Patent ID: 8244417

Claim:
A method for formation-keeping of a spacecraft in response to a displacement of the spacecraft to a displaced pose with respect to at least one direction of the displacement, wherein the spacecraft is configured to issue a compensative force, comprising the steps of: determining the compensative force as a function of a sum of a base force configured for maintaining the spacecraft in the displaced pose with respect to the direction of the displacement and an excess force configured for optimizing the formation-keeping with respect to the direction of the displacement of the spacecraft at the displaced pose, wherein the compensative, the base and the excess forces have a quantization resolution, the displaced pose borders an error range along the direction of the displacement; determining a magnitude of the base force according to Δ ⁢ ⁢ V base = ⌈  v x  q ⌉ ⁢ q , wherein ΔV base is the magnitude of the base force along the direction of the displacement x, v x is a veloci of the spacecraft along the direction of the displacement, and q is the quantization resolution; determining a magnitude of the excess force from a discrete control set of magnitudes, wherein a largest element maxU of the discrete control set is determined according to max ⁢ ⁢ U = ⌈ Δ ⁢ ⁢ v q ⌉ , wherein Δv is Δ ⁢ ⁢ v = 2 ⁢ d max ⁢ range 2 , wherein range is an extent of the error range, and d max is an upper bound of a displacement force; and generating a command to issue the compensative force, wherein the steps of the method are performed by a processor.