The bell-shaped lift distribution (BSLD) wing design methodology advanced by Ludwig Prandtl in 1932 was proposed as providing the minimum induced drag. This study used this method as the basis to analyze its characteristics in two wing formation flight. Of specific interest are the potential efficiency savings and the optimal positioning for formation flight. Additional comparison is made between BSLD wings and bird flight in formation. This study utilized Computational Flow Dynamics (CFD) simulations on a geometric modeling of a BSLD wing, the Prandtl-D glider. The results were validated by modified equations published by Prandtl, by CFD modeling published by others, and by Trefftz plane analysis. For verification, the results were compared to formation flight research literature on aircraft and birds, as well as published research on non-formation BSLD flight. The significance of this research is two part. One is that the BSLD method has the potential for significant efficiency in formation flight. The optimal position for a trailing wing was determined to be partially overlapping the leading wing vortex core. For a BSLD wing these vortices are located inboard from the wingtips resulting in wingtip overlap and have a wider impact downstream than the elliptical lift distribution (ELD) wingtip vortices. A second aspect is that avian research has traditionally been studied assuming the ELD model for bird flight, whereas this study proposes that bird flight would be better informed using the BSLD.

Experimental methods for the investigation of trailing vortex strengths, total lift, and lift distributions for three-dimensional wings in close proximity flight were developed. With these experiments we model compound aircraft flight either docked tip-to-tip, or flying in formation. There is a distinct lack of experimental formation flight data using three-dimensional wing models for tests. The absence of fixed walls on either end of the wing permits the development of the asymmetric shedding of vortices, and the determination of the asymmetric circulation distribution induced by the proximity of the leading wing. The pair consisted of a swept NACA-0012 non-cambered wing simulating one half of a leading aircraft and a rectangular cambered NACA 63-420 wing simulating the trailing aircraft. Important aspects of the work included theoretical development, experimental setup, data acquisition and processing, and results validation. Experimentally determining the lift for formation flight, in addition to the local flow behavior for a pair of wings, can provide valuable insight for the proposition of flying actual aircraft in formation to increase mission efficiency. To eliminate the need for bulky mounting stings and direct load measurement devices that can potentially interfere with the local flowfield, a minimally invasive velocity probe method is developed. A series of experiments were performed to assist with the development of the method. Velocity and vorticity distributions obtained along a near-field plane were processed to calculate wingtip vortex strengths. Additionally, vortex position instabilities and the shedding of vorticity inboard of the wingtips were observed. To determine the circulation distributions for the trailing wing, the initial method is modified. By processing velocity information acquired in a near-field plane, both the lift and induced drag were calculated for the trailing airfoil. Comparisons are made to directly measured loads and to results reported earlier. Directly measured lift and drag coefficients were found to agree with existing literature. / Master of Science

The advantages of UAVs in the aviation arena have led to extensive research activities on autonomous technology of UAVs to achieve specific mission objectives. This thesis mainly focuses on the development of a mission-based guidance system. Among various missions expected of UAVs for future needs, autonomous formation flight (AFF) and obstacle avoidance within safe operation limits are investigated. In the design of an adaptive guidance system for AFF, the leader information except position is assumed to be unknown to a follower. Thus, the only measured information related to the leader is the line-of-sight range and angle. Adding an adaptive element with neural networks into the guidance system provides a capability to effectively handle leader's velocity changes. Therefore, this method can be applied to the AFF control systems that use passive sensing methods. The simulation and flight test results clearly show that the adaptive guidance control system is a promising solution for autonomous formation flight of UAVs. The successful flight evaluations using the GTMax rotary wing UAV also demonstrate unique maneuvering aspects associated with rotary wing UAVs in formation flight. In the design of an autonomous obstacle avoidance system, an integrated approach is proposed to resolve the conflict between aggressive maneuvering needed for obstacle avoidance and the constrained maneuvering needed for envelope protection. A time-optimal problem with obstacle and envelope constraints is used for an integrated approach for obstacle avoidance and envelope protection. The Nonlinear trajectory generator (NTG) is used as a real-time optimization solver. The computational complexity arising from the obstacle constraints is reduced by converting the obstacle constraints into a safe waypoint constraint along with an implicit requirement that the horizontal velocity during the avoidance maneuver must be non-negative. The issue of when to initiate a time-optimal avoidance maneuver is addressed by including a requirement that the vehicle must maintain its original flight path to the maximum extent possible. The simulation results using a rotary wing UAV demonstrate the feasibility of the proposed approach for obstacle avoidance with envelope protection.

Les mini-drones à propulsion électrique sont susceptibles d’avoir une endurance inférieure à celle de drones plus grands.L’exploitation des interactions aérodynamiques, inspirée par les oiseaux migratoires, ainsi que le ravitaillement en vol , sont des approches prometteuses pour améliorer l’endurance des mini-drones. La commande par modes glissants d’ordre supérieur en temps continu (CTHOSM) a été considérée comme un candidat prometteur à ce problème ouvert difficile et a été appliquée avec succès à des modèles cinématiques simples. Dans nos travaux, nous étudions les implications de la présence de la dynamique de la boucle interne et de l’implémentation en temps discret à des taux d’échantillonnage modérés et constatons alors que l’application de la commande CTHOSM devient impossible. Nous proposons donc un schéma de guidage prédictif discret par modes glissants pour approximer les performances de la commande CTHOSM pour une dynamique réaliste du drone. On propose également un problème de référence accessible pour d'autres chercheurs. Les algorithmes de localisation probabilistes existants ne permettent pas la caractérisation de régions de confiance garanties de la position des autres membres de la formation. Dans ce contexte, nous proposons un nouveau filtre ensembliste caractérisant de telles régions de confiance sous forme ellipsoïdale. Nos premières évaluations ont montré que les efforts de calcul induits par cette mise en œuvre restent parfaitement compatibles avec les contraintes des systèmes avioniques des petits drones. / Small, electrically driven unmanned aircraft are likely to suffer from inferior endurance compared to their larger counterparts. Upwash exploitation by tight formation flight, as well as aerial recharging are the most promising control-driven approaches to mitigate this disadvantage. Continuous time higher order sliding mode control (CTHOSM) has been considered as a candidate for this challenging open problem and was successfully applied to simple kinematic models in simulation, where excellent relative position tracking performance can be demonstrated. In this work we study the implications of the presence of inner loop dynamics and discrete implementation at moderate sampling rates and we find that it precludes the application of CTHOSM control to fixed-wing UAS. We propose a predictive discrete sliding mode guidance scheme to approximate the performance of CTHOSM control assuming realistic fixed-wing UAS dynamics. We show that the proposed guidance scheme in combination with inner load factor tracking loops and a disturbance observer allows for relative position tracking performance compatible with the requirements of upwash exploitation. We propose as well an openly accessible benchmark problem. Existing probabilistic localization algorithms cannot provide guaranteed confidence regions of the relative position between UAS. We present a set membership filter that provides ellipsoidal regions guaranteed to contain the relative positions of the other UAS. It is compatible with the hardware constraints of small low-cost UAS. Simulations suggest computational efforts compatible with the computational resources typically available onboard small UAS.

The Auroral Acceleration Region (AAR) is a key region in understanding the interactionbetween the Magnetosphere and Ionosphere. To understand the physical, spatial, and temporal features of the region, multi-point measurements are required. Distributed small-satellite missions such as constellations of multiple nano satellites (for example multi-unit CubeSats) would enable such type of measurements. The capabilities of such a mission will highly depend on the number of satellites - one reason that makes low-cost platforms like CubeSats a very promising choice. In a previous study, the state-of-the-art of miniaturized payloads for AAR measurements was analyzed and evaluated on the capabilities of different multi-CubeSat configurations equipped with such payloads in addressing different open questions in AAR. This thesis will provide the mission analysis of such a multi-CubeSat mission to the AAR and possible mission design. This includes defining the mission scenario and associated requirements, developing a mathematical description of AAR that allows for specific regions in space to be targeted, an optimisation process for designing orbits targeting these regions, conversion of a satellite formation to appropriate orbits, verifying the scientific performance of this formation and the various costs associated with entering, maintaining, and exiting these orbits.

There is growing interest in commercial aircraft formation flight as a means of reducing both airspace congestion and the carbon footprint of air transportation. Wake vortex surfing has been researched extensively and proven to have significant fuel-saving benefits, however, commercial air transportation has yet to take advantage of these formation benefits due to understandable safety concerns. The realization of these formations requires serious consideration of formation contingencies and safety during closer-in maneuvering of large commercial aircraft. Formation contingency scenarios are much more complex than those of individual aircraft and have not yet been studied in depth. This thesis investigates the utility of optimization modeling in providing insight into generation of aircraft escape paths for formation contingency planning. Three high-altitude commercial aircraft formation scenarios are presented; formation join, formation emergency exit, and formation escape. The model-generated paths are compared with pilot-generated escape plans using the author’s pilot expertise. The model results compare well with pilot intuition and are useful in presenting solutions not previously considered, in evaluating separation requirements for improvement of escape path planning and in confirming the viability of the pilot-generated plans. The novel optimization model formulation presented in this thesis is the first model shown to be capable of generating escape paths comparable to pilot- generated escape plans and is also the first to incorporate avoidance of persistent and drifting wake turbulence within the formation.

No description available.

Formation flying of satellites describes a mission in which a set of satellites arrange their position with respect to one another. In this paper, satellite formation flying guidance and control algorithms are investigated in terms of required velocity increment Delta-v, and tracking error for a Chief/Deputy satellite system. Different control methods covering continuous and impulsive laws are implemented and tested for Low Earth Orbit (LEO). Sliding Mode, Feedback Linearization and Model Predictive Controllers are compared to an Impulsive Feedback Law which tracks the mean orbital element differences. Sliding Mode and Feedback Linearization controllers use the same dynamic model which includes Earth Oblateness perturbations. On the other hand, Model Predictive Control with Multi-Objective Cost Function is based on the Clohessy–Wiltshire equations, which do not account for any perturbation and do not cover the eccentricity of the orbit. The comparison was done for two different missions both including Earth Oblateness effects only. A relative orbit mission, which was based on the Prisma Satellite Mission and a rendezvous mission, was implemented. The reference trajectory for the controllers was generated with Yamanaka and Ankersen’s state transition matrix, while a separate method was used for the Impulsive Law. In both of the missions, it was observed that the implemented Impulsive Law outperformed in terms of Delta-v, 1.2 to 3.5 times smaller than the continuous control approaches, while the continuous controllers had a smaller tracking error, 2 to 8.3 times less, both in terms of root mean square error and maximum error in the steady state. Finally, this study shows that the tracking error and Delta-v has inversely proportional relationship. / Formationsflygning av satelliter innebär att en grupp satelliter flyger tillsammans och anpassar sina relativa lägen i förhållande till varandra. I detta examensarbete studerades regleralgoritmer för formationsflygande satelliter med fokus på bränsleförbrukning och positionsavvikelse genom ”Chief & Deputy”-metoden. Olika reglermetoder har studerats, t.ex. Sliding Mode- och Feedback Linearization-reglering för formationsflygningsfall i låg jordbana med J2-störning samt en Model Predictive-reglering för fall med relativ rörelse baserad på Clohessy-Wiltshire-ekvationerna. Vidare studerades en reglermetod baserad på impulsframdrivning. De fyra reglermetoderna implementerades på två olika rymduppdrag. Först ett uppdrag baserat på Prisma-satelliterna för två satelliter i relativ omloppsbana och sedan ett Rendezvous-uppdrag. Referensbanan för alla reglermetoder, utom för implusmetoden, har tagits fram med hjälp av Yamanakas och Ankersens tillståndsmatris. Resultaten visar att den implementerade impulsmetoden presterar bättre med avseende på bränsleförbrukning, medan de kontinuerliga reglermetoderna producerade mindre relativ positionsavvikelse, både med avseende på kvadratiskt medelvärde och maximalt värde.

This dissertation develops the visual pursuit method for air-to-air tracking and rendezvous of unmanned aircraft systems. It also shows the development of vector-field and proportional-integral methods for controlling UAS flight in formation with other aircraft. The visual pursuit method is a nonlinear guidance method that uses vision-based line of sight angles as inputs to the algorithm that produces pitch rate, bank angle and airspeed commands for the autopilot to use in aircraft control. The method is shown to be convergent about the center of the camera image frame and to be stable in the sense of Lyapunov. In the lateral direction, the guidance method is optimized to balance the pursuit heading with respect to the prevailing wind and the location of the target on the image plane to improve tracking performance in high winds and reduce bank angle effort. In both simulation and flight experimentation, visual pursuit is shown to be effective in providing flight guidance in strong winds. Visual pursuit is also shown to be effective in guiding the seeker while performing aerial docking with a towed aerial drogue. Flight trials demonstrated the ability to guide to within a few meters of the drogue. Further research developed a method to improve docking performance by artificially increasing the length of the line of sight vector at close range to the target to prevent flight control saturation. This improvement to visual pursuit was shown to be an effective method for providing guidance during aerial docking simulations. An analysis of the visual pursuit method is provided using the method of adjoints to evaluate the effects of airspeed, closing velocity, system time constant, sensor delay and target motion on docking performance. A method for predicting docking accuracy is developed and shown to be useful for predicting docking performance for small and large unmanned aircraft systems.