Abstract: The landing-phase guidance of launch vehicle is a typical nonlinear optimal control problem. With the convex optimization method, the landing-phase guidance can be effectively realized by being converted into a convex programming problem, while satisfying constraints. However, due to the nonlinearity of the landing-phase guidance, the optimal solution by convex optimization would oscillate and could not converge if only successive linearization is used. On the other hand, if variable substitution and relaxation convexification techniques are employed, the optimal solution can be clearly improved. However, different convexification techniques should be used for different convex optimization problems, lacking versatility. To address this issue, the bias proportional guidance and convex optimization are integrated to solve the landing-phase guidance of launch vehicle with the terminal track angle, velocity and thrust constraints. With the proposed method, normal guidance and tangential guidance are separated. The former adopts bias proportional guidance to satisfy the constraints on the terminal track angle and the landing point. For the latter, convex optimization and receding horizon control are employed to satisfy the constraints on the terminal velocity and the thrust constraint, and the method to estimate time-to-go and approximate trajectory parameters based on cubic curves, which could provide the necessary approximate state, is presented. The simulation results indicate that the convex optimization guidance method combined with the proposed guidance can effectively satisfy the constraints, and compared with the existing guidance method that directly adopts convex optimization and receding horizon control, the proposed method clearly improves the solution efficiency and smoothness of the control quantity. Therefore, it is more applicable to practical engineering.

Key words: rocket vertical landing, bias proportional guidance, convex optimization, receding horizon control, trajectory optimization