Kinematic feasibility analysis of 3D grasps

We present a solution to the problem of determining if it is possible for a given dexterous hand to grasp a polyhedral object at a desired topological configuration, subject to kinematic constraints. We refer to this problem as kinematic feasibility analysis. In our study, we define a desired grasp in terms of a set of contact pairs between the topological features of the hand and the object, and formulate a general algorithm that makes use of constrained optimization with nonlinear constraints to determine the feasibility. We first derive the conditions in order for the hand to make the desired contact and avoid undesirable collision. These conditions are expressed in terms of equalities and inequalities in the configuration variables of the hand and object, which can then easily be transformed into a constrained nonlinear optimization problem. Numerical examples are provided to illustrate the solution.