Fast collision detection of ellipses by approximating Minkowski sum of them with superellipse

Abstract

In this paper, we propose an accurate and fast method checking collision of ellipses. Ellipse collision detection techniques are used in various applications such as robot collision avoidance and material packing. Our proposed collision detection method is based on the Minkowski sum, which is the union of two ellipses as a subset. Ours approximates the Minkowski sum of ellipses in the form of a superellipse. We evaluate the accuracy and computation time of the Minkowski sum for various combinations of ellipses and describe the simplicity of the collision determination.