Dynamics and Optimal Control of Quadcopter

One of the primary difficulties encountered by researchers when dealing with quadcopters is the inherent coupling of their dynamics, which involve passive dynamics and MIMO nonlinear systems. The quadcopter's intricacy is heightened by the fact that it operates in six degrees of freedom, encompassing three rotational movements and three translational and. However, it is controlled using only four independent inputs, specifically the rotor speeds. This mismatch between the degrees of freedom and control inputs leads to highly nonlinear dynamics for the quadcopter, particularly when accounting for the intricate aerodynamic influences that come into play. The objective of this article is to develop appropriate techniques for stabilizing, and controlling the trajectory of a quadcopter. The paper discusses control and planning of robotic flight in three-dimensional environments for aerial vehicles, with an emphasis on quadrotors. The first step derives a nonlinear mathematical model and obtain a linearized version of the model. The second step derive the optimal controller, which is used to stabilize the quadcopter's four basic movements: altitude, pitch, roll, and yaw angles. The LQR controller balances the performance of the drone and the energy it consumes by specifying the weighting matrix of performance cost Q and control cost R to calculate an optimized controller. Increasing the performance cost leads to a faster responding drone, while increasing the control cost leads to a more energy-efficient drone.