Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T10:30:44.514Z Has data issue: false hasContentIssue false
  • English
  • Français

A linear optimal tracker designed for omnidirectional vehicle dynamics linearized based on kinematic equations

Published online by Cambridge University Press:  15 January 2010

Kuo-Yang Tu
Kuo-Yang Tu*
Affiliation:
Institute of System Information and Control, National Kaohsiung First University of Science and Technology, 2, Juoyue Rd., Nantsu, Kaohsiung 811, Taiwan, R. O. C.
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

It is difficult to design controllers for the complicated dynamics of omnidirectional vehicles steered by multiple wheels with distributed traction force. In this paper, the dynamic model of a three-wheel omnidirectional vehicle, which is linearized to simplify controller design, is developed. The conditions of making its dynamics linear are derived first. Then, a strategy of planning wheel velocities to satisfy these conditions is proposed. Consequently, three-wheel omnidirectional vehicle can be easily treated by classical linear control theories. Finally, a linear optimal tracker is designed to control the omnidirectional vehicle for desired movement trajectories. In particular, the dynamic model includes the motors installed in the three-wheel omnidirectional vehicle, making it a practical model. Three kinds of vehicle trajectories illustrate the planning of wheel trajectories for linearizing the vehicle dynamics, and simulations demonstrate the performance of the linear optimal tracker. In addition, experimental results of a practical three-wheel omnidirectional vehicle are also included.

Keywords

Omnidirectional vehiclesVehicle dynamicsVehicle controlKinematic constraintOptimal tracking controlTracking controlTrajectory planning
Type
Article
Information
Robotica , Volume 28 , Issue 7 , December 2010 , pp. 1033 - 1043
Copyright
Copyright © Cambridge University Press 2010

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.Balakrishna, R. and Ghosal, A., “Modeling of slip for wheeled mobile robots,” IEEE Trans. Robot. Autom. 11 (1), 126–132 (1995).CrossRefGoogle Scholar
2.Bétourné, A. and Campion, G., “Dynamic Modeling and Control Design of a Class of Omnidirectional Mobile Robots,” IEEE Int. Conf. on Robotics and Automation (1996) pp. 2810–2815.Google Scholar
3.Borenstein, J., Everett, H. R. and Feng, L., “Mobile robot positioning: Sensors and techniques,” J. Robot. Syst. 14, 231–249 (1997).3.0.CO;2-R>CrossRefGoogle Scholar
4.Canudas de Wit, C., “Trends in mobile robot and vehicle control,” Control Problems in Robotics and Automation 151–175 (1998).Google Scholar
5.D'Andrea, R., Kalmár-Nagy, T., Ganguly, P. and Babish, M., “The Cornell RoboCup Team,” In: Robot Soccer World Cup IV, Lecture Notes in Artificial Intelligence (Kraetzschmar, G., Stone, P. and Balch, T., eds.) vol. 2019, (Springer, Berlin, 2001), pp. 41–51.Google Scholar
6.D'Andréa-Novel, B., Bastin, G. and Campion, , “Modelling and Control of Non Holonomic Wheeled Mobile Robots,” IEEE Int. Conf. on Robotics and Automation (1991) pp. 1130–1135.Google Scholar
7.Faiz, N. and Agrawal, S. K., “Trajectory Planning of Robots with Dynamics and Inequalities,” IEEE Int. Conf. on Robotics and Automation (2000) pp. 3976–3982.Google Scholar
8.Ferrière, L., Campion, G. and Raucent, B., “POLLMOBS, a new drive system for omnimobile robots,” Robotica 19, 1–9 (2001).CrossRefGoogle Scholar
9.Fierro, R. and Lewis, F. L., “Control of a nonholonomic mobile robot: backstepping kinematics into dynamics,” J. Robot. Syst. 14 (3), 149–163 (1997).3.0.CO;2-R>CrossRefGoogle Scholar
10.Fraichard, T. and Scheuer, A., “From Reeds and Shepp's to continuous-curvature paths,” IEEE Trans. Robot. Autom. 20, 1025–1035 (2004).CrossRefGoogle Scholar
11.Frazzoli, E., Dahleh, M. A. and Feron, E., “Real-time motion planning for agile autonomous vehicles,” J. Guid. Control Dyn. 25 (1), 116–129 (2001).CrossRefGoogle Scholar
12.Fukao, T., Nakagawa, H. and Adachi, N., “Adaptive tracking control of a nonholonomic mobile robot,” IEEE Trans. Robot. Autom. 16 (5), 609–615 (2000).CrossRefGoogle Scholar
13.Gracia, L. and Tornero, J., “A new geometric approach to characterize the singularity of wheeled mobile robots,” Robotica 25, 627–638 (2007).CrossRefGoogle Scholar
14.Gracia, L. and Tornero, J., “Kinematic models and isotropy analysis of wheeled mobile robots,” Robotica 26, 587–599 (2008).CrossRefGoogle Scholar
15.Huang, H. C. and Tsai, C. C., “Simultaneous tracking and stabilization of an omnidirectional mobile robot in polar coordinates: a unified control approach,” Robotica 27, 1–12 (2008).Google Scholar
16.Jiang, Z.-P. and Nijmeijer, H., “Tracking control of mobile robots: a case study in backstepping,” Automatica 33 (7), 1393–1399 (1997).Google Scholar
17.Kalmár-Nagy, T., D'Andrea, R. and Ganguly, P., “Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle,” Robot. Auton. Syst. 46, 47–64 (2004).CrossRefGoogle Scholar
18.Lewis, F. L. and Syrmos, V. L., Optimal Control, ch. 42nd ed. (J. Wiley & Sons, 1995), Canada.Google Scholar
19.Li, Z., Chen, J. and Feng, J., “Design of an omni-directional mobile microrobot (OMMR-I) for a micro-factory with 2 mm electromagnetic micromotors,” Robotica 23, 45–49 (2005).CrossRefGoogle Scholar
20.Moore, K. L. and Flann, N. S.,, “A six-wheeled omnidirectional autonomous mobile robot,” IEEE Control Syst. Mag. 20 (6), 53–66 (2000).Google Scholar
21.Muñoz, V., Ollero, A., Prado, M. and Simón, A., “Mobile robot trajectory planning with dynamic and kinematic constraints,” Proc. of the IEEE Intern. Conf. on Robotics and Autom. 4, 2802–2807 (1994).Google Scholar
22.Pin, F. G. and Killough, S. M., “A new family of omnidirectional and holonomic wheeled platforms for mobile robot,” IEEE Trans. Robot. Autom. 19 (4), 480–489 (1994).CrossRefGoogle Scholar
23.Purwin, O. and D'Andrea, R., “Trajectory Generation for Four Wheeled Omnidirectional Vehicles,” Proceedings of American Control Conf. (2005) pp. 4979–4984.Google Scholar
24.Tsai, P.-S., Wang, L.-S., Chang, F.-R. and Wu, T.-F., “Systematic Backstepping Design for B-Spline Trajectory Tracking Control of the Mobile Robot in Hierarchical Model,” Proceedings of IEEE Int. Conf. on Networking, Sensing and Control (2004) pp. 713–718.Google Scholar
25.Williams, R. L. II, Carter, B. E., Gallina, P. and Rosati, G., “Dynamic model with slip for wheeled omnidirectional robots,” IEEE Trans. Robot. Autom. 18 (3), 185–293 (2002).CrossRefGoogle Scholar