Energy- and time-optimal reconfiguration of spacecraft clusters with collision avoidance

Spacecraft cluster reconfiguration is one of the enabling technologies to ensure non-traditional attributes of distributed space systems. This work treats energy- and time-optimal reconfiguration problems for both circular and eccentric reference orbits. Furthermore, typical local and coupling constraints have been taken into account. Particularly, focus is given to two coupling constraints: final configuration constraints and collision avoidance constraints. For final configuration constraints, a parameterization method is applied to ensure that the reconfiguration problem can be solved as only one optimization problem, rather than a large number of optimization problems resulting from the traditional discretization method. A generalized formulation is proposed for non-convex collision avoidance constraints, which are then convexified via linearization and convex restriction technology. This method provides the affine approximation as a special case. After incorporating above constraints, the reconfiguration problem is formulated as an open-loop optimal control problem, which is solved via the Gauss pseudospectral method (GPM). By virtue of elegant features of GPM, those solutions can serve as a counterpart and stepping stone for a distributed implementation of reconfiguration algorithms. Various simulations demonstrate that minimum-energy/time cluster reconfiguration problems with collision avoidance for circular and eccentric reference orbits can be solved effectively and efficiently using GPM.