This paper considers a satellite inspection mission where the deputy satellite is required to remain a fixed distance away from the chief satellite. This constraint on the deputy’s state is modeled as the surface of a sphere. Finding minimum energy solutions to travel from one point to another point on the sphere requires solving a nonconvex optimal control problem. Various novel suboptimal algorithms are proposed that can guarantee a feasible solution. These algorithms are benchmarked by optimal values obtained via a global continuation method, and their computational performance is analyzed in a statistical setting.
This paper considers the problem of a deputy spacecraft constrained to remain a fixed distance from another spacecraft. The relative dynamics of the deputy spacecraft are derived from a velocity-dependent potential function. A constant of motion is presented that aids in the development of multiple Lyapunov functions and stabilizing control laws. Through both numerical and analytical methods, estimates of the region of attraction are presented for each of the control laws. These regions of attraction serve as domains on which it is conclusively known that the equilibrium points are stabilizable. Lastly, a control law with a spatially maximal region of attraction is presented that can be used to track a time-varying trajectory.
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