A modified proportional navigation scheme for rendezvous and docking with tumbling targets: The Planar case

A two-phase proportional navigation scheme is developed for the case of two rigid bodies engaged in a rendezvous/docking maneuver. The target vehicle is nonmaneuvering, but does have constant nonzero angular and linear velocities. Under these conditions, it is shown that previously obtained solutions are not applicable. Analytical solutions are obtained leading to relationships between the transverse and LOS navigation constants. It is shown that the transverse navigation constant for the second phase of the maneuver must be 2. Also, initial conditions necessary for rendezvous are presented.