New computational method for three-fingered force-closure test

This paper proposes an efficient implementation of a force-closure test for frictional three-finger grasps. The implementation is based on a condition that transforms force-closure testing into the problem of convex hull intersection in projective space. The proposed implementation further reduces the problem into the problem of computing whether a line segment intersects a convex hull of at most four points. Implementation results are presented along with a thorough performance analysis and comparison with several existing methods. The results are also verified with arbitrary precision floating point computation. This provides comparison of qualitative error resulting from floating point roundoff. The result shows that the proposed implementation outperforms other methods in terms of speed and precision.