Design of Guidance and Algorithms for Space Rendezvous Maneuvers

CubeSat technology has been widely studied in the last 20 years, especially for missions in Low-Earth-Orbit (LEO). It represents an interesting alternative to multisatellite missions with bigger spacecrafts thanks to their superior agility and low cost. When these nanosatellites are operating to achieve a docking mission, it is essential to carefully plan rendezvous maneuvers and proximity operations to ensure mission safety and success. The aim of this research is to design and evaluate the performance of guidance and control algorithms for orbital rendezvous maneuvers. Zero-Effort-Mission/Zero-Effort-Velocity (ZEM-ZEV) guidance and Linear Quadratic Regulator (LQR) control are investigated to achieve position and attitude control for two 3U CubeSats in different scenarios. The first mission scenario considers the chaser in an initial station keeping point behind the target on a lower orbit. The approach trajectory starts with a homing phase to rise the chaser altitude and get to the target orbit, then a closing phase decreases the distance with the target until a final station keeping point is reached. A ZEM-ZEV guidance is implemented to control the chaser position during the target approach. This guidance, commonly applied to asteroids intercept and landing, is an optimum law only if the target gravitational field is a function of time. Moreover, this algorithm has a good accuracy, low fuel consumption, and effectiveness in presence of external disturbances. The ZEM-ZEV guidance is modified to adapt it to the rendezvous problem. In order to ensure that the chaser actually follows the defined trajectory, the actual position and velocity of the spacecraft are compared with the ideal ones at each time step. This method also allows low control accelerations. The second scenario is a short range maneuver. As before a homing phase followed by the closing phase is executed to reach a final station keeping point few meters behind the target. The objective of this mission is to test the precision of the Guidance, Navigation and Control (GNC) system during proximity operations before a docking. Therefor, a collision avoidance maneuver is also implemented where the chaser moves away from the target along a semicircular trajectory. An LQR law is proposed to control the chaser position along the maneuver. The LQR feedback gain is computed from the Hill equations of the relative motion and the cost weighting matrices are chosen from a trade-off in order to balance the requirements of following the desired trajectory and minimize the fuel consumption. An attitude control system is finally studied for the chaser to ensure the possibility to hold or modify the orientation throughout the maneuver, acting against the external torques. Euler’s equations are formulated for the dynamics while the kinematics is based on quaternions to avoid rotational sequences and singularities at any attitude. The feedback control exploits an LQR method based on the linearized dynamics equations. The work is completed with a proposed combination of attitude control and position control for the second scenario.