Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T15:20:26.077Z Has data issue: false hasContentIssue false
  • English
  • Français

Motion planning for multiple non-holonomic robots: a geometric approach

Published online by Cambridge University Press:  01 July 2008

Elias K. Xidias  and
Nikos A. Aspragathos
Elias K. Xidias*
Affiliation:
Department of Mechanical and Aeronautics Engineering, University of Patras, Patras, 26500Greece
Nikos A. Aspragathos
Affiliation:
Department of Mechanical and Aeronautics Engineering, University of Patras, Patras, 26500Greece
*
*Corresponding author. E-mail: xidias@mech.upatras.gr
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, a geometrical approach is developed to generate simultaneously optimal (or near-optimal) smooth paths for a set of non-holonomic robots, moving only forward in a 2D environment cluttered with static and moving obstacles. The robots environment is represented by a 3D geometric entity called Bump-Surface, which is embedded in a 4D Euclidean space. The multi-motion planning problem (MMPP) is resolved by simultaneously finding the paths for the set of robots represented by monoparametric smooth C2 curves onto the Bump-Surface, such that their inverse images onto the initial 2D workspace satisfy the optimization motion-planning criteria and constraints. The MMPP is expressed as an optimization problem, which is solved on the Bump-Surface using a genetic algorithm. The performance of the proposed approach is tested through a considerable number of simulated 2D dynamic environments with car-like robots.

Keywords

Multi-motion planningDynamic environmentNon-holonomic robotsOptimal pathsConstraintsBump-Surfaces
Type
Article
Information
Robotica , Volume 26 , Special Issue 4: Geometry in Robotics: Sensing , July 2008 , pp. 525 - 536
Copyright
Copyright © Cambridge University Press 2007

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.Latombe, J. C., Robot Motion Planning (Kluwer Academic, Boston, MA 1991).CrossRefGoogle Scholar
2.Kolmanovsky, I. and Mc Clamroch, N. H., “Developments in nonholonomic control problems,” IEEE Control Sys., 20–36 (1995).Google Scholar
3.Zelinsky, A. and Dowson, I., “Continuous Smooth Path Execution for an Autonomous Guided Vehicle.” Proceedings of the IEEE Region 10 Conf. (1992), pp. 871–875.Google Scholar
4.Aydin, S. and Temeltas, H., “A novel approach to smooth trajectory planning of a mobile robot,” IEEE AMC, 472–477 (2002).Google Scholar
5.Dubins, L. E., “On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents,” Am. J. Math., 497–516 (1957).Google Scholar
6.Reeds, J. A. and Shepp, L. A., “Optimal paths for a car that goes both forwards and backwards,” Pacific J. Math., 367–393 (1990).Google Scholar
7.Souères, P. and Laumond, J. P., “Shortest paths synthesis for a car-like robot,” IEEE Trans. Automat. Contr., 672–688 (1996).Google Scholar
8.Lamiraux, F. and Laumond, J. P., “Smooth motion planning for car-like vehicles,” IEEE Trans. Robot Auto., 498–502 (2001).Google Scholar
9.Fleury, S., Soueres, P., Laumond, J. P. and Chatila, R., “Primitives for smoothing mobile robot trajectories,” IEEE Trans. Robot. Autom., 441–448 (1995).Google Scholar
10.Nagatani, K., Iwai, Y. and Tanaka, Y., “Sensor based navigation for car-like mobile robots using generalized voronoi graph,” IEEE/RSJ IROS, 1017–1022 (2001).Google Scholar
11.Leven, P. and Hutchinson, S., “A framework for real-time path planning in changing environments,” Int. J. Robot Res., 999–1030 (2002).Google Scholar
12.La Valle, M. S., Planning Algorithms (University of Illinois, IL, 2004).Google Scholar
13.Perez, L., “Spatial planning: A configuration space approach,” IEEE Trans. Comput., 108–120 (1983).Google Scholar
14.Barraquand, J., Langlois, B. and Latombe, J., “Numerical potential field techniques for robot path planning,” IEEE Trans. Syst., Man Cybern., 1012–1017 (1992).Google Scholar
15.Egerstedt, M. and Hu, X., “Formation Constrained Multi-Agent Control,” Proceedings of the IEEE Conference on Robotics and Automation, Seoul, Korea (May 2001), pp. 3961–3966.Google Scholar
16.Kavraki, L. E., Svestka, P., Latombe, J. C. and Mark, H. Overmars, “Probabilistic roadmaps for path planning in high-dimensional configuration spaces,” IEEE Trans. Robot Automat., 566–580 (1996).Google Scholar
17.Sánchez, G. and Latombe, J. C., “On delaying collision checking in PRM planning: Application to multi-robot coordination,” Int. J. Robot. Res., 5–26 (2002).Google Scholar
18.Hsu, D., Randomized, Single-Query Motion Planning in Expansive Spaces Ph.D. Thesis (Stanford, CA: Computer Science Department, Stanford University, May 2000).Google Scholar
19.Alami, R., Robert, F., Ingrand, F. and Suzuki, S., “Multi-Robot Cooperation Through Incremental Plan-Merging,” Proceedings of The IEEE International Conference on Robotics and Automation, (1995), pp. 2573–2678.Google Scholar
20.Erdmann, M. and Lozano-Perez, T., “On Multiple Moving Objects,” Proceedings of the IEEE International Conference on Robotics and Automation (1986), pp. 1419–1424.Google Scholar
21.Bennewitz, M., Burgard, W. and Thrun, S., “Optimizing Schedules for Prioritized Path Planning of Multi-Robot Systems,” Proceedings of the International Conference on Robotics and Automation (2001), pp. 271–276.Google Scholar
22.Kreher, D. L. and Stinson, D. R., Combinatorial Algorithms: Generation, Enumeration and Search (CRC press, Boca Raton, FL, 1998).Google Scholar
23.Guo, Y. and Parker, L. E., “A Distributed and Optimal Motion Planning Approach for Multiple Mobile Robots,” Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC (2002), pp. 2612–2619.Google Scholar
24.Clark, C. M., Rockand, S. M. and Latombe, J. C., “Motion Planning for Mobile Robots Using Dynamic Networks,” Proceedings of the IEEE International Conference on Robotics and Automation (2003), pp. 4222–4227.Google Scholar
25.Li, T. Y. and Chou, H. C., “Motion Planning for a Crowd of Robots,” Proceedings of the IEEE International Conference on Robotics and Automation (2003), pp. 4215–4221.Google Scholar
26.Azariadis, P. and Aspragathos, N., “Obstacle representation by Bump-Surface for optimal motion-planning,” J. Robot Auton. Syst., 129–150 (2005).Google Scholar
27.Xidias, E. K., Azariadis, P. N. and Aspragathos, N. A., “Energy-minimizing motion design for nonholonomic robots amidst moving obstacles,” J. Comput Aided Des. Appl., 165–174 (2006).Google Scholar
28.Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning (Addison Wesley, Reading, MA, 1989).Google Scholar
29.Piegl, L. and Tiller, W., The NURBS Book (Springer-Verlag, Berlin, Heidelberg, 1997).CrossRefGoogle Scholar
30.Garey, M. R. and Johnson, D. S., Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, CA, 1979).Google Scholar
31.Reif, J. and Wang, H., “The Complexity of the Two Dimensional Curvature Constrained Shortest-Path Problem”, Proceedings of the Third Workshop on the Algorithmic Foundations of Robotics on Robotics: The Algorithmic Perspective, Houston, Texas (1998), pp. 49–57.Google Scholar
32.Xidias, E. K., Nearchou, A. C. and Aspragathos, N. A., “Single vehicle routing in reconfigurable manufacturing environments using the Bump-Surface concept”, Proceedings of the 2007 I*PROMS NoE Virtual International Conference on Intelligent Production Machines and Systems.Google Scholar
33.Xidias, E. K., Zacharia, P. Th. and Aspragathos, N. A., “Task Scheduling with Obstacle Avoidance for Industrial Manipulators Operating in 3D Environments,” Proceedings of the 2007 I*PROMS NoE Virtual International Conference on Intelligent Production Machines and Systems.Google Scholar
34.Xidias, E. K. and Aspragathos, N. A., “Path Planning in Weighted Regions Using the Bump-Surface Concept,” Proceedings of the 2006 I*PROMS NoE Virtual International Conference on Intelligent Production Machines and Systems, pp. 590–595.Google Scholar
35.Song, G. and Amato, N. M., “Randomized Motion Planning for Car-Like Robots with C-PRM,” Proceedings of the International Conference on Intelligent Robots and Systems (IROS), Hawaii (2001), pp. 37–42.Google Scholar
36.Xidias, E. and Aspragathos, N., “Bump-Hypersurfaces for Optimal Motion Planning in 3D Spaces,” Proceedings of the International Workshop on Robotics in Alpe-Adria-Danube Region Brno (2004), pp. 172–177.Google Scholar
37.Bishop, R. and Goldberg, S., Tensor Analysis on Manifolds (Dover, New York, 1980).Google Scholar
38.Preparata, F. P. and Shamos, M. I., Computational Geometry (Springer-Verlag, New York, 1985).CrossRefGoogle Scholar
39.Cooper, L. and Steinberg, D., Introduction to Methods of Optimization (Saunders, Philadelphia, PA, 1970).Google Scholar