A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

Assessments of training load in elite youth soccer

One of the most popular sports globally, soccer has seen a rise in the demands of the game over recent years. An increase in intensity and playing demands, coupled with growing social and economic pressures on soccer players means that optimal preparation is of paramount importance. Recent research has found the modern game, depending on positional role, to consist of approximately 60% more sprint distance in the English Premier League, which was also found to be the case for frequency and success of discrete technical actions (Bush et al., 2015). As a result, the focus on soccer training and player preparedness is becoming more prevalent in scientific research. By designing the appropriate training load, and thus periodization strategies, the aim is to achieve peak fitness in the most efficient way, whilst minimising the risk of injury and illness. Traditionally, training intensity has been based on heart rate responses, however, the emergence of tracking microtechnology such as global positioning system (GPS) and inertial sensors are now able to further quantify biomechanical load as well as physiological stress. Detailed pictures of internal and external loading indices such as these then combine to produce a more holistic view of training load experience by the player during typical drills and phases of training in soccer. The premise of this research is to gain greater understanding of the physical demands of common training methodologies in elite soccer to support optimal match performance. The coaching process may then benefit from being able to prescribe the most effective training to support these. The first experimental chapter in this thesis began by quantify gross training loads of the pre-season and in-season phases in soccer. A broader picture of the training loads inherent in these distinct phases brought more detail as to the type and extent of external loading experienced by soccer players at these times, and how the inclusion of match play influences weekly training rhythms. Training volume (total distance) was found to be high at the start compared to the end of pre-season (37 kilometres and 28 kilometres), where high cardiovascular loads were attained as part of the conditioning focus. This progressed transiently, however, to involve higher-speed, acceleration and change-of-direction stimuli at the end of pre-season compared to the start and to that in-season (1.18 kilometres, 0.70 kilometres and 0.42 kilometres high-intensity running; with 37, 25 and 23 accelerations >3m/s2 respectively) . The decrease in volume and increase in maximal anaerobic activity was evident in the training focus as friendly matches were introduced before the competitive season. The influence of match-play as being a large physical dose in the training week may then determine the change in weekly periodisation and how resulting training loads applied and tapered, if necessary. The focus of research was then directed more specifically to the most common mode of training in soccer, that also featured regularly in the pre-season period in the present study, small-sided games (SSG). The subsequent studies examined numerous manipulations of this specific form of soccer conditioning, such as player numbers as well as absolute and relative playing space available. In contrast to some previous literature, changing the number of players did not seem to influence training responses significantly, although playing format in the possession style brought about larger effects for heart rate (89.9%HRmax) and average velocity (7.6km/h-1). However, the following studies (Chapters 5, 6 and 7) revealed a greater influence of relative playing space available to players in SSG. The larger area at their disposal brought about greater aerobic responses (~90%HRmax), by allowing higher average and peak velocities (>25km/h-1), as well as greater distance acceleration behaviour at greater thresholds (>2.8m/s2). Furthermore, the data points towards space as being a large determinant in strategy of the player in small-sided games (SSG), subsequently shaping their movement behaviour and resulting physical responses. For example, higher average velocities in a possession format (8km/h-1) reflects higher work rate and heart rate load but makes achieving significant neuromuscular accelerations at a high level difficult given higher starting velocities prior to the most intense accelerations (4.2km/h-1). By altering space available and even through intentional numerical imbalances in team numbers, it may be easier for coaches to achieve the desired stimulus for the session or individual player, whether that is for aerobic and neuromuscular conditioning. Large effects were found for heart rate being higher in the underloaded team (85-90%HRmax) compared to the team with more players (80-85%HRmax) as well as for RPE (5AU versus 7AU). This was also apparent for meterage and therefore average velocity. It would also seem neuromuscular load through high acceleration and deceleration efforts were more pronounced with less numbers (given the need to press and close down opponents, and in a larger area relative to the number of players on the underloaded team. The peak accelerations and deceleration achieved was also higher when playing with less players (3-6.2m/s2 and 3-6.1m/s2) Having detailed ways in which to reach desired physical loading responses in common small training formats, Chapter 8 compared SSG to larger 9v9 formats with full-size 11v11 friendly matches. This enabled absolute and relative comparisons to be made and to understand the extent to which smaller training formats are able to replicate the required movements to be successful in competition. In relative terms, it was revealed that relative acceleration distance and Player Load were higher in smaller 4v4 games than match-play (1.1m.min-1 and 0.3m.min-1 >3m/s2; 16.9AU versus 12AU). Although the smallest format did not replicate the high-velocity demands of matches, the results confirmed their efficacy in providing significant neuromuscular load during the training week, which may then be supplemented by high-intensity interval running in order to gain exposure to more maximal speed work. In summary, the data presented provide valuable information from GPS and inertial sensor microtechnology which may then be used to understand training better to manipulate types of load according to physical conditioning objectives. For example, a library of resources to direct planning of drills of varying cardiovascular, neuromuscular and perceptual load can be created to give more confidence in session outcomes. Combining external and internal load data of common soccer training drills, and their application across different phases and training objectives may give coaches a powerful tool to plan and periodize training.

A comparison of the physiological demands of rugby union match-play when determined by absolute (ABS) or individual (IND) velocity bands in Global Positioning System (GPS) analysis

Since turning professional in 1995 there have been considerable advances in the research on the demands of rugby union, largely using Global Positioning System (GPS) analysis over the last 10 years. A systematic review on the use of GPS, particularly the setting of absolute (ABS) and individual (IND) velocity bands in field based, intermittent, high-intensity (HI) team sports was undertaken. From 3669 records identified, 38 studies were included for qualitative analysis. Little agreement on the definition of movement intensities within team sports was found, only three papers, all on rugby union, had used IND bands, with only one comparing ABS and IND methods. Thus, the aim of this study was to determine if there is a difference in the demands within positions when comparing ABS and IND methods for GPS analysis and if these differences are significantly different between the forward and back positional groups. A total of 214 data files were recorded from 26 players in 17 matches of the 2015/2016 Scottish BT Premiership. ABS velocity zones 1-7 were set at 1) 0-6, 2) 6.1-11, 3) 11.1-15, 4) 15.1-18, 5) 18.1-21, 6) 21.1-15 and 7) 25.1-40km.h-1 while IND zones 1-7 were 1) <20, 2) 20-40, 3) 40-50, 4) 50-70, 5) 70-80, 6) 80-95 and 7) 95-100% of player’s individually determined maximum velocity (Vmax). A 40m sprint test measured Vmax using OptaPro S4 10 Hz (catapult, Australia) GPS units to derive IND bands. The same GPS units were worn during matches. GPS outputs analysed were % distance, % time, high intensity efforts (HIEs) over 18.1 km.h-1 / 70% max velocity and repeated high intensity efforts (RHIEs) which consists of three HIEs in 21secs. General linear model (GLM) analysis identified a significant difference in the measurement of % total distance covered, between the ABS and IND methods in all zones for forwards (p<0.05) and backs (p<0.05). This difference was also significant between forwards and backs in zones 1, shown as mean difference ± standard deviation (3.7±0.7%), 6 (1.2±0.4%) and 7 (1.0±0.0%) respectively (p<0.05). Percentage time estimations were significantly different between ABS and IND analysis within forwards in zones 1 (1.7±1.7%), 2 (-2.9±1.3%), 3 (1.9±0.8%), 4 (-1.4±0.8%) and 5 (0.2±0.4%), and within backs in zones 1 (-10±1.5%), 2 (-1.2±1.1%), 3 (1.8±0.9%) and 5 (0.6±0.5%) (p<0.05). The difference between groups was significant in zones 1, 2, 4 and 5 (p<0.05). The number of HIEs was significantly different between forwards and backs in zones 6 (6±2) and 7 (3±2). RHIEs were significantly different between ABS and IND for forwards (1±2, p<0.05) although not between groups. Until more research on the differences in ABS and IND methods is carried out, then neither can be deemed a criterion method. In conclusion, there are significant differences between the ABS and IND methods of GPS analysis of the physical demands of rugby union, which must be considered when used to inform training load and recovery to improve performance and reduce injuries.

Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft

The idea of spacecraft formations, flying in tight configurations with maximum baselines of a few hundred meters in low-Earth orbits, has generated widespread interest over the last several years. Nevertheless, controlling the movement of spacecraft in formation poses difficulties, such as in-orbit high-computing demand and collision avoidance capabilities, which escalate as the number of units in the formation is increased and complicated nonlinear effects are imposed to the dynamics, together with uncertainty which may arise from the lack of knowledge of system parameters. These requirements have led to the need of reliable linear and nonlinear controllers in terms of relative and absolute dynamics. The objective of this thesis is, therefore, to introduce new control methods to allow spacecraft in formation, with circular/elliptical reference orbits, to efficiently execute safe autonomous manoeuvres. These controllers distinguish from the bulk of literature in that they merge guidance laws never applied before to spacecraft formation flying and collision avoidance capacities into a single control strategy. For this purpose, three control schemes are presented: linear optimal regulation, linear optimal estimation and adaptive nonlinear control. In general terms, the proposed control approaches command the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory (TVNT), while the threat of collision between the followers is reduced by repelling accelerations obtained from the collision avoidance scheme during the periods of closest proximity. Linear optimal regulation is achieved through a Riccati-based tracking controller. Within this control strategy, the controller provides guidance and tracking toward a desired TVNT, optimizing fuel consumption by Riccati procedure using a non-infinite cost function defined in terms of the desired TVNT, while repelling accelerations generated from the CAS will ensure evasive actions between the elements of the formation. The relative dynamics model, suitable for circular and eccentric low-Earth reference orbits, is based on the Tschauner and Hempel equations, and includes a control input and a nonlinear term corresponding to the CAS repelling accelerations. Linear optimal estimation is built on the forward-in-time separation principle. This controller encompasses two stages: regulation and estimation. The first stage requires the design of a full state feedback controller using the state vector reconstructed by means of the estimator. The second stage requires the design of an additional dynamical system, the estimator, to obtain the states which cannot be measured in order to approximately reconstruct the full state vector. Then, the separation principle states that an observer built for a known input can also be used to estimate the state of the system and to generate the control input. This allows the design of the observer and the feedback independently, by exploiting the advantages of linear quadratic regulator theory, in order to estimate the states of a dynamical system with model and sensor uncertainty. The relative dynamics is described with the linear system used in the previous controller, with a control input and nonlinearities entering via the repelling accelerations from the CAS during collision avoidance events. Moreover, sensor uncertainty is added to the control process by considering carrier-phase differential GPS (CDGPS) velocity measurement error. An adaptive control law capable of delivering superior closed-loop performance when compared to the certainty-equivalence (CE) adaptive controllers is finally presented. A novel noncertainty-equivalence controller based on the Immersion and Invariance paradigm for close-manoeuvring spacecraft formation flying in both circular and elliptical low-Earth reference orbits is introduced. The proposed control scheme achieves stabilization by immersing the plant dynamics into a target dynamical system (or manifold) that captures the desired dynamical behaviour. They key feature of this methodology is the addition of a new term to the classical certainty-equivalence control approach that, in conjunction with the parameter update law, is designed to achieve adaptive stabilization. This parameter has the ultimate task of shaping the manifold into which the adaptive system is immersed. The performance of the controller is proven stable via a Lyapunov-based analysis and Barbalat’s lemma. In order to evaluate the design of the controllers, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) are implemented, extending the number of elements in the formation into scenarios with reconfigurations and on-orbit position switching in elliptical low-Earth reference orbits. An extensive analysis and comparison of the performance of the controllers in terms of total Δv and fuel consumption, with and without the effects of the CAS, is presented. These results show that the three proposed controllers allow the followers to asymptotically track the desired nominal trajectory and, additionally, those simulations including CAS show an effective decrease of collision risk during the performance of the manoeuvre.