The contact location and the coefficient of friction are two of the main uncertainties that rise in the robotic grasping force analysis problem. In many robotic tasks, we seek robust solutions to problem, where the problem data suffer from known statistical uncertainty, that is, a solution minimizes the objective function for the worst-case while satisfying the constraints for every possible case. Our objective is to reveal the effect of the uncertainty on the optimal solution. First we propose an uncertain point contact model (UPCM), which can describe the contact location uncertainty. Then together with the robotic grasping constraints, we formulate the constrained grasping force optimization problem as an unconstrained least-squares problem based on exterior penalty method. Finally, a numerical example is given to illustrate the method.
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