Lambert Guidance Routine Designed to Match Position and Velocity of Ballistic Target

A three-degree-of-freedom interceptor missile simulation designed to rendezvous with a ballistic target is presented. The guidance scheme is designed to match the position and velocity of a ballistic target so that the interceptor will follow the target after the rendezvous. The guidance routine uses Lambert guidance to control the missile during the boost phase and put it on course to meet the ballistic target trajectory. After a long ballistic coast phase, shortly before rendezvous with the ballistic target, a short fourth-stage burn is scheduled to match the velocity of the ballistic target. The two-dimensional Lambert guidance equations are generalized to a three-dimensional coordinate system with the appropriate transformation matrix. The derivation of the equations for the miss distance created by the ∆V maneuver and required modifications to Lambert guidance are presented. Powell’s method is used to optimize the missile time of flight to reduce the maneuver ∆V requirements. The missile simulation is used to produce several trajectories and explore the ∆V requirements as a function of downrange and crossrange launch position of the interceptor.