An Algorithm for Computing Grasp Force Solutions in Power Grasps Considering Errors in Elastic Contact Model

Abstract

Power grasp or enveloping grasp enables a multifingered robot hand to grasp an object firmly by constraining the object with multiple contacts on its surfaces. The equilibrium equation in power grasp is not enough to determine the grasp force solution uniquely. It is known that if the contacts are elastic and their stiffness values are known, the grasp force solution can be computed uniquely. However, if they are not known, such computation is impossible. A more realistic assumption is that the range of the contact stiffness rather than its single value is known. Then the problem is to compute the corresponding set of grasp force solutions. This paper analyzes the solution as the function of stiffness parameters. We prove that each force component in the solution is maximum or minimum for a combination of the minimum or maximum values of the stiffness parameters. The number of such combinations is two to the n-th power where n is the number of the stiffness parameters. The ratio of the friction to normal forces at each contact is of the same function. Numerical examples show the effectiveness of the proposed algorithm.