Compliant motion in a simple polygon

We consider motion planning under the compliant motion model, in which a robot directed to walk into a wall may slide along it. We examine several variants of compliant motion planning for a point robot inside a simple polygon with n sides, where the goal is a fixed vertex or edge. For the case in which the robot moves with perfect control, we build a data structure that lets us in O (log n ) time determine the range of directions in which the robot can move from a query point to the goal in a single step. This structure lets us solve a variety of other problems: we can find a similar query data structure for multi-step paths; we can solve single-step problems allowing uncertainty in control and position sensing; and we can explicitly compute the set of all points that can reach the goal in a single step, even allowing uncertainty in control. Our algorithms run in O ( n log n ) time and linear space; they use a novel method for maintaining convex hulls of simple paths that may be of independent interest.

[1]  Leonidas J. Guibas,et al.  An efficient algorithm for finding the CSG representation of a simple polygon , 1988, SIGGRAPH.

[2]  Avraham A. Melkman,et al.  On-Line Construction of the Convex Hull of a Simple Polyline , 1987, Inf. Process. Lett..

[3]  John F. Canny,et al.  New lower bound techniques for robot motion planning problems , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[4]  Robert E. Tarjan,et al.  An O(n log log n)-Time Algorithm for Triangulating a Simple Polygon , 1988, SIAM J. Comput..

[5]  Micha Sharir,et al.  Planning, geometry, and complexity of robot motion , 1986 .

[6]  John F. Canny,et al.  A new algebraic method for robot motion planning and real geometry , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[7]  Godfried T. Toussaint,et al.  On a convex hull algorithm for polygons and its application to triangulation problems , 1982, Pattern Recognit..

[8]  F. Frances Yao,et al.  Finding the Convex Hull of a Simple Polygon , 1983, J. Algorithms.

[9]  Bruce Randall Donald.  The complexity of planar compliant motion planning under uncertainty , 1988, SCG '88.

[10]  Kenneth L. Clarkson,et al.  A fast las vegas algorithm for triangulating a simple polygon , 1989, Discret. Comput. Geom..

[11]  Jean Latombe.  Motion Planning with Uncertainty: The Preimage Backchaining Approach , 1988 .

[12]  Leonidas J. Guibas,et al.  Optimal Point Location in a Monotone Subdivision , 1986, SIAM J. Comput..

[13]  Leonidas J. Guibas,et al.  On the general motion-planning problem with two degrees of freedom , 2015, SCG '88.

[14]  Gordon T. Wilfong,et al.  Planning constrained motion , 1988, STOC '88.

[15]  Stephen J. Buckley.  Planning and teaching compliant motion strategies , 1987 .

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

[17]  B. Natarajan.  On Moving and Orienting Objects , 1986 .

[18]  Kenneth L. Clarkson,et al.  A fast Las Vegas algorithm for triangulating a simple polygon , 1988, SCG '88.

[19]  Alain Fournier,et al.  Triangulating Simple Polygons and Equivalent Problems , 1984, TOGS.

[20]  Michael A. Erdmann,et al.  Using Backprojections for Fine Motion Planning with Uncertainty , 1986 .

[21]  David G. Kirkpatrick,et al.  Optimal Search in Planar Subdivisions , 1983, SIAM J. Comput..

[22]  Matthew T. Mason,et al.  An exploration of sensorless manipulation , 1986, IEEE J. Robotics Autom..