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We compute the reach-avoid set for space vehicle rendezvous and docking under continuous thrust. We model the space vehicle dynamics through the Clohessy-Wiltshire-Hill (CWH) equations, resulting in a switched hybrid system with affine, time-invariant dynamics. We exploit a closed-form solution to the CWH equations to analytically determine evolution of the boundary of the reach-avoid set, then modify...
A new set of relative orbit elements (ROEs) is used to derive a new analytical optimal formation control strategy. The control of in-plane and out-of-plane relative motions can be completely decoupled using the ROEs-based impulsive feedback control law. The effects of the earth gravity harmonics perturbation (mainly J2) on the relative orbit are derived. Subsequently a formation optimal control approach...
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