An Iterative Convex Programming Method for Rocket Landing Trajectory Optimization
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An Iterative Convex Programming Method for Rocket Landing Trajectory Optimization Jinbo Wang 1 & Huixu Li 1 & Hongbo Chen 1 Accepted: 11 September 2020 / / # American Astronautical Society 2020
Abstract A rapid trajectory optimization method is proposed to solve the fuel-optimal Earth-landing problem of reusable rockets, in which the nonlinear aerodynamic drag force is non-negligible. To enable the online and autonomous operation ability, the method is designed based on convex optimization, which features rapid and deterministic convergence properties, and a homotopic-iterative strategy is proposed to convexify the nonlinear system dynamics of the rocket. In the proposed iterative algorithm, the problem is first solved based on the lossless convexification method while the drag force is considered to be zero. Then, during subsequent iterations, the drag profile is approximated by the last solution and homotopically added to the problem. Thus, the nonlinear drag is gradually included while the problem remains convex. Because the convexification of the nonlinear terms is not based on linearization, no reference trajectory or initial guess is needed, which greatly enhances the autonomy of the algorithm. Numerical experiments are provided to demonstrate the effectiveness, rapidness, and accuracy of the proposed algorithm. Keywords Reusable rocket landing . Online trajectory optimization . Convex optimization
. Lossless convexification . Homotopy method
* Jinbo Wang [email protected] Huixu Li [email protected] Hongbo Chen [email protected]
1
School of Systems Science and Engineering, Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
The Journal of the Astronautical Sciences
Introduction Reusable launch vehicles (RLVs) are effective tools for fulfilling the demands of low cost and fast access to space. Since the era of the space shuttle, many different types of RLVs have been developed and studied. In recent years, with the rapid progress of commercial aerospace companies, such as SpaceX and Blue Origin, vertical takeoff vertical landing (VTVL) RLVs that have evolved from conventional launch vehicles have received increased attention. Vertical landing is a significant feature that characterizes a VTVL rocket. This paper focuses on the online landing trajectory optimization of VTVL rockets, which would enable advanced and autonomous landing guidance. With the development of computing technology and advanced theories and algorithms, computational methods have become popular for solving aerospace guidance and control problems [21]. In particular, real-time trajectory optimization is a promising and essential approach for achieving optimal and autonomous guidance under complex environments and constraints [7]. In general, numerical methods for trajectory optimization can be categorized into indirect and direct methods [5], where direct methods can be more easily applied to problems with complex vehicle dynamics and constraints. Compared with other direct methods, methods b
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