Optimal, impulsive, time-fixed orbital rendezvous and interception with path constraints

Minimum-fuel, impulsive, time-fixed extremal solutions are obtained for the problem of orbital rendezvous and interception with path constraints. The coplanar case and a restricted class of path constraints are analyzed. A theory based on the extended problem of Bolza in the calculus of variations has been established to determine optimal impulsive trajectories with state variable inequality constraints (SVIC). According to this newly developed theory, all the necessary conditions including the optimal corner conditions have been obtained for both constrained and unconstrained arcs. The constrained extremal solutions, including the optimal number of impulses, their times and positions have been studied under a conjecture proposed for the minimization process on the constrained arc. The fundamental problems such as the existence of boundary arcs or boundary points, absorbing boundaries or non-absorbing boundaries, and the continuity of the Hamiltonian function with a scleronomic constraint in infinite control problems have been studied and answered in this research. A bifurcation phenomenon and the non-uniqueness of the extremal solutions having the same cost have been found during the research. The extended principles of dynamical reversibility and reflectability of the impulsive solution have been developed to obtain the conjugate solutions belonging to the same cost function. In addition, the local-optimal time-fixed solutions obtained can be used to perform time versus fuel trade-offs for missions which have time constraints.U of I OnlyETDs are only available to UIUC Users without author permissio