (3), 686–700 (2009).Google Scholar
12. Chen, J., Sun, D., Yang, J. and Chen, H., “Leader-follower formation control of multiple non-holonomic mobile robots incorporating a receding-horizon scheme,” Intl. J. Rob. Res. 29 (6), 727–747 (2010).Google Scholar
13. Desai, J. P., Ostrowski, J. P. and Kumar, V., “Modeling and control of formations of nonholonomic mobile robots,” IEEE Trans. Rob. Autom. 17 (6), 905–908 (2001).Google Scholar
14. Dimarogonasa, D. V. and Kyriakopoulos, K. J., “A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems,” Automatica 44, 2648–2654 (2008).Google Scholar
15. Dixon, W. E., Dawson, D. M., Zergeroglu, E. and Behal, A., Nonlinear Control of Wheeled Mobile Robots (Springer, London, 2001).Google Scholar
16. Do, K. D. and Pan, J., “Nonlinear formation control of unicycle-type mobile robots,” Robot. Autonom. Syst. 55 (3), 191–204 (2007).Google Scholar
17. Dong, W. and Farrell, J. A., “Cooperative control of multiple nonholonomic mobile agents,” IEEE Trans. Autom. Contr. 53 (6), 1434–1448 (2008).Google Scholar
18. Dong, W. and Farrell, J. A., “Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty,” Automatica 45 (3), 706–710 (2009).Google Scholar
19. Dörfler, F. and Francis, B., “Geometric analysis of the formation problem for autonomous robots,” IEEE Trans. Autom. Contr. 55 (10), 2379–2384 (2010).Google Scholar
20. Gazi, V., Fidan, B., Ordóñez, R. and Köksal, M. I., “A target tracking approach for nonholonomic agents based on artificial potentials and sliding model control,” ASME J. Dyn. Syst. Measur. Contr. 134 (11), Paper 061004 (2012).Google Scholar
21. Han, Z., Wang, L., Lin, Z. and Zheng, R., “Formation control with size scaling via a complex Laplacian-based approach,” IEEE Trans. Cyber. 46 (10), 2348–2359 (2016).Google Scholar
22. Kanayama, Y., Kimura, Y., Miyazaki, F. and Noguchi, T., “A Stable Tracking Control Method for an Autonomous Mobile Robot,” Proceedings of IEEE Conference on Robotics Automation, Cincinnati, OH, USA (1990) pp. 384–389.Google Scholar
23. Khaledyan, M. and de Queiroz, M., “Formation Maneuvering Control of Nonholonomic Multi-Agent Systems,” Proceedings of the ASME Dynamic System Control Conference, Minneapolis, MN, USA (2016) Paper No. DSCC2016-9616.Google Scholar
24. Khalil, H. K., Nonlinear Systems (Prentice Hall, Englewood Cliffs, NJ, 2002).Google Scholar
25. Khoo, S., Xie, L. and Man, Z., “Robust finite-time consensus tracking algorithm for multirobot systems,” IEEE/ASME Trans. Mechatron. 14 (2), 219–228 (2009).Google Scholar
26. Kostić, D., Adinandra, S., Caarls, J., van de Wouv, N. and Nijmeijer, H., “Saturated Control of Time-Varying Formations and Trajectory Tracking for Unicycle Multi-Agent Systems,” Proceedings of the IEEE Conference on Decision Control, Atlanta, GA, USA (2010) pp. 4054–4059.Google Scholar
27. Kostić, D., Adinandra, S., Caarls, J. and Nijmeijer, H., “Collision-Free Motion Coordination of Unicycle Multi-Agent Systems,” Proceedings of the American Control Conference, Baltimore, MD, USA (2010) pp. 3186–3191.Google Scholar
28. Krick, L., Broucke, M. E. and Francis, B. A., “Stabilization of infinitesimally rigid formations of multi-robot networks,” Intl. J. Contr. 83 (3), 423–439 (2009).Google Scholar
29. Krstić, M., Kanellakopoulos, I. and Kokotović, P., Nonlinear and Adaptive Control Design (John Wiley & Sons, New York, NY, 1995).Google Scholar
30. Lawson, C. L. and Hanson, R. J., Solving Least Squares Problems (Prentice Hall, Englewood Cliffs, NJ, 1974).Google Scholar
31. Lee, D. and Li, P. Y., “Passive decomposition approach to formation and maneuver control of multiple rigid-Bodies,” ASME J. Dyn. Syst., Measur., Contr., 129 (5), 662–677 (2007).Google Scholar
32. Liang, Y. and Lee, H.-H., “Decentralized Formation Control and Obstacle Avoidance for Multiple Robots with Nonholonomic Constraints,” Proc. Amer. Contr. Conf., Minneapolis, MN, USA (2006) pp. 5596–5601.Google Scholar
33. Mastellone, S., Stipanovic, D. M., Graunke, C. R., Intlekofer, K. A. and Spong, M. W., “Formation control and collision avoidance for multi-agent non-holonomic systems: Theory and experiments,” Intl. J. Robot. Res. 27 (1), 107–125 (2008).Google Scholar
34. Moshtagh, N., Michael, N., Jadbabaie, A. and Daniilidis, K., “Vision-based, distributed control laws for motion coordination of nonholonomic robots,” IEEE Trans. Rob. 25 (4), 851–860 (2009).Google Scholar
35. Narendra, K. S. and Annaswamy, A. M., Stable Adaptive Systems (Dover, Mineola, NY, 2005).Google Scholar
36. Ögren, P., Fiorelli, E. and Leonard, N. E., “Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment,” IEEE Trans. Autom. Contr. 49 (8), 1292–1302 (2004).Google Scholar
37. Oh, K.-K. and Ahn, H.-S., “Distance-Based Control of Cycle-Free Persistent Formations,” Proceedings of the IEEE Multi-Conference on Systems and Control, Denver, CO (2011) pp. 816–821.Google Scholar
38. Olfati-Saber, A., “Flocking for multi-agent dynamic systems: Algorithm and theory,” IEEE Trans. Autom. Contr. 51 (3), 401–420 (2006).Google Scholar
39. Paige, C. C. and Strakoš, Z., “Bounds for the Least Squares Residual Using Scaled Total Least Squares,” In: Total Least Squares and Errors-in-Variables Modeling (Van Huffel, S. and Lemmerling, P., eds.) (Springer, Dordrecht, 2002) pp. 35–44.Google Scholar
40. Pereira, A. R., Hsu, L. and Ortega, R., “Globally Stable Adaptive Formation Control of Euler–Lagrange Agents via Potential Functions,” Proceedings of the American Control Conference, St. Louis, MO, USA (2009) pp. 2606–2611.Google Scholar
41. Pickem, D., Lee, M. and Egerstedt, M., “The GRITSBot in its Natural Habitat—A Multi-Robot Testbed,” Proceedings of the IEEE International Conference on Robotics Automation, Seattle, WA, USA (2015) pp. 4062–4067.Google Scholar
42. Pickem, D.et al., “The Robotarium: A Remotely Accessible Swarm Robotics Research Testbed,” Proceedings of the IEEE International Conference on Robotics and Automation, Singapore (2017) pp. 1699–1709.Google Scholar
43. Qu, Z., Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles (Springer-Verlag, London, U.K., 2009).Google Scholar
44. Rozenheck, O., Zhao, S. and Zelazo, D., “A Proportional-Integral Controller for Distance Based Formation Tracking,” Proceedings of the European Control Conference, Linz, Austria (2015) pp. 1693–1698.Google Scholar
45. Sadowska, A., Kostić, D., van de Wouw, N., Huijberts, H. and Nijmeijer, H., “Distributed Formation Control of Unicycle Robots,” Proceedings of the IEEE International Conference on Robotics Automation, Saint Paul, MN, USA (2012) pp. 1564–1569.Google Scholar
46. Stilwell, D. J., Bishop, B. E. and Sylvester, C. A., “Redundant Manipulator Techniques for Partially Decentralized Path Planning and Control of Platoon of Autonomous Vehicles,” IEEE Trans. Syst., Man, and Cybern. - Part B 35 (5), 842–848 (2005).Google Scholar
47. Sun, D., Wang, C., Shang, W. and Feng, G., “A Synchronization Approach to Trajectory Tracking of Multiple Mobile Robots While Maintaining Time-Varying Formations,” IEEE Trans. Rob. 25 (5), 1074–1086 (2009).Google Scholar
48. Thorvaldsen, C. F. L. and Skjetne, R., “Formation Control of Fully-Actuated Marine Vessels Using Group Agreement Protocols,” Proceedings of the IEEE Conference on Decision Control, Orlando, FL, USA (2011) pp. 4132–4139.Google Scholar
49. Yao, J., Ordóñez, R. and Gazi, V., “Swarm tracking using artificial potentials and sliding mode control,” ASME J. Dyn. Syst., Meas., Control 129 (5), 749–754 (2007).Google Scholar
50. Zhang, P., de Queiroz, M. and Cai, X., “3D dynamic formation control of multi-agent systems using rigid graphs,” ASME J. Dyn. Syst. Measur. Contr. 137 (11), Paper no. 111006 (2015).Google Scholar
51. Zhao, X. and Huang, T., “On the inverse of a general pentadiagonal matrix,” Appl. Math. Comp. 202 (2), 639–646 (2008).Google Scholar
52. Zhu, J., Lu, J. and Yu, X., “Flocking of multi-agent nonholonomic systems with proximity graphs,” IEEE Trans. Circ. Syst. I 60 (1), 199–210 (2013).Google Scholar
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