Guidance law of spacecrafts for orbital rendezvous problem

For the space rendezvous process, the hypothesis of pulse thrust will always not be satisfied, which causes a big deviation between the actual and nominal optimal trajectory. After providing the approach of the ordinary differential equation (ODE) integration with differential algebraic (DA), a DA method is used to obtain the nominal velocity pulse value by iteration and get the position deviation between the end of the actually finite thrust arc and the nominal trajectory. Then DA is used to get the small velocity correct values which act at the end of the finite thrust arc, using this kind of velocity correction value, the spacecraft can reach the nominal final position and avoid the complex computing process of iteration and ODE integration in every guidance circle.