A Review of Spacecraft Aeroassisted Orbit Transfer Approaches

Abstract

Aerodynamic manoeuvring technology for spacecraft actively utilizes aerodynamic forces to alter orbital trajectories. This approach not only substantially reduces propellant consumption but also expands the range of accessible orbits, representing a key technological pathway to address the demands of increasingly complex yet cost-effective space missions. The theoretical prototype of this technology was proposed by Howard London. Over the course of more than half a century of development, it has evolved into four distinct modes: aeroglide, aerocruise, aerobang, and aerogravity assist. These modes have been engineered and applied in scenarios such as in-orbit manoeuvring of reusable vehicles, rapid response to space missions, and interplanetary exploration. Our research centers on two core domains: trajectory optimization and control guidance. Trajectory optimization employs numerical methods such as pseudo-spectral techniques and sequential convex optimization to achieve multi-objective optimization of fuel and time under constraints, including heat flux and overload. Control guidance focuses on standard orbital guidance and predictive correction guidance, progressively evolving into adaptive and robust control to address atmospheric uncertainties and the challenges of strong nonlinear coupling. Although breakthroughs have been achieved in deep-space exploration missions, critical challenges remain, including constructing high-fidelity models, enhancing real-time computational efficiency, ensuring the explainability of artificial intelligence methods, and designing integrated framework architectures. As these technical hurdles are progressively overcome, this technology will find broader engineering applications in diverse space missions such as lunar return and in-orbit servicing, driving continuous innovation in the field of space dynamics and control.

1. Introduction

With the increasing demand for orbital manoeuvres and prolonged stays in orbit of spacecraft such as hypersonic vehicles and very low Earth orbit satellites, research on aeroassisted orbit transfer approaches has been continuously and intensively promoted. Hypersonic vehicles must be able to flexibly adjust their orbits during re-entry. Very low Earth orbit satellites must cope with orbital decay caused by atmospheric drag. Aeroassisted orbit transfer approaches can use aerodynamic power to reduce fuel consumption. This effectively enhances manoeuvrability and the economy of in-orbit service. Currently, the relevant research results have been thoroughly verified through numerical simulation and technical validation. For example, the aeroassisted orbit transformation program of hypersonic re-entry vehicles has been verified by experiments. This method can significantly reduce fuel consumption and improve the stealth of manoeuvres [1,2]. The aeroassisted orbital control strategy for very low Earth orbit satellites has achieved precise maintenance of orbital elements [3].

Aeroassisted orbital manoeuvring harnesses atmospheric forces to actively alter spacecraft trajectories, enabling orbital transfers and delivering superior manoeuvring capability. In this context, aerobraking specifically utilizes atmospheric drag to reduce a spacecraft’s velocity, thereby decreasing its orbital energy, shortening the semi-major axis, and primarily affecting the apogee altitude [4]. Traditionally, the atmosphere has been regarded as a dissipative medium, with aerodynamic forces considered obstacles to be controlled. However, their effective utilization can reduce fuel consumption and expand accessible domains. The process of pneumatic-assisted track switching can be observed in Figure 1.

As space missions grow increasingly complex and cost-efficiency demands intensify, aerodynamic manoeuvring has garnered attention for its potential to conserve propellant and enhance manoeuvring capabilities. This technique combines aerodynamic forces with propulsion systems to alter orbits, demonstrating significant potential across diverse space missions. However, challenges such as thermal flux control persist, making it a crucial research focus within contemporary space dynamics and control studies.

This article reviews the research progress of aeroassisted orbit transfer approaches since their inception, focusing on the new breakthroughs achieved in this century and research on the near-Earth space range [5]. This review is expected to provide a special perspective for researchers in related fields to promote the further development and engineering application of aeroassisted orbit transfer technology for spacecraft. The structure of this article is shown in Figure 2.

2. Current Status of Aeroassisted Orbit Change Research for Spacecraft

Aeroassisted orbital transfer has garnered significant attention for its substantial propellant savings. It has emerged as a key technological pathway to enhance spacecraft economy and mission flexibility. The increasing diversity and complexity of industrial projects, such as in-orbit missions, space rendezvous [6], in-orbit services [7], and space rescues [8], have put forward higher requirements for reusable vehicles and spacecraft orbital manoeuvring capabilities. Orbital transfer propulsion methods vary. These include traditional approaches such as finite thrust and single-, double-, or N-impulse manoeuvres.

The theoretical origins of this technology trace back to the core concept proposed by Howard London: utilizing the aerodynamic forces of planetary atmospheres to achieve orbital manoeuvres with minimal propellant expenditure. Early feasibility analyses indicated that aerobraking could reduce fuel consumption by approximately 60% compared to classical Hohmann transfers [9], a substantial potential that rapidly spurred in-depth research in this field. After over half a century of development, aeroassisted orbital transfer has crystallized into four primary modes: aeroglide [10], aerocruise [11], aerobang [12], and aerogravity assist [13]. The core distinction between these modes lies in the force characteristics experienced during atmospheric flight segments [14].

2.1. Aeroglide Mode

The aeroglide mode achieves mission objectives through unpowered atmospheric flight, controlling the spacecraft via the angle of attack and bank angle rather than using thrust.

The theoretical foundations of aeroglide were established early, with Vinh et al. [10,15] modelling unpowered atmospheric glide trajectories as optimal control problems and identifying principles of orbital energy management. Later research extended this framework to evaluate performance parameters for objectives like minimizing fuel consumption [16,17], reducing transfer time [18], and optimizing for various missions [19,20].

The lift-to-drag ratio is a pivotal parameter for assessing orbital manoeuvrability, indicating the energy required to change a spacecraft’s orbital inclination via aerodynamic forces. While increasing this ratio boosts fuel economy [21,22], it also heightens atmospheric friction and thermal loads. Thus, engineering solutions must balance fuel savings and protection system weight to find the optimal trade-off [20,23].

Aeroglide’s effectiveness depends on atmospheric density, achieving significant controllability and optimization only below 100 km, where conditions are dense enough. At higher altitudes, weak aerodynamic forces render control parameters ineffective [24]. Theoretical analysis indicates the optimal trajectory approximates a parabolic or elliptical orbit [25,26,27].

Research on aeroglide has progressed from simple to advanced manoeuvres as mission complexity increases. Studies [28,29,30,31,32,33,34,35,36] confirm the feasibility of non-coplanar aeroglide, analyzing how parameters such as the angle of attack, bank angle, aspect ratio, and lift coefficient affect inclination changes and propellant usage [28,37].

Multiple atmospheric passages are used to meet stringent thermal and overload constraints. Ma [34] reports that spreading thermal loads with several shallow re-entries maintains transfer effectiveness, albeit at the cost of longer mission times and increased exposure to the Van Allen belts, which disfavors manned missions.

On the algorithmic front, solution methods have shifted from early indirect approaches to direct methods, including the Gaussian pseudo-spectral method [37,38] and intelligent algorithms [39]. These enable efficient treatment of dynamic complexities and non-convex path constraints, optimizing trajectories to satisfy engineering demands.

2.2. Aerocruise Mode and Aerobang Mode

Synergetic manoeuvres (SMs) [40,41] address the manoeuvrability limitations of aeroglide modes caused by the harsh aerothermal environment. By enabling coordinated interaction between spacecraft engine thrust and atmospheric aerodynamic forces, SM allows for more efficient and flexible orbital manoeuvres while controlling thermal loads, leading to significant fuel savings.

Aerocruise and aerobang are two thrust-coordinated modes for spacecraft manoeuvring within the atmosphere. In cruise mode, the spacecraft maintains engine operation after entry, using low thrust to counteract drag, enabling prolonged quasi-steady flight at high altitudes with a stable guidance environment, which supports precise orbital adjustments such as large inclination changes [32]. This mode highlights sustainability and controllability. In contrast, the aerobang mode emphasizes extreme, instantaneous manoeuvrability by maximizing lift-to-drag re-entry, firing engines at peak thrust before atmospheric exit, and combining thrust with aerodynamic forces to abruptly modify velocity for rapid response or interception. Both modes manage altitude using thrust to avoid deep atmospheric penetration and high heat flux, reducing thermal protection demands and mitigating the trade-off between manoeuvrability and thermal management in pure glide modes [42].

Early studies, such as Nyland’s work [43], have qualitatively demonstrated that aerodynamic–thrust combinations can save 30–50% of fuel compared to pure propulsion. Teams, including Vinh [44] and Mease [45], further quantified the capability of aerocruise modes to alter orbital inclination, confirming their superiority for high-inclination maneuvers.

However, thrust coordination introduces new complexities. The primary challenge is singular optimal control problems [46]. When thrust becomes a continuously variable control variable, the optimal solution directly derived from traditional Pontryagin maximization principles may lie along the boundary of control constraints (i.e., thrust neither assumes its zero value nor its maximum value, but an intermediate value), forming a “singular arc” that renders problem-solving exceptionally complex. Ross and his collaborators, alongside Bruce [47], McDanell and Powers [48], Park [49], and others, made foundational contributions in this field. They not only introduced the concept of aerobang but also systematically derived the conditions for singular arc existence and its stitching theory, providing a critical theoretical foundation for subsequent numerical optimization.

Secondly, multi-constraint trade-offs arise. Research indicates that the benefits of thrust-cooperative manoeuvring are closely linked to the aircraft’s lift-to-drag ratio, typically requiring a ratio exceeding 1.0 to demonstrate advantages [20]. However, a high lift-to-drag ratio also entails increased total heat flux, necessitating consideration of thermal constraints in thrust-cooperative manoeuvring studies [50]. Spriesterbach and Ross [51] pioneered the quantification of the “thermal limit-fuel gain” curve, demonstrating that fuel savings from thrust coordination diminish as local heat flux decreases, corroborating prior research. Recent studies employ advanced numerical optimization tools, such as sequential quadratic programming [52] and pseudo-spectral methods [53,54], to directly address these complex constraints. For instance, Shi X.N.’s [53] optimization results indicate that under peak heat flux and time constraints, the aerobang mode may exhibit superior overall performance compared to aerocruise and glide modes, while satisfying the overload requirements for manned flight, thereby validating its engineering feasibility.

2.3. Aerogravity Assist Mode

The application of aeroassisted orbit-changing techniques has extended into interplanetary exploration, giving rise to the aerogravity assist mode. This mode integrates aerodynamic forces with planetary gravity, significantly enhancing the manoeuvrability of interplanetary gravity assists. It offers greater design flexibility and higher fuel efficiency for deep-space exploration missions.

Traditional gravity assist has limitations. In pure gravity assist, the deflection angle and velocity change during a planetary flyby depend on the spacecraft’s approach speed and the planet’s characteristics. This produces fixed values that limit manoeuvrability. To overcome this, the Jet Propulsion Laboratory (JPL) proposed aerogravity assist. In this method, the spacecraft deliberately enters a planet’s atmosphere during a flyby. Using aerodynamic lift, it actively adjusts its flyby path. This enables controlled changes to the deflection angle and velocity. Aerogravity assist provides more flexible manoeuvring than pure gravity assist. Common related approaches are aerobraking [55] and aerocapture [56].

Aerodynamic manoeuvre technology has found extensive application in interplanetary navigation, with the Magellan Venus probe marking the first successful implementation of aerodynamic descent techniques [57]. Subsequent Mars missions, including Mars Global Surveyor (MGS) [58], Mars Odyssey [59], and Mars Reconnaissance Orbiter (MRO) [60], employed aerodynamic descent techniques to achieve their target orbits. These engineering applications have demonstrated the technique’s significant value in substantially conserving propellant and reducing overall mission costs [5].

Bonfiglio [61], Lohar [13], Qiao [62], and Han [63] have investigated the prospects of aerogravity-assisted transfer technology for deep-space exploration missions. By integrating numerical optimization methods, they explored the conditions and methodologies for orbital splicing during spacecraft missions, confirming that this technology can effectively reduce the launch costs of deep-space exploration missions. This opens new avenues for designing more complex exploration orbits and undertaking diversified deep-space exploration missions. The characteristics of the four models are presented below in

Table 1. Comparison of characteristics and advantages/disadvantages of four modes.

Mode Type	Characteristics	Control Variable	Advantages	Disadvantages	Application
Aeroglide	No thrust	Angle of attack, sideslip angle	Simple structure, significant fuel savings	Limited manoeuvrability, high heat flux	CAV 1, X-37B
Aerocruise	Sustained low thrust + aerodynamic synergy	Angle of attack, sideslip angle + thrust throttling	Strong pitch change capability, controllable heat flux	Control complexity, presence of singular arcs	X-37B
Aerobang	Short-duration high thrust + aerodynamic force synergy	Angle of attack, sideslip angle + maximum thrust	Rapid heterogenous manoeuvres, suitable for interception missions	High thermal flux and peak g-force	Rapid Response Space Mission (ORS 2)
Aerogravity Assist	Aerodynamic force + planetary gravity	Lift direction + perigee altitude	Substantial Fuel Savings	Highly demanding orbital window requirements	Magellan, MRO, Mars Odyssey

¹ CAV—Common aero vehicle; ² ORS—operationally responsiveness space.

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3. Key Approaches for Aeroassisted Orbit Manoeuvring

Research into aeroassisted orbit manoeuvres focuses on optimizing trajectories to reduce fuel use and increase payload and on controlling guidance to keep the spacecraft on the planned path. Foundational work by Vinh [64] and extensions by Mease [65], Miele [66], and Naidu [67] built the core framework for this field.

3.1. Trajectory Optimization

Trajectory optimization is essential for missions involving aerodynamic orbital changes, as it seeks to improve fuel efficiency or reduce flight times while accounting for required constraints. The problem’s complexity results from nonlinear dynamics, uncertainties, and multiple constraints, making it a high-dimensional nonlinear control challenge.

3.1.1. Optimization Problem Modelling

The trajectory optimization problem for aeroassisted re-orbiting is typically modelled as a continuous-time optimal control problem. Its core components comprise the spacecraft’s dynamic equations, control variables, state variables, performance metrics, and constraint conditions.

(1) Dynamics Model: The spacecraft’s motion within the atmosphere is typically described using a three-degree-of-freedom or six-degree-of-freedom (DOF) model, accounting for the combined effects of gravity, atmospheric drag, lift, thrust, etc. [68,69].

1.

Equations of motions

$$\left\{\begin{array}{l}{\displaystyle \frac{\mathrm{d}r}{\mathrm{d}t}}=V\mathrm{s}\mathrm{i}\mathrm{n}\gamma \\ {\displaystyle \frac{\mathrm{d}\varphi }{\mathrm{d}t}}={\displaystyle \frac{V\mathrm{c}\mathrm{o}\mathrm{s}\psi \mathrm{c}\mathrm{o}\mathrm{s}\gamma }{r}}\\ {\displaystyle \frac{\mathrm{d}\theta }{\mathrm{d}t}}={\displaystyle \frac{V\mathrm{s}\mathrm{i}\mathrm{n}\psi \mathrm{c}\mathrm{o}\mathrm{s}\gamma }{r\mathrm{c}\mathrm{o}\mathrm{s}\varphi }}\\ {\displaystyle \frac{\mathrm{d}V}{\mathrm{d}t}}=-{\displaystyle \frac{S\rho Cp\left(a\right)V^2}{2m}}-g\mathrm{s}\mathrm{i}\mathrm{n}\gamma \\ {\displaystyle \frac{\mathrm{d}\gamma }{\mathrm{d}t}}={\displaystyle \frac{S\rho C_L\left(a\right)V^2\mathrm{c}\mathrm{o}\mathrm{s}\sigma }{2Vm}}+\left({\displaystyle \frac{V^2-rg}{Vr}}\right)\mathrm{c}\mathrm{o}\mathrm{s}\gamma \\ {\displaystyle \frac{\mathrm{d}\psi }{\mathrm{d}t}}={\displaystyle \frac{S\rho C_L\left(a\right)V^2\mathrm{s}\mathrm{i}\mathrm{n}\sigma }{2Vm\mathrm{c}\mathrm{o}\mathrm{s}\gamma }}+{\displaystyle \frac{V}{r}}\mathrm{t}\mathrm{a}\mathrm{n}\varphi \mathrm{c}\mathrm{o}\mathrm{s}\gamma \mathrm{s}\mathrm{i}\mathrm{n}\psi \end{array}\right.$$

(1)

Equation (1) is the 3-DOF model referring to the translational equations of motion (EMOs). Variables appearing in this equation are $r,\varphi ,\theta ,V,\gamma ,\psi ,\alpha ,\sigma ,S,{ C}_D,g,C_L,\mathrm{a}\mathrm{n}\mathrm{d} \rho$, representing the radius, latitude, longitude, speed, flight path angle (FPA), azimuth angle, angle of attack (AOA), bank angle, reference area, deg coefficient, gravity, lift coefficient, and atmosphere density, respectively.

$$\left\{\begin{array}{c}\begin{array}{c}{\displaystyle \frac{\mathrm{d}\tau }{\mathrm{d}t}}=q-\rho \mathrm{t}\mathrm{a}\mathrm{n}\beta \mathrm{c}\mathrm{o}\mathrm{s}\alpha -\nu \mathrm{t}\mathrm{a}\mathrm{n}\beta \mathrm{s}\mathrm{i}\mathrm{n}\alpha +{\displaystyle \frac{\mathrm{s}\mathrm{i}\mathrm{n}\alpha }{\mathrm{c}\mathrm{o}\mathrm{s}\beta }}\dot{(\psi }\mathrm{c}\mathrm{o}\mathrm{s}\gamma -\dot{\varphi }sin\psi sin\gamma \\ +\dot{\theta }cos\varphi cos\psi sin\gamma -\dot{\theta }sin\varphi cos\gamma )\\ -{\displaystyle \frac{cos\alpha }{cos\alpha }}\left(\dot{\gamma }-\dot{\varphi }cos\psi -\dot{\theta }cos\varphi cos\varphi sin\psi \right)\\ {\displaystyle \frac{\mathrm{d}\sigma }{\mathrm{d}t}}=-p\mathrm{c}\mathrm{o}\mathrm{s}\alpha \mathrm{c}\mathrm{o}\mathrm{s}\beta -q\mathrm{s}\mathrm{i}\mathrm{n}\beta -\nu \mathrm{s}\mathrm{i}\mathrm{n}\alpha \mathrm{c}\mathrm{o}\mathrm{s}\beta +\dot{\alpha }\mathrm{s}\mathrm{i}\mathrm{n}\beta \\ -\dot{\psi }cos\gamma -\dot{\varphi }sin\psi cos\gamma +\dot{\theta }sin\varphi sin\gamma \\ +\dot{\theta }cos\psi cos\varphi cos\gamma \\ {\displaystyle \frac{\mathrm{d}\beta }{\mathrm{d}t}}=p\mathrm{s}\mathrm{i}\mathrm{n}\alpha -\nu \mathrm{c}\mathrm{o}\mathrm{s}\alpha +\mathrm{s}\mathrm{i}\mathrm{n}\sigma [\dot{\gamma }-\dot{\varphi }\mathrm{c}\mathrm{o}\mathrm{s}\psi +\dot{\theta }\mathrm{c}\mathrm{o}\mathrm{s}\varphi \mathrm{s}\mathrm{i}\mathrm{n}\psi \\ +cos\sigma (\dot{\psi }cos\gamma -\dot{\varphi }sin\psi sin\gamma \\ -\dot{\theta }cos\varphi cos\psi sin\gamma -\dot{\theta }sin\varphi cos\gamma )]\\ {\displaystyle \frac{\mathrm{d}p}{\mathrm{d}t}}={\displaystyle \frac{M_x}{I_{xx}{I}_{zz}-{\displaystyle I_{xz}^2}}}{I}_{zz}+I_{xz}\left({\displaystyle \frac{M_z}{I_{xx}{I}_{zz}-{\displaystyle I_{xz}^2}}}+qp{\displaystyle \frac{I_{xx}+I_{zz}-I_{yy}}{I_{xx}{I}_{zz}-{\displaystyle I_{xz}^2}}}\right)\\ +qv{\displaystyle \frac{\left(I_{yy}{I}_{zz}-I_{zz}{I}_{zz}-I_{xz}\right)}{I_{xx}{I}_{zz}-{\displaystyle I_{xz}^2}}}\end{array}\\ {\displaystyle \frac{\mathrm{d}q}{\mathrm{d}t}}={\displaystyle \frac{I_{xz}}{I_{yy}}}\left(v^2-p^2\right)+{\displaystyle \frac{M_y}{I_{yy}}}+pv{\displaystyle \frac{I_{zz}-I_{xx}}{I_{yy}}}\\ \begin{array}{c}{\displaystyle \frac{dv}{dt}}=I_{xZ}\left[{\displaystyle \frac{M_x}{I_{xx}{I}_{zz}-{\displaystyle I_{xz}^2}}}+{\displaystyle \frac{qv\left(I_{yy}-I_{xx}-I_{zz}\right)}{l_{xxx}{L}_{xxx}-L_{xx}}}\right]\\ +I_{xx}{\displaystyle \frac{M_z}{I_{xx}{I}_{zz}-{\displaystyle I_{xz}^2}}}+pq{\displaystyle \frac{{{\displaystyle I_{xx}^2}-I}_{yy}{I}_{xx}-I_{xz}}{I_{xx}{I}_{zz}-{\displaystyle I_{xz}^2}}}\end{array}\end{array}\right.$$

(2)

To establish the rotation motion equations for the high-order 6-DOF model of an aeroassisted vehicle, Equation (2) can be formulated. Rotational variables appearing in these EMOs are $\beta ,p,q$, and $\nu$, respectively. $\beta$ denotes the sideslip angle of the vehicle; $p,q$, and $r$ represent the roll rate, pitch rate, and yaw rate, respectively; $m$ is the mass of the vehicle; $S$ is the reference area; $M_{\mathrm{i}} \left(i = x, y, z\right)$ denotes the angular moments acting on the vehicle about the corresponding axes; $I_{\mathrm{i}\mathrm{j}} \left(i, j = x, y, z\right)$ denotes the moments of inertia of the vehicle about the respective axes.

2.

Aerodynamic model

During the aeroassisted orbit transfer process, the vehicle’s speed is extremely high, typically exceeding Mach 5. In order to simplify the problem, for the aerodynamic model of the vehicle, it was decided to ignore the effect of the Mach number, Reynolds number, etc., and the aerodynamic drag coefficients and lift coefficients obeyed a parabolic-type drag pole formula [70], which is related to the following formula:

$$C_D=C_{D0}+K{\displaystyle C_L^2}$$

(3)

where $C_{D0}$ is the zero drag coefficient, and $K$ is the induced drag factor, both of which are constants. Moreover, the maximum lift-to-drag ratio $E^{\ast }$ can be obtained for a given $C_{D0}$ and $K$.

$$E^{\ast }={\displaystyle \frac{1}{2\sqrt[2]{C_{D0}}}}$$

(4)

Aerodynamic lift and aerodynamic drag are expressed as

$$L={\displaystyle \frac{\rho V^{2}s}{2}}{C}_L,D={\displaystyle \frac{\rho V^{2}s}{2}}{C}_{D0}$$

(5)

where $\rho$ is the current atmospheric density, $V$ is the velocity of the vehicle relative to the atmosphere, and $s$ is the reference area.

For very low Earth orbit (VLEO) satellites [71], expressions for the force coefficients must be obtained by combining the atmospheric drag model, the orientation of the joint surface elements, and the pressure and shear coefficients. For a flat plate object, the force coefficient is the sum of the normal and tangential components of the pressure and shear coefficients, so the drag coefficient CD and lift coefficient CL are related to the angle of incidence $\theta$ as

$$\left\{\begin{array}{c}{C}_D=-(Cpsin\theta +C\tau cos\theta )\\ C_L=-Cpcos\theta +C\tau sin\theta \end{array}\right.$$

(6)

where $Cp$ is the pressure coefficient, and $C\tau$ is the shear coefficient.

The air resistance acceleration of a satellite moving through the atmosphere can be expressed as

$$f_a=-{\displaystyle \frac{1}{2}}{\displaystyle \frac{C_{D}A}{m}}\rho {\displaystyle {\upsilon }_a^2}$$

(7)

where $C_D$ is the drag coefficient found above, $A$ is the cross-sectional area, $\rho$ is the atmospheric density, and ${\upsilon }_a$ is the velocity of the satellite relative to the atmosphere.

3.

Atmospheric Density Model

The atmospheric density model commonly used in the study is as follows:

$$\rho ={\rho }_{s}exp\left[-\beta \left(R-R_s\right)\right]$$

(8)

where ${\rho }_s$ is the standard atmospheric density at sea level, which takes the value of 1.22 $\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$; $\beta$ is the reciprocal of the sea level elevation, which takes the value of 1/6900 ${\mathrm{m}}^{-1}$; and $R_s$ is the mean radius of the earth at sea level, which takes the value of 6378 $\mathrm{k}\mathrm{m}$.

4.

Standing Point Heat Flow Model

During the aeroassisted orbit transfer process, due to the violent friction between the spacecraft and the atmosphere, a standing-point heat flow is generated on the spacecraft’s surface. The aerodynamic heating equation of the spacecraft usually adopts the Chapman equation [70,72], and its standing heat flow Q is calculated as follows:

$$\dot{Q}=9.437\times {10}^{-5}{\rho }^{0.5}{\displaystyle V_a^{1.15}}$$

(9)

where $\dot{Q}$ is in units of $\mathrm{W}/{\mathrm{m}}^2$, $\rho$ is the atmospheric density at the current position of the vehicle, and $V_a$ is the magnitude of the spacecraft’s velocity relative to the atmosphere.

(2) Control Variables: These variables primarily encompass the angle of attack, bank angle, thrust magnitude, and thrust direction. By adjusting these variables, the spacecraft modifies its aerodynamic forces and thrust to achieve trajectory control. For instance, the bank angle is primarily employed for lateral manoeuvres and altering orbital inclination [25,26], while the angle of attack influences the lift-to-drag ratio and aerothermal heating.

(3) Performance Metrics: Common objectives include minimum fuel consumption [73,74,75,76], shortest flight duration [74], and minimal thermal loads [65,73,77], often requiring multi-objective trade-offs. Detailed performance indicators and their connotations can be found in

Table 2. Different performance metrics and their implications.

Performance Metric	Implication	References
Minimum fuel consumption	Reduction in propellant consumption through aerodynamic optimization	[19,35,65,73]
Minimum flight duration	Minimizing flight duration for certain emergency or time-sensitive missions	[74]
Minimum heat flux/thermal load	Spacecraft re-entering the atmosphere undergoes intense aerothermal heating; limiting maximum heat flux density or total thermal load ensures structural integrity of the spacecraft.	[64,65,73,76]
Minimum overload	Limiting the maximum overload experienced by spacecraft to protect the spacecraft structure and internal equipment.	[53,76]
Terminal state constraints	Ensuring that the spacecraft ultimately reaches its target orbit while satisfying specific orbital parameters (such as perigee, apogee, inclination, phase, etc.) and arrival time requirements	[73,78]

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(4) Path Constraints: Beyond the aforementioned performance metrics, trajectory optimization must also account for a series of path constraints, including physical limits such as dynamic pressure, heat flux density, and overload. These are critical for ensuring flight safety [69,73]. The four path constraints and their implications are shown in

Table 3. Four constraints and their contents.

Category	Content	References
Dynamic pressure constraint	Limits the maximum dynamic pressure experienced by spacecraft during atmospheric flight to prevent structural damage	[18,79]
Heat flux density constraint	Limiting the maximum heat flux density on the spacecraft surface to prevent ablation	[16]
G-force constraint	Limits the maximum acceleration a spacecraft can endure, safeguarding equipment and crew	[53,80]
Control variable constraints	Physical limitations on control variables such as angle of attack, roll angle, and thrust	[25,26]

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3.1.2. Optimization Methods

The advent of the maximum principle marked a significant shift in trajectory optimization, moving from analytical methods toward predominantly numerical techniques capable of handling complex nonlinear problems. These numerical methods work by discretising the continuous-time optimal control problem and converting it into a parameter optimization problem. Specific algorithms are then employed to solve these parameter problems. Overall, numerical trajectory optimization research consists of two main components: transforming the original problem and choosing suitable parameter-solving algorithms.

Optimization Problem Transformation Methods

Betts summarized early research progress in trajectory optimization, classifying methods into direct and indirect approaches [81]. In direct methods, continuous optimal control problems are parameterized and discretized into non-linear programming (NLP) problems, which are then solved by established NLP solvers. This approach eliminates the need to derive optimality conditions from extremum principles, offers high solution accuracy, and effectively handles complex constraints and high-dimensional problems. As such, direct methods are predominant in current AOT trajectory optimization. Indirect methods, by contrast, are grounded in Pontryagin’s minimum principle for optimal control. They yield numerical solutions for both optimal trajectories and controls by solving two-point boundary value problems (TPBVPs), providing necessary conditions for optimality and theoretically achieving global optimality. However, indirect methods are highly sensitive to initial guesses for state variables, struggle with complex path constraints and boundary conditions, and are prone to singular arcs when penalty functions are introduced. These characteristics complicate constraint satisfaction and solution stability, limiting their regular use in practical AOT problems. The following sections outline several methods with demonstrated performance in AOT applications.

• Pseudospectral Methods (PSMs)

The PSM represents one of the most mature and widely applied techniques for spacecraft trajectory optimization. In this method, state and control variables are approximated using orthogonal polynomials at selected configuration points. This process transforms differential equation constraints into algebraic constraints, facilitating efficient solutions to NLP problems. For example, Anil V. Rao [82] applied PSM to trajectory planning in rapid-response launch missions; similarly, Ref. [83] addressed multi-orbit trajectories in aeroassisted orbital transfers.

The Gaussian pseudospectral method (GPM), which utilizes Gaussian–Lobatto configuration points, provides high accuracy and convergence. It is widely used in AOT trajectory optimization. For instance, Chai [76] employed multi-stage global configuration techniques with GPM to solve the minimally fueled aeroassisted regional reconnaissance spacecraft problem. Fu [84] used GPM to address spacecraft HEO-LEO coplanar transfer problems, deriving suboptimal trajectories for the atmospheric flight segment under thermal flux and control constraints. Compared to indirect methods, GPM offers greater efficiency and optimization performance in these contexts.

Another commonly used technique is the Radau pseudospectral method, which differs from GPM mainly in the selection of configuration points and weight calculations. For particular problems, it may exhibit better performance. For example, Chai [69] employed a variable-order Radau pseudospectral method, combined with a pipeline optimization strategy, to investigate high-fidelity trajectory optimization. By employing grid-adaptive iteration, they improved both the smoothness and convergence of the resulting trajectories.

The hp-adaptive pseudospectral method further innovates by adaptively adjusting both the polynomial degree (p) and the configuration point distribution (h) [85]. This approach enhances accuracy and efficiency. For example, Han [74] applied it to optimize AOT rendezvous and intercept trajectories between non-coplanar elliptical orbits, which led to robust convergence and fuel savings compared to conventional manoeuvres. Similarly, Darby and Rao [73] demonstrated in the LEO-LEO minimum-fuel AOT problem that optimal solutions often involve two atmospheric entries when using this method.

PSM’s main advantage is its high accuracy and ability to manage complex constraints. However, it is computationally intensive, so it is most suitable for offline trajectory planning [86].

• Sequential Convex Optimization (SCP)

SCP enhances computational efficiency by iteratively converting non-convex problems into a series of convex subproblems. This iterative convexification makes SCP suitable for real-time trajectory optimization tasks.

Ben [87] developed a rapid SCP-based algorithm for spacecraft aerodynamic transfer, which showed efficient and robust performance when compared to pseudospectral methods. Building on this, Feng [88] and Teng [89] extended SCP to multi-lap AOT trajectory optimization by incorporating adaptive trust regions and dynamic penalties, which improved convergence and robustness. Lu [90] proposed the nonlinearity-kept convexification (NKKC) method for atmospheric ascent, which splits complex subproblems and utilizes sequential approximations to achieve rapid convergence while preserving model nonlinearity—a crucial factor for handling strong aerodynamics in AOT. In summary, SCP is distinguished by its rapid solutions and precise constraint management, making it well-suited for real-time online trajectory optimization [91,92,93].

• Other Optimization Methods

Miele [94] addressed the LEO-LEO AOT optimal trajectory problem using the Sequential Gradient-Restoration Algorithm, targeting objectives such as minimizing energy, maximizing flight time, and limiting peak heat flux for various orbital changes. Their analysis recommended a “Nearly-grazing solution” to balance energy and heat constraints. Separately, Ben [95] reframed AOT as a parameter estimation problem, developing a numerical solution based on the UKF parameter estimation method. This approach eliminates the need to initialize co-state variables, thus improving computational efficiency and robustness.

Parameter Solution Algorithms

After the optimization problem is transformed, parameter optimization is performed. Solutions for this step fall into two categories: exact algorithms that use gradients and modern heuristic algorithms that rely on intelligent decision-making processes. Exact algorithms are highly precise but tend to be slower, whereas heuristic algorithms are more flexible but may produce less accurate results in practice.

Exact algorithms require favorable properties in the objective or constraint functions, such as differentiability, continuity, and a convex feasible region. Typical examples include Sequential Quadratic Programming (SQP), interior-point methods, and dynamic programming. Among these, SQP is the most widely applied, though interior-point methods are gaining attention with the increased focus on convex optimization.

Gill proposed the sparse sequential quadratic programming (SQP) algorithm, which exhibits quadratic convergence speed. The SNOPT software package [96], based on this algorithm, is extensively used for trajectory optimization. For example, Yun [97] combined a point-matching method with SQP to solve aeroassisted optimal orbital transfer problems. Additionally, gradient descent, trust-region methods, and penalty function approaches are commonly employed to solve NLP problems.

Modern heuristic algorithms are inspired by human simulations of natural phenomena. Their update strategies for searching optimal solutions do not depend on system gradient information, making them less likely to become trapped in local minima and thus applicable to a broader range of problems. Algorithms such as genetic algorithms, simulated annealing, and particle swarm optimization have been applied to spacecraft trajectory optimization [98] for their potential in global optimum search and robust performance. For example, Fu [39] used a genetic algorithm to calculate manoeuvre points for aeroassisted elliptical orbital transfers. Additionally, article [99] addressed trajectory optimization for aeroassisted manoeuvring spacecraft under complex constraints using the NSGA-II multi-objective genetic algorithm, which yielded favorable results. However, genetic algorithms tend to have low search efficiency and slow convergence, limiting their suitability for rapid real-time trajectory optimization.

Beyond the aforementioned parameter optimization algorithms, artificial intelligence methods such as neural networks, deep learning, and reinforcement learning are also extensively employed [100,101,102,103,104]. Neural network approaches integrate seamlessly with minimax principles, utilizing neural network approximation techniques to solve two-point boundary value problems and thereby ensuring the global optimality of the solution. This neural network-based optimization framework effectively overcomes the technical bottleneck of initial value estimation inherent in indirect methods, holding significant theoretical research value and promising engineering applications. Celestini [100] proposed a Transformer-based model predictive control, employing sequence modelling for trajectory optimization. This approach significantly reduced solver iterations and runtime whilst maintaining performance. Subsequently, they further proposed universal spacecraft trajectory generation through multimodal learning with Transformers, enhancing convergence speed and performance [101]. Takubo [102] introduced a robust spacecraft trajectory optimization method based on Transformers, enhancing feasibility rates and convergence speed by providing near-optimal initial guesses. These studies demonstrate that AI technologies hold promise for delivering novel solutions in AOT trajectory optimization and real-time guidance, particularly when handling complex environments and autonomous decision-making. However, during the practical parameterization of problem-solving, the engineering application of such methods still faces numerous challenges due to the complexity of mathematical modelling and the uncontrollable nature of the objective function’s finite-time diminishing returns. The comparison of several optimisation methods is shown in

Table 4. Comparison of core performance of trajectory optimization methods.

Methods	Computational Complexity	Convergence Reliability	Path Constraint Handling Capability	Sensitivity to Initial Values	Typical Application Scenarios
PSM	High	Strong	Medium	Low	Fuel-optimal and multi-stage coupled trajectory planning
SCP	Low	Medium	Medium	Low	Spacecraft atmospheric flight phase path adjustment and fast multi-constraint optimization
SQP	Medium	Strong	Strong	Medium	Multi-objective and multidisciplinary collaborative optimization, thermal protection–aerodynamic shape coupled design
AI	High (training); low (inference)	Medium	Medium	/	Fast trajectory generation and multi-constraint approximate optimization

.

3.2. Control Guidance

3.2.1. Control Strategy

Optimizing control strategies is essential for aeroassisted orbit manoeuvres. This area focuses on selecting and refining control parameters such as the lift-to-drag ratio, angle of attack, bank angle, and roll angle. Recent studies explore adaptive and model predictive control methods to address real-time trajectory tracking, uncertainty management, and constraint satisfaction. There is an increasing emphasis on resilience and operational effectiveness. In control system design, time-domain analysis examines system responses over time, such as transient and steady-state behavior, while frequency-domain analysis evaluates system performance across different input frequencies, such as gain and phase margins. These two approaches, when combined, provide a comprehensive and complementary view for control design.

Time-domain analysis tracks how the system state or output changes over time. It examines the system’s response to standard input signals, such as steps, pulses, or slopes. This helps evaluate transient performance indicators, such as response speed, time to peak, and overshoot. It also considers steady-state accuracy indicators, such as steady-state bias. Controller design uses theoretical tools. These include Lyapunov stability criteria, state-space models, and optimal control theories, such as the linear quadratic regulator (LQR).

Frequency-domain analysis uses the Fourier transform to map a signal into the frequency domain. It analyses amplitude–frequency and phase–frequency characteristics. The primary objective is to investigate how the system responds to different frequency components of the input. Controllers are then designed to optimize the system’s frequency response characteristics. This ensures that the system meets stability and performance requirements. Common analytical tools include the Porter’s diagram, Nyquist diagram, and Nichols diagram. Typical strategies include PID regulation, the root locus method, and H∞/H₂ frequency domain optimization.

Time-domain methods, such as LQR and model predictive control (MPC), use equations directly to control systems, allowing them to handle time-varying dynamics, nonlinearities, and multiple constraints. In contrast, frequency-domain methods, such as classical PID regulation and H∞ robust control, rely on transfer functions and frequency responses to analyze control performance. Time-domain methods are well-suited for tracking how system trajectories change over time, addressing specific constraints like heat flow and control input limits. Frequency-domain methods, meanwhile, are effective at suppressing disturbances in selected frequency bands, such as blocking high-frequency turbulence or low-frequency solar radiation pressure, and they are particularly useful for evaluating system stability margins and robustness [105,106].

For example, Fu [107] introduced an optimal control law for non-planar manoeuvres using aerodynamic forces. In a related development, Yan [108] highlighted the importance of the lift-to-drag ratio and roll angle. Extending this line of inquiry, Li [109] investigated minimizing fuel usage by optimizing the angle of attack, bank angle, and frontal area. Furthermore, Yao [110] proposed an adaptive approach that tracks the reference trajectory under uncertainties and constraints by tuning the angle of attack and bank angle, employing an inverse method to construct control laws.

Notably, MPC is particularly valuable for high-dynamic, multi-constrained scenarios owing to its effective handling of constraints and time-domain optimization [111]. By solving a finite-time optimal control problem at each step and executing the initial action, MPC ensures real-time trajectory alignment with mission objectives. The MPC is capable of explicitly handling system constraints and multi-objective optimization. Hayes and Caverly [112] proposed an estimation and control framework for target re-entry of drag-modulated spacecraft under uncertain atmospheric densities, where a model predictive control strategy enhances tracking and robustness.

MPC also plays an important role in trajectory tracking with its ability to handle multiple-input multiple-output systems and various constraints. Building on this, Ji [113] further advanced tracking in challenging initial states by integrating rolling-horizon control with MPC to address environmental complexities. Reinforcement learning has also been applied in conjunction with MPC [114]. Lang [115] proposed a neural network adaptive iterative learning control scheme for spacecraft proximity manoeuvres with uncertainty by integrating simple adaptive algorithms into the spacecraft dynamics and using iterative learning control to improve tracking performance.

3.2.2. Guidance Strategy

A well-defined guidance strategy is essential for precise outcomes in aeroassisted orbit manoeuvres. Guidance methods are classified as perturbation or predictive correction. Predictive correction suits more complex missions. Each method is chosen based on mission objectives and required performance.

Standard orbital guidance utilizes a reference trajectory and adjusts controls to maintain the spacecraft’s alignment with its intended path in response to in-flight errors. This approach ensures real-time tracking despite disturbances and underpins advanced guidance improvements [107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123].

Building on these foundational strategies, several advanced guidance approaches address spacecraft noise and disturbance. For example, Naidu [116] addressed boundary-value disturbances, state noise, and measurement noise using the Linear Quadratic Gaussian (LQG) method, which produces filter and control gains for accurate guidance. Similarly, ZealSain Kuo [117] used an enhanced Matched Asymptotic Expansion (MAE) to improve precision in reference trajectory estimates. In addition, Zhang [118] presented a performance-based tracking law validated by simulations for hypersonic gliders, confirming adaptability and robustness. Reinforcement learning has also been applied to trajectory tracking: Luo [119] proposed a robust 3D trajectory tracking control scheme for hypersonic gliding vehicles with time-varying uncertainties and proved the uniform eventual boundedness of the closed-loop system.

To ensure robust performance amid bounded uncertainties, widely adopted methods such as Sliding Mode Control (SMC), also known as Variable Structure Control (VSC) [120], offer resilience to uncertainties and disturbances. H₂ control and H∞ control are classical approaches in linear robust control. Both have been thoroughly studied and are widely used for mitigating system uncertainty. The main difference is that H₂ control minimizes the average (energy-based) system response to disturbances, focusing on typical-case scenarios using the L₂ norm, while H∞ control seeks to minimize the worst-case (peak) response to disturbances, using the L∞ norm, and is aimed at maximizing robustness against the largest possible disturbance. In the frequency domain, H₂ control corresponds to quadratic performance index optimization, whereas H∞ control involves great-minimal optimization.

In the spacecraft aeroassisted trajectory change scenario, H₂ control can effectively reduce the impact of small random fluctuations in aerodynamic parameters on trajectory tracking accuracy. Unstructured factors such as sudden changes in atmospheric density and modeling deviations in aerodynamic coefficients may lead to the degradation of system performance. The H∞ controller has a significant suppression advantage over such disturbances. Building on these, Zhang [121] combined SMC and robust controllers in an SMC-H₂ guidance algorithm, improving tracking and robustness while meeting operational constraints. H∞ control is also often combined with multi-objective optimization in aerodynamically assisted orbit change missions for deep space exploration. For example, Zhou [122] combined H∞ performance with pole placement and fuel optimization in orbit transfer control for hovering at an elliptical orbital target. Zhou solved the controller using the LMI method to achieve high-precision orbital control under parameter uncertainty and external disturbances. Guadagnini [123] developed an end-to-end GNC solution for reusable launch vehicles, integrating advanced onboard trajectory optimization and H∞ control for robust performance.

A key advancement is predictive correction guidance, which utilizes numerical trajectory analysis to predict the spacecraft’s final state and applies corrections to design parameters. This minimizes terminal errors and enables highly precise orbits. Unlike strategies relying on nominal trajectories, predictive correction allows adaptive adjustments and precise navigation under varied initial conditions. Thus, it supports the precision needed for spacecraft re-entry and orbit changes [124,125,126,127].

Miele and Wang [124] developed a two-stage Gamma guidance law. This law employs linear path inclination guidance during descent and constant path inclination during ascent. The improved scheme introduces predictive-correction guidance. It adjusts the switching speed of the correction algorithm and the target path inclination angle. This enhances trajectory stability. In another paper [125], Miele proposed a robust predictive-correction guidance method for aeroassisted manoeuvres. He detailed a procedure for determining the sideslip angle of the exit-phase control variable using a specialized predictive-correction technique. Zhang [126] designed zero-order and first-order closed-loop guidance laws. Their simulation validation demonstrated superior robustness compared to trajectory-optimized open-loop algorithms. Higher-order laws exhibited greater precision. Wu [127] provided a phased synthesis of trajectory optimization and guidance methods for aeroassisted problems. They proposed three primary guidance approaches: predictive correction, explicit guidance, and energy controller methods. These aim to satisfy requirements for accuracy, stability, and robustness. Xi and Li [111] summarized the principles of predictive control qualitative synthesis theory. They reviewed major achievements concerning stability and performance-guaranteed predictive control over the past decade. Efficient predictive control research has gradually become a focal point in this field. Predictive guidance now exhibits two developmental trends: model predictive control and adaptive predictive-correction guidance. Lin [1] used an energy-balancing strategy combined with aeroassistance for orbital manoeuvres in hypersonic vehicles. They adopted a fully-coefficient adaptive predictive-corrective aeroassisted guidance technique to reduce computational complexity and enhance engineering feasibility. This method adapts to uncertainties by correcting predictive models or parameters online.

3.2.3. Discussion

Atmospheric uncertainty is a key source of external perturbation during spacecraft flight. It significantly affects spacecraft modelling by directly changing aerodynamic environment parameters and indirectly affecting dynamics. The atmosphere in near-Earth space is shaped by kinetic, radiative, and photochemical processes [128]. These cause complex temporal and spatial variations. Perturbations in core parameters, such as density and temperature, can trigger chain effects through aerodynamic load transfer. This creates a multi-dimensional impact on spacecraft design and operation.

At the modelling level, spatial and temporal perturbation of atmospheric density causes core model uncertainty. Zeng [129] found that the density prediction of classical models like USSA-76 and NRLMSISE-00 at 70~110 km altitude can deviate up to 50% from measured data. Atmospheric density perturbation, as a function of latitude and date, peaks near 78 km. Perturbation with local time increases with altitude. Such deviations directly distort aerodynamic parameters such as lift and drag coefficients based on ideal atmosphere assumptions. This, in turn, undermines the credibility of the dynamical model.

At the control effect level, atmospheric uncertainty affects control reliability through aerodynamic load fluctuation and thermal environment deterioration. Peng [130] noted that deviations in atmospheric density trigger the uptake of aerodynamic parameters. This leads to reduced robustness in the control system. Traditional controllers are prone to oscillation and dispersion when parameter deviation exceeds 20%. Random perturbations, such as turbulence and gravity waves, introduce non-modelled dynamic disturbances. These require robust control methods [131], like H∞ hybrid sensitivity control or adaptive sliding mode control. Otherwise, attitude tracking accuracy and flight stability are reduced. Atmospheric uncertainty can cause trajectory deviation and orbit offset that mismatch control commands. This challenges model reliability and requires robust design, disturbance suppression, or online compensation mechanisms in control methods.

The LQR/LQG control method utilizes a linearized model of spacecraft dynamics and represents uncertainty as Gaussian white noise. It minimizes secondary performance indicators such as trajectory deviation and control energy consumption. This is achieved by combining state estimation, using Kalman filtering in LQG, with optimal feedback control. However, the method’s effectiveness depends on linear assumptions. When these assumptions fail, the system becomes susceptible to trajectory dispersion, and reliability decreases significantly [132].

In contrast to LQR/LQG, SMC sliding mode control forces the system state to follow a preset trajectory by designing a sliding mode surface. Unlike methods that focus on precise system modelling, SMC emphasizes “disturbance suppression”. This makes it inherently robust to parameter changes and external disturbances. While this robustness is beneficial, SMC’s main drawback is the jitter problem. Jitter can cause frequent aerodynamic attitude adjustments and increased fuel consumption. Thus, designing the sliding mode surface requires balancing robustness and control smoothness. Poor design may reduce trajectory tracking accuracy [133].

Further advancing uncertainty management, MPC is effective at handling uncertainty under multiple constraints. The atmospheric density-compensated MPC specifically improves performance. In a Monte Carlo simulation, it achieves 98.4% of cases with a trajectory error of less than 100 km. The average positioning error of the re-entry interface is only 12.1 km. This makes it more suitable for complex mission scenarios [109,134].

A different approach, the H∞ control, is extremely robust and quantitatively suppresses uncertainty, particularly when compared to methods such as LQR/SMC. While H∞ achieves high-precision control under strong perturbations, multi-coupling, and variable operating conditions by utilizing both frequency-domain optimization and time-domain constraints, it has disadvantages: The controller design is more complicated, computational complexity is medium to high, and real-time performance is slightly inferior to LQR/SMC. Unlike these alternatives, H∞’s core value in aerodynamic-assisted trajectory change lies in its capacity to incorporate aerodynamic coefficient uncertainty, wind field perturbation, and other nondeterministic factors within a unified control framework. This approach safeguards mission reliability through quantitative robustness indexes [135,136]. The hybrid guidance algorithm based on SMC-H₂/H∞ in [121] has been validated by engineering simulation and shows excellent robustness in aerodynamic uncertainty scenarios.

Beyond traditional control methods, AI methods have also been tried in the field of control guidance. One is the Physical Information Neural Network (PINN). It writes the coupled orbit–attitude–aerodynamic equations into a loss function-embedded network. It achieves perturbation prediction and compensation by recognizing aerodynamic parameters online and remains insensitive to measurement noise. This has pressed the aerodynamic coefficient error to within 1% in the terminal guidance section of the re-entry glider [137]. The other method is reinforcement learning (RL), which uses the framework of ‘Reference Trajectory + Error Dynamics’. RL converts multiple constraints—including residual range, thermals, and overload—into reward signals. It continuously outputs corrections for the angle of attack and tilt angle with a single evaluation network. This method can adapt to strong nonlinear uncertainties in real time. It reduces the gliding segment point-circle probability error by one order of magnitude compared to LQR [119].

Despite these advances, both approaches have significant advantages, but their reliability is still limited by the boundaries of the training data. For example, if the offline samples do not cover extreme scenarios such as solar storms, there will be “out-of-distribution failures”. In a Mars re-entry simulation, PINN-MPC still fails to converge the altitude error under severe solar wind perturbations. The offline training of RL requires ten million high-fidelity simulations. Engineering still requires parallelism with robust control or predictive correction laws to meet safety certification levels for manned or planetary sampling missions.

Control guidance is the critical element for successful aeroassisted orbit manoeuvres. When atmospheric density varies and aerodynamic effects are uncertain, guidance must also handle external disturbances and system constraints. It is imperative to ensure flight stability and mission completion. Guidance and control for aeroassisted orbit manoeuvres confront unique challenges. These include uncertainty, strong nonlinearity, tight coupling, multiple constraints, and real-time demands. Algorithms are evolving from fundamental control laws towards model adaptation and robustness. Adaptive approaches combine parameter adaptation with neural network adaptation. These methods address system uncertainties, including variations in aerodynamic parameters and errors in atmospheric density models. They also address external disturbances through online estimation or adjustment of control parameters. Robustness enhancements are primarily achieved through the use of more resilient modern control algorithms. A comparison of several control methods is shown in

Table 5. Comparison of uncertainty adaptability and reliability of control algorithms.

Methods	Uncertainty Adaptability	Core Reliability Advantages	Reliability Shortcomings	References
LQR/LQG	Small disturbances and linear scenarios	High computational efficiency, mature engineering application	Prone to divergence under nonlinear/ large-amplitude disturbances	[132]
SMC	Large disturbances and nonlinear scenarios	Intrinsically robust, outstanding anti-interference capability	Chattering leads to increased fuel consumption	[133]
MPC	Multi-constraints and dynamic disturbances	Online compensation, good constraint compatibility	High computational complexity, real-time performance limited	[120,134]
H∞	Bounded disturbances and worst-case scenarios	Optimal robustness, guaranteed stability	High conservatism, high fuel consumption	[135,136]
AI	Complex nonlinear disturbances	Adapts to spatiotemporal non-stationary uncertainties	Data-dependent, insufficient out-of-distribution reliability	[115,137]

.

4. Hardware and Software Platform Model Tests and Validation

The engineering implementation of the approach relies on rigorous model validation and tests, and the effectiveness, robustness, and engineering suitability of the algorithms can be systematically assessed through standardized benchmark problems and dedicated validation platforms.

4.1. Typical Benchmark Cases

The choice of a recognized benchmark case is a central precondition for validating an algorithm, and two classic scenarios are listed below.

4.1.1. GTO-GEO Aeroassisted Transfer Mission

The low-energy orbit transfer mission from geostationary transfer orbit (GTO) to geostationary orbit (GEO) is widely used to verify the effectiveness of spacecraft orbit optimization algorithms.

The core parameters and constraints of the mission scenario are as follows: The initial orbit is a typical GTO (perigee altitude of about 200 km, apogee altitude of about 35,786 km, and orbital inclination angle of 28.5°), and the target orbit is a circular GEO (orbital altitude of 35,786 km, orbital inclination angle of 0°). The spacecraft employs a high-lift-to-drag-ratio aerodynamic configuration and may undergo multiple upper atmosphere traversals, during which the atmospheric entry angle and perigee altitude are strictly controlled (perigee altitude is typically constrained to the dilute atmospheric region of 100–120 km) to minimize excessive aerodynamic heating and orbit deviation.

The validation core indexes include the following: total transfer time, fuel consumption, peak heat flow control accuracy, orbit transfer accuracy, and convergence stability of the trajectory optimization algorithm [138].

4.1.2. Mars Aerocapture Deceleration Mission

Typical aerocapture and deceleration benchmark test cases in Mars exploration missions are core verification links of the planetary entry, descent, and landing (EDL) technology system. These tests are widely used in the standardized testing of aerodynamic thermal protection design, guidance control algorithms, and deceleration system performance.

The mission scenarios are commonly based on the NASA Mars Exploration Mission Common Standard. The initial state of entry is the Mars atmospheric interface at an altitude of about 125 km. The initial velocity is 5.5 km/s. The entry angle ranges from −12° to −15°. The spacecraft features a blunt aerodynamic shape and must withstand the extreme aerodynamic heating and pressure loads associated with the Mars atmospheric environment. Core constraints include peak aerodynamic heating, surface pressure, and attitude angle deviation during deceleration. Ultimately, the spacecraft must decelerate to subsonic speed on the surface of Mars and maintain a stable orbit near the fire point altitude to satisfy the initial conditions of the subsequent descent phase [139].

The core validation metrics include deceleration efficiency, peak heat flow control, trajectory dispersion, and robustness under atmospheric parameter uncertainty. The mission serves as a core validation benchmark for NASA’s (MRO probe) and ESA’s (ExoMars) purposes. It enables full testing of the algorithm’s adaptability to complex environments with stringent constraints [60].

4.2. Mainstream Validation Methods and Metrics

The existing literature categorizes validation methods for aeroassisted orbit transfer processes of spacecraft into three main types, each corresponding to distinct validation approaches.

4.2.1. Numerical Simulation Verification

Reproduce the physical process through high-precision numerical models (e.g., CFD, trajectory integration) to verify the theoretical accuracy of aerodynamic models and guidance algorithms [140], including the two categories of “Model Fidelity Verification” and “Trajectory Prediction Accuracy Verification”. Commonly used software tools include STK, GPOPS, SNPORT, PaGMO toolkit, and so on [73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98].

4.2.2. Monte Carlo Simulation Analysis

Monte Carlo simulation (MCS) [141,142] is a core method for uncertainty validation by generating many samples with random uncertainties (e.g., atmospheric density, initial state, aerodynamic parameter dispersion), simulating complex perturbations in real flight, and statistically evaluating algorithms/models for robustness, accuracy, and engineering constraint satisfaction. Aerodynamic parameter identification validation, aerocapture, and guidance validation can be performed [54,55,56,57,58,59,60,61,62,63,111,112,113,114,115,116,117,118,119,120,121,122,123].

4.2.3. Real Experiments and Verification

Verifying the effectiveness of models or algorithms in real-world applications through real-world physical environments such as wind tunnel tests or actual flight data such as radar tracking and sensor measurements is a core validation step in the Numerical-Engineering Transformation (NET) process, where the applicability of algorithms in real-world engineering applications can be assessed by comparing real-world mission-relevant data such as aerodynamic parameters of the Apollo lunar return and SpaceX starship return landing data. By comparing mission-relevant data, such as the aerodynamic parameters of the Apollo lunar return and the SpaceX Starship return landing, the applicability of the algorithms to real-world engineering can be assessed [143].

4.3. Aerospace Verification and Validation Tests Beds

Verification and validation tests are crucial, as formal experiments are necessary to confirm that the model or system has been correctly constructed for industrial use [144]. For a complex technology such as aeroassisted orbit transfer, purely theoretical analyses and high-fidelity simulations are not sufficient to fully guarantee its reliability in real missions. The testbed, as a controlled, non-commercial experimental environment capable of simulating real-space operating conditions, is a key infrastructure for conducting rigorous, transparent, and repeatable tests. It can be categorized into mathematical simulation testbeds (focusing on algorithm verification), hardware-in-the-loop testbeds (incorporating real components), and semi-physical simulation testbeds. The typical platforms are as follows:

• ESA ESTEC Digital Twin Platform:

It integrates high-fidelity atmospheric and thermal protection digital twins, with a large space simulator (LSS) and supporting data processing system, which can complete thermal vacuum, mechanics, and other environmental tests; the “Space Rider” project studies the re-entry problem and designs a digital twin for validating the descent and landing mission phases. The “Space Rider” project studies the re-entry problem and designs a systematic airborne test for validating the descent and landing mission phases [145].

• NASA AMES Hardware-in-the-Loop (HIL) platform:

It utilizes guidance hardware to interact with the simulation environment in real-time, simulating sensor noise, actuator latency, and digital twins. Indeed, digital twins and HIL methods are extensively used in projects such as electric aircraft propulsion and spacecraft health monitoring [146].

• Zero-G Lab Multi-Purpose Space Operations Simulation Facility:

It is built by the Interdisciplinary Centre for Security, Reliability, and Trust (SnT) of the University of Luxembourg, focusing on the simulation of space operations in a gravity-less/microgravity environment. The facility supports Software- and Hardware-in-the-Loop (SIL/HIL) test modes, with test capabilities covering core missions such as rendezvous and docking, in-orbit refueling, space debris removal, and attitude trajectory control, among others [147,148].

• DLR Multidisciplinary HIL Facility:

The facility integrates full-flow testing of aerodynamic-thermodynamic and structural dynamics, featuring a built-in Monte Carlo module to assess the robustness of extreme operating conditions. It has a long history of conducting coupled aerodynamic-thermal-structural testing and Monte Carlo robustness assessments [149].

4.4. Main Practice Directions for the Industries

In the field of aeroassisted orbit transfer approaches, the world’s major space agencies have formed a research and development pattern with different focuses according to their mission objectives and technology accumulation. The following table provides a systematic overview of the focus of representative institutions in this field.

Table 6. Research objectives and technical features of major space institutions.

Research Institutions	Primary Research Objectives and Application Scenarios	Typical Methods/Technical Features	References
NASA 1	Deep space exploration (Mars)	The aerobraking technology has been successfully applied in missions such as Mars Global Surveyor and Mars Odyssey. The probe repeatedly passes through the upper Martian atmosphere to gradually reduce orbital energy.	[57,58,59,60]
ESA 2/DLR 3	Reusable aerospace vehicles (e.g., SpaceLiner)	Experimental vehicles verify key technologies during re-entry, including aerodynamics and thermal protection (e.g., active cooling technology), laying the foundation for commercial operation.	[150,151,152]
TsAGI 4	New-generation aerospace systems, heavy-lift capacity, and hypersonic spaceplanes (e.g., MRKN program)	Focus on overall aerodynamic layout design; conduct wind tunnel tests to investigate full-envelope aerodynamic characteristics and thermal management issues covering subsonic and hypersonic regimes.	[153,154]
Chinese Space Agencies	Deep space exploration and space transportation	Systematically research engineering-oriented practical technologies including orbital strategy design, aerothermal environment analysis, and capture corridor optimization.	[155,156]

¹ NASA—National Aeronautics and Space Administration; ² ESA—European Space Agency; ³ DLR—the German Aerospace Center; ⁴ TsAGI—the Central Aerohydrodynamic Institute named after N.E. Zhukovsky.

has more details.

The primary driver for aeroassisted orbit transfer approaches in industry is their ability to deliver significant fuel savings, resulting in improved mission economics or increased payload capacity. Industry practice is centered around two main scenarios.

The first scenario is atmospheric braking in deep space exploration missions. This approach is currently the most mature technology and the most widely used area. For example, in Mars exploration missions, utilizing the Mars atmosphere for deceleration has become the preferred option due to the characteristics of the Mars gravitational field and the stringent mass constraints of the mission. NASA has successfully verified and applied this technology in several of its prestigious missions.

The second scenario focuses on future reusable space transport systems. For spacecraft that are frequently transported between Earth orbits (e.g., orbital transfer vehicles travelling to and from space stations and different orbital platforms), AOT technology is seen as a key technology path to reduce operating costs and achieve reusability.

5. Conclusions and Future Developments

Aerodynamic manoeuvring technology for spacecraft has evolved over more than six decades, during which hundreds of scientific papers have been published. Overseas research peaked in the 1980s, whilst domestic studies reached their zenith, particularly in the 1990s and 2010s. In recent years, the field has witnessed remarkable progress, marked by a continuous increase in both the quantity and quality of newly proposed methodologies. With the four major modes having completed the transition from theoretical exploration to simulation validation, aerodynamic manoeuvring technology—leveraging its distinctive orbital adjustment capabilities—is poised for practical application in diverse missions such as lunar return, Mars exploration, and regional reconnaissance.

This review systematically examines the research advancements in aeroassisted orbit manoeuvring, delving into the two pivotal technologies: trajectory optimization and control guidance.

Regarding trajectory optimization, researchers have developed multiple efficient numerical methods to address the complex nonlinear, multi-constraint optimization problems inherent in aeroassisted orbit manoeuvring tasks. Direct methods such as Gaussian pseudo-spectral methods, hp-adaptive pseudo-spectral methods, Radau pseudo-spectral methods, and Sequential Convex Programming have become mainstream due to their advantages in handling complex dynamics and multiple constraints. Pseudo-spectral methods enable high-precision offline trajectory design, while SCP enhances computational efficiency and real-time capability by decomposing non-convex problems into convex sub-sequences, demonstrating significant potential in online trajectory planning [89,90,91,92,93,94]. Moreover, artificial intelligence techniques, particularly Transformer-based models, have recently been introduced into AOT trajectory optimization. These offer novel approaches for tackling high-dimensional, unstructured problems and generating high-quality initial guesses, thereby enhancing algorithmic efficiency and performance [101,102,103,104,105,106,107], though their application remains limited. Such methods provide feasible optimal trajectories for diverse mission scenarios under constraints including minimum fuel consumption, minimum time, and strict requirements such as heat flux and overload limits.

In guidance and control, researchers have introduced advanced strategies to solve challenges such as atmospheric uncertainty, variable aerodynamic effects, strong nonlinear couplings, and strict path constraints. MPC, a form of predictive guidance, is effective for re-entry tracking and system robustness because it manages system constraints and optimizes multiple objectives [106,107]. Adaptive guidance and robust control strategies, including sliding mode control and H∞ control, increase system reliability against uncertainties and disturbances through online parameter estimation or worst-case design [106,118,119]. Artificial intelligence is also making strides in this domain. For example, reinforcement learning has been applied to trajectory tracking control and shows promise for autonomously learning optimal control laws in complex dynamic settings [120].

At the level of technology validation and engineering landing, the model testing and validation system of hardware and software platforms provides an important guarantee for the practical application of aeroassisted orbit transfer approaches. With the help of standardized validation mission scenarios, such as the GTO-GEO transfer and the Mars aerocapture, three types of validation combining numerical simulation, Monte Carlo analysis, and physical tests are adopted [143,144,145,146,147]. Based on the ESA digital twin platform, NASA hardware-in-the-loop facility and zero-gravity laboratory, and other major test environments, the comprehensive evaluation of algorithm feasibility and system stability is completed, and at the same time, engineering practices in the field of global spaceflight, such as the atmospheric braking technology for NASA’s deep-space exploration and the development of ESA’s reusable spacecraft, are used to promote scenarios for the application of the technology and to create favorable conditions for the implementation of the subsequent mission engineering.

However, despite these technological advances, several key research gaps persist in aerodynamic manoeuvring for spacecraft. Addressing these gaps is urgent and will require future breakthroughs:

• During modelling, simplified models are often used, while high-fidelity models do not quantify uncertainties well. They also struggle to accurately model or respond to extreme disturbances, such as changes in atmospheric density over time and space, or solar storms. In the future, we can construct high-fidelity atmospheric models that are fused with multi-source data, and research cutting-edge technologies related to the quantification of uncertainty and robust modeling.
• Real-time performance and computational efficiency struggle to meet the demands of complex, multi-channel, multi-constraint missions for onboard applications. We can then research lightweight hybrid optimization algorithms and develop adaptive model downscaling techniques for the future.
• Global coordination for multi-objective optimization (e.g., fuel usage, mission timelines, and heat flux limits) across all mission phases (e.g., deorbiting, atmospheric flight, and re-entry insertion) is not yet mature, particularly in integrating coupling effects between phases. Thus, we can establish a multi-stage and multi-objective synergistic optimization model in the future and research layered and decoupled optimization methods.
• Integrating AI methods with scenarios can enhance their interpretability while satisfying multiple constraints. In the future, AI models embedded with physics-informed information can be developed, and hybrid architectures combining AI with traditional control or convex optimization can be constructed to leverage the strengths of both.
• The integrated design framework needs to be optimized, and the co-optimization of aerodynamic shape, thermal protection, and guidance, navigation, and control (GNC) systems is insufficient, so it is necessary to build a systematic design with multi-disciplinary analysis methods and a multi-disciplinary unified modelling and co-optimization platform and develop an integrated design tool chain.