Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T13:37:35.077Z Has data issue: false hasContentIssue false
  • English
  • Français

Feedback control framework for car-like robots using the unicycle controllers

Published online by Cambridge University Press:  25 July 2011

Maciej Michałek  and
Krzysztof Kozłowski
Maciej Michałek*
Affiliation:
Chair of Control and Systems Engineering, Poznan University of Technology (PUT), Piotrowo 3A, 60-965 Poznań, Poland
Krzysztof Kozłowski
Affiliation:
Chair of Control and Systems Engineering, Poznan University of Technology (PUT), Piotrowo 3A, 60-965 Poznań, Poland
*
*Corresponding author. E-mail: maciej.michalek@put.poznan.pl
Get access Rights & Permissions [Opens in a new window]

Summary

The paper introduces a novel general feedback control framework, which allows applying the motion controllers originally dedicated for the unicycle model to the motion task realization for the car-like kinematics. The concept is formulated for two practically meaningful motorizations: with a front-wheel driven and with a rear-wheel driven. All the three possible steering angle domains for car-like robots—limited and unlimited ones—are treated. Description of the method is complemented by the formal stability analysis of the closed-loop error dynamics. The effectiveness of the method and its limitations have been illustrated by numerous simulations conducted for the three main control tasks, namely, for trajectory tracking, path following, and set-point regulation.

Keywords

Wheeled mobile robotsKinematicsFeedback control
Type
Articles
Information
Robotica , Volume 30 , Issue 4 , July 2012 , pp. 517 - 535
Copyright
Copyright © Cambridge University Press 2011

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.Aicardi, M., Casalino, G., Bicchi, A. and Balestrino, A., “Closed loop steering of unicycle-like vehicles via Lyapunov techniques,” IEEE Robot. Autom. Mag. 2, 27–35 (1995).CrossRefGoogle Scholar
2.Angeles, J., “An innovative drive for wheeled mobile robots,” IEEE/ASME Trans. Mechatronics 10 (1), 43–49. (2005).CrossRefGoogle Scholar
3.Astolfi, A., “Exponential Stabilization of a Car-like Vehicle,” Proceedings of the IEEE International Conference on Robotics and Automation, Nagoya, Aichi, Japan (1995) pp. 1391–1396.Google Scholar
4.Astolfi, A., “Exponential Stabilization of a Wheeled Mobile Robot via Discontinuous Control,” Proceedings of the Nonlinear Control System Design Symposium, Lake Tahoe, USA (1995) pp. 741–746.Google Scholar
5.Bhat, S. P. and Bernstein, D. S., “Finite-time stability of continuous autonomous systems,” SIAM J. Control Optim. 38 (3), 751–766 (2000).CrossRefGoogle Scholar
6.de Wit, C. Canudas, Khennouf, H., Samson, C. and Sordalen, O. J., “Nonlinear Control Design for Mobile Robots,” In: Recent Trends in Mobile Robots (Zheng, Y. F., ed.) (World Scientific, Singapore, 1993) vol. 11, chapter 5, pp. 121–156.Google Scholar
7.Cherubini, A., Chaumette, F. and Oriolo, G., “Visual servoing for path reaching with nonholonomic robots,” Robotica. Available on CJO 2011, doi: 10.1017/S0263574711000221.CrossRefGoogle Scholar
8.Corradini, M. L. and Orlando, G., “Control of mobile robots with uncertainties in the dynamical model: A discrete time sliding mode approach with experimental results,” Control Eng. Pract. 10, 23–34 (2002).CrossRefGoogle Scholar
9.d'Andrea Novel, B., Campion, G. and Bastin, G., “Control of nonholonomic wheeled mobile robots by state feedback linearization,” Int. J. Robot. Res. 14, 543–559 (1995).CrossRefGoogle Scholar
10.de Wit, C. Canudas, Siciliano, B. and Bastin, G., Theory of Robot Control (Springer-Verlag, New York, 1996).CrossRefGoogle Scholar
11.Dixon, W. E., Dawson, D. M., Zergeroglu, E. and Behal, A., Nonlinear Control of Wheeled Mobile Robots (Springer, London, 2001).Google Scholar
12.Gomez-Bravo, F., Cuesta, F. and Ollero, A., “Parallel and diagonal parking in nonholonomic autonomous vehicles,”. Eng. Appl. Artif. Intell. 14, 419–434 (2001).CrossRefGoogle Scholar
13.Gonzalez, R., Fiacchini, M., Alamo, T., Guzman, J. L. and Rodriguez, F., “Adaptive control for a mobile robot under slip conditions using an LMI-based approach,” Eur. J. Control 16 (2), 144–155 (2010).CrossRefGoogle Scholar
14.Khalil, H. K., Nonlinear Systems, 3rd ed. (Prentice-Hall, Upper Saddle River, New Jersey, 2002).Google Scholar
15.Kim, B. M. and Tsiotras, P., “Controllers for unicycle-type wheeled robots: theoretical results and experimental validation,” IEEE Trans. Robot. Autom. 18 (3), 294–307 (2002).Google Scholar
16.Lefeber, E. and Nijmeijer, H., “Adaptive Tracking Control of Nonholonomic Systems: An Example,” Proceedings of the 38th Conference on Decision and Control, Phoenix, USA (1999) pp. 2094–2099.Google Scholar
17.De Luca, A. and Oriolo, G., “Modeling and Control of Nonholonomic Mechanical Systems,” In: Kinematics and Dynamics of Multi-Body Systems (Angeles, J. and Kecskementhy, A., eds.) (Springer-Verlag, Wien, 1995) chapter 7, pp. 277–342.CrossRefGoogle Scholar
18.De Luca, A., Oriolo, G. and Samson, C., “Feedback Control of a Nonholonomic Car-Like Robot,” In: Robot Motion Planning and Control (Laumond, J. P., ed.) (Springer-Verlag, New York, Inc., 1998) chapter 4, pp. 170–253.Google Scholar
19.Michalek, M. and Kozlowski, K., “Vector-field-orientation feedback control method for a differentially driven vehicle,” IEEE Trans. Control Syst. Technol. 18 (1), 45–65 (2010).CrossRefGoogle Scholar
20.Morin, P. and Samson, C., “Trajectory Tracking for Non-Holonomic Vehicles: Overview and Case Study,” Proceedings of the 4th International Workshop On Robot Motion and Control, Puszczykowo, Poland (2004) pp. 139–153.Google Scholar
21.Morin, P. and Samson, C., “Trajectory Tracking for Nonholonomic Vehicles,” In: Robot Motion and Control. Recent Developments, Lecture Notes in Control and Information Sciences (Springer, 2006) vol. 335, pp. 3–23.CrossRefGoogle Scholar
22.Morin, P. and Samson, C., “Motion Control of Wheeled Mobile Robots,” In: Springer Handbook of Robotics (Siciliano, B. and Khatib, O., eds.) (Springer, 2008) pp. 799–826.CrossRefGoogle Scholar
23.Morin, P. and Samson, C., “Control of nonholonomic mobile robots based on the transverse function approach,” IEEE Trans. Robot. 25 (5), 1058–1073 (2009).CrossRefGoogle Scholar
24.Oriolo, G., De Luca, A. and Venditteli, M., “WMR control via dynamic feedback linearization: Design, implementation and experimental validation,” IEEE Trans. Control Syst. Technol. 10, 835–852 (2002).CrossRefGoogle Scholar
25.Pomet, J. B., “Explicit design of time varying stabilization control laws for a class of controllable systems without drifts,” Syst. Control Lett. 18, 147–158 (1992).CrossRefGoogle Scholar
26.Rosales, A., Scaglia, G., Mut, V. and di Sciascio, F., “Trajectory tracking of mobile robots in dynamic environments—A linear algebra approach,” Robotica 27, 981–997 (2009).CrossRefGoogle Scholar
27.Samson, C., “Path Following and Time-varying Feedback Stabilization of a Wheeled Mobile Robot,” Proceedings of the International Conference (ICARCV '92), Singapur (1992) pp. 13.1.1–13.1.5.Google Scholar
28.Samson, C., “Time-varying feedback stabilization of car-like wheeled mobile robots,” Int. J. Robot. Res. 12, 55–64 (1993).CrossRefGoogle Scholar
29.Samson, C., “Control of chained systems; application to path following and time-varying point-stabilization of mobile robots,” IEEE Trans. Autom. Control 40, 64–77 (1995).CrossRefGoogle Scholar
30.Siegwart, R. and Nourbakhsh, I. R., Introduction to Autonomous Mobile Robots (The MIT Press, 2004).Google Scholar
31.Sørdalen, O. J. and Egeland, O., “Exponential stabilization of nonholonomic chained systems,” IEEE Trans. Autom. Control 40 (1), 35–49 (1995).CrossRefGoogle Scholar
32.Sordalen, O. J. and de Wit, C. Canudas, “Exponential control law for a mobile robot: Extention to path following,” IEEE Trans. Robot. Autom. 9 (6), 837–842 (1993).CrossRefGoogle Scholar
33.Teimoori, H. and Savkin, A. V., “A biologically inspired method for robot navigation in a cluttered environment,” Robotica 28, 637–648 (2010).CrossRefGoogle Scholar
34.Toibero, J. M.Roberti, F. and Carelli, R., “Stable contour-following control of wheeled mobile robots” Robotica 27, 1–12 (2009).CrossRefGoogle Scholar
35.Wang, D. and Xu, G. “Full-state tracking and internal dynamics of nonholonomic wheeled mobile robots,” IEEE Trans. Mechatronics 8 (2), 203–214 (2003).CrossRefGoogle Scholar
36.Werling, M. and Gröll, L., “Low-Level Controllers Realizing high-Level Decisions in an Autonomous Vehicle,” Proceedings of the 2008 IEEE Intelligent Vehicles Symposium, Eindhoven, The Netherlands (2008) pp. 1113–1118.CrossRefGoogle Scholar
37.Werling, M., Gröll, L. and Bretthauer, G., “Invariant trajectory tracking with a full-size autonomous road vehicle,” IEEE Trans. Robot. 26 (4), 758–765 (2010).CrossRefGoogle Scholar
38.Yi, J., Song, D., Levandowski, A. and Jayasuriya, S., “Trajectory Tracking and Balance Stabilization Control of Autonomous Motorcycles,” Proceedings of the 2006 IEEE International Conference on Robotics and Automation, Orlando, USA (2006) pp. 2583–2588.Google Scholar