Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-12T19:47:32.608Z Has data issue: false hasContentIssue false
  • English
  • Français

Modeling and trajectory tracking control of a two-wheeled mobile robot: Gibbs–Appell and prediction-based approaches

Published online by Cambridge University Press:  01 August 2018

Hossein Mirzaeinejad  and
Ali Mohammad Shafei
Hossein Mirzaeinejad
Affiliation:
Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran. E-mail: [email protected]
Ali Mohammad Shafei*
Affiliation:
Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran. E-mail: [email protected]
*
*Corresponding author: E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

This study deals with the problem of trajectory tracking of wheeled mobile robots (WMR's) under non-holonomic constraints and in the presence of model uncertainties. To solve this problem, the kinematic and dynamic models of a WMR are first derived by applying the recursive Gibbs–Appell method. Then, new kinematics- and dynamics-based multivariable controllers are analytically developed by using the predictive control approach. The control laws are optimally derived by minimizing a pointwise quadratic cost function for the predicted tracking errors of the WMR. The main feature of the obtained closed-form control laws is that online optimization is not needed for their implementation. The prediction time, as a free parameter in the control laws, makes it possible to achieve a compromise between tracking accuracy and implementable control inputs. Finally, the performance of the proposed controller is compared with that of a sliding mode controller, reported in the literature, through simulations of some trajectory tracking maneuvers.

Keywords

Trajectory trackingWMRNon-holonomic constraintPredictive controlOptimization
Type
Articles
Information
Robotica , Volume 36 , Issue 10 , October 2018 , pp. 1551 - 1570
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Asif, M., Khan, M. J. and Cai, N., “Adaptive sliding mode dynamic controller with integrator in the loop for nonholonomic wheeled mobile robot trajectory tracking,” Int. J. Control 87, 964–975 (2014).Google Scholar
2. Blazic, S., “A novel trajectory tracking control law for wheeled mobile robots,” Robot. Autonomous Syst. 59, 1001–1007 (2011).Google Scholar
3. Khatib, O., Yokoi, K., Chang, K., Ruspini, D., Holmberg, R., Casal, A. and Baader, A., “Force Strategies for Cooperative Tasks in Multiple Mobile Manipulation Systems,” In: The 7th International Symposium on Robotics Research 7 (Giralt, G. and Hirzinger, G., eds.) (Springer, Berlin, 1996) pp. 333–342.Google Scholar
4. Wiens, G. J., “Effects of Dynamic Coupling in Mobile Robotic Systems,” Proceedings of SME Robotics Research World Conference, Gaithersburg, Maryland (1989) pp. 43–57.Google Scholar
5. Saha, S. K. and Angeles, J., “Dynamics of non-holonomic mechanical systems using a natural orthogonal complement,” Trans. ASME, J. Appl. Mech. 58, 238–243 (1991).Google Scholar
6. Hootsmanns, N. and Dubowsky, S., “The Motion Control of Manipulators on Mobile Vehicles,” Proceedings of the IEEE Conference on Robotics and Automation (1991) pp. 2336–2341.Google Scholar
7. Liu, K. and Lewis, F. L., “Decentralized Continuous Robust Controller for Mobile Robots,” Proceedings of the IEEE Conference on Robotics and Automation, Cincinnati, OH (1990) pp. 1822–1827.Google Scholar
8. Chen, M. W. and Zalzala, A. M. S., “Dynamic modeling and genetic-base trajectory generation for nonholonomic mobile manipulators,” Control Eng. Practice 5, 39–48 (1997).Google Scholar
9. Yamamoto, Y. and Yun, X., “Coordinating locomotion and manipulation of a mobile manipulator,” IEEE Trans. Autom. Control 39, 1326–1332 (1994).Google Scholar
10. Thanjavur, K. and Rajagopalan, R., “Ease of Dynamic Modeling of Wheeled Mobile Robots (WMRs) Using Kane's Approach,” Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, New Mexico (1997) pp. 2926–2931.Google Scholar
11. Tanner, H. G. and Kyriakopouos, K. J., “Mobile manipulator modeling with Kane's approach,” Robotica 19, 675–690 (2001).Google Scholar
12. Korayem, M. H. and Shafei, A. M., “A new approach for dynamic modeling of n-viscoelastic-link robotic manipulators mounted on a mobile base,” Nonlinear Dyn. 79 2767–2786 (2015).Google Scholar
13. Korayem, M. H. and Shafei, A. M., “Motion equation of nonholonomic wheeled mobile robotic manipulator with revolute-prismatic joints using recursive Gibbs–Appell formulation,” Appl. Math. Modeling 39, 1701–1716 (2015).Google Scholar
14. Korayem, M. H., Shafei, A. M. and Seidi, E., “Symbolic derivation of governing equations for dual-arm mobile manipulators used in fruit-picking and the pruning of tall trees,” Comput. Electron. Agricultur. 105, 95–102 (2014).Google Scholar
15. Korayem, M. H., Shafei, A. M. and Shafei, H. R., “Dynamic modeling of nonholonomic wheeled mobile manipulators with elastic joints using recursive Gibbs–Appell formulation,” Scientia Iranica Trans. b-Mech. Eng. 19, 1092–1104 (2012).Google Scholar
16. Huang, J., Wen, C., Wang, W. and Jiang, Z. P., “Adaptive output feedback tracking control of a nonholonomic mobile robot,” Automatica 50, 821–831 (2014).Google Scholar
17. Canudas, C. de Wit, H. Khennouf, C. Samson and Sordalen, O. J., “Nonlinear control design for mobile robots,” In: Recent Trends in Mobile Robots (Zheng, Y. F., ed.) (Singapore, World Scientific, 1993) pp. 121–156.Google Scholar
18. Oriolo, G., Luca, A. and Vandittelli, M., “WMR control via dynamic feedback linearization: Design, implementation, and experimental validationv,” IEEE Trans. Control Syst. Technol. 10, 835–852 (2002).Google Scholar
19. Keighobadi, J., Menhaj, M. B. and Kabganian, M., “Feedback-linearzation and fuzzy controllers for trajectory tracking of wheeled mobile robots,” Kybernetes 39, 83–106 (2010).Google Scholar
20. Xu, R. and Özgüner, Ü., “Sliding mode control of a class of underactuated systems,” Automatica 44, 233–241 (2008).Google Scholar
21. Morin, P. and Samson, C., “Application of backstepping techniques to time-varying exponential stabilization of chained systems,” Eur. J. Control 3 15–36 (1997).Google Scholar
22. Tamba, T. A., Hong, B. and Hong, K. S., “A path following control of an unmanned autonomous forklift,” Int. J. Control, Automat. Syst. 7, 113–122 (2009).Google Scholar
23. Canudas de Wit, C. and Sordalen, O. J., “Exponential stabilization of mobile robots with nonholonomic constraints,” IEEE Trans. Automat. Control 37, 1791–1797 (1992).Google Scholar
24. Marchand, N. and Alamir, M., “Discontinuous exponential stabilization of chained form systems,” Automatica 39, 343–348 (2003).Google Scholar
25. Scaglia, G., Rosales, A., Quintero, L., Mut, V. and Agarwal, R., “A linearinterpolation-based controller design for trajectory tracking of mobile robots,” Control Eng. Practice 18, 318–329 (2010).Google Scholar
26. Shojaei, Kh., “Neural adaptive output feedback formation control of type (m, s) wheeled mobile robots,” IET Control Theory Appl. 21, 504–515 (2016). DOI: 10.1049/iet-cta.2016.0952Google Scholar
27. Chwa, D., “Fuzzy adaptive tracking control of wheeled mobile robots with state-dependent kinematic and dynamic disturbances,” IEEE Trans. Fuzzy Syst. 20, 587–593 (2012).Google Scholar
28. Shojaei, K., Shahri, A. R. M, and Tarakameh, A. R., “Adaptive feedback linearizing control of nonholonomic wheeled mobile robots in presence of parametric and nonparametric uncertainties,” Robot. Comput.- Integr. Manuf. 27, 149–204 (2011).Google Scholar
29. Shojaei, K. and Shahri, A. M., “Output feedback tracking control of uncertain non-holonomic wheeled mobile robots: A dynamic surface control approach,” IET Control Theory & Appl. 6, 216–228 (2012).Google Scholar
30. Defoort, M., Floquet, T., Kokosy, A. and Perruquetti, W., “Integral sliding mode control for trajectory tracking of a unicycle type mobile robot,” Integr. Comput.-Aided Eng. 13, 277–288 (2006).Google Scholar
31. Zdešar, A., Škrjanc, I. and Klančar, G., “Visual trajectory-tracking model-based control for mobile robots,” Int. J. Adv. Robot. Syst. 10, 1–13 (2013).Google Scholar
32. Xin, L., Wang, Q., She, J. and Li, Y., “Robust adaptive tracking control of wheeled mobile robot,” Robot. Autonomous Syst. 78, 36–48 (2016).Google Scholar
33. Keymasi Khalaji, A., Ali, S. and Moosavian, A., “Dynamic modeling and tracking control of a car with n trailers,” J. Multi-body Syst. Dyn. 37, 211–225 (2016).Google Scholar
34. Chwa, D., “Sliding-mode tracking control of nonholonomic wheeled mobile robots in polar coordinates,” IEEE Trans. Control Syst. Technol. 12, 637–644 (2004).Google Scholar
35. Keymasi Khalaji, A., Ali, S. and Moosavian, A., “Adaptive sliding mode control of a wheeled mobile robot towing a trailer,” Proc. Institut. Mech. Eng., I: J. Syst. Control Eng. 229, 169–183 (2015).Google Scholar
36. Azizi, M. R. and Keighobadi, J., “Robust sliding mode trajectory tracking controller for a nonholonomic spherical mobile robot,” IFAC Proc. Vol. 47, 4541–4546 (2014).Google Scholar
37. Park, B. S., Yoo, S. J., Park, J. B. and Choi, Y. H., “A simple adaptive control approach for trajectory tracking of electrically driven nonholonomic mobile robots,” IEEE Trans. Control Syst. Technol. 18, 1199–1206 (2010).Google Scholar
38. Rashid, R., Elamvazuthi, I., Begam, M. and Arrofiq, M., “Fuzzy based navigation and control of a non-holonomic mobile robot,” J. Comput. 2, 130–137 (2010).Google Scholar
39. Tzafestas, S. G., Deliparaschos, K. M. and Moustris, G. P., “Fuzzy logic path tracking control for autonomous non-holonomic mobile robots: Design of system on a chip,” Robot. Autonomous Syst. 58, 1017–1027 (2010).Google Scholar
40. Keighobadi, J. and Menhaj, M. B., “From nonlinear to fuzzy approaches in trajectory tracking control of wheeled mobile robots,” Asian J. Control 14, 960–973 (2012).Google Scholar
41. Gu, D. and Hu, H., “Neural predictive control for a car-like mobile robot,” Int. J. Robot. Autonomous Syst. 39, 73–86 (2002).Google Scholar
42. Azizi, M. R. and Keighobadi, J., “Point stabilization of nonholonomic spherical mobile robot using nonlinear model predictive control,” Robot. Autonomous Syst. 98, 347–359 (2017).Google Scholar
43. Lu, P., “Optimal predictive control of continuous nonlinear system,” Int. J. Control 62, 633–649 (1995).Google Scholar
44. Mirzaeinejad, H. and Mirzaei, M., “A novel method for non-linear control of wheel slip in anti-lock braking systems,” Control Eng. Practice 18, 918–926 (2010).Google Scholar
45. Mirzaeinejad, H. and Mirzaei, M., “A new approach for modelling and control of two-wheel anti-lock brake systems,” Proc. Institut. Mech. Eng., Part K: J. Multi-body Dyn. 225, 179–192 (2011).Google Scholar
46. Mirzaeinejad, H., Mirzaei, M. and Kazemi, R., “Enhancement of vehicle braking performance on split-k roads using optimal integrated control of steering and braking systems,” Proc. Institution Mech. Eng., Part K: J Multi-body Dynamics. 230, 401–415 (2016).Google Scholar
47. Mirzaei, M. and Mirzaeinejad, H., “Fuzzy scheduled optimal control of integrated vehicle braking and steering systems,” IEEE/ASME Trans. Mechatron. 22, 2369–2379 (2017).Google Scholar
48. Slotine, J. J. E. and Li, W., Applied Nonlinear Control (Englewood Cliffs, Prentice-Hall, New Jersey, 1991).Google Scholar
49. Chen, W. H., Ballance, D. J. and Gawthrop, P. J., “Optimal control of nonlinear systems: A predictive control approach,” Automatica 39, 633–641 (2003).Google Scholar
50. Khalil, H., Nonlinear Systems, 2nd ed. (Prentice Hall, New Delhi, 1996).Google Scholar
51. Li, Y., Zhu, L., Wang, Z. and Liu, T., “Trajectory Tracking for Nonholonomic Wheeled Mobile Robots based on an Improved Sliding Mode Control Method,” Proceedings of the ISECS International Colloquium on Computing, Communication, Control, and Management (2009) pp. 55–58.Google Scholar
52. Vishnu Prasad, S. S., Pottakulath, V. and Ajmal, M. S., “Development of Backstepping Sliding Mode Tracking Control for Wheeled Mobile Robot,” Proceedings of the IEEE International Conference on Advanced Communication Control and Computing Technologies (ICACCCT) (2014) pp. 1013–1018.Google Scholar