Least cost paths with algebraic cost functions. Part 1

Abstract

An idea of planning safer paths for robot motion is outlined. Use is made of algebraic cost functions of clearance to obstacles. A parameter k, safety factor, controls the balance between safety and length of the resultant paths. Analytical solutions are given for a polygon world by using calculus of variations. Results are reported about simple regions only. Another fundamental idea of the 'equivalence classes' of paths is introduced.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>