Design and simulation of an optimal missile trajectory with constraints of impact time and impact angle

For the nonlinear characteristics of cruise missile's kinematic model, we present an optimal cruise trajectory with constraints of impact angle and impact time. Section 1 of the full paper designs a guidance law of initial guidance stage based on the variable structure control theory; eqs. (6) and (8), both proposed by us, are the control overloads of lateral channel and longitudinal channel respectively. Section 2 firstly transforms the missile's nonlinear kinematic model flexibly without linearization, and then designs a guidance law of mid-course guidance stage using the minimum principle of optimal control theory and considering the impact angle and impact time constraints; eq. (14) is the control law we used. Section 3 designs a guidance law of terminal guidance stage, its core consists of: (1) the projecting of the missile and target speeds to the visual coordinate; (2) the improved 3D proportional guidance law (eq. (18)); (3) the missile-target relative movement model (eq. (19)). The simulation results, presented in Figs. 3 through 7, show that the designed trajectory can hit the target precisely and satisfy both the impact time and impact angle constraints.