Fingertip position planning for a multifingered hand

Discusses problems relating to planning fingertip positions of a multifingered hand. The fundamental problem is to compute a fingertip range within which the fingers can exert equilibrium forces. In two dimensions, the effect of changing a fingertip position along an edge is equivalent to the effect of changing fingertip forces of the fingers fixed at both ends of the edge. When the object to be grasped is a polygon and the edges on which fingers are positioned are given, this equivalence reduces the problem to a fractional programming problem which in turn is reduced to an LP problem. When the edge selection is also taken into account, this problem can be formulated as a combinatorial programming problem with either-or constraints. This paper also discusses optimum grasps taking both finger forces and positions into account