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This paper proposes a novel approach to the solution of optimal control problems under uncertainty (OCPUUs). OCPUUs are first cast in a general formulation that allows the treatment of uncertainties of different nature, and then solved with a new direct transcription method that combines multiple shooting with generalised polynomial algebra to model and propagate extended sets. The continuity conditions on extended sets at the boundary of two adjacent segments are directly satisfied by a bounding approach. The Intrusive Polynomial Algebra aNd Multiple shooting Approach (IPANeMA) developed in this work can handle optimal control problems under a wide range of uncertainty models, including nonparametric, epistemic, and imprecise probability ones. In this paper, the approach is applied to the design of a robust low-thrust trajectory to a Near-Earth Object with uncertain initial conditions. It is shown that the new method provides more robust and reliable trajectories than the solution of an analogous deterministic optimal control problem.

This work proposes a high-speed Light Detection and Ranging (LIDAR) based navigation architecture that is appropriate for uncooperative relative space navigation applications. In contrast to current solutions that exploit 3D LIDAR data, our architecture transforms the odometry problem from the 3D space into multiple 2.5D ones and completes the odometry problem by utilizing a recursive filtering scheme. Trials evaluate several current state-of-the-art 2D keypoint detection and local feature description methods as well as recursive filtering techniques on a number of simulated but credible scenarios that involve a satellite model developed by Thales Alenia Space (France). Most appealing performance is attained by the 2D keypoint detector Good Features to Track (GFFT) combined with the feature descriptor KAZE, that are further combined with either the H∞ or the Kalman recursive filter. Experimental results demonstrate that compared to current algorithms, the GFTT/KAZE combination is highly appealing affording one order of magnitude more accurate odometry and a very low processing burden, which depending on the competitor method, may exceed one order of magnitude faster computation.

The deceleration of a supersonic flow to the subsonic regime inside a high-speed engine occurs through a series of shock waves, known as a shock train. The generation of such a flow structure is due to the interaction between the shock waves and the boundary layer inside a long and narrow duct. The understanding of the physics governing the shock train is vital for the improvement of the design of high-speed engines and the development of flow control strategies. The present paper analyses the sensitivity of the shock train configuration to a back-pressure variation. The complex characteristics of the shock train at an inflow Mach number M = 2 in a channel of constant height are investigated with two-dimensional RANS equations closed by the Wilcox k-ω turbulence model. Under a sinusoidal back-pressure variation, the simulated results indicate that the shock train executes a motion around its mean position that deviates from a perfect sinusoidal profile with variation in oscillation amplitude, frequency, and whether the pressure is first increased or decreased.

The traditional method used for handling qualities assessment of manned space vehicles is too time-consuming to meet the requirements of an increasingly fast design process. In this study, a rendezvous and docking inverse simulation system to assess the handling qualities of spacecraft is proposed using a previously developed model-predictive-control architecture. By considering the fixed discrete force of the thrusters of the system, the inverse model is constructed using the least squares estimation method with a hyper-ellipsoidal restriction, the continuous control outputs of which are subsequently dispersed by pulse width modulation with sensitivity factors introduced. The inputs in every step are deemed constant parameters, and the method could be considered as a general method for solving nominal, redundant, and insufficient inverse problems. The rendezvous and docking inverse simulation is applied to a nine-degrees-of-freedom platform, and a novel handling qualities evaluation scheme is established according to the operation precision and astronauts' workload. Finally, different nominal trajectories are scored by the inverse simulation and an established evaluation scheme. The scores can offer theoretical guidance for astronaut training and more complex operation missions.

Lightweight deployable space webs have been proposed as platforms or frames for a construction of structures in space where centrifugal forces enable deployment and stabilization. The Suaineadh project was aimed to deploy a 2×2m2 space web by centrifugal forces in milli-gravity conditions and act as a test bed for the space web technology. Data from former sounding rocket experiments, ground tests and simulations were used to design the structure, the folding pattern and control parameters. A developed control law and a reaction wheel were used to control the deployment. After ejection from the rocket, the web was deployed but entanglements occurred since the web did not start to deploy at the specified angular velocity. The deployment dynamics was reconstructed from the information recorded in inertial measurement units and cameras. The nonlinear torque of the motor used to drive the reaction wheel was calculated from the results. Simulations show that if the Suaineadh started to deploy at the specified angular velocity, the web would most likely have been deployed and stabilized in space by the motor, reaction wheel and controller used in the experiment.

This paper introduces the concept of Resilience Engineering in the context of space systems design and a model of Global System Reliability and Robustness that accounts for epistemic uncertainty and imprecision. In particular, Dempster-Shafer Theory of evidence is used to model uncertainty in both system and environmental parameters. A resilience model is developed to account for the transition from functional to degraded states, and back, during the operational life and the dependency of these transitions on system level design choices and uncertainties. The resilience model is embedded in a network representation of a complex space system. This network representation, called Evidence Network Model (ENM), allows for a fast quantification of the global robustness and reliability of system. A computational optimisation algorithm is then proposed to derive design solutions that provide an optimal compromise between resilience and performance. The result is a set of design solutions that maximise the probability of a system to recover functionalities in the case of a complete or partial failure and at the same time maximises the belief in the desired target value of the performance index.

With the recent progress toward the application of commercially-available hardware to small-scale space missions, it is now becoming feasible for groups of small, efficient robots based on low-power embedded hardware to perform simple tasks on other planets in the place of large-scale, heavy and expensive robots. In this paper, we describe design and programming of the Beaver micro-rover developed for Northern Light, a Canadian initiative to send a small lander and rover to Mars to study the Martian surface and subsurface. For a small, hardware-limited rover to handle an uncertain and mostly unknown environment without constant management by human operators, we use a Bayesian network of discrete random variables as an abstraction of expert knowledge about the rover and its environment, and inference operations for control. A framework for efficient construction and inference into a Bayesian network using only the C language and fixed-point mathematics on embedded hardware has been developed for the Beaver to make intelligent decisions with minimal sensor data. We study the performance of the Beaver as it probabilistically maps a simple outdoor environment with sensor models that include uncertainty. Results indicate that the Beaver and other small and simple robotic platforms can make use of a Bayesian network to make intelligent decisions in uncertain planetary environments.

Libration Point Orbits (LPOs) and Highly Elliptical Orbits (HEOs) are often selected for astrophysics and solar terrestrial missions. No guidelines currently exist for their end-of-life disposal. However, as current and future missions are planned to be placed on these orbits, it is a critical aspect to clear these regions at the end of operations to avoid damage to other spacecraft and ensure on-ground safety. This paper presents an analysis of possible disposal strategies for LPO and HEO missions as a result of a European Space Agency study. The dynamical models and the design approach are presented for each disposal option. Five current missions are selected as test cases Herschel, Gaia, SOHO as LPOs, and INTEGRAL and XMM-Newton as HEOs. A trade-off on the disposal options is made considering technical feasibility, as well as the sustainability context.

This paper investigates displaced periodic orbits at linear order in the circular restricted Earth-Moon system (CRTBP), where the third massless body utilises a hybrid of solar sail and solar electric propulsion (SEP). A feedback linearisation control scheme is implemented to perform stabilisation and trajectory tracking for the nonlinear system. Next, attention is directed to binary asteroid systems as an application of the restricted problem. The idea of combining a solar sail with an SEP auxiliary system to obtain a hybrid sail system is important especially due to the challenges of performing complex trajectories.

The combined effect of solar radiation pressure, Earth oblateness and atmospheric drag on the orbital dynamics of satellites-on-a-chip (SpaceChips) is investigated for future swarm mission concepts. The natural evolution of the swarm is exploited to perform spatially distributed measurements of the upper layers of the atmosphere. The energy gain from asymmetric solar radiation pressure can be used to balance the energy dissipation from atmospheric drag. An algorithm for long-term orbit control is then designed, based on changing the reflectivity coefficient of the SpaceChips. The subsequent modulation of the solar radiation pressure allows stabilisation of the swarm in the orbital element phase space. It is shown that the orbit lifetime for such devices can be extended through the interaction of solar radiation pressure and atmospheric drag and indeed selected and the end-of-life re-entry of the swarm can be ensured, by exploiting atmospheric drag.

The effect of solar radiation pressure and atmospheric drag on the orbital dynamics of satellites-on-a-chip (SpaceChips) is exploited to design equatorial long-lived orbits about the oblate Earth. The orbit energy gain due to asymmetric solar radiation pressure, considering the Earth's shadow, is used to balance the energy loss due to atmospheric drag. Future missions for a swarm of SpaceChips are proposed, where a number of small devices are released from a conventional spacecraft to perform spatially distributed measurements of the conditions in the ionosphere and exosphere. It is shown that the orbit lifetime can be extended and indeed selected through solar radiation pressure and the end-of-life re-entry of the swarm can be ensured, by exploiting atmospheric drag.

In this paper, displaced geostationary orbits using hybrid low-thrust propulsion, a complementary combination of Solar Electric Propulsion (SEP) and solar sailing, are investigated to increase the capacity of the geostationary ring that is starting to become congested. The SEP propellant consumption is minimized in order to maximize the mission lifetime by deriving semi-analytical formulae for the optimal steering laws for the SEP and solar sail accelerations. By considering the spacecraft mass budget, the performance is also expressed in terms of payload mass capacity. The analyses are performed both for the use of pure SEP and hybrid low-thrust propulsion to allow for a comparison. It is found that hybrid low-thrust control outperforms the pure SEP case both in terms of payload mass capacity and mission lifetime for all displacements considered. Hybrid low-thrust propulsion enables payloads of 255 to 487 kg to be maintained in a 35 km displaced orbit for 10 to 15 years. Adding the influence of the J2 and J22 terms of the Earth’s gravity field has a small effect on this lifetime, which becomes almost negligible for small values of the sail lightness number. Finally, two SEP transfers that allow for an improvement in the performance of hybrid low-thrust control are optimized for the propellant consumption by solving the accompanying optimal control problem using a direct pseudospectral method. The first type of transfer enables a transit between orbits displaced above and below the equatorial plane, while the second type of transfer enables customized service for which a spacecraft is transferred to a Keplerian parking orbit when geostationary coverage is not needed. While the latter requires a modest propellant budget, the first type of transfer comes at the cost of an almost negligible SEP propellant consumption.

This paper proposes a way to model uncertainties and to introduce them explicitly in the design process of a preliminary space mission. Traditionally, a system margin approach is used in order to take them into account. In this paper, Evidence Theory is proposed to crystallise the inherent uncertainties. The design process is then formulated as an Optimisation Under Uncertainties (OUU). Three techniques are proposed to solve the OUU problem: (a) an evolutionary multi-objective approach, (b) a step technique consisting of maximising the belief for different levels of performance, and (c) a clustering method that\ud firstly identifes feasible regions. The three methods are applied to the BepiColombo mission and their\ud effectiveness at solving the OUU problem are compared.

Plans for interplanetary manned space missions imply significant risks arising from human's exposure to the hostile space environment. Thus the design of reliable protection systems against the ionizing cosmic radiation becomes one of the most relevant issues. In this paper the composition and magnitude of the atmospheric radiation on the planetary surface and for typical interplanetary transfer configurations have been analyzed. The investigation based on prior NASA and ESA mission results, using a manned mission to planet Mars as a case study. According to this, the time-dependent character of the consistency of cosmic radiation has been taken into account, which is justified by the interdependence of the radiation magnitude to the solar cycle. With regard to this paper it implies even solar particle events. The results have been compared to the protective character of different materials potentially usable as a habitat's structural shell and for interplanetary spacecrafts. The investigation aimed on particle energy degradation rates and reduction of secondary particle production. In this regard the physical process of absorbing effectiveness against particle radiation has been examined by analytical calculation and given scientific results, depending on thickness and molecular composition of the materials. The most suitable materials have been used for shield design proposals using different configurations, evaluating the use of aluminium, water tanks and polyethylene bricks.

This paper reports on the results of the experiment PULSAR (Pulsating and Rotating Instabilities in Oscillatory Marangoni Flows), performed on the MAXUS 3 Sounding Rocket launched last November from the Swedish base in Kiruna. Aim of the experiment was the study of the oscillatory Marangoni convection in a cylindrical liquid bridge of silicone oil with kinematic viscosity of 5cSt. The experiment was motivated by preliminary on-ground numerical simulations and microscale experimental studies, that have pointed out that the oscillatory Marangoni instability appears at the beginning in the form of a pulsating regime, caused by a hydro-thermal standing wave, and then it turns to a rotating regime, caused by a traveling wave. The height of the bridge was equal to the disk diameter (20mm), and the imposed temperature difference was 15K during the first 460 s and 20K in the second part of the experiment, until the end of the microgravity period. The analysis of the temperature profiles, measured by thermocouples located near the disks at the same radial and axial coordinate but at different azimuthal coordinates (shifted at 90°), and the surface temperature distribution, measured by an infrared thermocamera, show that a pulsating and a mixed pulsating-rotating regimes have been established during the experiment. Unfortunately during the flight the accelerations level caused by two centrifuges with some biological samples in an adjacent module were above the expected values, so that disturbing g-jitter were encountered at different times during the microgravity mission. The effects are clearly visible and the numerical simulations had to make different assumptions to correlate the experimental results

The effect of atmospheric drag on spacecraft dynamics is considered one of the predominant sources of uncertainty in Low Earth Orbit. These effects are characterised in part by the atmospheric density, a quantity highly correlated to space weather. Current atmosphere models typically account for this through proxy indices such as the F10.7, but with variations in solar radio flux forecasts leading to significant orbit differences over just a few days, prediction of these quantities is a limiting factor in the accurate estimation of future drag conditions, and consequently orbital prediction. In this work, a novel deep residual architecture for univariate time series forecasting, N-BEATS, is employed for the prediction of the F10.7 solar proxy on the days-ahead timescales relevant to space operations. This untailored, pure deep learning approach has recently achieved state-of-the-art performance in time series forecasting competitions, outperforming well-established statistical, as well as statistical hybrid models, across a range of domains. The approach was found to be effective in single point forecasting up to 27-days ahead, and was additionally extended to produce forecast uncertainty estimates using deep ensembles. These forecasts were then compared to a persistence baseline and two operationally available forecasts: one statistical (provided by BGS, ESA), and one multi-flux neural network (by CLS, CNES). It was found that the N-BEATS model systematically outperformed the baseline and statistical approaches, and achieved an improved or similar performance to the multi-flux neural network approach despite only learning from a single variable.