The purpose of the guidance control is to release a payload into a prescribed target orbit (PTO) accurately. The parameters that determine an orbit are called orbital elements (OEs), which include the semi-major axis a, the eccentricity e, the argument of perigee $$\omega $$
ω
, the inclination angle i, and the longitude of ascending node (LAN) or the right ascension of ascending node (RAAN) $$\Omega $$
Ω
, where a and e can be converted to the perigee height $$h_p$$
h
p
and the apogee height $$h_a$$
h
a
. Thus, the guidance mission of a launcher is a typical optimal control problem with multi-terminal constraints, which requires complex iterative calculations. Considering various constraints in practical applications, such as the accuracy of inertial navigation systems and the performances of embedded computing devices (speed and storage capacity), guidance methods need to balance the mission requirements, hardware resources, and algorithm complexity. A variety of guidance methods has been developed with distinct era characteristics.