| Three most important problems in dextrous manipulation by multifingered robotic hands are the optimal grasp synthesis problem, real-time grasping force optimization problem, and coordinated manipulation with finger gaiting.; (a) Optimal grasp synthesis problem. Given an arbitrary object and the corresponding friction models, plan a set of contacts for the hand such that the grasp is force closure if such grasp exists. Moreover it is optimal in some sense. Traditional heuristic approaches, although being successfully applied to several classical manipulation examples, encounter difficulties in systems with more than 2 fingers and complex object geometries. In Chapter 3, we introduce several candidate grasp quality functions and formulate the grasp synthesis problem as a Max-transfer, a Max-normal-grasping-force, and a Min-analytic-center problem. (b) Real-time grasping force optimization problem. Given a set of contact points of the hand, the external wrench, and the corresponding friction models, determine an optimal grasping force in real-time with respect to a given objective function. In Chapter 4, we formulate the grasping force optimization as a convex optimization problem on the Riemannian manifold of positive definite matrices subject to linear constraints, for which five algorithms are developed and their respective step size selection are discussed in detail. (c) Coordinated manipulation with finger gaiting. Given a periodic motion of the object, the geometry of the object and fingers, and the workspaces of fingers of the hand, determine if finger gaits are necessary. If that, how to plan a sequence of discrete events (fingers make or break contacts with the object) as well as the trajectories of fingers and contacts between any two events such that (1) all finger trajectories are contained in their respective workspaces; (2) at any time, whatever number of fingers are in contact with objects, the respective grasp keeps force closure. In Chapter 5, we give some preliminary results on this problem. We first use stratified configuration spaces to model the manipulation system with finger gaiting. Then, for a given gait and a periodic motion of the object, we construct two behavior basis for each finger of the hand corresponding to the contact and non-contact states. (Abstract shortened by UMI.)... |
