Convexification of Aerodynamic-Constraints for Reusable-Rockets Reentry-Burn Guidance

This paper presents a convexification method for aerodynamic constraints used in guiding a reusable rocket’s first stage during its reentry burn. Following upper stage separation, the first stage performs a reentry burn to mitigate excessive aerodynamic loads, then coasts to a predefined position and velocity for the final landing burn ignition, relying on atmospheric deceleration. Consequently, minimizing fuel consumption during the reentry burn requires maximizing aerodynamic deceleration while strictly adhering to vehicle aerodynamic constraints. However, these constraints, which include dynamic pressure (Max-Q), angle of attack (Max-α), and their product (Max-Qα), are highly nonlinear functions of the vehicle’s position, velocity, and inertial attitude. Consequently, generating guidance trajectories via sequential convex optimization using linear constraint approximations often leads to convergence issues. To address this challenge, we propose a convexification method for the aerodynamic constraints that employs an atmospheric density approximation, control input variable transformation, and dynamic pressure linearization. The method is formulated around discrete trajectory points, using the L2 norm and second-order cone constraints. It specifically ensures that the original nonlinear constraints are fully satisfied for the Max-Q and Max-Qα constraints. The reentry burn guidance problem is modeled using a point-mass system. Numerical examples are presented for the first-stage return guidance of a large rocket, including a parameter study of the impact of initial position errors after the separation.