An algorithm for computing fingertip positions of a spatial equilibrium grasp with a multifingered hand

This paper proposes an algorithm for computing the fingertip positions of an equilibrium grasp for a polyhedral object. The authors has already developed such an algorithm for a planar grasp where the problem can be 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 two virtual fingers, one fixed at each edge endpoint. This equivalance 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 and nonlinear constraints. The nonlinear constraints still remain, but exhibit the same properties as the integer requirement in an integer programming problem. This paper proposes an algorithm based on the branch-and-bound method that decomposes each finger region until the nonlinear constraint associated with the finger is satisfied. Numerical examples show that the algorithm effectively solves problems of practical size