This paper presents an accurate solution of finite-time Cartesian trajectory tracking control problem of a quadrotor system by designing and implementing a novel robust flight-control algorithm. The quadrotor is subject to nonlinearities, unmodeled dynamics, parameters' uncertainties, and external time-varying disturbances. To reject the disturbances and enhance the control system's robustness, a terminal sliding mode-based active antidisturbance control (TSMBAADC) approach is proposed for rotational and translational subsystems. To improve the tracking performance, a nonlinear continuous terminal sliding manifold and a fast reaching law are proposed in this work to quickly drive the systems' states to the equilibrium point even in the presence of lumped disturbances. The convergence time of the states can be pretuned based on the parameters of the sliding manifold and the reaching law. Lyapunov theorem is used to provide a rigorous stability proof for the feedback control system. Numerical simulations and processor-in-the-loop (PIL) experiments are conducted to validate and implement the designed flight control algorithm on real autopilot hardware. The novelty of the proposed research lies in hardware implementation of a sophisticated version of modern control technique that exhibits a multitude of distinguishing features including but not limited to (i) finite-time tracking stability featuring fast convergence is ensured, (ii) chattering and singularity problems in sliding mode control (SMC) are avoided, and (iii) null steady-state error is achieved along with enhanced robustness. Finally, the proposed control law is compared with two recently reported research works. Results of performance comparison in term of the integral of square error (ISE) and the absolute value of the derivative of the input ut (IADU) dictate that the proposed technique overperforms by precision and chattering alleviation.