# Optimal piecewise linear motion of an object among obstacles

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## Abstract

We present an algorithm for determining the shortest restricted path motion of a polygonal object amidst polygonal obstacles. The class of motions which are allowed can be described as follows: a designated vertex,*P*, of the polygonal object traverses a piecewise linear path, whose breakpoints are restricted to the vertices of the obstacles. The distance measure being minimized is the length of the path traversed by*P*. Our algorithm runs in time*O*(*n* ^{4}kog*n*). We also discuss a variation of this algorithm which minimizes any positive linear combination of length traversed by*P* and angular rotation of the ladder about*P*. This variation requires*O*(*n* _{5}) time.

### Key words

Shortest-path motion Motion planning Piano movers problem## Preview

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© Springer-Verlag New York Inc. 1987