Dextrous manipulation with multifingered robotic hands is an important problem in the study of robotics and has applications in a wide variety of areas. Given a robotic hand and an object to be manipulated by the hand in an environment containing obstacles, the main objectives of dextrous manipulation are to have the hand grasp the object and transfer it from a start configuration to a goal configuration while simultaneously avoiding collisions, respecting governing physical laws and system limits.; We show that nonlinear friction cone constraints, which have been one major stumbling block in the study of grasp statics, can be cast into Linear Matrix Inequality (LMI) constraints. This observation enables us to formulate a set of fundamental grasp statics problems as convex optimization problems involving LMIs, which can be efficiently solved by interior-point algorithms with polynomial time complexity. The numerical study results show the simplicity and efficiency of our LMI approach.; We point out that one common approach of applying instantaneous manipulation kinematics in manipulation planning has severe drawbacks, which may cause the generation of infeasible or undesirable trajectories that cannot be successfully implemented by the robotic system. We derive dextrous manipulation kinematics and incorporate kinematic feasibility constraints as well as all kinematic variables (object, contacts and finger joints) into manipulation planning.; We present a modular Control System Architecture for Multi-fingered Manipulation (CoSAM2), which is inspired by our results in manipulation kinematics. The modularity of the control architecture facilitates easy incorporation of functional modules. The experimental results show that CoSAM2 can successfully fulfill complicated manipulation tasks by incorporating the manipulation kinematics and statics with proper sensory data inputs.; We propose a probabilistic roadmap planner for manipulation with fixed grasps, which can be viewed as a system involving closed chains. Our planner uses kinematics to tackle the closure constraints, which have been problematic for previous closed chain planners. Furthermore, The planner adopts a novel two-stage probabilistic roadmap approach to amortize the expensive computation cost associated with closure constraints. The results show that our approach can reduce the computation costs and improve the connectivity of resulting roadmaps.
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