Abstract
For path planning, an optimal path is defined both by its length and by its clearance from obstacles. Many motion planning techniques such as the roadmap method, the cell decomposition method, and the potential field method generate low quality paths with redundant motions which are post-processed to generate high quality approximations of the optimal path. In this paper, we present a O(h 2(logn + k)) algorithm to optimize a path between a source and a destination in a plane based on a preset clearance from obstacles and overall length, where h is a multiple of the number of vertices on the given path, n is a multiple of the number of obstacle vertices, and k is the average number of obstacle edges against which the clearance check is done for each of the O(h 2) queries to determine whether a potential edge of the path is collision-free. This improves the running time of the geometric algorithm presented by Bhattacharya and Gavrilova (2007) which already generates a high quality approximation of the optimal path.
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References
Berglund, T., Erikson, U., Jonsson, H., Mrozek, K., Söderkvist, I.: Automatic Generation of Smooth Paths Bounded by Polygonal Chains. In: International Conference on Computational Intelligence for Modeling Control and Automation (2001)
Lamireaux, F., Bonnafous, D., Geem, C.V.: Path Optimization for Nonholonomic Systems: Application to Reactive Obstacle Avoidance and Path Planning. In: Workshop on Control Problems in Robotics and Automation, pp. 1–18 (2002)
Lamiraux, F., Laumond, J.P.: Smooth Motion Planning for Car-like Vehicles. IEEE Transactions on Robotics and Automation 17(4), 188–208 (2001)
Yamamoto, M., Iwamura, M., Mohri, A.: Quasi-Time-Optimal Motion Planning of Mobile Platforms in the Presence of Obstacles. In: IEEE International Conference on Robotics and Automation, pp. 2958–2963. IEEE Computer Society Press, Los Alamitos (1999)
Song, G., Amato, N.: Randomized Motion Planning for Car-like Robots with C-PRM. In: IEEE International Conference on Intelligent Robots and Systems, IEEE Computer Society Press, Los Alamitos (2001)
Baginski, B.: Efficient Motion Planning in High Dimensional Spaces: The Parallelized Z3-Method. In: International Workshop on Robotics in the Alpe-Adria-Danube Region, pp. 247–252 (1997)
Baginski, B.: Motion Planning for Manipulators with Many Degrees of Freedom - The BB-Method. Ph.D. dissertation, Technische Universität München (1998)
Bohlin, R.: Motion Planning for Industrial Robots. Ph.D. dissertation, Göteborg University (1999)
Hsu, D., Latombe, J.C., Sorkin, S.: Placing a Robot Manipulator amid Obstacles for Optimized Execution. In: IEEE International Symposium on Assembly and Task, pp. 280–285. IEEE Computer Society Press, Los Alamitos (1999)
Geem, C., Simeon, T., Laumond, J.P., Bouchet, J.L., Rit, J.F.: Mobility Analysis for Feasibility Studies in CAD Models of Industrial Environments. In: IEEE International Conference on Robotics and Automation, pp. 1770–1775. IEEE Computer Society Press, Los Alamitos (1999)
Nieuwenhuisen, D., Overmars, M.: Motion Planning for Camera Movements. Utrecht University, Technical Report 2003-004 (2003)
Song, G., Amato, N.: Using Motion Planning to Study Protein Folding Pathways. Journal of Computational Biology 9(2), 149–168 (2002)
Kuffner, J., Nishiwaki, K., Kagami, S., Inaba, M., Inoue, H.: Motion Planning for Humanoid Robots Under Obstacle and Dynamic Balance Constraints. In: IEEE International Conference on Robotics and Automation, pp. 692–698. IEEE Computer Society Press, Los Alamitos (2001)
Geraerts, R., Overmars, M.H.: Clearance Based Path Optimization for Motion Planning. In: IEEE International Conference on Robotics and Automation, vol. 3, pp. 2386–2392. IEEE Computer Soceity Press, Los Alamitos (2004)
Bhattacharya, P.: Optimal Path Planning using Spatial Neighborhood Properties. M.Sc. Thesis, University of Calgary, Canada (2007)
Bhattacharya, P., Gavrilova, M.L.: Voronoi Diagram in Optimal Path Planning. In: 4th International Symposium on Voronoi Diagrams in Science and Engineering, IEEE Computer Society Press, Los Alamitos (2007)
Amato, N., Wu, Y.: A Randomized Roadmap Method For Path And Manipulation Planning. In: IEEE International Conference on Robotics and Automation, pp. 113–120. IEEE Computer Society Press, Los Alamitos (1996)
Ibarra-Zannatha, J.M., Sossa-Azuela, J.H., Gonzalez-Hernandez, H.: A New Roadmap Approach to Automatic Path Planning for Mobile Robot Navigation. In: IEEE International Conference on Systems, Man, and Cybernetics, Humans, Information and Technology, vol. 3, pp. 2803–2808 (1994)
Nolborio, H., Naniwa, T., Arimoto, S.: A Quadtree-Based Path-Planning Algorithm for a Mobile Robot. Journal of Robotic Systems 7(4), 555–574 (1990)
Chen, D.Z., Szczerba, R.J., Uhran, Jr., J.J: A Framed-Quadtree Approach for Determining Euclidean Shortest Paths in a 2-D Environment. IEEE Transactions on Robotics and Automation 13(5) (1997)
Koren, Y., Borenstein, J.: Potential Field Methods and their Inherent Limitations for Mobile Robot Navigation. In: Proceedings of the IEEE Conference on Robotics and Automation, pp. 1398–1404. IEEE Computer Society Press, Los Alamitos (1991)
Warren, C.W.: Global Path Planning using Artificial Potential Fields. In: Proceedings of IEEE Conference on Robotics and Automation, pp. 316–321. IEEE Computer Society Press, Los Alamitos (1989)
Masehian, E., Amin-Naseri, M.R.: A Voronoi Diagram - Visibility Graph - Potential Field Compound Algorithm for Robot Path Planning. Journal of Robotic Systems 21(6) (2004)
Yang, D.H., Hong, S.K.: A Roadmap Construction Algorithm for Mobile Robot Path Planning using Skeleton Maps. Journal of Advanced Robotics 21(1), 51–63 (2007)
Wein, R., van den Berg, J.P., Halperin, D.: The Visibility-Voronoi Complex and its Applications. In: Proceedings of the 21st Annual Symposium on Computational geometry, pp. 63–72 (2005)
Kim, J., Pearce, R.A., Amato, N.M.: Extracting Optimal Paths from Roadmaps for Motion Planning. In: IEEE International Conference on Robotics & Automation, pp. 2424–2429. IEEE Computer Society Press, Los Alamitos (2003)
Chen, P., Hwang, Y.: SANDROS: A Dynamic Graph Search Algorithm for Motion Planning. IEEE Transactions on Robotics and Automation 14(3), 390–403 (1998)
Kavraki, L., Latombe, J.C.: Probabilistic Roadmaps for Robot Path Planning. In: Gupta, K., del Pobil, A. (eds.) Practical Motion Planning in Robotics: Current Approaches and Future Directions, pp. 33–53. John Wiley, New York, NY (1998)
Švestka, P.: Robot Motion Planning using Probabilistic Road Maps. Ph.D. dissertation, Utrecht University (1997)
Sánchez, G., Latombe, J.-C.: On Delaying Collision Checking in PRM Planning – Application to Multi-Robot Coordination. International Journal of Robotics Research 21(1), 5–26 (2002)
Sekhavat, S., Švestka, P., Laumond, J.P, Overmars, M.: Multilevel Path Planning for Nonholonomic Robots using Semiholonomic Subsystems. International Journal of Robotics Research 17, 840–857 (1998)
Isto, P.: Constructing Probabilistic Roadmaps with Powerful Local Planning and Path Optimization. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2323–2328. IEEE Computer Society Press, Los Alamitos (2002)
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Hasan, M., Gavrilova, M.L., Rokne, J.G. (2007). A Geometric Approach to Clearance Based Path Optimization. In: Gervasi, O., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2007. ICCSA 2007. Lecture Notes in Computer Science, vol 4705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74472-6_11
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DOI: https://doi.org/10.1007/978-3-540-74472-6_11
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