A nonlinear control algorithm is given for a class of quadrotors operating in small angles. The control of 6-DOF moving platform using only four actuators results in an under-actuated control system. In order to transform the dynamics in affine form, an additional constraint is applied on the actuation mechanism that reduces the independent control signals even further. In this paper, the system is decomposed in to three fully actuated subsystems; in pitch, roll and yaw domains. Local subcontrollers are designed using partial feedback linearization. The proposed multi Lyapunov function based switching control algorithm is employed to achieve tracking of Cartesian space motion and the heading angle of the quadrotor. Local stability of the closed-loop system is shown in the flight region of interest. The performance of the proposed controller is illustrated to follow a desired position, velocity and the heading angle of quadrotor.