A labeling system employs a multi-processing computer control system which includes a computer control host processor (536), a motion control processor (520) and a container tracking processor (528). The system is responsive to the physical position of the labels and the physical position of containers or similar objects to which the labels are applied. The label application motion controller identifies the machine position and performs the mathematical calculations needed to create a piecewise continuous function motion profile required to achieve label contact at a predefined contact point on the surface of each container. Because the position of the label is based on the position of the container and a motion profile is calculated for each application, a fixed initial staging position of the label prior to application is not needed.