Approximating polylines by curved paths

This paper examines a problem related to motion planning of steering constrained robots. Many existing path planning algorithms provide paths represented by series of line segments. These segments join at angles that a steering constrained robot may not be able to follow. Further, the entire path is not differentiable, requiring the robot to stop and realign its wheels. Path planners that do output curved paths, use curved paths in configuration space and are much less efficient. We suggest path planning can be achieved by using a fast planner, then transforming the straight line output to a curved path. In this paper, an algorithm is presented to transform a polyline path to a differentiable path of straight segments and circular arcs. The arcs are formed by varying sized circles, with radius no smaller than a specified minimum value. The entire output path is also guaranteed to be no further than a chosen value ε from the input.