Physical Dynamics and Model

The goal of this project was to create a usercontrollable quadcopter that would receive user reference variables for x, y, and z velocities via radio and respond by moving in the appropriate direction. The project incorporated two major concepts introduced in EE149: Modeling of physical dynamics and simulation strategies. To find reasonable values for quadcopter motor outputs, a simulation was crucial — with no simulation, the quadcopter would most likely fail to perform any kind of aerodynamic feet. In order to simulate the physical dynamics of the quadcopter, though, a mathematical model of the physical dynamics was needed. Once equations describing the state of the quadcopter over time was obtained, Matlab tools such as Simulink was applied to obtain theoretical evolution of the state of the quadcopter. Physical Dynamics and Model In this project, we implemented the quadcopter configured to fly in the x-orientation, following the righthand rule 3-dimensional coordinate system. Much of the mathematical derivations and physical assumptions used in this project were derived in parallel to Andrew Gibiansky’s paper, ”Quadcopter Dynamics, Simulation, and Control”; differences in quadcopter configuration and coordinate systems were incorporated into the original calculations performed in that paper. Such differences manifested itself in the equations of quadcopter torque, as well as the rotation matrix utilized to transform the derived quadcopter dynamics from the quadcopter body frame to the inertial frame. The final rederived equations successfully described the 9 state variables of interest as differential equations. The equations that describe the evolution of linear acceleration, angular velocity, and the time derivative of roll, pitch, and yaw follow: ẍ = −kd m ẋ+ k m (sφsψ + cψsθcφ)(ω 2 1 + ω 2 2 + ω 2 3 + ω 2 4)