Convergence analysis and experimental study of geometric algorithms for real-time grasping force optimization

Real-time grasping force optimization problem can be naturally formulated as a convex optimization problem on the Riemannian manifold of positive definite matrices subject to linear constraints for which many algorithms, including gradient algorithms, Newton algorithms, and interior point algorithms, have been developed. In all these algorithms we need to specify a step size in every iteration. In this paper we propose several strategies for selecting such a step size according to the properties of each algorithm. By investigating the structure of the affine-scaling vector fields associated with the optimization problem, we give a detailed convergence analysis of these algorithms. Experimental results show the different performance of these algorithms from convergence rates.