TY - JOUR

T1 - On the general motion-planning problem with two degrees of freedom

AU - Guibas, Leonidas J.

AU - Sharir, Micha

AU - Sifrony, Shmuel

PY - 1989/12

Y1 - 1989/12

N2 - We show that, under reasonable assumptions, any collision-avoiding motion-planning problem for a moving system with two degrees of freedom can be solved in time O(λs(n) log2n), where n is the number of collision constraints imposed on the system, s is a fixed parameter depending, e.g., on the maximum algebraic degree of these constraints, and λs(n) is the (almost linear) maximum length of (n, s) Davenport-Schinzel sequences. This follows from an upper bound of O(λs(n)) that we establish for the combinatorial complexity of a single connected component of the space of all free placements of the moving system. Although our study is motivated by motion planning, it is actually a study of topological, combinatorial, and algorithmic issues involving a single face in an arrangement of curves. Our results thus extend beyond the area of motion planning, and have applications in many other areas.

AB - We show that, under reasonable assumptions, any collision-avoiding motion-planning problem for a moving system with two degrees of freedom can be solved in time O(λs(n) log2n), where n is the number of collision constraints imposed on the system, s is a fixed parameter depending, e.g., on the maximum algebraic degree of these constraints, and λs(n) is the (almost linear) maximum length of (n, s) Davenport-Schinzel sequences. This follows from an upper bound of O(λs(n)) that we establish for the combinatorial complexity of a single connected component of the space of all free placements of the moving system. Although our study is motivated by motion planning, it is actually a study of topological, combinatorial, and algorithmic issues involving a single face in an arrangement of curves. Our results thus extend beyond the area of motion planning, and have applications in many other areas.

UR - http://www.scopus.com/inward/record.url?scp=0001748030&partnerID=8YFLogxK

U2 - 10.1007/BF02187744

DO - 10.1007/BF02187744

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0001748030

SN - 0179-5376

VL - 4

SP - 491

EP - 521

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 1

ER -