We present an algorithm to model the workspace obstacles of a circular robot. Based on robot radius, we apply local geometry to model the obstacles and the operation is called offsetting. Result of our algorithm constructs an efficient configuration space and helps planning high-quality motion paths. Our method works in two major steps: it finds the raw offset curve for both lines and circular arcs in O(n) times and then removes the global invalid loops in O((n + k)logm) times, 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 method is very fast, mathematically well defined, and overall complexity is approximately linear. By applying our simple and efficient approach, offsetting any shape of obstacles is possible to construct a configuration space that ensures optimized motion planning.