Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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A Geometric Proof on Shortest Paths of Bounded Curvature

제한된 곡률을 갖는 최단경로에 대한 기하학적 증명

  • 안희갑 (세종대학교 컴퓨터공학과) ;
  • 배상원 (한국과학기술원 전산학과) ;
  • 정지원 (한국과학기술원 전산학과)
  • Published : 2007.04.15
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Abstract

A point-wise car-like robot moving in the plane changes its direction with a constraint on turning curvature. In this paper, we consider the problem of computing a shortest path of bounded curvature between a prescribed initial configuration (position and orientation) and a polygonal goal, and propose a new geometric proof showing that the shortest path is either of type CC or CS (or their substring), where C specifies a non-degenerate circular arc and S specifies a non-degenerate straight line segment. Based on the geometric property of the shortest path, the shortest path from a configuration to a polygonal goal can be computed in linear time.

평면상에서 이동하는 자동차와 같은 로봇은 이동방향을 변경할 때 제한된 곡률(curvature)로 서서히 방향을 바꿀 수밖에 없다. 본 논문은 물체의 동선의 곡률이 제한되어 있을 경우, 한 구성에서 출발하여 목표점에 이르는 최단경로는 CC 혹은 CS 타입(C는 원호(circular arc), S는 선분(line segment)을 의미한다), 혹은 이들의 부분문자열 타입이 된다는 사실을 기하학적 성질만을 이용하여 증명하였다. 본 연구결과를 이용하여, 시작점 구성에서 출발하여 목표점, 혹은 목표다각형에 도달하는 최단경로는 다각형의 공간복잡도의 선형시간에 계산 가능하다.

Keywords

References

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