Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-16T12:19:30.875Z Has data issue: false hasContentIssue false
  • English
  • Français

Formation control and trajectory tracking of mobile robotic systems – a Linear Algebra approach

Published online by Cambridge University Press:  05 May 2010

Andrés Rosales ,
Gustavo Scaglia ,
Vicente Mut  and
Fernando di Sciascio
Andrés Rosales*
Affiliation:
Instituto de Automática (INAUT). Universidad Nacional de San Juan, Av. Libertador San Martín 1109 (oeste) – J5400ARL, San Juan, Argentina
Gustavo Scaglia
Affiliation:
Instituto de Automática (INAUT). Universidad Nacional de San Juan, Av. Libertador San Martín 1109 (oeste) – J5400ARL, San Juan, Argentina
Vicente Mut
Affiliation:
Instituto de Automática (INAUT). Universidad Nacional de San Juan, Av. Libertador San Martín 1109 (oeste) – J5400ARL, San Juan, Argentina
Fernando di Sciascio
Affiliation:
Instituto de Automática (INAUT). Universidad Nacional de San Juan, Av. Libertador San Martín 1109 (oeste) – J5400ARL, San Juan, Argentina
*
*Corresponding author. E-mail: androsaco@gmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

A novel approach for trajectory tracking of a mobile-robots formation by using linear algebra theory and numerical methods is presented in this paper. The formation controller design is based on the formation states concept and the dynamic model of a unicycle-like nonholonomic mobile robot. The proposed control law designed is decentralized and scalable. Simulations and experimental results confirm the feasibility and the effectiveness of the proposed controller and the advantages of using the dynamic model of the mobile robot. By using this new strategy, the formation of mobile robots is able to change its configuration (shape and size) and follow different trajectories in a precise way, minimizing the tracking and formation errors.

Keywords

Dynamic modelFormation statesLinear algebraMulti-robot systemNumerical methodsTrajectory tracking
Type
Article
Information
Robotica , Volume 29 , Issue 3 , May 2011 , pp. 335 - 349
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.Antonelli, G. and Chiaverini, S., “Kinematic Control of a Platoon of Autonomous Vehicles,” IEEE International Conference on Robotics and Automation, Taipei, Taiwan (Sep. 2003) pp. 1464–1469.Google Scholar
2.Balch, T. and Arkin, R., “Behavior-based formation control for multi-robot teams,” IEEE Trans. Rob. Autom. 14, 926–939 (1998).CrossRefGoogle Scholar
3.Balch, T. and Hybinette, M., “Social Potentials for Scalable Multi-Robot Formations,” IEEE International Conference on Robotics and Automation, San Francisco, CA (April 2000) pp. 73–80.Google Scholar
4.Belta, C. and Kumar, V., “Trajectory Design for Formations of Robots by Kinetic Energy Shaping,” IEEE International Conference Robotics and Automation, Washington, DC (May 2002) pp. 2593–2598.Google Scholar
5.Brooks, R. A., “A robust layered control system for a mobile robot,” IEEE J. Rob. Autom. 2 (1), 14–23 (1986).CrossRefGoogle Scholar
6.Carelli, R., Nasisi, O., Roberti, F. and Tosetti, S., “Direct Visual Tracking Control of Remote Cellular Robots,” 13th. International Symposium on Measurement and Control in Robotics – Towards Advanced Robots: Design, Sensors, Control, Applications – ISMCR, Madrid, España (Dec. 2003) pp. 11–12.Google Scholar
7.Chung, J. H., Yi, B. J., Kim, W. K. and Lee, H., “The Dynamic Modeling and Analysis for an Omnidirectional Mobile Robot With Three Caster Wheels,” Proceedings of IEEE International Conference on Robotics and Automation, Taipei, Taiwan (Sep. 2003) pp. 521–527.Google Scholar
8.Cowan, N., Shakerina, O., Vidal, R. and Sastry, S., “Vision-Based Follow-the-Leader,” Proc. IEEE/RSJ Int. Conf. Intell. Robot. Syst. 2, 1796–1801 (2003).Google Scholar
9.Das, A., Fierro, R., Kumar, V., Ostrowski, J., Spletzer, J. and Taylor, C., “A vision-based formation control framework,” IEEE Trans. Robot. Automat. 18, 813–825 (2002).CrossRefGoogle Scholar
10.De la Cruz, C. and Carelli, R., “Dynamic model based formation control and obstacle avoidance of multi-robot systems,” Robotica – Camb. 26 (3), 345–356 (2008).CrossRefGoogle Scholar
11.Del Rio, F., Jiménez, G., Sevillano, J., Amaya, C. and Balcells, A., “Error Adaptive Tracking for Mobile Robots,” Proceedings of the 28th Annual Conference IEEE Industrial Electronics Society, Sevilla, España (Nov. 2002) pp. 2415–2420.Google Scholar
12.Desai, J. P., Ostrowski, J. and Kumar, V., “Controlling Formations of Multiple Mobile Robots,” IEEE International Conference on Robotics and Automation (1998) pp. 2864–2869.Google Scholar
13.Dong, W. J., Guo, Y. and Farrell, J. A., “Formation Control of Nonholonomic Mobile Robots,” Proceedings of American Control Conference, Minneapolis, MN (2006), pp. 5602–5607.Google Scholar
14.Dongbing, G., “A differential game approach to formation control,” IEEE Trans. Cont. Syst. Technol. 16, 85–93 (2008).Google Scholar
15.Fierro, R., Song, P., Das, A. and Kumar, V., “Cooperative Control of Robot Formations,” InCooperative Control and Optimization, vol. 5 (Kluwer, The Nederlands, 2002) pp. 73–93.CrossRefGoogle Scholar
16.Fredslund, J. and Mataric, M. J., “Robot Formations Using Only Local Sensing and Control,” IEEE International Symposium on Computational Intelligence in Robotics and Automation (2001), pp. 308–313.Google Scholar
17.Fukao, T., Nakagawa, H. and Adachi, N., “Adaptive tracking control of a nonholonomic mobile robot,” IEEE Trans. Robot. Automat. 16, 609–615 (2000).CrossRefGoogle Scholar
18.Hentschel, M., Lecking, D. and Wagner, B., “Deterministic Path Planning and Navigation for an Autonomous Fork Lift Truck,” 6th IFAC Symposium on Intelligent Autonomous Vehicles – IAV (2007a).CrossRefGoogle Scholar
19.Hentschel, M., Wulf, O. and Wagner, B., “A hybrid feedback controller for car-like robots – combining reactive obstacle avoidance and global re-planning,” Integr. Comput.-Aided Eng. 14, 3–14 (2007b).CrossRefGoogle Scholar
20.Hwang, C. L. and Chang, L. J., “Trajectory tracking and obstacle avoidance of car-like mobile robots in an intelligent space using mixed H 2/H ∞ decentralized control,” IEEE Trans. Mechatron. 12 (3), 345–352 (2007).CrossRefGoogle Scholar
21.Lawton, J., Beard, R. and Young, B., “A decentralized approach to formation maneuvers,” IEEE Trans. Robot. Automat. 19, 933–941 (2003).CrossRefGoogle Scholar
22.Lee, S. and Park, J. H., “Virtual Trajectory in Tracking Control of Mobile Robots,” Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronic, AIM, Kobe, Japan (July 2003).Google Scholar
23.Monteiro, S., Vaz, M. and Bicho, E., “Attractor Dynamics Generates Robot Formations: From Theory to Implementation,” Proceedings of IEEE International Conference on Robotics and Automation, Barcelona, España (April 2004) pp. 2582–2587.Google Scholar
24.Naffin, D., Multi-Robot Formations: Rule-Based Synthesis and Stability Analysis Doctoral Thesis (University of Southern California, 2006).Google Scholar
25.Normey-Rico, J., Alcalá, I., Gomez-Ortega, J. and Camacho, E., “Mobile robot path tracking using PID controller,” Cont. Eng. Pract. 9 (11), 1209–1214 (2001).CrossRefGoogle Scholar
26.Normey-Rico, J., Gomez-Ortega, J. and Camacho, E., “A Smith-Predictor-based generalized predictive controller for mobile robot path-tracking,” Control Eng. Pract. 7 (6), 729–740 (1999).CrossRefGoogle Scholar
27.Ojeda, L. and Borenstein, J., “Reduction of Odometry Errors in Over-Constrained Mobile Robots,” Proceedings of the UGV Technology Conference at the SPIE AeroSense Symposium, Orlando, FL (April 2003) pp. 21–25.Google Scholar
28.Ren, W. and Beard, R. W., “A Decentralized Scheme for Spacecraft Formation Flying via the Cirtual Structure Approach,” Proceedings of the American Control Conference, Denver, CO (June 2003) pp. 1746–1751.Google Scholar
29.Rosales, A., Scaglia, G., Mut, V. and di Sciascio, F., “Controller Designed by Means of Numeric Methods for a Benchmark Problem: RTAC (Rotational Translational Actuator),” IEEE – Electronics, Robotics and Automotive Mechanics Conference, Cuernavaca, Mexico (Sep. 2006) pp. 97–104.CrossRefGoogle Scholar
30.Rosales, A., Scaglia, G., Mut, V. and di Sciascio, F., “Trajectory tracking of mobile robots in dynamic environments – A linear algebra approach,” Robot. 27, 981–997 (2009).CrossRefGoogle Scholar
31.Scaglia, G., Mut, V., Rosales, A. and Quintero, O., “Tracking Control of a Mobile Robot Using Linear Interpolation,” International Conference on Integrated Modeling & Analysis in Applied Control & Automation – IMAACA, Buenos Aires, Argentina (Jan. 2007).Google Scholar
32.Scaglia, G., Quintero, O., Mut, V. and di Sciascio, F., Numerical Methods Based Controller Design for Mobile Robots (Robotica – Cambridge University Press, Cambridge, UK, 2008a).CrossRefGoogle Scholar
33.Scaglia, G., Quintero, O., Mut, V. and di Sciascio, F., “Numerical Methods Based Controller Design for Mobile Robots,” IFAC World Congress, Korea (2008b).Google Scholar
34.Scharf, D. P., Hadaegh, F. Y. and Ploen, S. R., “A Survey of Space Formation Flying Guidance and Control (Part 2),” Proceedings of the American Control Conference, Boston, MA (Dec. 2004) pp. 1733–1739.Google Scholar
35.Strang, G., Linear Algebra and Its Applications, 3rd ed. (Academic Press MIT, New York, 1980).Google Scholar
36.Tan, K. H. and Lewis, M. A., “Virtual Structures for High-Precision Cooperative Mobile Robotic Control,” Int. Conf. Intell. Robot. Syst. 1, 132–139 (1996).Google Scholar
37.Wang, T. and Tsai, C., “Adaptive Trajectory Tracking Control of a Wheeled Mobile Robot via Lyapunov Techniques,” Annual Conference of IEEE Industrial Electronics Society, Busan, Korea (Nov. 2004) pp. 389–394.Google Scholar
38.Yamaguchi, H., Arai, T. and Beni, G., “A distributed control scheme for multiple robotic vehicles to make group formations,” Robot. Autonom. Syst. 36, 125–147 (2001).CrossRefGoogle Scholar
39.Yang, X., He, K., Guo, M. and Zhang, B., “An Intelligent Predictive Control Approach to Path Tracking Problem of Autonomous Mobile Robot,” IEEE International Conference on Robotics and Automation, Leuven, Belgium (May 1998) pp. 3301–3306.Google Scholar