On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers

Jacob T. Schwartz, Micha Sharir

Research output: Contribution to journalArticlepeer-review

Abstract

We present an algorithm that solves a two‐dimensional case of the following problem which arises in robotics: Given a body B, and a region bounded by a collection of “walls”, either find a continuous motion connecting two given positions and orientations of B during which B avoids collision with the walls, or else establish that no such motion exists. The algorithm is polynomial in the number of walls (O(n5) if n is the number of walls), but for typical wall configurations can run more efficiently. It is somewhat related to a technique outlined by Reif.

Original languageEnglish
Pages (from-to)345-398
Number of pages54
JournalCommunications on Pure and Applied Mathematics
Volume36
Issue number3
DOIs
StatePublished - May 1983

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