Control of a Quadrotor Using Linear Quadratic Regulator: Mathematical Modeling and Implementation Approach

This paper presents a comprehensive study on quadrotor control using the Linear Quadratic Regulator (LQR) technique. Quadrotors, widely employed as autonomous aerial vehicles and drones, require sophisticated control strategies for stable flight operations. The LQR method serves as a fundamental optimal control approach for linear systems and proves highly applicable to quadrotor stabilization. The implementation typically involves deriving a linearized state-space model from the nonlinear dynamics, then computing optimal feedback gains through Riccati equation solutions. Key implementation steps include: 1) System linearization around hover conditions using Jacobian matrices, 2) Designing Q and R weighting matrices for state/control trade-offs, 3) Calculating optimal gain matrix K=lqr(A,B,Q,R) in MATLAB, and 4) Implementing state feedback control u=-Kx. This research thoroughly details the control methodology from mathematical modeling based on Newton-Euler equations to experimental validation results, including attitude stabilization and trajectory tracking performance metrics.