This paper deals with the acquisition of an object by a manipulator arm when there is significant uncertainty concerning the position and orientation of the object. The key operation is planning the grasp. Objects are modelled using constraint sets. A constraint manipulation system is employed to maintain a more efficient representation. These models combine all sources of uncertainty in the position, orientation and size of objects. Geometric reasoning is applied to the hand and object models to find a suitable grasp configuration. This involves predicting a probable configuration and checking for feasibity. Trajectory planning which enables the hand to achieve the grasp smoothly, without collision with other objects is also discussed.