Thrust Integrated Trajectory Optimization for Multipulse Rocket Missiles Using Convex Programming

In this paper, a thrust integrated trajectory optimization algorithm for multipulse rocket missiles is proposed. Maximizing terminal velocity is selected as a performance index for achieving high maneuverability in the homing stage. To incorporate the optimization of thrust profile, thrust parameters are also considered as optimization variables with several thrust constraints such as impulse conservation and maximum/minimum thrust level. The original trajectory optimization problem is reformulated using new independent variables and timescale variables. This method simplifies the dynamics and makes the impulse conservation constraint disappear. Then, a control-affine system is established by defining the angle of attack and its square as new control inputs. The admissible input set is relaxed to a convex set, and mathematical proof is provided to show that the relaxation preserves the solution. The problem is discretized by applying a pseudospectral method for each subinterval. The solution is then obtained using sequential convex programming (SCP). A quadratic variable trust-region constraint is used for robust convergence of SCP. The proposed method robustly optimizes the thrust parameters and trajectory of the multipulse rocket missile within 1 s. Numerical simulation shows the feasibility and effectiveness of the proposed method.