On the Impulsive Formation Control of Spacecraft Under Path Constraints

This paper deals with the impulsive formation control of spacecraft in the presence of constraints on the position vector and time. Determining a set of path constraints can increase the safety and reliability in an impulsive relative motion of spacecraft. Specially, the feasibility problem of the position norm constraints is considered in this paper. Under assumptions, it is proved that if a position vector be reachable, then the reach time and the corresponding time of impulses are unique. The trajectory boundedness of the spacecraft between adjacent impulses are analyzed using the Gerschgorin and the Rayleigh-Ritz theorems as well as a finite form of the Jensen's inequality. Some boundaries are introduced regarding the Jordan-Brouwer separation theorem which are useful in checking the satisfaction of a constraint. Two numerical examples (approximate circular formation keeping and collision-free maneuver) are solved in order to show the applications and visualize the results.