Orbital rendezvous enables spacecraft to perform missions to service satellites, remove space debris, resupply space stations, and return samples from other planets. These missions are often considered high risk due to concerns that the two spacecraft will collide if the maneuvering capability of one spacecraft is compromised by a fault.<br>In this thesis, a passive safety analysis is used to evaluate the probability that a fault that compromises maneuvering capability results in a collision. For a rendezvous<br>mission, the chosen approach trajectory, state estimation technique, and probability of collision calculation each impact the total collision probability of the mission. This<br>thesis presents a modular framework for evaluating the comparing the probability of collision of rendezvous mission design concepts.<br>Trade studies were performed using a baseline set of approach trajectories, and a Kalman Filter for relative state estimation and state estimate uncertainty. The state covariance matrix following each state update was used to predict the resulting probability of collision if a fault were to occur at that time. These trade studies emphasize that the biggest indicator of rendezvous mission risk is the time spent on a nominal intercept trajectory.

No / Abstract: Avoiding collision among contending customer premise equipments (CPEs) attempting to associate with a base station (BS), the only available solution in IEEE 802.22 standard is binary exponential random backoff process in which the contending CPEs retransmit their association requests. The number of attempts the CPEs sends their requests to the BS are fixed in IEEE 802.22 network. This paper presents a mathematical framework for helping the BS in determining at which attempt the majority of the CPEs become the part of wireless regional area network (WRAN) from a particular number of contending CPEs at a given initial contention window size.

The topic of this thesis is on-board estimation of spacecraft collision probability for orbital rendezvous and proximity operations. All of the examples shown in this work assume that the satellite dynamics are described by the Clohessy-Wiltshire equations, and that the spacecraft are spherical. Several collision probability metrics are discussed and compared. Each metric can be placed into one of three categories. The first category provides an estimate of the instantaneous probability of collision, and places an upper bound on the total probability of collision. The second category provides an estimate of total collision probability directly. The last category uses Monte Carlo analysis and a novel Pseudo Monte Carlo analysis algorithm to determine total collision probability. The metrics are compared and their accuracy is determined for a variety of on-orbit conditions. Lastly, a method is proposed in which the metrics are arranged in a hierarchy such that those metrics that can be computed quickest are calculated first. As the proposed algorithm progresses the metrics become more costly to compute, but yield more accurate estimates of collision probability. Each metric is compared to a threshold value. If it exceeds the limits determined by mission constraints, the algorithm computes a more accurate estimate by calculating the next metric in the series. If the threshold is not reached, it is assumed there is a tolerable collision risk and the algorithm is terminated. In this way the algorithm is capable of adapting to the level of collision probability, and can be sufficiently accurate without needless calculations being performed. This work shows that collision probability can be systematically estimated.

The collision probability approach to neutron transport can be used to obtain the energy-dependent neutron spectrum in nuclear reactor systems as well as other quantities of interest. This method makes the approximation that the neutron distribution is constant within homogeneous regions, or cells, in the system. This assumption restricts geometries that can be modeled by the collision probability approach. The geometry modeled is typically an infinite lattice of two homogeneous cells: a fuel pin cylinder and the coolant that surrounds it. The transport of neutrons between the homogeneous cells is done using probabilities describing the chance that a neutron having a collision in one cell has its next collision in another cell. These collision probabilities can be cast in terms of escape and transmission probabilities for each cell. Some methods exist that extend the collision probability approach to systems composed of more than two homogeneous cells. In this work, we present a novel collision probability method, based on previous work by Schneider et al. (2006a), for an arbitrary number of cells. The method operates by averaging the transmission probabilities across cells of the same shape, and thus assumes a certain level of homogeneity across all cells. When using multigroup cross sections, which the collision probability approach requires, it is necessary to consider the effect that a system's geometry and composition has on those multigroup cross sections. The cross sections must be computed in a way that accounts for the resonance self-shielding that may reduce the reaction rates in the resonance region. The process of developing self-shielded cross sections in a heterogeneous system utilizes an escape cross section. We compute this escape cross section using the same collision probabilities used to obtain the energy spectrum. Results are presented for simple two-cell systems, and preliminary results for four-cell simulations are also given. An extension to the method is provided that accounts for the fact that in thermal systems the assumption of homogeneity is not always valid. / text

This work develops a one dimensional, slab geometry, multigroup collision probability code named Oklo which solves both criticality calculations and fixed source problems. The code uses the classical collision probabilities approach where the first flight collision probabilities are calculated analytically for void, reflected and periodic boundary conditions. The code has been verified against analytical criticality benchmark test sets from Los Alamos National Laboratory, which have been used to verify MCNP amongst other codes. The results from the code show a good agreement with the benchmark test sets for the critical systems presented in this report. The results from the code also match the infinite multiplication factors k and average scalar flux ratios for infinite multiplicative systems from the benchmark test sets. The criticality results and the fixed source results from the Oklo code have been compared with criticality results and fixed source results from a discrete ordinates code and the results for both types of problems show a good agreement with the results from the discrete ordinates code as we increase the N for the discreet ordinates code. / Thesis (M.Sc. Engineering Sciences (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2012.

This work develops a one dimensional, slab geometry, multigroup collision probability code named Oklo which solves both criticality calculations and fixed source problems. The code uses the classical collision probabilities approach where the first flight collision probabilities are calculated analytically for void, reflected and periodic boundary conditions. The code has been verified against analytical criticality benchmark test sets from Los Alamos National Laboratory, which have been used to verify MCNP amongst other codes. The results from the code show a good agreement with the benchmark test sets for the critical systems presented in this report. The results from the code also match the infinite multiplication factors k and average scalar flux ratios for infinite multiplicative systems from the benchmark test sets. The criticality results and the fixed source results from the Oklo code have been compared with criticality results and fixed source results from a discrete ordinates code and the results for both types of problems show a good agreement with the results from the discrete ordinates code as we increase the N for the discreet ordinates code. / Thesis (M.Sc. Engineering Sciences (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2012.

This thesis can be viewed as two parts. The first part focuses on performance analysis of millimeter wave (mmWave) communications. We investigate how the interference behaves in the outdoor mesh network operating at 60-GHz when block age and shadowing are present using the probability of collision as a metric, under both the protocol model and the physical model. In contrast with results reported in mmWave mesh networks at 60-GHz that advocates that interference has only a marginal effect, our results show that for a short-range link of 100 m, the collision probability gets considerably larger (beyond 0.1) at the signal-to-interference-plus-noise ratio (SINR) of interest (for example, the reference value is chosen as 15 dB for uncoded quadrature phase shift keying (QPSK)). Compensation or compromise should be made in order to maintain a low probability of collision, either by reducing transmitter node density which is to the detriment of the network connectivity, or by switching to a compact linear antenna array with more at-top elements, which places more stringent requirements in device integration techniques. The second part of this thesis focuses on finding the optimal unmanned aerial vehicle (UAV) deployment in the sense that it can maximize over specific network connectivity. We have introduced a connectivity measure based on the commonly used network connectivity metric, which is refered to as global soft connectivity. This measure can be easily extended to account for different propagation models, such as Rayleigh fading and Nakagami fading. It can also be modified to incorporate the link state probability and beam alignment errors in highly directional networks. As can be shown, under the line-of-sight (LOS) and Rayleigh fading assumptions, the optimization regarding the global soft connectivity can be expressed as a weighted sum of the square of link distances between the nodes within the network, namely the ground-to-ground links, the UAV-to-UAV links and the ground-to-UAV links. This can be shown to be a quadratically constrained quadratic program (QCQP) problem with non-convex constraints. We have also extended our global connectivity to other types of connectivity criteria: network k-section connectivity and k-connectivity. In all the three cases, we have proposed a heuristic and straightforward way of finding the suboptimal UAV locations. The simulation results have shown that all these methods can improve our network connectivity considerably, which can achieve a gain of up to 30% for a five UAV scenario.

yes / The only available solution in the IEEE 802.22 standard for avoiding collision amongst various contending customer premises equipment (CPEs) attempting to associate with a base station (BS) is binary exponential random backoff process in which the contending CPEs retransmit their association requests. The number of attempts the CPEs send their requests to the BS are fixed in an IEEE 802.22 network. This paper presents a mathematical framework that helps the BS in determining at which attempt the majority of the CPEs become part of the wireless regional area network from a particular number of contending CPEs. Based on a particular attempt, the ranging request collision probability for any number of contending CPEs with respect to contention window size is approximated. The numerical results validate the effectiveness of the approximation. Moreover, the average ranging success delay experienced by the majority of the CPEs is also determined. / The full text will be available at the end of the publisher's embargo: 7th Aug 2018

The development of the IEEE 802.22 standard is aimed at providing broadband access in rural areas by effectively utilizing the unused TV band, provided no harmful interference is caused to the incumbent operation. This thesis presents the analytical framework to evaluate the number of active customer premise equipments (CPEs) in a wireless regional area network. Initial ranging is the primary process in IEEE 802.22 networks for CPEs to access the network and establish their connections with the base station (BS). A comprehensive analysis of initial ranging mechanism is provided in this work and initial ranging request success probability is derived based on the number of contended CPEs and the initial contention window size. Further, the average ranging success delay is derived for the maximum backoff stages. The collision probability is highly dependent on the size of the initial contention window and the number of contended CPEs. To keep it at a specific level, it is necessary for the BS to schedule the required size of the initial contention window to facilitate the maximum number of CPEs to establish their connections with reasonable delay. Therefore, the optimized initial window size is proposed that meets the collision probability constraint for a particular number of contended CPEs. An analytical model is also developed to estimate the ranging request collision probability depending upon the size of initial contention window and the number of contended CPEs. Moreover, this approximation provides the threshold size for contention window to start the initial ranging process in the IEEE 802.22 network.

Na área de robótica móvel autônoma é importante que o robô siga uma trajetória livre de obstáculos. Estes podem ser desde obstáculos estáticos, como paredes e cadeiras em um ambiente interno, ou mesmo obstáculos móveis, como pessoas caminhando na calçada e carros passando pela rua, quando consideramos ambientes externos. No caso de um ambiente estático, o problema pode ser resolvido planejando uma trajetória livre de colisões, sendo que não é necessário um replanejamento se todos os obstáculos estáticos foram considerados. Para ambientes onde os obstáculos estão em constante movimento, é necessário um constante replanejamento da trajetória para que se evite colisões. Alternativamente, pode ser verificada a possibilidade de se manter na rota planejada, alterando apenas a velocidade de cruzeiro do robô para que este desvie dos obstáculos móveis. Este trabalho propõe uma metodologia para calcular uma velocidade de cruzeiro para o robô de forma a minimizar a probabilidade de colisão com os obstáculos detectados pelos seus sensores. A escolha da variação de velocidade para o robô considera a sua velocidade atual, e as velocidades estimadas para os obstáculos. A metodologia para resolução deste problema é apresentada considerando incertezas na posição do robô e obstáculos. São apresentados resultados de simulação que exemplificam a aplicação da metodologia. / Following a free path is an important issue in the area of autonomous mobile robotics. The obstacles can be anything from walls and chairs in an indoor environment, or they can also be people walking on the sidewalk and cars moving through the street. In the case of a static environment, the problem can be solved by planning a path free from collisions, thus it is not essential another path planning as all static obstacles were considered. For an environment were the obstacles are constantly moving, it is necessary an unceasing path replanning to avoid possible collisions. Alternatively, keeping the robot on the previously calculated path can be verified modifying the robot\'s traffic velocity to avoid moving obstacles. Our proposal is to calculate a velocity for the robot which minimizes its collision probability with moving obstacles detected by its sensors. Varying the robot\'s velocity takes into account its current velocity and the estimated velocities of obstacles. The methodology for solving this problem is presented regarding uncertainties in robots and obstacles\' positions. Results from simulations that exemplifies an application for the methodology are presented.