Grasping force optimization for multi-fingered robot hands

For dextrous robotic hand grasping a key goal is to balance external and internal grasping forces to assure a stable grasp and low grasping energy. In this paper, we view the task of grasping force optimization as a linearly constrained semidefinite programming problem for which there are known globally exponentially convergent solutions via gradient flows. A key observation is that the nonlinear friction constraint at each contact point is equivalent to the positive definiteness of a suitable matrix containing the contact wrench intensities. A recursive version is presented, and numerical examples demonstrate the simplicity, the good numerical properties, and optimality of the approach.