A fast procedure for computing the distance between complex objects in three-dimensional space

An algorithm for computing the Euclidean distance between a pair of convex sets in R/sup m/ is described. Extensive numerical experience with a broad family of polytopes in R/sup 3/ shows that the computational cost is approximately linear in the total number of vertices specifying the two polytopes. The algorithm has special features which makes its application in a variety of robotics problems attractive. These features are discussed and an example of collision detection is given. >

[1]  E. Gilbert.  An Iterative Procedure for Computing the Minimum of a Quadratic Form on a Convex Set , 1966 .

[2]  E. Gilbert,et al.  Some efficient algorithms for a class of abstract optimization problems arising in optimal control , 1969 .

[3]  R. Barr.  An Efficient Computational Procedure for a Generalized Quadratic Programming Problem , 1969 .

[4]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[5]  Philip Wolfe,et al.  Finding the nearest point in A polytope , 1976, Math. Program..

[6]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[7]  John W. Boyse,et al.  Interference detection among solids and surfaces , 1979, CACM.

[8]  Jacob T. Schwartz,et al.  Finding the Minimum Distance Between Two Convex Polygons , 1981, Information Processing Letters.

[9]  Francis Y. L. Chin,et al.  Optimal Algorithms for the Intersection and the Minimum Distance Problems Between Planar Polygons , 1983, IEEE Transactions on Computers.

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

[11]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[12]  W. Edward Red,et al.  Minimum distances for robot task simulation , 1983, Robotica (Cambridge. Print).

[13]  Elmer Gilbert,et al.  The application of distance functions to the optimization of robot motion in the presence of obstacles , 1984, The 23rd IEEE Conference on Decision and Control.

[14]  D. T. Lee,et al.  Computational Geometry—A Survey , 1984, IEEE Transactions on Computers.

[15]  Franco P. Preparata,et al.  Correction to "Computational Geometry - A Survey" , 1985 .

[16]  Rodney A. Brooks,et al.  A subdivision algorithm in configuration space for findpath with rotation , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  Bruce Randall Donald,et al.  On motion planning with six degrees of freedom: Solving the intersection problems in configuration space , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[18]  Herbert Edelsbrunner,et al.  Computing the Extreme Distances Between Two Convex Polygons , 1985, J. Algorithms.

[19]  Stephen Cameron,et al.  A study of the clash detection problem in robotics , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[20]  Elmer G. Gilbert,et al.  Distance functions and their application to robot path planning in the presence of obstacles , 1985, IEEE J. Robotics Autom..

[21]  Elmer Gilbert,et al.  Minimum time robot path planning in the presence of obstacles , 1985, 1985 24th IEEE Conference on Decision and Control.

[22]  David G. Kirkpatrick,et al.  A Linear Algorithm for Determining the Separation of Convex Polyhedra , 1985, J. Algorithms.

[23]  Larry J. Leifer,et al.  A Proximity Metric for Continuum Path Planning , 1985, IJCAI.

[24]  Vladimir J. Lumelsky,et al.  On Fast Computation of Distance Between Line Segments , 1985, Information Processing Letters.

[25]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1986 .

[26]  S. A. Cameron,et al.  Determining the minimum translational distance between two convex polyhedra , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[27]  Karl G. Kempf,et al.  A collision detection algorithm based on velocity and distance bounds , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[28]  Walter Meyer,et al.  Distances between boxes: Applications to collision detection and clipping , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[29]  John F. Canny,et al.  Collision Detection for Moving Polyhedra , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  S. Sathiya Keerthi,et al.  A fast procedure for computing the distance between complex objects in three space , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.