The purpose of this paper is to design and simulate a linearized attitude stabilizer based on linear quadratic regulator theory (LQR) using the multiplicative definition of the attitude.
The attitude is modeled by the modified Rodriguez parameters that provide a minimal representation of attitude and always invertible kinematics. The nonlinear model of the satellite attitude dynamics is linearized around the origin and an LQR is proposed for the linearized design. They are also simulated using the original nonlinear satellite dynamics in order to verify that the controller is operating properly. Simulations include randomly selected initial conditions to justify the stability against various initial conditions.
Theoretically, the resultant controllers are locally stable around the origin. However, the simulation results show that the attitude is well regulated in the presence of both inertia uncertainties and random initial conditions.
The originality of this work is due to its demonstration that complicated attitude regulators are not the solution for proper satellite or spacecraft attitude stabilization.
