From movement analysis literature, such as the work of Bartenieff, and motion capture and anatomical evidence, it is known that the core of human body plays an important role in walking motion. Motivated by these findings, a biped robot with core-located actuation, which causes the center of mass to change, has been proposed. In this paper, a planar model of the core-located actuation platform and its simulation results are presented. This simple model utilizes actuation near its center of mass in order to achieve forward progress. A stable walking gait is derived using the method of feedback linearization and virtual constraints to define desired walking behavior. The results of this modeling and control analysis are presented here. This initial work lays the framework for a humanoid platform that utilizes actuation strategies more closely akin to those employed by virtuosic movers, who focus on core training and initiation, allowing biped robotic platforms to achieve more robust and stylistically adjustable gaits.