Optimal hybrid Coulomb control for on-track rendezvous and docking of spacecraft

This paper investigates the dynamics of on-track rendezvous and docking of two spacecraft, and stabilization using hybrid Coulomb control. Modeling electrostatic forces and torques for control of complex spacecraft geometries like cylinders is challenging. Point mass assumption of the spacecraft that disregards the chaser dynamics will lead to errors in force estimation during the terminal docking phase, resulting in a mission failure. This paper uses the effective sphere method to model Coulomb interactions between the chaser and the target. The method is coupled with the chaser's tumbling motion about its body axes to develop a relationship between electrostatic force and attitude. The relative attitude dynamics of the chaser is then derived and incorporated into the system dynamics. Differential gravity and hybrid thrusters are used to stabilize the relative attitude of the two bodies. The charge-voltage relations are used to compute potential variations for the Coulomb control. An optimal linear quadratic tracking control is proposed for tracking a reference trajectory generated using solutions of Clohessy-Wiltshire-Hill's equations. Numerical simulations are carried out for both non-linear and linear models of the Coulomb spacecraft to validate the proposed concept. Results have also been compared with an existing voltage feedback controller to demonstrate the merits and challenges of electrostatic actuation for rendezvous and docking.