Optimal guidance trajectories for a nanosat docking with a non-cooperative resident space object

There has been an increasing interest in on-orbit autonomous servicing and repair of satellites as well as controlled active debris removal (ADR) in the space industry recently. One of the most challenging tasks for servicing/repair as well as for ADR is the rendezvous and docking with a non-cooperative tumbling resident space object (RSO). This paper presents a propellant optimal maneuver profile for a servicing spacecraft to perform proximity operations and eventually dock with a non-cooperative target. The strategy is to find an optimal trajectory which will guide the servicing spacecraft to approach the tumbling satellite such that the two vehicles will eventually have no relative motion. Therefore, a subsequent docking or capture operation can be safely performed. The research described here elaborates on the previous work that studied the minimum-control-effort for a 3-D docking to a tumbling object considering a full six-degree-of-freedom model of both chaser and target. The current work expands the scope by adding new set of linearized equations of motion that capture the effect of the J
₂
geopotential disturbance force. Typically, Hill's linearized equation of relative motion have been used for this analysis, but they fail to capture the effect of J
₂
disturbance force on the chaser satellite. Firstly, the effects of the J
₂
disturbance force is added to the linearized equations of motion by the addition of the J
₂
terms. Secondly, minimum-control-effort optimality condition is examined and propellant optimal trajectories for a relative motion problem are then numerically solved, by using a direct collocation method based on the Gauss pseudospectral approach. The simulation results shows the effect of errors caused by the oblateness of the earth (as described by the J
₂
potential) on the described relative motion problem. Furthermore, effect of J
₂
disturbance on the optimal trajectory is discussed for the minimum propellant-consumption optimality condition.