Abstract
In this paper, a method based on the successive convexification is proposed to solve the ascent trajectory optimization problem, the algorithm converges to the optimal solution quickly even if the initial guess is coarse. A three-dimensional motion is formulated with complex aerodynamics and terminal constraints. Based on the modified aerodynamic coefficients, the new auxiliary control variables are designed to deal with the complex aerodynamics and non-smooth of control variables in the discrete optimization problem. The inner nonconvex constraints between the new control are relaxed to be convex without loss. The artificial infeasibility and unboundedness caused by linearization are tackled by the virtual controls and soft constraint for trust region in the successive convexification. The good convergence of the proposed method is illustrated by the iterative solutions of the ascent trajectory optimization problem for a small guided rocket, the accuracy is verified by the comparison with the optimal solution given by the typical optimal control solvers, and the feasibility and stability are demonstrated by optimal solutions of the ascent trajectory optimization problems under different missions and dispersed conditions. These excellent performances validated by the adequate simulations indicate that the proposed algorithm can be implemented online.
Highlights
The ascent trajectory optimization problem has been developed over decades and attracting wide interests and research attention, it is of great significance for the rockets or vehicles to reconstruct the trajectory adaptively when the mission changes or the non-fatal fault occurs during the flight [1]
The associate editor coordinating the review of this manuscript and approving it for publication was Shanying Zhu. Especially, they were effective in the vacuum ascent trajectory optimization problem, of which the optimal solution was the explicit expression about the initial variable [8]
Compared with the previous works on the sequential convex programming (SCP) method used in the trajectory optimization, the primary contributions of the paper are drawn as three points: 1) the 3 degree of freedom (3-Dof) formulation with accurate and tractable aerodynamics is feasible to different ascent trajectory optimization problems; 2) the proposed new control facilitates the convergence to the optimal solution; 3) the soft constraint of the trust region avoids the non-convergence of the sequential iterations
Summary
The ascent trajectory optimization problem has been developed over decades and attracting wide interests and research attention, it is of great significance for the rockets or vehicles to reconstruct the trajectory adaptively when the mission changes or the non-fatal fault occurs during the flight [1]. The direct methods were combined with the intelligent algorithms to solve the trajectory optimization problems, Jiang et al [18] proposed a hybrid optimization strategy by taking the advantages of particle swarm optimization (PSO) and Gauss pseudospectral method, Chai et al [19], [20] utilized the ‘‘discretization + optimization’’ strategies to solve the reentry trajectory planning, such as violation learning deferential evolution-based hp-adaptive pseudo-spectral method and multiple-shooting discretization technique with the newest NSGA-III optimization algorithm, besides, a violation learning deferential evolution method was designed to generate the appropriate initial guess These works illustrated that pseudospectral methods were effective to discrete the trajectory optimization problems. Compared with the previous works on the SCP method used in the trajectory optimization, the primary contributions of the paper are drawn as three points: 1) the 3 degree of freedom (3-Dof) formulation with accurate and tractable aerodynamics is feasible to different ascent trajectory optimization problems; 2) the proposed new control facilitates the convergence to the optimal solution; 3) the soft constraint of the trust region avoids the non-convergence of the sequential iterations.
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