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.
Highlights
Reusable rocket is becoming an important space vehicle due to its low launch cost [1]
Due to nonlinear dynamics and various nonconvex state and control constraints, the landing trajectory planning problem is highly nonconvex, which makes it difficult to be solved in real time via existing nonconvex optimization algorithms
One of the main reasons is that the angle of attack (AOA) constraint is a nonconvex-nonconcave inequality constraint which is difficult to be handle by lossless convexification and successive linearization method
Summary
Reusable rocket is becoming an important space vehicle due to its low launch cost [1]. Due to nonlinear dynamics and various nonconvex state and control constraints, the landing trajectory planning problem is highly nonconvex, which makes it difficult to be solved in real time via existing nonconvex optimization algorithms. One of the main reasons is that the AOA constraint is a nonconvex-nonconcave inequality constraint which is difficult to be handle by lossless convexification and successive linearization method. The CFS method was first proposed to address the obstacle avoidance problem in robot motion planning [24]–[26], in which the key idea is to find a CFS of the original problem Using this method, we find out a convex feasible subset in the AOA constraint by introducing the quadratic concave function. The lossless convexification is employed to address the thrust constraint, and the successive linearization is performed to handle the nonlinear dynamics.
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