On the fuel optimality of maneuvers for multi-spacecraft interferometric imaging systems
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In this paper, we study the design of minimum fuel maneuvers for multi-spacecraft interferometric imaging systems. We show that the underlying optimization problem is computationally intractable, by mapping it into a Generalized Traveling Salesman Problem, and that it is necessary to resort to heuristics in order to solve the problem. We consider the design of minimum fuel spiral maneuvers and formulate the "Minimum Fuel Double Pantograph Problem". We show that the geometric design problem, the optimization problem obtained by fixing the angular rate of the spiral, and the kinematic design problem, obtained by fixing the spiraling rate of the spiral, are both convex, under certain assumptions. Further, we show that these conditions are satisfied by two important cases of dynamical systems: free space and linear systems. It is also shown that an equilibrium of the minimum fuel problem is obtained by solving an alternating sequence of the kinematic and geometric design problems.
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