This survey is aligned toward controlling quadrotors in the application of aerial manipulation or surveillance of tunnels, windmills, transmission lines, and other constrained spaces, where human presence would be inefficient, hazardous, or infeasible. Quadrotors have opened many opportunities in research, especially in control applications owing to their coupled underactuated dynamics. In a typical aerial manipulation application, the quadrotor must have an appropriate size and shape to perform dexterous operations without colliding with the environment. Identifying and operating in problematic regions demand ample flight time. The constraint on the robot's size necessitates a reduction in the mass of the robot and the power consumption. So, the robot has to carry minimal hardware, including sensors, actuators, power supply, and processor.
Most existing control techniques are unusable in real applications because they rely too much on localization accuracy. However, the current techniques in visual-inertial localization methods require heavy processing capabilities. So, research is shifting toward remotely operated UAVs (drones over IP), enabling a human to teleoperate an aerial manipulator with visual aids. In such a scenario, the controller must be robust to time-varying delays. Further, the operations of the manipulator introduce additional forces and moments along with the existing parametric uncertainties and external disturbances. Therefore, we present a survey of current works on controlling quadrotor UAVs in such applications in the presence of parametric uncertainties, disturbances, and time-varying delays.