The paper presents a control oriented dynamic formulation for constrained robotic systems. We refer to this formulation as control oriented since it can be directly applied to design a model-based tracking control strategy. It enables one to obtain dynamic models for systems subjected to material constraints and non-material referred to as program constraints. The dynamic model for a constrained robot, where equations of program constraints specify tasks and motion requirements, is used as a program motion planner for a controller design. The formulation provides a theoretical framework, which is a basis for the study of robot performance of constrained tasks. Examples of developments of control oriented dynamic models are presented, and their applications for control are demonstrated and discussed.