The primary goal of this project is to analyze the kinematics and dynamics of a quadcopter, a type of mobile robot. Using this kinematic and dynamic model, classical methods such as PD controllers and optimal control techniques will be explored. The performance of each control scheme will be evaluated through simulations in MATLAB.
The simulation setup and the MATLAB script for this project are available at the following GitHub link.
https://github.com/MinThihaSoe/Design-and-Modelling-of-Quadcopter
Drone designs, particularly multi-copters, started from the Da Vinci era. Throughout the years, many attempts were made to improve the control and dynamic of the multi-copter system, most notable attempts were made by contributors like Breguet brothers in 1907 and Oehmishen and Bothezat in 1920s. With each successive attempt, further understanding of the multi-copter dynamic and control were gained, which led to the commercialization of the drone technology in the 2010s (Mendoza-Mendoza, Gonzalez-Villela, Aguilar-Ibañez, & Fonseca-Ruiz, 2021).
The standard to link between the theory and the sensor components was established by ISO 1151-2:1985 (Mendoza-Mendoza, Gonzalez-Villela, Aguilar-Ibañez, & Fonseca-Ruiz, 2021). The quadcopters were mainly developed photography, research in artificial vision or artificial intelligence algorithms, research in automatic control algorithms for aircraft flight, and agricultural purposes.
As the name suggests, the quadcopters have four motors which are oriented 90 degrees apart from each other. Brushless DC motors are commonly used in the quadcopter application due to their fast response time. The speed of the brushless motor can be controlled via RC-PWM as brushless motor is usually a multiphase motor. Aside from the motors, propellers and the base frame, the quadcopters can have various measuring components, such us IMU, GPS, gyroscopes, accelerometers, LIDARs and cameras to aid the control of the quadcopter. Quadcopters may also be equipped with telemetry and RC modules for communication and manual control and some type of microcontroller for autopilot functionality. Power components like batteries, power distributor, power module and battery indicator are also important components to consider during the designing phase of the quadcopter.
In this section, a common configuration of the quadcopter was investigated. To simplify the modelling, the aerodynamics of the propellers are ignored, and the quadcopter operates in open space; far away from walls and objects. Figure 2 shows how the forces are acting on a quadcopter.
There are three frames of modelling associated with the quadcopter, namely the world frame, the vehicle body frame, and the motor frame. World frame is the fixed frame where the vehicle moves with respect to this fixed reference frame. The body frame is attached to the quadcopter, usually placed at the center of gravity and mass. The translation and rotations of the quadcopter are measured from the body frame with respect to the world frame. Motor frames are placed on each of the motors to model the force and torque distribution of the quadcopter with respect to the vehicle reference frame.
The orientation of the vehicle with respect to the global frame can be related with rotation matrices. The rotation matrix associated with roll is $R_{z\psi}$ (where z is the roll axis) and it can be expressed as:
$$ R_{z\psi}=\begin{bmatrix} \cos\psi & -\sin\psi & 0\\ \sin\psi & \cos\psi & 0\\ 0 & 0 & 1\\ \end{bmatrix} $$