Dynamic coverage optimal control for interferometric imaging spacecraft formations (part II): the nonlinear case

This is the second of a two paper series on the dynamic coverage problem first introduced in Hussein, II and Bloch, AM (2004). Dynamic coverage optimal control is a new class of optimal control problems motivated by multi-spacecraft interferometric imaging applications. The dynamics is composed of N second order differential equations representing N fully actuated particles. To be minimized is a cost functional that is a weighted sum of the total fuel expenditure, the relative speeds between the particles and the measure of a given set whose size is a function of the particles' trajectories. In this paper, we extend the analysis to formations evolving on non-linear manifolds. We derive the necessary optimality conditions and give an example of a non-rigid two spacecraft formation evolving on a paraboloidal surface.