Modeling any obstacle shapes for motion planning of circular robots

This paper presents an algorithm to model the workspace obstacles of a circular robot. An obstacle of any shape can be represented by line and circular arc segments. Based on robot radius, geometric representation is applied for both line and circular arcs and the operation is known as offsetting. Result of our algorithm creates an efficient configuration space and helps planning high-quality motion paths. Our method works differently for line and circular arc segments. Two major steps are: (i) finding the raw offset curve for both lines and circular arcs and (ii) removing the global invalid loops. The process takes O(n) times to find the raw offset curve and O((n + k) log m) times to remove global invalid loops, where n is the number of vertices in the original polygon, k is the number of self-intersections, and m is the number of segments in the raw offset curve and always m ≤ n. Local invalid loops are removed before generating the raw offset curve by invoking a pair-wise intersection detection test (PIDT). Our algorithm is very fast and computational complexity is approximately linear.