Exact calculation for disturbance force rejection grasp quality measure

We propose a novel method to calculate scalar version of the grasp quality measure proposed, which is the magnitude of minimal disturbance force applied to the object that breaks the grasp. This measurement is adopted in several works but all of them are essentially calculated by enumerating over discretized directions of forces. Our proposed method does not need to discretize the direction, rendering the method more complete. The key idea of our method is that the measure is formulated as a function which depends on object vertices, disturbance force direction and hyperplanes of Unit grasp wrench space(UGWS). We proved that the reciprocal of this function is indeed concave over disturbance force direction, for a fixed object and fixed hyperplane of UGWS. Hence, we can derive analytical solution that find the global minimum of this function. A numerical example was carried out and the result shows that our proposed method can outperform the original computation in term of accuracy and efficiency.