This paper focuses on the mathematical modeling of a bench-quadcopter system. We present an approach for estimating the viscous friction coefficient in the test bench’s hinge joint. For the considered test bench-quadcopter system model, we have synthesized a covariance controller that stabilizes the system at its top unstable equilibrium point. A dataset was annotated the keypoint detection task, and a YOLOv8 model was trained and tested for HPE to establish the relationship between thrust forces generated by UAV motors and PWM signals. The synthesized algorithms were tested, and the experimental results obtained from the physical system are presented in the final section of this work.