A novel materials handling system is being developed at CarnegieMellon University's Mechanical EngineeringDepartment. This systems contains an array of cells, each of which has two actuators. The two actuators are orthogonally oriented motorized roller wheels which, in combination, can generate a vector of motion in any planar direction. This work develops control laws for transporting and manipulating objects which rest on the array. Towards this goal, we consider the dynamics of parcel transport and manipulation. The parcel dynamics are based on an exact discrete representation of the system, unlike other methods where a continuity assumption is made. Two types of contact models are considered. This work extends the previous one-dimensional discrete model into two-dimensions.