A Preliminary Study of Optimal Thrust-Limited Path-Constrained Maneuvers
Fuel-optimal maneuvers of a constant-specific-impulse, thrust-limited
spacecraft in field-free space are analyzed. The simple problem of an optimal
maneuver from a state of rest at one location to a state of rest at another
location becomes very complex when a path constraint is introduced. Solutions
are obtained using a direct numerical optimization method that combines
Hermite-Simpson transcription and non-linear programming. The resulting
Lagrange multipliers provide a discrete approximation to the primer vector.
The necessary conditions for an optimal solution can then be checked to
validate the solution. Fundamental concepts, such as the existence of boundary
arcs or boundary points and the optimal number of coast arcs, are examined.
A comprehensive solution is obtained for symmetric rest-to-rest maneuvers.
More general maneuvers are also examined.