Planning optimal independent contact regions for two-fingered force-closure grasp of a polygon

This paper addresses the problem of optimizing the maximal independent contact region for two-fingered force- closure grasp of a rigid object in 2D. Existing methods for optimizing this criterion considered only independent graspable regions on a given pair of edges. We propose an algorithm that takes nearby edges into consideration so that larger independent contact regions can be obtained. Our method takes the input polygons, computes graspable regions for each pair of edges, merge all adjacent regions together, and then find the best independent contact region inscribed in those regions. Two different criteria to define the best independent contact region are studied. The first criterion maximizes area of the axis-parallel rectangle in the configuration space, while the other criterion maximizes the smaller side´s length of the rectangle. For a given object with n vertices, the first criterion can be optimized using the algorithm from Karen Daniels et al. in O(n² log² n) time, while the other criterion can be optimized using the algorithm from Evanthia Papadopoulou and D. T. Lee in O(n² log n) time.