Analysis of indeterminate force in multi-contact friction grasp based on potential energy minimization

Prediction of contact forces is a central issue in robotic grasping analysis and the indetermination of the contact force is one of the most important characteristic for the object-hand system. In this paper, we provide a unified framework to determine the contact force in robotic grasping. First, a nonlinear mapping, based on the Hertz contact theory, was used to build the force-deformation relationship. Then we combine the elastic contact constraint and friction constraint to formulate the grasping force analysis problem as a constrained optimization problem by minimizing the potential energy. Further, we transform the constrained optimization problem into an unconstrained optimization process using the Augmented Lagrangian Method. Finally, a numerical example is given to illustrate the method.