A framed-quadtree approach for determining Euclidean shortest paths in a 2-D environment

In this paper we investigate the problem of finding a Euclidean (L/sub 2/) shortest path between two distinct locations in a planar environment. We propose a novel cell decomposition approach which calculates an L/sub 2/ distance transform through the use of a circular path-planning wave. The proposed method is based on a new data structure, called the framed-quadtree, which combines together the accuracy of high resolution grid-based path planning techniques with the efficiency of quadtree-based techniques, hence having the advantages of both. The heart of this method is a linear time algorithm for computing certain special dynamic Voronoi diagrams. The proposed method does not place any unrealistic constraints on obstacles or on the environment and represents an improvement in accuracy and efficiency over traditional path planning approaches in this area.

[1]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[2]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[3]  Hanan Samet,et al.  Neighbor finding techniques for images represented by quadtrees , 1982, Comput. Graph. Image Process..

[4]  J. Schwartz,et al.  On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers , 1983 .

[5]  G. Borgefors.  Distance transformations in arbitrary dimensions , 1984 .

[6]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[7]  Larry S. Davis,et al.  Multiresolution path planning for mobile robots , 1986, IEEE J. Robotics Autom..

[8]  Terrance E. Boult.  Updating Distance Maps When Objects Move , 1987, Other Conferences.

[9]  Hiroshi Noborio,et al.  A fast path-planning algorithm by synchronizing modification and search of its path graph (mobile robots) , 1988, Proceedings of the International Workshop on Artificial Intelligence for Industrial Applications.

[10]  Hobart R. Everett,et al.  Survey of collision avoidance and ranging sensors for mobile robots , 1989, Robotics Auton. Syst..

[11]  R. Mehrotra,et al.  Obstacle-free path planning for mobile robots , 1989 .

[12]  Christos H. Papadimitriou,et al.  Finding Feasible Paths for a Two-Point Body , 1989, J. Algorithms.

[13]  Hanan Samet,et al.  A hierarchical strategy for path planning among moving obstacles [mobile robot] , 1989, IEEE Trans. Robotics Autom..

[14]  Karen Trovato.  Differential a*: an Adaptive Search Method Illustrated with Robot Path Planning for Moving Obstacles and Goals, and an uncertain Environment , 1990, Int. J. Pattern Recognit. Artif. Intell..

[15]  Hiroshi Noborio,et al.  A quadtree-based path-planning algorithm for a mobile robot , 1990, J. Field Robotics.

[16]  Rodney A. Brooks,et al.  Solving the Find-Path Problem by Good Representation of Free Space , 1983, Autonomous Robot Vehicles.

[17]  Carme Torras,et al.  2D Path Planning: A Configuration Space Heuristic Approach , 1990, Int. J. Robotics Res..

[18]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[19]  Jean-Claude Latombe,et al.  Numerical potential field techniques for robot path planning , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[20]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[21]  Peter Kwong-Shun Tam,et al.  Robot navigation in unknown terrains via multi-resolution grid maps , 1991, Proceedings IECON '91: 1991 International Conference on Industrial Electronics, Control and Instrumentation.

[22]  Alexander Zelinsky,et al.  A mobile robot exploration algorithm , 1992, IEEE Trans. Robotics Autom..

[23]  Paul M. Griffin,et al.  Path planning for a mobile robot , 1992, IEEE Trans. Syst. Man Cybern..

[24]  Narendra Ahuja,et al.  Gross motion planning—a survey , 1992, CSUR.

[25]  Lynne E. Parker.  Designing control laws for cooperative agent teams , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[26]  Yoshio Kawauchi,et al.  A principle of distributed decision making of Cellular Robotic System (CEBOT) , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[27]  Anthony Stentz,et al.  Optimal and efficient path planning for partially-known environments , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[28]  J. Y. S. Luh,et al.  Coordination and control of a group of small mobile robots , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[29]  Danny Z. Chen,et al.  Determining conditional shortest paths in an unknown 3-D environment using framed-octrees , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[30]  Danny Ziyi Chen,et al.  Planning conditional shortest paths through an unknown environment: a framed-quadtree approach , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[31]  Akihiro Matsumoto,et al.  Development of an omni-directional mobile robot with 3 DOF decoupling drive mechanism , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[32]  Ichiro Suzuki,et al.  Distributed algorithms for formation of geometric patterns with many mobile robots , 1996, J. Field Robotics.