A Convex Programming Method for Rocket Powered Landing With Angle of Attack Constraint

Abstract

Real time trajectory planning is vital in rocket precision powered landing guidance. Due to the nonconvex angle of attack (AOA) constraint and other constraints, including nonlinear dynamics and thrust constraint, the powered landing trajectory planning problem is highly nonconvex, which makes it difficult to be solved in real time via existing nonconvex optimization algorithms. As the main contribution of this paper, the AOA constraint is taken into account in the problem. A convex feasible set method is presented to handle it, in which a quadratic concave function is introduced to find a convex feasible subset in the original AOA constraint and the second order term of this function is estimated by Gersgorin disc theorem. For the remaining nonconvexities, the lossless convexification is employed to address the thrust constraint, and the successive linearization is performed to handle the nonlinear dynamics. Thus, a convex optimization problem with AOA constraint for landing trajectory planning is built. The optimal solution to the original problem is obtained by iteratively solving convex problems. Numerical simulations show that the proposed method can find a feasible landing trajectory where the AOA constraint is satisfied and has a better convergence performance compared with the traditional linearization method. INDEX TERMS Convex feasible set, angle of attack constraint, powered landing.

Design of the landing guidance for the retro-propulsive vertical landing of a reusable rocket stage

“…In the present work, a linearization using its first-order Taylor approximation has been considered. However, future work could include linearization of the constraint using second-order Taylor approximation, and a convex feasible set (CFS) method [14]. In addition to virtual control and trust region, and to avoid infeasibilities and to enhance convergence, AoA and terminal state constraints have been relaxed.…”

Fault-Tolerant Guidance of Rocket Vertical Landing Phase Based on MPC Framework

“…There are two commonly used coordinate systems for modeling rocket vertical landing problems, the velocity coordinate system [16][17][18][19][20] and the landing point coordinate system [21][22][23][24][25]. In this paper, the three-degree-of-freedom dynamics of the rocket are derived based on the landing point coordinate system.…”

“…In Ref. [24], a convex feasible set (CFS) method is proposed to convexify the angle of attack constraint which is a nonconvex-nonconcave inequality. Ref.…”