A Conflict Detection Method for Ellipsoidal Safety Regions

A novel pairwise comparison algorithm that determines whether a pair of ellipsoids is overlapping, touching, or separated by exploiting two new Mahalanobis distance conditions is presented. These conditions are filtering steps prior to a previously proposed method that transforms the intersection query problem into a least squares minimization over a sphere. The algorithm introduced here is shown to be more computationally efficient than previous methods, which either solve the least squares minimization over a sphere or check the signs of the roots of a fourth order polynomial. The proposed method may be applied in cases when an ellipsoid is an appropriate safety region. The resulting algorithm is useful in applications including, but not limited to, collision detection and avoidance.