ATTITUDE CONTROL OF 3D RIGID PENDULUM BASED ON MODIFIED RODRIGUES PARAMETERS

The 3D rigid pendulum is a simplified mechanical model of the GEO (Geostationary) stationary spacecraft, and it is a rigid body with three rotational degrees of freedom, connected with a fixed pivot without consideration of the friction. The attitude dynamics equations of the 3D rigid pendulum based on the modified Rodrigues parameters are derived in this paper. For the 3D rigid pendulum's attitude and angular velocity stability as a nonlinear control design problem, by using the energy method, the system controller is designed based on the passive control theory. It is shown that the system can meet the passive condition. By constructing the system's Lyapunov function, the attitude control law of the 3D rigid pendulum is obtained by using the energy method, and the LaSalle invariant principle is used to prove the asymptotic stability of the control law. The simulation results show that the attitude and angular velocity are asymptotically stable in the case of the inverted equilibrium and the simulation results verify the reliability of the method.