Fast grasp quality evaluation with partial convex hull computation

We present Partial Quick Hull (PQH), an algorithm to efficiently compute one of the most commonly used grasp quality metrics. The metric relies on the computation of the convex hull of a set of points in a six dimensional space. Built on top of widely used QuickHull algorithm, PQH exploits the relationship between the convex hull and the grasp quality metric to avoid computing the whole convex hull. PQH determines at run time when the computation can be ended because the grasp quality metric can be already determined from a partially computed convex hull - hence the name of the algorithm. This improvement greatly accelerates grasp quality evaluation for force closure grasps. When the grasp is not force closure, the partial computation does not apply and PQH then behaves exactly like QuickHull. A large set of experimental tests show how PQH largely outperforms QuickHull and better scales with the size of the input.