Some Collision Avoidance Problems in the Plane

Spurred by developments in spatial planning in robotics, computer graphics, and VLSI layout, considerable attention has been devoted recently to the problem of moving sets of objects, such as line segments and polygons in the plane or polyhedra in three dimensions, without allowing collisions between the objects. One class of such problems considers the separability of sets of objects under different kinds of motions and various definitions of separation. This paper surveys this new area of research in a tutorial fashion, presents new results, and provides a list of open problems and suggestions for further research for the case of two dimensions only.

[1]  Leo Moser.  Moving Furniture Through a Hallway , 1966 .

[2]  G. Toussaint.  Solving geometric problems with the rotating calipers , 1983 .

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

[4]  D. T. Lee,et al.  Visibility of a simple polygon , 1983, Comput. Vis. Graph. Image Process..

[5]  Godfried T. Toussaint.  On a Simple Minkowski Metric Classifier , 1970, IEEE Trans. Syst. Sci. Cybern..

[6]  Godfried T. Toussaint,et al.  SOME NEW RESULTS ON MOVING POLYGONS IN THE PLANE. , 1983 .

[7]  R. J. Dawson.  On Removing a Ball Without Disturbing the Others , 1984 .

[8]  Raimund Seidel,et al.  Some methods of computational geometry applied to computer graphics , 1984, Comput. Vis. Graph. Image Process..

[9]  Bernard Chazelle,et al.  The Complexity and Decidability of Separation , 1984, ICALP.

[10]  Michael Goldberg.  Moving Furniture Through a Hallway (Leo Moser) , 1969 .

[11]  Robert E. Tarjan,et al.  A linear-time algorithm for triangulating simple polygons , 1986, STOC '86.

[12]  D. T. Lee,et al.  An Optimal Algorithm for Finding the Kernel of a Polygon , 1979, JACM.

[13]  Gilbert Strang.  The Width of a Chair , 1982 .

[14]  Franco P. Preparata,et al.  Testing a Simple Polygon for Monotonicity , 1981, Inf. Process. Lett..

[15]  Godfried T. Toussaint,et al.  Computing the Width of a Set , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  William E. Howden,et al.  The sofa problem , 1968, Comput. J..

[17]  Godfried T. Toussaint.  Shortest Path Solves Translation Separability of Polygons , 1986, IAS.

[18]  Thomas Ottmann,et al.  On translating a set of line segments , 1983, Comput. Vis. Graph. Image Process..

[19]  Godfried T. Toussaint,et al.  Separation of two monotone polygons in linear time , 1984, Robotica.

[20]  David Avis,et al.  A Linear Algorithm for Computing the Visibility Polygon from a Point , 1981, J. Algorithms.

[21]  James D. Sebastian.  Moving Furniture Through a Hallway (Leo Moser) , 1970 .

[22]  Leonidas J. Guibas,et al.  On translating a set of rectangles , 1980, STOC '80.

[23]  Sue Whitesides,et al.  Computational Geometry and Motion Planning , 1985 .

[24]  Godfried T. Toussaint.  Polynomial Representation of Classifiers with Independent Discrete-Valued Features , 1972, IEEE Transactions on Computers.

[25]  Martin E. Dyer,et al.  Linear Time Algorithms for Two- and Three-Variable Linear Programs , 1984, SIAM J. Comput..

[26]  Jorg-Rudiger Wolfgang Sack,et al.  Rectilinear computational geometry , 1984 .

[27]  J. Stoer,et al.  Convexity and Optimization in Finite Dimensions I , 1970 .

[28]  Thomas M. Cover,et al.  Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition , 1965, IEEE Trans. Electron. Comput..