Circumscribed Douglas-Peucker Polygonal Approximation for Curvilinear Obstacle Representation

Abstract

ECD (Exact Cell Decomposition) based path planning is not applicable in curvilinear obstacles environment. Therefore, after the curvilinear obstacles are approximated to the polygons by using DP (Douglas-Peucker) algorithm, which is a polygon approximation algorithm, the ECD method is applied. However, there is a case of not including all the existing obstacles' area and ignoring the outer area, when it comes to the curvilinear obstacles, approximated to the polygons by using the DP algorithm. In this case, path planning of ECD method cannot guarantee the clearance. This paper proposes a CDP (Circumscribed DP) algorithm to solve this problem. The CDP algorithm has a disadvantage of having more inner area than the DP algorithm, but it can guarantee the clearance because of the fact the algorithm always has 0(%) of outer area (OA). In order to confirm this, the polygonal approximation of DP and CDP algorithms was compared in the same curvilinear obstacles and the result was as the following: When each ε value is 0.05, 0.08, 0.11(m), each result of the inner area ratio (IA) was 2.45, 4.89, 7.19(%) by DP algorithm, 16.3, 18.39, 32.58(%) by CDP algorithm, and result of the outer area ratio (OA) was 0.7, 1.17, 1.54(%) by DP Algorithm, 0, 0, 0(%) by CDP Algorithm. Also, it can be confirmed that the CDP algorithm has always guaranteed for clearance.