Partial convex hull algorithms for efficient grasp quality evaluation

Abstract

We present two algorithms to efficiently determine the value of two grasp quality metrics formerly proposed in literature. The first one is heavily used in practice but has some drawbacks, e.g., it is not scale invariant and it does not focus on the disturbance forces that will occur in practice when the robot grasps an object. The second one overcomes these limitations, but is rarely used because it is computationally too demanding. The two algorithms we propose are based on the common intuition that both metrics can be efficiently computed through a modified version of the QuickHull algorithm that is commonly used to compute convex hulls. In both cases it is possible to establish when enough information has been generated to determine the desired value, and then stop the construction of a suitably defined convex hull. Extensive numerical evaluations demonstrate that our algorithms provide substantial computational gains when compared with the state of the art. The speedup provides an immediate benefit to planners using grasp quality metrics to guide the search through the space of possible grasps.

Research on two-stage grasping planning method for multifingered dexterous hand

“…The traditional force closure evaluation method is inefficient, and the amount of calculation increases with the number of fingers (Dan et al , 2001). The partial convex hull algorithms designed by Liu et al only have a speed-up effect on the solution of force closure conditions (Liu and Carpin, 2016). Analytical methods are mainly used for a specific grasp type (Hegedus et al , 2022), and it is difficult to be transplanted into the actual scene (Bohg et al , 2014).…”

“…The force closure evaluation score adopts the L 1 (Liu and Carpin, 2016). The comprehensive evaluation score for the grasped solution is defined as: …”

A Two-stage Learning Architecture that Generates High-Quality Grasps for a Multi-Fingered Hand

“…While the original definition assumes the same force at each contact, we show how the contact forces can be scaled realistically based on their location. To speed up the computation of the metric, the Partial Convex Hull algorithm only computes the part of the convex hull that is necessary for determining the weakest wrench [13]. We additionally manage to efficiently incorporate the more realistic Minkowski sum formulation of the metric into the algorithm.…”

“…We use the efficient implementation proposed by Borst et al [15]. d) Computing the metric including Minkowski sum: We make use of the partial convex hull algorithm (PQH) to efficiently determine the smallest distance from the origin to the convex hull [13]. Here, the convex hull is built using the qhull algorithm, which, starting from an initial guess, sequentially adds points to the convex hull until no points are left outside.…”

“…with d(p) being the distance of a point to the facet with normal n and offset o: d(p) = n • p + o. By reformulating (13), this computationally expensive combinatorial problem can be drastically simplified:…”