Rocket landing guidance using convex optimization and proportional navigation considering performance-limited engine

In recent years, convex optimization has been widely applied in aircraft trajectory optimization and guidance. For rocket vertical landing, the dynamics are highly nonlinear, which easily causes convergence issues in convex optimization. Moreover, for the existing convex optimization methods, it is difficult to implement landing guidance with a performance-limited engine in which the thrust cannot be continuously and instantly regulated. To address these two issues, a novel rocket vertical landing guidance method is developed, in which the guidance in the normal and tangential planes with respect to the rocket velocity is separated to enhance the convergence property of convex optimization. Normal guidance adopts biased proportional navigation to easily satisfy the pinpoint landing with the required attitude angles. For tangential guidance, convex optimization and model predictive control are employed to optimize the thrust command that satisfies the landing velocity limit. Based on this, an impulse equivalent transformation method is designed to derive thrust commands that satisfy the engine limits. Simulation results indicate that the proposed guidance method can achieve precise landing and satisfy various constraints while being highly robust to uncertainties. Moreover, the efficiency, convergence property, and control smoothness are significantly improved.