Examining the Robustness of Grasping Force Optimization Methods Using Uncertainty Analysis

The development of robust and adaptable methods of grasping force optimization (GFO) is an important consideration for robotic devices, especially those which are designed to interact naturally with a variety of objects. Along with considerations for the computational efficiency of such methods, it is also important to ensure that a GFO approach chooses forces which can produce a stable grasp even in the presence of uncertainty. This paper examines the robustness of three methods of GFO in the presence of variability in the contact locations and in the coefficients of friction between the hand and the object. A Monte Carlo simulation is used to determine the resulting probability of failure and sensitivity levels when variability is introduced. Two numerical examples representing two common grasps performed by the human hand are used to demonstrate the performance of the optimization methods. Additionally, the method which yields the best overall performance is also tested to determine its consistency when force is applied to the object's center of mass in different directions. The results show that both the nonlinear and linear matrix inequality (LMIs) methods of GFO produce acceptable results, whereas the linear method produces unacceptably high probabilities of failure. Further, the nonlinear method continues to produce acceptable results even when the direction of the applied force is changed. Based on these results, the nonlinear method of GFO is considered to be robust in the presence of variability in the contact locations and coefficients of friction.