Abstract
This paper proposes an algorithm for computing the tip positions of fingers maintaining equilibrium when they grasp a polyhedral object. The author has already developed an algorithm for a planar grasp. The problem in a planar grasp is reduced to a linear programming problem using the static equivalence; the effect of changing a fingertip position along an edge is equivalent to the effect of changing the fingertip forces of the virtual fingers fixed at both ends. This equivalence makes the moment equilibrium equation in the planar grasp linear. In a spatial grasp, introducing such virtual fingers to the faces of the object decomposes the moment equilibrium equation into linear constraints and nonlinear constraints. The nonlinear constraints still remain, but they exhibit the same properties as the integer requirement in an integer programming problem. We propose an algorithm based on the branch and bound method. The algorithm decomposes each finger region until the nonlinear constraint associated with the finger is satisfied. Numerical examples show that the algorithm efficiently solves problems of practical size.
