Guidance, Navigation and Control for Satellite Proximity Operations using Tschauner-Hempel Equations

In this paper, the development of relative navigation, guidance, and control algorithms of an autonomous space rendezvous and docking system are presented. These algorithms are based on using the analytical closed-form solution of the Tschauner-Hempel equations that is completely explicit in time. The navigation system uses an extended Kalman filter based on Tschauner-Hempel equations to estimate the relative position and velocity of the chaser vehicle with respect to the target vehicle and the chaser attitude and gyros biases. This filter uses the range and angle measurements of the target relative to the chaser from a simulated LIDAR system along with the star tracker and gyro measurements of the chaser. The corresponding measurement models, process noise matrix and other filter parameters are provided. The guidance and control algorithms are based on the glideslope used in the past for rendezvous and proximity operations of the Space Shuttle with other vehicles. These algorithms are used to approach, flyaround, and to depart form a target vehicle in elliptic orbits. The algorithms are general and able to translate the chaser vehicle in any direction, decelerate while approaching the target vehicle, and accelerate when moving away. Numerical nonlinear simulations that illustrate the relative navigation, attitude estimation, guidance, and control algorithms performance and accuracy are evaluated in the current paper. The analyses include the navigations errors, trajectory dispersions and attitude dispersions.