## 4 Simulations  
As mentioned in Section 3, a dynamics model of a commercial aerial robot (Parrot) was selected and implemented in the simulator environment as an aerial robot under control to test the effectiveness of the proposed control architecture in controlling an aerial robot. The AR Drone 2.0, the Rolling Spider, and Mambo are all Parrot products that can be programmed using MATLAB [51]. The AR Drone 2.0 toolbox was developed and distributed by researchers. In addition, a MATLAB Simulink Support Package for Rolling Spider is available as an add-on development package based on MIT's Aerospace Blockset supporting simulation, hardware code generation, and interface for Parrot Minidrones [52]. The Parrot Mambo (6-DOF small quadcopter) comes with ultrasonic, accelerometer, gyroscope, air pressure, and down-facing camera sensors. It allows algorithms to be applied to the robot via a Bluetooth link over a Personal Area Network (PAN).The Simulink Support Package for Parrot Minidrones [53], which is developed using the UAV toolbox from Mathworks [54], was utilized in this research study to simulate the quadrotor. The aerodynamics effect was deemed minor for the purpose of simplicity, hence the block associated with the aerodynamics effect was deactivated throughout the simulations. Furthermore, during the simulations, parameters of the environment (such as air pressure at various elevations) were also assumed to be constant. A UAV waypoint follower block (included in the UAV toolbox) was employed to generate several successive waypoints. In the Simulink environment, two experiments were carried out to evaluate the performance of the proposed control architecture, compared to that of typical PID controllers. The experiments aimed at evaluating the effectiveness of the controller in controlling the aerial robot in the presence of weight disturbances affecting the dynamics model of the robot. When a payload is attached to a quadrotor, three main changes may happen. The overall mass of the system increases. The fluctuations in the mass of the robot can also shift the gravitational center, and therefore the inertia. In the experiments, the payload was considered to be an isotropic symmetric stiff solid mass connected to the aerial robot, rather than being suspended. Another assumption was that the physical dimensions of the attached mass were smaller than the dimensions of the quadrotor. The distance between the center of gravity of the robot and the center of gravity of the load is associated with the shape and the weight distribution of the connector, as well as with the shape and the weight distribution of the load. In our experiments, this distance was assumed to be zero. As a result, the effects of changes in inertia and gravity were deemed insignificant. Therefore, the focus of our article was solely on analyzing the effects of mass variation on the performance of the controller. When the robot is executing a logistic task, the mass could be in two stable states: one before the load comes into contact with the quadrotor, and the other when the payload mass is integrated into the system. Depending on the gripping technique and the qualities of the surface of the load, there may be many profiles of mass fluctuation between these two states. We assumed that there was no gripping and the mass was connected to the robot body directly. Another assumption was that the load had a non-deformable surface; therefore, a single step profile for the mass disturbance could be used, as it was implemented in many prior publications. The variations in the mass were simulated by adding a term named \(Mass_{dist}\) to (16)-(18), resulting in Equations (54)-(56). \(Mass_{dist}\) is calculated using Equation (57).