Velocity estimation for spacecraft with immersion and invariance observers

This paper investigates the control problem of the spacecraft with only position and attitude measurement via coupled liner velocity and angular velocity observers. In the first instance, the coupled six degrees of freedom dynamics of a single spacecraft described by dual numbers (quaternions) are established. Then, a velocity observer is designed utilizing the immersion and invariance(I&I) methodology. The cross terms caused by angular velocity are absorbed by the high-gain injection. This observer takes into account the gravity gradient torque, gravitational force, measurement noise. The convergence of the observer states and the boundedness of injection gain are analyzed theoretically by Lyapunov function, and the exponential stability of the observer is proved. Furthermore, a PD position and attitude tracking controller is designed. The asymptotic stability of the closed-loop system of this observer-controller cascade structure is analyzed. Finally, the simulations are demonstrated to show the effectiveness of the theoretical results.