Soit X une courbe projective lisse et irréductible munie d'une involution σ. Dans cette thèse, nous étudions les fibrés vectoriels invariants and anti-invariants sur X sous l'action induite par σ. On introduit la notion de modules σ-quadratiques et on l'utilise, avec GIT, pour construire ces espaces de modules, puis on en étudie certaines propriétés. Ces espaces de modules correspondent aux espaces de modules de G-torseurs parahoriques sur la courbe X/σ , pour certains schémas en groupes parahoriques G de type Bruhat-Tits, qui sont twistés dans le cas des anti-invariants. Nous développons les systèmes de Hitchin sur ces espaces de modules et on les utilise pour dériver une classification de leurs composantes connexes en les dominant par des variétés de Prym. On étudie aussi le fibré déterminant sur les espaces de modules des fibrés vectoriels anti-invariants. Dans certains cas, ce fibré en droites admet certaines racines carrées appelées fibrés Pfaffiens. On montre que les espaces des sections globales des puissances de ces fibrés en droites (les espaces des fonctions thêta généralisées) peuvent être canoniquement identifier avec les blocs conformes associés aux algèbres de Kac-Moody affines twistées de type A(2). / Let X be a smooth irreducible projective curve with an involution σ. In this dissertation, we studythe moduli spaces of invariant and anti-invariant vector bundles over X under the induced action of σ. We introduce the notion of σ-quadratic modules and use it, with GIT, to construct these moduli spaces, and than we study some of their main properties. It turn out that these moduli spaces correspond to moduli spaces of parahoric G-torsors on the quotient curve X/σ, for some parahoric Bruhat-Tits group schemes G, which are twisted in the anti-invariant case.We study the Hitchin system over these moduli spaces and use it to derive a classification of theirconnected components using dominant maps from Prym varieties. We also study the determinant of cohomology line bundle on the moduli spaces of anti-invariant vector bundles. In some cases this line bundle admits some square roots called Pfaffian of cohomology line bundles. We prove that the spaces of global sections of the powers of these line bundles (spaces of generalized theta functions) can be canonically identified with the conformal blocks for some twisted affine Kac-Moody Lie algebras of type A(2).

<p>This thesis describes the development of a low-cost, low-power, accurate sensor designed for precise, feedback control of an autonomous vehicle to a hitch. Few studies have been completed on the hitching problem, yet it is an important challenge to be solved for vehicles in the agricultural and transportation industries. Existing sensor solutions are high cost, high power, and require modification to the hitch in order to work. Other potential sensor solutions such as LiDAR and Digital Fringe Projection suffer from these same fundamental problems. </p> <p>The solution that has been developed uses an active stereo vision system, combining classical stereo vision with a laser speckle projection system, which solves the correspondence problem experienced by classic stereo vision sensors. A third camera is added to the sensor for texture mapping. As a whole, the system cost is $188, with a power usage of 2.3 W.</p> <p>To test the system, a model test of the hitching problem was developed using an RC car and a target to represent a hitch. In the application, both the stereo system and the texture camera are used for measurement of the hitch, and a control system is implemented to precisely control the vehicle to the hitch. The system can successfully control the vehicle from within 35⁰ of perpendicular to the hitch, to a final position with an overall standard deviation of 3.0 mm of lateral error and 1.5⁰ of angular error. Ultimately, this is believed to be the first low power, low cost hitching system that does not require modification of the hitch in order to sense it. </p>

Žemės ūkio paskirties traktorių pagrindinis tikslas yra atlikti tempimo darbus esant įvairioms sąlygoms ir skirtingiems kelio paviršiams. Traukos jėga priklauso nuo traktoriaus eksploatacinių rodiklių, tokių kaip: ratų sukibimas su paviršiumi ir jų buksavimo dydis, traktoriaus išvystoma traukos galia ir t.t. Visi šie rodikliai kinta kintant traktoriaus bendrajai masei tuo pačiu ir vertikaliosioms apkrovoms veikiančioms kiekvieną iš traktoriaus ratų. Todėl atliekant įvairius žemės ūkio darbus, reikia tinkamai įvertinti traktorių veikiančias statines bei dinamines apkrovas. Magistrinio darbo tema – išanalizuoti traktoriaus ratus veikiančias reakcijos jėgas, esant skirtingiems agregato prikabinimo aukščiams ir kampams. Atlikus tyrimus, gautos priklausomybės rodo, jog didinant traukos jėgą priešinga kryptimi negu traktorius juda, apkrovos, veikiančios traktoriaus galinius ratus didėja, o priekinius – mažėja. Veikiant traukos jėga nukreipta horizontaliu kampu (imituojant posūkį į kairę pusę) kairės pusės traktoriaus ratus veikiančios apkrovos kito intensyviau negu dešinės pusės ratų. / The main purpose for agricultural tractor is to make pulling actions in various conditions and on various surfaces. Tractor pulling force depends on tractor performances such as: wheel grip with surface and their slippage value, tractor traction force etc. These performances depends on tractor weight and on its vertical wheel loads. Seeking for the best tractor efficiency while doing agricultural work it is necessary to sum up static and dynamic loads effecting tractor. Chosen Master thesis is designed to investigate tractor wheel static load, when simulating implement pull with different hitching heights and angles. After the research it can be stated that the increasing pulling force with the direction opposite tractor movement, rear wheel loads increase, while front wheel loads decrease. While pulling force with horizontal angle is increased (turning to the left is simulated), left side wheel loads varies with greater values than loads of the right side wheel.