Skip to main content Accessibility help

Finding a High-Quality Initial Solution for the RRTs Algorithms in 2D Environments

  • Jiankun Wang (a1), Wenzheng Chi (a2), Mingjie Shao (a1) and Max Q.-H. Meng (a1)


In this paper, we propose a bioinspired path planning algorithm for finding a high-quality initial solution based on the pipeline of the Rapidly exploring Random Tree (RRT) method by modifying the sampling process. The modification mainly includes controlling the sampling space and using the probabilistic sampling with the two-dimensional Gaussian mixture model. Inspired by the tropism of plants, we use a Gaussian mixture model to imitate the tree’s growth in nature. In a 2D environment, we can get an approximate moving point’s probabilistic distribution, and the initial path can be found much quickly guided by the probabilistic heuristic. At the same time, only a small number of nodes are generated, which can reduce the memory usage. As a meta-algorithm, it can be applicable to other RRT methods and the performance of underlying algorithm is improved dramatically. We also prove that the probabilistic completeness and the asymptotic optimality depend on the original algorithm (other RRTs). We demonstrate the application of our algorithm in different simulated 2D environments. On these scenarios, our algorithm outperforms the RRT and the RRT* methods on finding the initial solution. When embedded into post-processing algorithms like the Informed RRT*, it also promotes the convergence speed and saves the memory usage.


Corresponding author

*Corresponding author. E-mail:


Hide All
1. Willms, A. R. and Yang, S. X., “An efficient dynamic system for real-time robot-path planning,” IEEE Trans. Syst. Man Cybern. B Cybern. 36(4), 755766 (2006).10.1109/TSMCB.2005.862724
2. Yang, J., Qu, Z., Wang, J. and Conrad, K., “Comparison of optimal solutions to real-time path planning for a mobile vehicle,” IEEE Trans. Syst. Man Cybern. A Syst. Hum. 40(4), 721731 (2010).10.1109/TSMCA.2010.2044038
3. Li, H., Yang, S. X. and Seto, M. L., “Neural-network-based path planning for a multirobot system with moving obstacles,” IEEE Trans. Syst. Man Cybern. C Appl. Rev. 39(4), 410419 (2009).10.1109/TSMCC.2009.2020789
4. Khatib, O., “Real-time obstacle avoidance for manipulators and mobile robots,” Int. J. Rob. Res. 5(1), 9098 (1986).10.1177/027836498600500106
5. Hart, P. E., Nilsson, N. J. and Raphael, B., “A formal basis for the heuristic determination of minimum cost paths,” IEEE Trans. Syst. Sci. Cybern. 4(2), 100107 (1968).10.1109/TSSC.1968.300136
6. Stentz, A., “Optimal and Efficient Path Planning for Partially-known Environments,” Proceedings of the IEEE International Conference on Robotics and Automation, 1994, IEEE, San Diego, CA, USA (1994) pp. 33103317.10.1109/ROBOT.1994.351061
7. LaValle, S. M. and Kuffner, J. J. Jr., “Randomized kinodynamic planning,” Int. J. Rob. Res. 20(5), 378400 (2001).10.1177/02783640122067453
8. Kavraki, L. E., Svestka, P., Latombe, J.-C. and Overmars, M. H., “Probabilistic roadmaps for path planning in high-dimensional configuration spaces,” IEEE Trans. Robot. Autom. 12(4), 566580 (1996).10.1109/70.508439
9. Urmson, C. and Simmons, R., “Approaches for Heuristically Biasing RRT Growth,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2003, IROS 2003, Las Vegas, NV, USA vol. 2, IEEE (2003) pp. 11781183.
10. Shkolnik, A., Walter, M. and Tedrake, R., “Reachability-guided Sampling for Planning Under Differential Constraints,” IEEE International Conference on Robotics and Automation, 2009, ICRA’09, IEEE, Kobe, Japan (2009) pp. 28592865.10.1109/ROBOT.2009.5152874
11. Wang, J., Li, X. and Meng, M. Q.-H., “An Improved RRT Algorithm Incorporating Obstacle Boundary Information,” Proceedings of the IEEE International Conference on Robotics and Biomimetics (ROBIO), IEEE, Qingdao, China (2016) pp. 625630.
12. Kiesel, S., Burns, E. and Ruml, W., “Abstraction-guided Sampling for Motion Planning,” Proceedings of the Fifth Annual Symposium on Combinatorial Search, SoCS, Ontario, Canada (2012).
13. Wedge, N. A. and Branicky, M. S., “On Heavy-tailed Runtimes and Restarts in Rapidly-exploring Random Trees,” Twenty-Third AAAI Conference on Artificial Intelligence, Chicago, IL, USA (2008) pp. 127133.
14. Gammell, J. D., Srinivasa, S. S. and Barfoot, T. D., “Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (IROS 2014), IEEE, Chicago, IL, USA (2014) pp. 29973004.
15. Geraerts, R. andOvermars, M. H., “Creating high-quality paths for motion planning,” Int. J. Rob. Res. 26(8), 845863 (2007).10.1177/0278364907079280
16. Brunner, M., Brüggemann, B. and Schulz, D., “Hierarchical Rough Terrain Motion Planning Using an Optimal Sampling-based Method,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), IEEE, Karlsruhe, Germany (2013) pp. 55395544.
17. Palmieri, L., Koenig, S. and Arras, K. O., “RRT-based Nonholonomic Motion Planning Using Any-angle Path Biasing,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), IEEE, Stockholm, Sweden (2016) pp. 27752781.
18. Raveh, B., Enosh, A. and Halperin, D., “A little more, a lot better: Improving path quality by a path-merging algorithm,” IEEE Trans. Rob. 27(2), 365371 (2011).10.1109/TRO.2010.2098622
19. Arslan, O. and Tsiotras, P., “Use of Relaxation Methods in Sampling-based Algorithms for Optimal Motion Planning,” IEEE International Conference on Robotics and Automation (ICRA), IEEE, Karlsruhe, Germany (2013) pp. 24212428.
20. Dorigo, M. and Gambardella, L. M., “Ant colony system: A cooperative learning approach to the traveling salesman problem,” IEEE Trans Evol Comput 1(1), 5366 (1997).10.1109/4235.585892
21. Grefenstette, J., Gopal, R., Rosmaita, B. and Van Gucht, D., “Genetic Algorithms for the Traveling Salesman Problem,” Proceedings of the first International Conference on Genetic Algorithms and their Applications Pittsburgh, PA, USA (1985) pp. 160168.
22. Ferrante, E., Turgut, A. E., Huepe, C., Stranieri, A., Pinciroli, C. andDorigo, M., “Self-organized flocking with a mobile robot swarm: A novel motion control method,” Adapt. Behav. 20(6), 460477 (2012).10.1177/1059712312462248
23. Güzel, M. S., Kara, M. and Beyazkılıç, M. S., “An adaptive framework for mobile robot navigation,” Adapt. Behav. 25(1), 3039 (2017).10.1177/1059712316685875
24. Dean, T., Basye, K. and Shewchuk, J., “Reinforcement Learning for Planning and Control,” In: Machine Learning Methods for Planning, Minton, S. (ed.) (Elsevier, San Francisco, CA, USA, 1993) pp. 6792.10.1016/B978-1-4832-0774-2.50008-1
25. Kretzschmar, H., Spies, M., Sprunk, C. and Burgard, W., “Socially compliant mobile robot navigation via inverse reinforcement learning,” Int. J. Rob. Res. 35(11), 12891307 (2016).10.1177/0278364915619772
26. Karaman, S. and Frazzoli, E., “Sampling-based algorithms for optimal motion planning,” Int. J. Rob. Res. 30(7), 846894 (2011).10.1177/0278364911406761
27. Janson, L., Schmerling, E., Clark, A. and Pavone, M., “Fast marching tree: A fast marching sampling-based method for optimal motion planning in many dimensions,” Int. J. Rob. Res. 34(7), 883921 (2015).10.1177/0278364915577958
28. Li, Y., Littlefield, Z. and Bekris, K. E., “Sparse Methods for Efficient Asymptotically Optimal Kinodynamic Planning,” In: Algorithmic Foundations of Robotics XI Akin, H. L., Amato, N. M., Isler, V., van der Stappen, A. F. (eds.) (Springer, Istanbul, Turkey, 2015) pp. 263282.
29. Salzman, O. and Halperin, D., “Asymptotically near-optimal RRT for fast, high-quality motion planning,” IEEE Trans. Rob. 32(3), 473483 (2016).10.1109/TRO.2016.2539377
30. Ferguson, D. and Stentz, A., “Anytime RRTs,” IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE, Beijing, China (2006) pp. 53695375.10.1109/IROS.2006.282100
31. Naderi, K., Rajamäki, J. and Hämäläinen, P., “RT-RRT*: A Real-time Path Planning Algorithm Based on RRT,” Proceedings of the 8th ACM SIGGRAPH Conference on Motion in Games, ACM, New York, NY, USA (2015), pp. 113118.10.1145/2822013.2822036
32. Kleinbort, M., Salzman, O. and Halperin, D., “Efficient High-quality Motion Planning by Fast All-pairs r-nearest-neighbors,” IEEE International Conference on Robotics and Automation (ICRA), IEEE, Seattle, WA, USA (2015) pp. 29852990.10.1109/ICRA.2015.7139608
33. LaValle, S. M., Planning Algorithms (Cambridge University Press, New York, NY, USA, 2006).10.1017/CBO9780511546877
34. Bialkowski, J., Karaman, S., Otte, M. and Frazzoli, E., “Efficient Collision Checking in Sampling-based Motion Planning,” In: Algorithmic Foundations of Robotics X (Springer, Boston, MA, USA, 2013) pp. 365380.10.1007/978-3-642-36279-8_22



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed