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 rendezvous 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 a new set of linearized equations of motion that capture not only the effect of the J
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geopotential disturbance force but also quadratic drag force. Typically, Hill's linearized equations of relative motion have been used for this analysis, but they fail to capture the effect of J
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disturbance force and drag on the chaser satellite. It appears that there is a need for a set of linearized equations that are as easy and useful as Hills equations, but at the same time capture the effect of the J
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disturbance and drag force acting on the spacecrafts. The current paper presents a set of linearized, constant coefficient differential equations that capture the J
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and quadratic drag perturbation. The importance of these perturbations is studied by doing trajectory propagation. Finally, it is shown for a control problem, the effect on the control-solution due to the formulated high fidelity dynamical constraints with respect to the simplified Hill's equations.