Optimal Terminal Maneuver for a Cooperative Impulsive Rendezvous
In this Note, the optimal terminal maneuver is determined for a
cooperative impulsive rendezvous of two space vehicles.
The term "cooperative rendezvous"
implies that each vehicle is active, i.e., capable of
providing all or part of the total velocity change required for
This maneuver, which occurs at the point of interception
of the two vehicles, must be performed in an optimal manner
to be part of an overall optimal cooperative rendezvous solution.
The common velocity vector of the two vehicles after the
rendezvous is unspecified, and therefore free to be optimized.
Optimal rendezvous implies that the sum of the final masses of the
two vehicles is maximized.
This is synonymous with minimum total propellant consumption, but it
is not the same as minimum total ΔV because the masses and exhaust
velocities of the two vehicles are in general different.
The propellant mass fraction of each vehicle is assumed to be
constrained between a minimum value of zero and a specified maximum
value that is less than unity.
In the case of only one active vehicle, this is a moot point.
The active vehicle either has enough propellant to perform the rendezvous
or it does not.
By contrast, the two-active-vehicle case is more interesting.
If each vehicle has enough propellant to perform the rendezvous,
the more propellant-efficient vehicle will provide the total required
However, if the more efficient vehicle does not have enough propellant
to provide the total ΔV, the other vehicle must provide some, or
in some cases, all of the velocity change.
Illustrations of these cases are provided by numerical examples at the
end of this Note.