Optimization of Quaternion Based on Hybrid PID and $$\varvec{P}_{\varvec{\omega}} \varvec{ }$$ Control

The aim of this article is to present an optimization of full non-linear quaternion based on hybrid control scheme using Genetic Algorithm (GA). A comprehensive objective is used to find novel solutions to design hybrid controller based on PID and \(\varvec{ P}_{\varvec{\omega}}\) control so that the performance and functionality system and may be compromised. The proposed hybrid control algorithm and quadrotor attitude model have been implemented in the fully quaternion space without any conversion and calculations in the Euler’s angles. In this paper, the optimized quaternion with fitness function composed of \(\varvec{ K}_{\varvec{P}}\), \(\varvec{ K}_{\varvec{I}}\), \(\varvec{ K}_{\varvec{D}}\), and \(\varvec{ P}_{\varvec{\omega}}\) are proposed, and the output effective waveform is shown by simulations using MATLAB.