In this paper, modified versions of quadtree/octree, as structures used in path planning, are proposed which we call them cornered quadtree/octree. Also a new method of creating paths in quadtrees/octrees, once quadrants/octants to be passed are determined, is proposed both to improve traveled distance and path smoothness. In proposed modified versions of quadtree/octree, four corner cells of quadrants and eight corner voxels of octants are also considered as nodes of the graph to be searched for finding the shortest path. This causes better quadrant/octant selection during graph search relative to simple quadtrees and octrees. On the other hand, after that all quadrants/octants are determined, multiple gateways are nominated between each two selected nodes and path is constructed by passing through the gateway which its selection leads in shorter and smoother path. Proposed structures in this paper alongside the utilized path construction approach, creates better paths in terms of path length than those created if simple trees are used, somehow equal to the quality of the achieved paths by framed trees, meanwhile interestingly, consumed time and memory in our proposed method are closer to the used time and memory if simple trees are used.
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Huang, H. M., Pavek, K., Novak, B., Albus, J., & Messin, E. (2005). A framework for autonomy levels for unmanned systems (ALFUS). In Proceedings of AUVSI Unmanned Systems 2005.
Pehlivanoglu, Y. V. (2012). A new vibrational genetic algorithm enhanced with a Voronoi diagram for path planning of autonomous UAV. Aerospace Science and Technology, 16(1), 47–55.
Yahja, A., Stentz, A., Singh, S., & Brumitt, B. L. (1998). Framed-quadtree path planning for mobile robots operating in sparse environments. In Proceedings of IEEE International Conference on Robotics and Automation, 1998. (Vol. 1, pp. 650–655). IEEE.
Finkel, R. A., & Bentley, J. L. (1974). Quad trees a data structure for retrieval on composite keys. Acta Informatica, 4(1), 1–9.
Meagher, D. J. (1980). Octree encoding: A new technique for the representation, manipulation and display of arbitrary 3-d objects by computer. Electrical and Systems Engineering Department Rensseiaer Polytechnic Institute Image Processing Laboratory.
Chen, D. Z., Szczerba, R. J., & Uhran, J. J. (1995). Using framed-octrees to find conditional shortest paths in an unknown 3-d environment. Informe Técnico, 95–9.
Chen, D. Z., Szczerba, R. J., & Uhran J. J. Jr. (1995). Using framed-quadtrees to find conditional shortest paths in an unknown 2-D environment (Vol. 95, No. 2). Technical Report.
Chen, D. Z., Szczerba, R. J., & Uhran J. J. Jr. (1995). Planning conditional shortest paths through an unknown environment: A framed-quadtree approach. In Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems 95. ‘Human Robot Interaction and Cooperative Robots, 1995 (Vol. 3, pp. 33–38). IEEE.
Latombe, J. C. (2012). Robot motion planning (Vol. 124). Berlin: Springer Science & Business Media.
Lozano-Pérez, T., & Wesley, M. A. (1979). An algorithm for planning collision-free paths among polyhedral obstacles. Communications of the ACM, 22(10), 560–570.
Goerzen, C., Kong, Z., & Mettler, B. (2010). A survey of motion planning algorithms from the perspective of autonomous UAV guidance. Journal of Intelligent and Robotic Systems, 57(1–4), 65–100.
Howlet, J. K., Schulein, G., & Mansur, M. H. (2004). A practical approach to obstacle field route planning for unmanned rotorcraft.
Yahja, A., Singh, S., & Stentz, A. (2000). An efficient on-line path planner for outdoor mobile robots. Robotics and Autonomous systems, 32(2), 129–143.
Ghosh, S., Halder, A., & Sinha, M. (2011). Micro air vehicle path planning in fuzzy quadtree framework. Applied Soft Computing, 11(8), 4859–4865.
Vörös, J. (2001). Low-cost implementation of distance maps for path planning using matrix quadtrees and octrees. Robotics and Computer-Integrated Manufacturing, 17(6), 447–459.
Vörös, J. (1998). Using extended quadtrees in robot path planning. In Proceedings of the Seventh Workshop on Robotics in Alpe-Adria-Danube Region, Smolenice (pp. 451–456).
Guanglei, Z., & Heming, J. (2013). 3D path planning of AUV based on improved ant colony optimization. In 32nd Chinese Control Conference (CCC), 2013 (pp. 5017–5022). IEEE.
Xu, S., Honegger, D., Pollefeys, M., & Heng, L. (2015). Real-time 3D navigation for autonomous vision-guided MAVs. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2015 (pp. 53–59). IEEE.
Zhang, Q., Ma, J., & Xie, W. (2012). A framed-quadtree based on reversed d* path planning approach for intelligent mobile robot. Journal of Computers, 7(2), 464–469.
Zhang, Q., Ma, J., & Liu, Q. (2012). Path planning based quadtree representation for mobile robot using hybrid-simulated annealing and ant colony optimization algorithm. In 10th World Congress on Intelligent Control and Automation (WCICA), 2012 (pp. 2537–2542). IEEE.
Colombo, A., Fontanelli, D., Legay, A., Palopoli, L., & Sedwards, S. (2015). Efficient customisable dynamic motion planning for assistive robots in complex human environments. Journal of Ambient Intelligence and Smart Environments, 7, 617–633.
Abbadi, A., & Přenosil, V. (2015). Safe path planning using cell decomposition approximation. Distance Learning, Simulation and Communication, 2015, 8.
Hernandez, J. D., Vidal, E., Vallicrosa, G., Galceran, E., & Carreras, M. (2015). Online path planning for autonomous underwater vehicles in unknown environments. In IEEE International Conference on Robotics and Automation (ICRA), 2015 (pp. 1152–1157). IEEE.
Hornung, A., Wurm, K. M., Bennewitz, M., Stachniss, C., & Burgard, W. (2013). OctoMap: An efficient probabilistic 3D mapping framework based on octrees. Autonomous Robots, 34(3), 189–206.
Omar, F. S., Islam, M. N., & Haron, H. (2015). Shortest path planning for single manipulator in 2D environment of deformable objects. Jurnal Teknologi, 75(2), 33–37.
Zelinsky, A. (1992). A mobile robot exploration algorithm. IEEE Transactions on Robotics and Automation, 8(6), 707–717.
De Berg, M., Van Kreveld, M., Overmars, M., & Schwarzkopf, O. C. (2000). Computational geometry (pp. 1–17). Berlin: Springer.
Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269–271.
Hart, P. E., Nilsson, N. J., & Raphael, B. (1968). A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics, 4(2), 100–107.
Namdari, M. H., Hejazi, S. R., & Palhang, M. (2015). MCPN, Octree Neighbor Finding During Tree Model Construction Using Parental Neighboring Rule. 3D. Research, 6(3), 1–15.
Stentz, A. (1994). Optimal and efficient path planning for partially-known environments. In IEEE International Conference on Robotics and Automation, 1994. Proceedings (pp. 3310–3317). IEEE.
Koenig, S., & Likhachev, M. (2005). Fast replanning for navigation in unknown terrain. IEEE Transactions on Robotics, 21(3), 354–363.
Daniel, K., Nash, A., Koenig, S., & Felner, A. (2010). Theta*: Any-angle path planning on grids. Journal of Artificial Intelligence Research, 39, 533–579.
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Namdari, M.H., Hejazi, S.R. & Palhang, M. Cornered Quadtrees/Octrees and Multiple Gateways Between Each Two Nodes; A Structure for Path Planning in 2D and 3D Environments. 3D Res 7, 14 (2016). https://doi.org/10.1007/s13319-016-0092-9
- Path planning
- 2D/3D environments