This study proposes a novel model predictive control (MPC) based on receding horizon particle swarm optimisation (RHPSO) for formation control of non-holonomic mobile robots by incorporating collision avoidance and control input minimisation and guaranteeing asymptotic stability. In most conventional MPC approaches, the collision avoidance constraint is imposed by the 2-norm of a relative position vector at each discrete time step. Thus, multi-robot formation control problem can be formulated as a constrained non-linear optimisation problem. In general, traditional optimisation techniques suitable for addressing constrained non-linear optimisation problems take a longer computation time with an increase in the number of constraints. The traditional approaches therefore suffer from the computational complexity problem corresponding to an increase in the prediction horizon. To address this problem without a significant increase in computational complexity, a novel strategy for collision avoidance is proposed to incorporating a particle swarm optimisation. In addition, the stability conditions are derived in simplified forms that can be satisfied by selecting appropriate constant values for control gains and weight parameters. Numerical simulations verify the effectiveness of the proposed RHPSO-based formation control.

References

1. 1)
  - 15. Keviczky, T., Borrelli, F., Balas, G.J.: ‘Decentralized receding horizon control for large scale dynamically decoupled systems’, Automatica, 2006, 42, (12), pp. 2105–2115 (doi: 10.1016/j.automatica.2006.07.008).
2. 2)
  - 19. Turpin, M., Michael, N., Kumar, V.: ‘Trajectory design and control for aggressive formation flight with quadrotors’, Auton. Robots, 2012, 33, (1–2), pp. 143–156 (doi: 10.1007/s10514-012-9279-y).
3. 3)
  - 7. Ögren, P., Egerstedt, M., Hu, X.: ‘A control Lyapunov function approach to multiagent coordination’, IEEE Trans. Robot. Autom., 2002, 18, (5), pp. 847–851 (doi: 10.1109/TRA.2002.804500).
4. 4)
  - 4. Balch, T., Arkin, R.C.: ‘Behavior-based formation control for multirobot teams’, IEEE Trans. Robot. Autom., 1998, 14, (6), pp. 926–939 (doi: 10.1109/70.736776).
5. 5)
  - 3. Fukushima, H., Kon, K., Matsuno, F.: ‘Model predictive formation control using branch-and-bound compatible with collision avoidance problems’, IEEE Trans. Robot., 2013, 29, (5), pp. 1308–1317 (doi: 10.1109/TRO.2013.2262751).
6. 6)
  - 32. Bonyadi, M.R., Michalewicz, Z.: ‘A locally convergent rotationally invariant particle swarm optimization algorithm’, Swarm Intell., 2014, 8, (3), pp. 159–198 (doi: 10.1007/s11721-014-0095-1).
7. 7)
  - 21. Saska, M., Vonásek, V., Přeučil, L.: ‘Trajectory planning and control for airport snow sweeping by autonomous formations of ploughs’, J. Intell. Robot. Syst., 2013, 72, (2), pp. 239–261 (doi: 10.1007/s10846-013-9829-3).
8. 8)
  - 1. Desai, J.P., Ostrowski, J.P., Kumar, V.: ‘Modeling and control of formations of nonholonomic mobile robots’, IEEE Trans. Robot. Autom., 2001, 17, (6), pp. 905–908 (doi: 10.1109/70.976023).
9. 9)
  - 26. Duan, H., Luo, Q., Ma, G., Shi, Y.: ‘Hybrid particle swarm optimization and genetic algorithm for multi-UAV formation reconfiguration’, IEEE Comput. Intell. Mag., 2013, 8, (3), pp. 16–27 (doi: 10.1109/MCI.2013.2264577).
10. 10)
  - 22. Scholte, E., Campbell, M.E.: ‘Robust nonlinear model predictive control with partial state information’, IEEE Trans. Control Syst. Technol., 2008, 16, (4), pp. 636–651 (doi: 10.1109/TCST.2007.912120).
11. 11)
  - 8. Do, K.D.: ‘Formation tracking control of unicycle-type mobile robots with limited sensing ranges’, IEEE Trans. Control Syst. Technol., 2008, 16, (3), pp. 527–538 (doi: 10.1109/TCST.2007.908214).
12. 12)
  - 12. Fontes, F.A.C.C.: ‘A general framework to design stabilizing nonlinear model predictive controllers’, Syst. Control Lett., 2001, 42, (2), pp. 127–143 (doi: 10.1016/S0167-6911(00)00084-0).
13. 13)
  - 23. Wang, X., Yadav, V., Balakrishnan, S.N.: ‘Cooperative UAV formation flying with obstacle/collision avoidance’, IEEE Trans. Control Syst. Technol., 2007, 15, (4), pp. 672–679 (doi: 10.1109/TCST.2007.899191).
14. 14)
  - 29. Kennedy, J., Eberhart, R.C.: ‘Swarm intelligence’ (Morgan Kaufmann Publisher, 2001).
15. 15)
  - 28. Lee, S.-M., Kim, H., Myung, H.: ‘Cooperative coevolution-based model predictive control for multi-robot formation’, Proc. IEEE Int. Conf. Robot. Autom., 2013, pp. 1890–1895.
16. 16)
  - 20. Kushleyev, A., Mellinger, D., Powers, C., Kumar, V.: ‘Towards a swarm of agile micro quadrotors’, Auton. Robots, 2013, 35, (4), pp. 287–300 (doi: 10.1007/s10514-013-9349-9).
17. 17)
  - 25. Wang, S., Zheng, C.: ‘A hierarchical evolutionary trajectory planner for spacecraft formation reconfiguration’, IEEE Trans. Aerosp. Electron. Syst., 2012, 48, (1), pp. 279–289 (doi: 10.1109/TAES.2012.6129635).
18. 18)
  - 24. Duan, H.B., Liu, S.Q.: ‘Non-linear dual-mode receding horizon control for multiple unmanned air vehicles formation flight based on chaotic particle swarm optimisation’, IET Control. Theory Appl., 2010, 4, (11), pp. 2565–2578 (doi: 10.1049/iet-cta.2009.0256).
19. 19)
  - 16. Keviczky, T., Borrelli, F., Fregene, K., Godbole, D., Balas, G.J.: ‘Decentralized receding horizon control and coordination of autonomous vehicle formations’, IEEE Trans. Control Syst. Technol., 2008, 16, (1), pp. 19–33 (doi: 10.1109/TCST.2007.903066).
20. 20)
  - 11. Camponogara, E., Jia, D., Krogh, B.H., Talukdar, S.: ‘Distributed model predictive control’, IEEE Control Syst. Mag., 2002, 22, (1), pp. 44–52 (doi: 10.1109/37.980246).
21. 21)
  - 6. Lewis, M.A., Tan, K.-H.: ‘High precision formation control of mobile robots using virtual structures’, Auton. Robots, 1997, 4, (4), pp. 387–403 (doi: 10.1023/A:1008814708459).
22. 22)
  - 30. Gu, D., Hu, H.: ‘A stabilizing receding horizon regulator for nonholonomic mobile robots’, IEEE Trans. Robot., 2005, 21, (5), pp. 1022–1028 (doi: 10.1109/TRO.2005.851357).
23. 23)
  - 17. Richards, A., How, J.: ‘A decentralized algorithm for robust constrained model predictive control’. Proc. IEEE Amer. Control Conf., 2004, pp. 4261–4266.
24. 24)
  - 33. Dehdari, V., Oliver, D.S.: ‘Sequential quadratic programming for solving constrained production optimization – case study from Brugge field’, SPE J., 2012, 7, (3), pp. 874–884 (doi: 10.2118/141589-PA).
25. 25)
  - 10. Wang, P., Ding, B.: ‘Distributed RHC for tracking and formation of nonholonomic multi-vehicle systems’, IEEE Trans. Autom. Control, 2014, 59, (6), pp. 1439–1453 (doi: 10.1109/TAC.2014.2304175).
26. 26)
  - 27. Lee, S.-M., Kim, H., Myung, H., Yao, X.: ‘Cooperative coevolutionary algorithm-based model predictive control guaranteeing stability of multirobot formation’, IEEE Trans. Control Syst. Technol., 2015, 23, (1), pp. 37–51 (doi: 10.1109/TCST.2014.2312324).
27. 27)
  - 14. Dunbar, W.B., Caveney, D.S.: ‘Distributed receding horizon control of vehicle platoons: stability and string stability’, IEEE Trans. Autom. Control, 2012, 57, (3), pp. 620–633 (doi: 10.1109/TAC.2011.2159651).
28. 28)
  - 5. Lawton, J.R.T., Beard, R.W., Young, B.J.: ‘A decentralized approach to formation maneuvers’, IEEE Trans. Robot. Autom., 2003, 19, (6), pp. 933–941 (doi: 10.1109/TRA.2003.819598).
29. 29)
  - 9. Park, B.S., Park, J.B., Choi, Y.H.: ‘Robust adaptive formation control and collision avoidance for electrically driven non-holonomic mobile robots’, IET Control Theory Appl., 2011, 5, (3), pp. 514–522 (doi: 10.1049/iet-cta.2010.0353).
30. 30)
  - 18. Richards, A., How, J.: ‘Decentralized model predictive control of cooperating UAVs’. Proc. IEEE Conf., Decision Control, 2004, pp. 4286–4291.
31. 31)
  - 13. Dunbar, W.B., Murray, R.M.: ‘Distributed receding horizon control for multi-vehicle formation stabilization’, Automatica, 2006, 42, (4), pp. 549–558 (doi: 10.1016/j.automatica.2005.12.008).
32. 32)
  - 2. Chen, J., Sun, D., Yang, J., Chen, H.: ‘Leader-follower formation control of multiple non-holonomic mobile robots incorporating a receding-horizon scheme’, Int. J. Robot. Res., 2010, 29, (6), pp. 727–747 (doi: 10.1177/0278364909104290).
33. 33)
  - 31. Gu, D., Hu, H.: ‘Receding horizon tracking control of wheeled mobile robots’, IEEE Trans. Control Syst. Technol., 2006, 14, (4), pp. 743–749 (doi: 10.1109/TCST.2006.872512).

Receding horizon particle swarm optimisation-based formation control with collision avoidance for non-holonomic mobile robots

References

Related content