Finding all valid hand configurations for a given precision grasp

Planning a precision grasp for a robot hand is usually decomposed into two main steps. First, a set of contact points over the object surface must be determined, ensuring they allow a stable grasp. Second, the inverse kinematics of the robot hand must be solved to verify whether the contact points can actually be reached. Whereas the first problem has been largely solved in a general posing, the second one has only been tackled with local convergence methods. These methods only provide one solution to the problem, even if many are possible, and depending on the initial estimation they use, they may fail to converge, which results in grasp re-planning in situations where it could be avoided. This paper overcomes both issues by providing a complete method to solve the kinematics of human-like hands. The method is able to find all possible configurations that reach the specified contact points, even when positive-dimensional sets of such configurations are possible.