With the increasing interest in the Solar System's smaller bodies, quite a few missions have been sent to comets and asteroids, and more will be send in the near future. Due to the large distances involved, communication to command mission parameters takes a long time, which has a negative impact on operational safety. Autonomous navigation would be one of the key technologies that can make the mission more robust, safe, and cost effective. This is especially true if one considers the unknown fight environment when the spacecraft is first encountering the body. Most asteroids and comets have a very irregular shape and unknown mass distribution. Therefore, knowledge about its irregular gravity field will be directly beneficial as input to orbital corrections and manoeuvre planning. This paper addresses the estimation process of gravity-field parameters that could potentially be implemented in an autonomous navigation system. The focus is on a spherical-harmonic modelling of asteroid Eros-433, most notably outside the Brillouin sphere where the validity of the model is guaranteed. By using Kalman filtering it is shown that all degree and order coefficients up to degree 8 can be estimated with an error below 10%. This is the first step towards an autonomous navigation system that can operate in a highly-perturbed environment close to the asteroid.

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Within the last decade, the use of launch vehicles has increased as private companies have emerged in the space exploration industry. Compared to the early 1980s, the market for launch vehicles has become significantly more competitive, introducing the desire to have fully reusable launch vehicles. The true benefits of fully reusable launch vehicles can only be achieved once both stages are fully operational and recoverable. This stimulates the need for a comprehensive mission design. In this paper, this is achieved by revisiting the mission profiles of flyback boosters. An extensive analysis of the design-space is performed to identify the contributions of each decision variable to the trajectory design. The results concluded that such an approach supports achieving a more efficient optimization, with better convergence speed and solution performance. @en

This research performs a surrogate-assisted shape optimisation of hypersonic waveriders, where the trajectories of each shape are optimised with a multi-objective evolutionary algorithm for heat-load and cross-range. A study on the best evolutionary algorithm, node control strategy for angle of attack and bank angle profiles, and population size to use in the trajectory optimisation phase, are identified. The aerodynamics of the waveriders is computed with a new local surface inclination method blending the modified Newtonian and tangent wedge solutions, while the convective heat flux is computed for the leading edges using the Newton-Kays engineering model. Shape variability is introduced according to the layout of central composite designs, and analysis of variance is applied to identify the shape features driving the two objectives. Shock angle, leading edge radius and overall vehicle dimensions are the strongest drivers, while details on the planform shape are less relevant and should be left for posterior studies. The surrogates are a good approximation of the true fitness functions, so they were optimised in a single-objective framework, producing two optimal waverider designs.@en

This paper investigates the performance of an autonomous navigation system to navigate a spacecraft in the proximity of a binary asteroid system using optical and laser ranging measurements. The knowledge about the binary asteroid is limited to its orbital parameters and ellipsoid shape models. The accelerometer bias random walk is included in the estimation process. Over a four-hour landing maneuver starting from 6770 m altitude and ending at 550 m, the mean position estimation uncertainty is 41.6 m (3). It is shown that the navigation accuracy is sensitive to the Sun phase angle, the irregularity of the asteroid shape, and the goodness of fit of the ellipsoid shape model. The paper demonstrates that the navigation system is robust to large errors in the initialization of the extended Kalman filter state. The impact of image distortion and two types of image noise on the navigation performance are investigated.

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To limit the mass of the vehicle's thermal protection system, an optimal trajectory that minimises the total integrated heat load should be own. This means that the maximum heat-ux constraint is followed for as long as possible, until the maximum mechanical load is encountered. Flying as close to this load as possible contributes to minimising the heat load as well. The guidance system to track the path constraints includes two components: a semi-analytical guidance that produces nominal bank-angle commands and a tracking system based on non-linear dynamic inversion. The ight system under consideration is a hypersonic test vehicle of which the stagnation heat-ux should not exceed 1,700 kW/m2, with a limit of the mechanical load of 4.8 g. The preliminary results show that the tracking system extends the duration of heat-ux tracking and is able to tightly track the heat-ux constraint, but reduces the ight range because of that. A simultaneous optimisation of these two con icting objectives should be pursued to rene the guidance-system design in case both have requirements to be met. In none of the cases considered, the g-load constraint was violated, although a more detailed analysis is required to make this part of the guidance more robust.

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Objects travelling at hypersonic speeds typically experience significant mechanical loads, particularly during acceleration/deceleration. Excluding both technical and economic limitations, sub-orbital point-to-point travel is inevitably restricted to a group of individuals that are trained and whose health is certified prior to travel. This work seeks to explore the possibility of identifying, for a chosen route and reference vehicle, a set of parameters such that an individual could participate in hypersonic travel without health screenings or prior training. An open-loop guidance system is used with idealised navigation and control systems. The guidance method is based on node control with the assumption of instant implementation of commanded states. After an initial design space exploration is performed with various evolutionary algorithms, the Multi-objective Evolutionary Algorithm based on Decomposition with differential evolution (MOEA/D) (DE) is selected for further use, along with a preferred set of objective functions and a decision vector length. The subsequent optimisation strategy is separated into a coupled and decoupled phase approach, where the coupled approach combines the vehicle’s ascent and descent optimisations, while the decoupled approach performs a descent phase optimisation and attempts to link an ascent phase to the optimised descent phase. Decoupling, as performed, did not allow for the identification of a linkable trajectory. An optimal trajectory was identified with the coupled approach that required a significant amount of additional propellant and dry mass, yet maximum g₀-loads approached the constraint of an increase of 1 g₀. Recommendations are given to further the study.

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Attitude control of conventional launchers is relatively easy and straightforward and gives an adequate performance when applied to the nominal vehicle and mission. However, in the presence of environmental disturbances and vehicle design uncertainties, more robust types of controllers are required to guarantee stable attitudes. This chapter discusses the application of Simple Adaptive Control for the pitch control of a conventional flexible launcher. Because of the large number of design parameters, an optimisation procedure based on an evolutionary algorithm has been applied. With a floating-point representation for the design parameters, stochastic universal sampling selection, arithmetic crossover and non-uniform mutation, the performance of the controller is analysed, and it is identified how the developed methodology can streamline the (conceptual) design phase. Application of Pareto ranking enabled the simultaneous minimisation of the state deviation and the control effort, while the oscillation of the control has been used as an optimisation criterion. A conclusive simulation shows the controller performance for the flexible launch system.

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This paper focuses on the attitude control and propellant slosh suppression of aeroelastic launch vehicles in a turbulent atmosphere. For a ve-degree pitch-angle block command, the tracking performance of the selected Incremental Non-Linear Dynamic Inversion Sliding Mode Controller (INDI-SMC) shows excellent tracking performance. However, turbulence still inevitably leads to oscillatory behaviour in the swivel command. Various lter designs have been implemented to improve the smoothness of INDI-SMC. Using either a notch or band-pass lter in the sensor-feedback loops of pitch angle and pitch rate only marginally reduced the swivel oscillations, but did not solve the problem for the rigid-body control. For the exible launcher with slosh dynamics, ltering of the sensor-feedback signals reduced the oscillations in swivel command, and elastic and slosh motion signi cantly, but could not completely remove them. The preliminary design of a rigid-body state observer has been included, and the results show that the INDI-SMC controller remains stable in the presence of engine dynamics, sloshing, exible modes, input errors due to the use of rigid-body and slosh-state observers, while ying in a turbulent wind field.

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Parachute/flow interaction is dominant in evaluating a decelerator’s performance. Such interaction is characterized by nonlinear deformations and complex flow phenomena. While testing methods are available to investigate parachute performance, these are often costly and nonrepresentative of the desired flight conditions. To address the need for an accessible technique capable of modeling parachutes at the early design stages, this paper proposes a robust fluid/structure interaction methodology for three-dimensional subsonic simulations. This is attained by replacing the linear springs in Provot’s equation with polynomial expressions whose coefficients are fitted to tensile test data. The nonlinear cloth algorithm is coupled with the rhoPorousSimpleFoam solver in the open-source OpenFOAM toolbox, thereby establishing an iterative process that reaches steady-state convergence in at most six iterations. The transient response is obtained from the average distributed load of the steady-state pressure field and an inertial damping contribution. The simulations are performed for two disk-gap-band parachutes and a ringsail parachute over a velocity range of ring sail 5–30 m/s. The results are compared to the experimental data measured in the Open Jet Facility of Delft University of Technology, yielding errors below 5% for the steady-state cases and overestimations in peak loads of 4.4–12.4% for the transient simulations.@en

The beginning of the conceptual design phase of (re)entry missions requires aerodynamic methods to reduce the initial design space. For this purpose, full computational fluid dynamics (CFD) simulations are unsuitable due to their computational requirements. Rapid hypersonic methods are thus often employed to approximate the heat flux and skin friction on the most critical parts of the (re)entry vehicle, such as the nose and the leading edges. However, the vast majority of these rapid methods only allow for a computation of these parameters at specific fixed locations and not on the other parts of the vehicle. One method that overcomes this is the axisymmetric analogue method, that determines the entire viscous flowfield from the inviscid flowfield solution. This method has typically been coupled to inviscid Euler simulations, but even Euler simulations can still consume a lot of computational time. In earlier research, it was shown that a reasonable accuracy can also be obtained if this method is coupled with the inviscid flowfield computed via the modified Newtonian technique. In this paper, we extend the validation and estimation of the uncertainties of this method using CFD, evaluate the respective corrections for thermal and chemical fluxes separately, and apply these corrections back to the solver. The biconic DART vehicle, partial optimisation of which was presented in the previous paper, is revisited, here optimising only four parameters instead of five as originally intended, as using five parameters resulted in an unfeasible geometry. We perform a full response surface methodology and analysis of variance accounting for the CFD corrections and examine the final optimised design also again with the Newtonian/axisymmetric code. The proposed methodology leads to a small underestimate of the heat fluxes, but is considered sufficient for the conceptual design phase.@en

We present a 3 Degrees of Freedom mission design and analysis for in-situ probing of Uranus' atmosphere consisting of two un-propelled gliders and one orbiting spacecraft in continuous line of sight. We focus on the study of the gliders' navigation and science modules. Because of the lack of a Global Navigation Satellite System around Uranus and the ineffective use of optical sensors due to the planet's large distance to the Sun and high atmospheric opacity, the post-processing relation between the vehicles' estimated state and measured scientific data is investigated to yield accurate state estimations. In-situ probing by the two gliders will make it possible to measure spatially variable atmospheric properties over a flight duration of up to 12 Earth days, as compared to a few hours for a conventional descent probe. Future work will include a 6 Degrees of Freedom simulation of the vehicles' flight, the chosen planet's wind model, a Flush Air Data Sensor as an additional navigation sensor, and a band-pass filter to reduce the estimated variables' noise.@en

This paper proposes a two-stage optimization approach for aerocapture guidance. In classical entry guidance systems, deterministic optimization is used. Large-scale and short-scale density perturbations may strongly affect the performance of the guidance system, and variations in those are usually not accounted for when computing the command. In this work, perturbations that affect the trajectory at future time-steps are taken into consideration when computing the commanded bank angle. The chosen command is optimal based on a set of possible future perturbations, after the observation of which, a correction can be made. Both two-stage stochastic and two-stage robust optimization are proposed as a solution. In a Monte Carlo analysis consisting of 50 runs, the two-stage robust optimization guidance outperforms an optimal, deterministic, numeric predictor-corrector guidance. Excluding one outlier, also the two-stage stochastic optimization makes the guidance perform better than an optimal deterministic numeric predictor-corrector. With either approach, the computational demands are increased by about thirty times compared to an optimal numeric predictor-corrector. Much of the computation time increase may be reduced by parallelization. On the other hand, the extensive tuning required for the optimal numeric predictor-corrector is not needed for the two-stage optimization guidance, making this approach conceptually more robust. Better modeling of the environment may help further improve the performance. Finally, an approximation to the two-stage robust optimization approach is developed. The guidance has computational requirements only four times larger than those of the optimal numeric predictor-corrector guidance, but can be parallelized into two threads, and, except for two outliers, it offers improved performance.@en

Verified interval orbit propagation provides mathematically guaranteed solutions of satellite position and velocity over time. These verified solutions are useful for conjunction analysis and other space-situational-awareness activities. Unfortunately, verified methods suffer from overestimation and explosive interval growth, limiting the possible propagation time and thus their applicability. Different orbital-element state models have been shown to increase the maximum propagation time to a degree, but at the expense of significant overestimation introduced by the state transformations. This paper proposes the Dromo state model for verified integration. Dromo is a regularized variation-of-parameter formulation of the perturbed two-body equations of motion. Taylor models are implemented for both integration and transformation. Moreover, a technique is developed for dealing with time uncertainty resulting from verified regularized propagation. Dromo significantly prolongs the maximum forecasting window, producing verified trajectories of days up to weeks in duration for the low Earth orbit regime. A sensitivity analysis of the integrator settings identifies combinations that produce stable and computationally efficient solutions. A sensitivity study of the orbital parameters shows that the method is applicable to a large orbital regime, especially for low Earth orbit regions that contain high densities of space debris.

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Re-entry shape and trajectory optimisation studies typically require hundreds to thousands of flow solutions to resolve the heat transfer and skin friction. Due to the fact that full CFD simulations and even Euler simulations are typically very expensive, this work presents a development of a much simpler technique, in which the modified Newtonian approximation is coupled with the axisymmetric-analogue-based viscous method. Afterwards, the developed technique is applied to the shape optimisation study of the DART module originally conducted by Sudmeijer and Mooij in 2002. Large differences in heat fluxes are observed mainly owing to the fact that the present method estimates the transition region from approximate transition criteria while the original study assumes the transition point to be fixed at the interface between the cone and the flare. This emphasises the sensitivity of design optimisation studies on delicate parameters such as the location of transition, which typically cannot be accurately predicted during the conceptual phase. Finally, the limitations of the current method are identified and the areas in which the technique will be improved further are outlined.@en

Space safety and hazard-reduction techniques for space-transportation vehicles are becoming critical in the advent of commercial crewed launches and suborbital intercontinental travel. One way to mitigate risks is to use advanced guidance strategies to centralise mission planning, and guidance, navigation and control. Convex optimisation can be suitable for this purpose, as it solves second-order-cone programming problems sequentially in polynomial time. As atmospheric re-entry contains a large number of non-convexities, an advanced optimal-control optimiser based on successive convex optimisation was developed and analysed with a golden-section line-search method to enhance its convergence. A direct-linearisation approach, although slightly sensitive to initial guesses, was seen to be robust when compared in different objective formulations. However, a hybrid approach using a lossless convexification performed better for most problems, although it relied on a regularisation condition, which was sometimes difficult to satisfy. The reachability capabilities of the SPHYNX lifting body during orbital and descent aborts were analysed and showed that around 14 minutes are available to perform an abort to an alternative landing site for a nominal mission. While there is significant room for improvement, the study shows that successive convex optimisation could be potentially used for mission planning and on-board applications as an optimal trajectory planner during realistic re-entry missions.@en

In this paper a new drag-energy scheme for atmospheric entry guidance, based on the use of pseudospectral methods and convex optimization, is proposed. One of the most successful technologies to deal with atmospheric entry is the class of drag-tracking schemes, a direct heritage of the Space Shuttle program. The method that we propose exploits the drag-dynamics, and allows for an efficient automatic design of an optimal entry profile satisfying all the longitudinal constraints acting on the vehicle. A new representation of the entry-guidance problem, able to loss-less convexify the formulation, is provided. Numerical simulations confirm the validity of the proposed scheme as tool for further improving the autonomy of modern entry guidance systems, with a mean final range-to-go error at the end of entry phase smaller than 2 km, and the capability to re-compute a complete constrained trajectory to meet the mission requirements.

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This paper focuses on the attitude control and propellant slosh suppression of aeroelastic launch vehicles. Four candidate controllers are proposed: the Linear Quadratic Regulator (LQR), the Incremental Non-linear Dynamic Inversion (INDI) control, the Incremental Sliding Mode Control (INDI-SMC), and the Feedback Linearisation-based Sliding Mode Control (FL-SMC). Theoretical analyses show INDI itself is unable to deal with under-actuated systems. Therefore, when applied to the launch vehicle directly, it cannot simultaneously track the pitch command and effectively suppress the slosh dynamics. This issue is solved by INDI-SMC, which also has enhanced robustness against both matched and unmatched uncertainties. Furthermore, despite its reduced model dependency, INDI-SMC has better robustness against model uncertainties and external disturbances than FL-SMC. These merits of INDI-SMC are verified by various simulation results. First, when the nominal plant configuration is adopted, the system using INDI-SMC has the smallest pitch-angle tracking error. The slosh motion is also effectively damped out. Second, Monte-Carlo studies are used to test the robustness of LQR, INDI-SMC, and FL-SMC to parametric uncertainties. Among these three controllers, LQR shows the worst performance and largest control-effort outliers. On the contrary, both INDI-SMC and FL-SMC can resist a wider range of perturbations without significant performance degradation. Even so, the tracking and slosh damping performance of INDI-SMC is still the best. Finally, both INDI-SMC and FL-SMC show robustness against unmodeled dynamics, while the robust performance of INDI-SMC is superior. @en

Precision landing is an anticipated technology for future interplanetary missions. Autonomous spacecraft Entry, Descent and Landing (EDL) on the surface of a planetary body with a degree of precision in the order of meters is highly challenging. In this paper, a successive convexification guidance algorithm is utilized to simulate autonomous precision landing sequences on Saturn’s moon Titan. Due to its unique geophysical features, studying the science of matter within Titan’s atmosphere and beneath its surface is one of NASA’s most important planetary science objectives. As part of the Space Exploration Technology Directorate, a parafoil is proposed for landing on Titan due to its cost effectiveness, ease of deployment, low mass compared to the prospective payload and capabilities of precise autonomous delivery. This paper focuses on path optimization and guidance law development for high-fidelity dynamics parafoil tuning in the dense and adverse wind atmosphere of Titan, defined as a nonlinear and nonconvex optimal control problem. The powerful successive convexification method is used to solve the problem accordingly. The algorithm is designed such that the converged solution adheres to the nonlinear dynamics and kinematics in accordance with the original formulation, while respecting the state and control constraints. The six-degree-of-freedom (6DoF) simulations results show that this robust method is suitable for autonomous interplanetary applications.@en

In this paper, we combine the concepts of hyper-volume, ant colony optimization and nondominated sorting to develop a novel multi-objective ant colony optimizer for global space trajectory optimization. In particular, this algorithm is first tested on three space trajectory bi-objective test problems: an Earth-Mars transfer, an Earth-Venus transfer and a bi-objective version of the Jupiter Icy Moons Explorer mission (the first large-class mission of the European Space Agency's Cosmic Vision 2015-2025 programme). Finally, the algorithm is applied to a four-objectives low-thrust problem that describes the journey of a solar sail towards a polar orbit around the Sun. The results on both the test cases and the more complex problem are reported by comparing the novel algorithm performances with those of two popular multi-objective optimizers (i.e., a nondominated sorting genetic algorithm and a multi-objective evolutionary algorithm with decomposition) in terms of hypervolume metric. The numerical results of this study show that the multi-objective hypervolume-based ant colony optimization algorithm is not only competitive with the standard multi-objective algorithms when applied to the space trajectory test cases, but it can also provide better Pareto fronts in terms of hypervolume values when applied to the complex solar sailing mission.

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By simulating full lift-up and full lift-down trajectories, the limit initial conditions for which successful aerocapture is possible have been determined. These boundaries form the entry corridor for aerocapture, and have been developed for Earth, Mars, and Venus. Moreover, two different vehicles representative for either manned missions or sample return were studied. The vehicle configurations were varied to study the effect of mass and lift on the size of the entry corridor. From this investigation it was determined that increasing the lift produced by the vehicle is a more effective method of widening the entry corridor than decreasing the mass. Furthermore, it was found that a lift-up-lift-down bang-bang type of trajectory minimises both the total ∆V, the load factor, and the heat load. An optimisation scheme was set up to determine the optimal switch time, which showed that for nearly all initial conditions that fall within the boundaries specified by the developed entry corridors, optimal aerocapture could indeed be achieved with an apoapsis correcting manoeuvre with a ∆V smaller than 0.01 m/s.

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