Curvature-Based Computation of Antipodal Grasps
Yan-Bin Jia
Abstract
It is well known that antipodal grasps can be achieved on curved objects in the
presence of friction. This paper presents an efficient algorithm that finds, up
to numerical resolution, all pairs of antipodal points on a closed, simple, and
twice continuously differentiable planar curve. Dissecting the curve into
segments everywhere convex or everywhere concave, the algorithm performs
simultaneous marching on a pair of such segments with provable convergence and
interleaves marching with numerical bisection. The algorithm makes use of new
insights into the differential geometry at a pair of antipodal points. By
exploiting geometry of curves, we have avoided resorting to a traditional
nonlinear programming method that would be much less efficient and not guarantee
to find all antipodal points.