A comparative 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 and a valid initial point to start the recursion. In this paper we propose several strategies for selecting such a step size according to the properties of each algorithm and one method for searching a valid initial point. Simulation and experimental results show the different performances of these algorithms from computation time and convergence rates.