In the past decade, there has been much interest in operating quadrotors in uncertain and cluttered environments due to their simplicity. Executing precise agile quadrotor flight maneuvers is an important open research problem for navigating in such environment. Collisions can occur if actuator constraints are not considered in the trajectory tracker design. This paper presents a cascade nonlinear constrained control approach (CNCCA) for trajectory tracking with explicit consideration of actuator constraints, where the output signal of the position controller is converted into the desired command of the attitude controller. The proposed position control loop is shown to be stable and bounded, satisfying the total thrust limits. The proposed attitude tracking control loop is designed as a saturated control law based on a modified geometric controller in SO(3) space. A proof of its stability is provided. The simulation results also show good tracking performance of the proposed approach.