Fuel-Optimal Rocket Landing with Aerodynamic Controls

Liu, Xinfu

doi:10.2514/6.2017-1732

Cited by 16 publications

(11 citation statements)

References 9 publications

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“…This highly nonlinear and nonconvex optimization problem was solved by convex optimization after a constructive method was used to handle the nonlinear dynamics. To further broaden the application of convex optimization, Liu [40] extended convex optimization to the fuel-optimal rocket landing problem in which the engine thrust adds another freedom of controls in addition to the aerodynamic forces. Though the simultaneous presence of thrust and aerodynamics forces is still a challenge to be dealt with by convex optimization, it will find broad and important applications in atmospheric vehicles with propulsion.…”

Section: Applications In High-speed Atmospheric Vehiclesmentioning

confidence: 99%

“…The dynamics in Eq. (5) are nonlinear in many aerospace applications, such as in the hypersonic gliding and rocket landing problems [36,40]. The nonlinear dynamics will become nonlinear algebraic equality constraints after discretization and they may be the major sources of non-convexity.…”

Section: Non-convexitymentioning

confidence: 99%

“…These two variables are the control inputs. By change of variables the following nonconvex control constraint is obtained [40]:…”

Section: Relaxationmentioning

confidence: 99%

“…Note that a lower bound may also be imposed on the thrust magnitude [40]. The preceding constraints correspond to a nonconvex set (see Fig.…”

Section: Relaxationmentioning

confidence: 99%

“…3(b). The second method considers relaxing a nonconvex ũ3 Tmax/m (its feasible set is the whole solid in (b)) [40].…”

Section: Relaxationmentioning

confidence: 99%

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Survey of convex optimization for aerospace applications

2017

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Convex optimization is a class of mathematical programming problems with polynomial complexity for which state-of-the-art, highly efficient numerical algorithms with predeterminable computational bounds exist. Computational efficiency and tractability in aerospace engineering, especially in guidance, navigation, and control (GN&C), are of paramount importance. With theoretical guarantees on solutions and computational efficiency, convex optimization lends itself as a very appealing tool. Coinciding the strong drive toward autonomous operations of aerospace vehicles, convex optimization has seen rapidly increasing utility in solving aerospace GN&C problems with the potential for onboard real-time applications. This paper attempts to provide an overview on the problems to date in aerospace guidance, path planning, and control where convex optimization has been applied. Various convexification techniques are reviewed that have been used to convexify the originally nonconvex aerospace problems. Discussions on how to ensure the validity of the convexification process are provided. Some related implementation issues will be introduced as well.

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Section: Applications In High-speed Atmospheric Vehiclesmentioning

confidence: 99%

Section: Non-convexitymentioning

confidence: 99%

“…These two variables are the control inputs. By change of variables the following nonconvex control constraint is obtained [40]:…”

Section: Relaxationmentioning

confidence: 99%

“…Note that a lower bound may also be imposed on the thrust magnitude [40]. The preceding constraints correspond to a nonconvex set (see Fig.…”

Section: Relaxationmentioning

confidence: 99%

“…3(b). The second method considers relaxing a nonconvex ũ3 Tmax/m (its feasible set is the whole solid in (b)) [40].…”

Section: Relaxationmentioning

confidence: 99%

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Survey of convex optimization for aerospace applications

2017

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Gravity-Turn-Based Precise Landing Guidance for Reusable Rockets

Yang

Liu

2021

Lecture Notes in Electrical Engineering

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Autonomous Descent Guidance via Sequential Pseudospectral Convex Programming

Sagliano

Seelbinder

Theil

2023

Springer Series in Astrophysics and Cosmology

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This chapter expands our development of an autonomous descent guidance algorithm which is able to deal with both the aerodynamic descent and the powered landing phases of a reusable rocket. The method uses sequential convex optimization applied to a Cartesian representation of the equations of motion, and the transcription is based on the use of hp pseudospectral methods. The major contributions of the formulation are a more systematic exploitation and separation of convex and non-convex contributions to minimize the computation of the latter, the inclusion of highly nonlinear terms represented by aerodynamic accelerations, a complete reformulation of the problem based on the use of Euler angle rates as control means, an improved transcription based on the use of a generalized hp pseudospectral method, and a dedicated formulation of the aerodynamic guidance problem for reusable rockets. The approach is demonstrated for a 40 kN-class reusable rocket. Numerical results confirm that the methodology we propose is very effective and able to satisfy all the constraints acting on the system. It is therefore a valid candidate solution to solve the entire descent phase of reusable rockets in real-time.

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Fuel-Optimal Rocket Landing with Aerodynamic Controls

Cited by 16 publications

References 9 publications

Survey of convex optimization for aerospace applications

Survey of convex optimization for aerospace applications

Gravity-Turn-Based Precise Landing Guidance for Reusable Rockets

Autonomous Descent Guidance via Sequential Pseudospectral Convex Programming

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