A fast n-dimensional ray-shooting algorithm for grasping force optimization

We present an efficient algorithm for solving the ray-shooting problem on high dimensional sets. Our algorithm computes the intersection of the boundary of a compact convex set with a ray emanating from an interior point of the set and represents the intersection point as a convex combination of a set of affinely independent points. We use our intersection algorithm to compute two types of optimal grasping forces, where either the sum or the maximum of normal force components is minimized. In our simulation, the algorithm converges well and performs the computations in tens of milliseconds on a laptop.