Rolling manipulation is the manipulation of an object using a multifingered dextrous robotic hand by virtue of rolling contacts between the fingertips and the object. This dissertation examines the kinematics, statics, dynamics of the hand/object system and proposes a method of controlling the motion of the object, the motion of the fingers and the contact forces simultaneously.

Rolling, when restricted to the plane, is a holonomic motion - i.e. a motion which can be described by integrable constraints. In three dimensions, rolling is characterized by holonomic and non-holonomic constraints. Kinematics analysis has revealed two modes of rolling manipulation. In the manipulating mode, the fingertips move so as to impart motion onto the object without rotating themselves with respect to the inertial frame. In the re-locating mode, the fingertips roll on the object's surface without imparting any motion on it. This provides a way of re-orienting or re-locating the fingertips on the object surface.

An object is said to be completely manipulable if it can be moved through any instantaneous motion by the fingers grasping it. If the grasp also satisfies unisense and friction conditions, the object is said to be in a state of hand force closure. This implies that the fingers can exert arbitrary forces and moments on the object.

The dynamics of a non-holonomic system is characterized by the existence of a set of equilibrium points which are collectively called the equilibrium manifold. The system can be asymptotically stable only in the sense that its state will converge to this manifold with time. Herein, it is shown that Lyapunov's direct method can be used to analyze the stability of such a system.

Using separate PD controllers for the position and orientation of the object, and the orientations of the fingertips, as well as a force-balancing scheme to regulate the internal forces, a complete control law for rolling manipulation has been formed. This method is effective for both planar and three-dimensional rolling manipulation.