This paper presents a novel concept of a co-axial bi-rotor UAV which is controlled by moving its center of gravity. After deriving a 6DOF nonlinear model using the Euler-Newton method, we introduce a simplified 3DOF model for planar motion. Due to the limited available torque in pitch and roll channels, a linear quadratic regulator controller is designed for planar motion control, in order to evaluate the performance and maneuverability of the system while respecting the control limits. The simulation results of implementing an LQR controller on the nonlinear model for tracking problem shows that the system has convincing performance, and while control inputs are constrained, controlling the system is possible with no significant restrictions. Even with considering a first-order dynamic for the actuators, the implementation of the LQR controller for tracking an 8-shape trajectory considering different uncertainties shows that the system has high enough maneuverability for a wide range of applications, like Air Shipping and Delivery, Photography and Multimedia, Monitoring (Traffic, Wildlife, Industry, …), Search and Rescue, Weather Forecasting, etc.