Dual quaternion-based dynamics and control for gravity recovery missions

Abstract

A novel dual quaternion modeling and control approach is introduced as a better alternative to traditional modeling methods for formation flying spacecraft utilized for gravity recovery missions. The new formulation for the equations of motion for the relative dynamics of formation flying spacecraft and an interior test mass results in two coupled six degree-of-freedom models that show superior performance over traditional linearized and uncoupled methodologies. Utilizing data products from the Gravity Recovery and Climate Experiment Follow-On mission, a comparison of modeling methods is presented which demonstrates the advantage of the proposed dual quaternion-based modeling approach. Also, a dual quaternion-based Lyapunov controller is formulated and proven to control a test mass within specified gravitational reference sensor development requirements. Additional fidelity is added to the simulation by modeling the voltage-to-force and-torque equations of electrodes located within an electrode housing with appropriate white noise added to the commanded voltages. Equations are also derived and presented for modeling the coupling between the spacecraft and the test mass, and for modeling the density of the atmosphere so that the simulations of the spacecraft and test mass include both gravitational and nongravitational effects. This research ultimately lays the ground work and shows the need for, dual quaternions on future gravity recovery missions.