The clothoid, also known as the Cornu spiral, is a curve generated by linearly increasing or decreasing curvature as a function of arc length. The clothoid has been widely accepted as a logical curve for transitioning from straight segments to circle arcs in roads and railways, because a vehicle following the curve at constant speed will have a constant change of centripetal acceleration. Clothoids have also been widely adopted in planning potential paths for autonomous vehicle navigation. They have been viewed as useful representations of possible trajectories that are dynamically feasible. Surprisingly, the assumptions that underlie this choice appear to be lightly treated or ignored in past literature. This thesis will examine three key assumptions that are implicitly made when assuming that a vehicle will follow a clothoid path. The first assumption is that the vehicle's steering mechanism will produce a linear change in turning radius for a constant rate input. This assumption is loosely referred to as the "bicycle model" and it relates directly to the kinematic parameters of the steering mechanism. The second assumption is that the steering actuator can provide a constant steering velocity. In other words, the actuator controlling the steering motion can instantaneously change from one rate to another. The third assumption is that the vehicle is traveling at a constant velocity. By definition, the clothoid is a perfect representation of a vehicle traveling at constant velocity with a constant rate of change in steering curvature. The goal of this research was to examine the accuracy of these assumptions for a typical Ackermann-steered ground vehicle. Both theoretical and experimental results are presented. The vehicle that was used as an example in this study was a modified Club Car Pioneer XRT 1500. This Ackermann-steered vehicle was modified for autonomous navigation and was one of Virginia Tech's entries in the DARPA 2005 Grand Challenge. As in typical operation, path planning was conducted using the classic clothoid curve model. The vehicle was then commanded to drive a selected path, but with variations in speed and steering rate that are inherent to the real system. The validity of the three assumptions discussed above were examined by comparing the actual vehicle response to the planned clothoid. This study determined that the actual paths driven by the vehicle were generally a close match to the originally planned theoretical clothoid path. In this study, the actual kinematics of the Ackermann vehicle steering system had only a small effect on the driven path. This indicates that the bicycle model is a reasonable simplification, at least for the case studied. The assumption of constant velocity actuation of the steering system also proved to be reasonably accurate. The greatest deviation from the planned clothoid path resulted from the nonlinear velocity of the vehicle along the path, especially when accelerating from a stop. Nevertheless, the clothoid path plan generally seems to be a good representation of actual vehicle motion, especially when the planned path is updated frequently. / Master of Science

A curva de transição apresenta um raio de curvatura variando de um valor infinito no fim da tangente até um valor igual ao raio da curva circular no final da curva de transição. Nos projetos rodoviários, o tipo de curva mais utilizado é a clotóide, pois esta corresponde à trajetória descrita pelo veículo, com uma velocidade constante e o volante girando com velocidade angular constante. Consequentemente, é uma situação em que não requer esforço do motorista, proporciona uma trajetória mais natural e um aumento/redução da aceleração radial de um veículo de forma gradual. O presente trabalho admite que o comprimento desejável da espiral de transição em rodovias rurais e urbanas, baseado na recomendação da AASHTO (2011), é igual à distância correspondente a um tempo de percurso de 2 segundos ao longo da via à velocidade de projeto. É recomendável que o comprimento considerado como desejável seja suficiente para se realizar a transição da superelevação, e por outro lado, deve ser menor que o comprimento crítico de hidroplanagem, ou seja, comprimento a partir do qual o veículo passa a perder contato do pneu/pavimento em uma pista coberta com lâmina dágua, a uma velocidade crítica. Visto que os manuais brasileiros não introduzem a hidroplanagem como um dos fatores considerados para estabelecer estes comprimentos, pretende-se desenvolver uma ferramenta de trabalho que auxilia na determinação do comprimento desejável da espiral de transição, possibilitando uma análise do risco de ocorrência do fenômeno da hidroplanagem. No estudo de caso, são calculados comprimentos da espiral de transição de três curvas, onde serão feitas também simulações com diferentes parâmetros para analisar as situações críticas de hidroplanagem. Os resultados obtidos demonstram que comprimentos muito longos da espiral de transição, combinado com uma declividade longitudinal muito baixa pode aumentar o risco de hidroplanagem. / The transition curve has a radius of curvature varying from infinity at the end of the tangent to a value equal to the radius of the circular arc at the end of the transition curve. In highway design, clothoid is the most commonly used spiral type because it corresponds to the path described by the vehicle, with a constant speed and the less need for steering. Consequently, it\'s a situation that doesn\'t require driver effort, providing a more natural path and a gradual increase / reduction of the centrifugal force of a vehicle. Based on AASHTO (2011)\'s recommendation, this study establishes that the desired length of the spiral transition in highways and streets is equal to the distance traveled in 2 seconds in the design speed. It\'s recommended that the spiral length considered as desirable is sufficient to perform the superelevation runoff and on the other hand, should be shorter than the critical length of hydroplaning, in other words, it\'s a phenomenon caused by the increase of the water film above the contact pressure of tire and road. Since the manuals do not introduce hydroplaning as one of the criteria considered in establishing these lengths, a tool will be developed to define the desirable spiral length, allowing an analysis of the risk of hydroplaning. In the study, the lengths of three spiral transition curves are calculated; furthermore simulations with different parameters of these three curves are also calculated to analyze critical situations of hydroplaning. The results demonstrate that longer lengths of spiral transition combined with lower grades may increase the risk of hydroplaning.

A curva de transição apresenta um raio de curvatura variando de um valor infinito no fim da tangente até um valor igual ao raio da curva circular no final da curva de transição. Nos projetos rodoviários, o tipo de curva mais utilizado é a clotóide, pois esta corresponde à trajetória descrita pelo veículo, com uma velocidade constante e o volante girando com velocidade angular constante. Consequentemente, é uma situação em que não requer esforço do motorista, proporciona uma trajetória mais natural e um aumento/redução da aceleração radial de um veículo de forma gradual. O presente trabalho admite que o comprimento desejável da espiral de transição em rodovias rurais e urbanas, baseado na recomendação da AASHTO (2011), é igual à distância correspondente a um tempo de percurso de 2 segundos ao longo da via à velocidade de projeto. É recomendável que o comprimento considerado como desejável seja suficiente para se realizar a transição da superelevação, e por outro lado, deve ser menor que o comprimento crítico de hidroplanagem, ou seja, comprimento a partir do qual o veículo passa a perder contato do pneu/pavimento em uma pista coberta com lâmina dágua, a uma velocidade crítica. Visto que os manuais brasileiros não introduzem a hidroplanagem como um dos fatores considerados para estabelecer estes comprimentos, pretende-se desenvolver uma ferramenta de trabalho que auxilia na determinação do comprimento desejável da espiral de transição, possibilitando uma análise do risco de ocorrência do fenômeno da hidroplanagem. No estudo de caso, são calculados comprimentos da espiral de transição de três curvas, onde serão feitas também simulações com diferentes parâmetros para analisar as situações críticas de hidroplanagem. Os resultados obtidos demonstram que comprimentos muito longos da espiral de transição, combinado com uma declividade longitudinal muito baixa pode aumentar o risco de hidroplanagem. / The transition curve has a radius of curvature varying from infinity at the end of the tangent to a value equal to the radius of the circular arc at the end of the transition curve. In highway design, clothoid is the most commonly used spiral type because it corresponds to the path described by the vehicle, with a constant speed and the less need for steering. Consequently, it\'s a situation that doesn\'t require driver effort, providing a more natural path and a gradual increase / reduction of the centrifugal force of a vehicle. Based on AASHTO (2011)\'s recommendation, this study establishes that the desired length of the spiral transition in highways and streets is equal to the distance traveled in 2 seconds in the design speed. It\'s recommended that the spiral length considered as desirable is sufficient to perform the superelevation runoff and on the other hand, should be shorter than the critical length of hydroplaning, in other words, it\'s a phenomenon caused by the increase of the water film above the contact pressure of tire and road. Since the manuals do not introduce hydroplaning as one of the criteria considered in establishing these lengths, a tool will be developed to define the desirable spiral length, allowing an analysis of the risk of hydroplaning. In the study, the lengths of three spiral transition curves are calculated; furthermore simulations with different parameters of these three curves are also calculated to analyze critical situations of hydroplaning. The results demonstrate that longer lengths of spiral transition combined with lower grades may increase the risk of hydroplaning.

No description available.

Previous methods for planning clothoid based continuous curvature paths aim at minimizing path length. However, minimal length paths are not always smooth, natural, and drivable. A method of generating clothoid-based trajectories is discussed using constructive polylines. The goal of the motion planner is to create a path for a large car-like vehicle in human driving environments. Thus, the trajectories generated by the motion planner must be smooth, drivable, and natural such that the vehicle can follow the planned path on human roadways. Several examples are shown of trajectories developed for a DARPA Urban Challenge vehicle and a method of testing the motion planner and the vehicle controller is described.

Vehicle platooning is an advanced vehicle maneuver that allows for the simultaneous control of several vehicles traveling on the roadway cite{al2010experimental}. Automated platoons, when activated in tractor trailer convoys, have a high potential of increasing the fuel efficiency and improving the utilization of roadways by allowing more vehicles to share the road at the same time. The increased fuel efficiency translates to lower cost on goods and motivates a more environmentally friendly and sustainable economy. In order to achieve the promised fuel savings from vehicle platooning, the vehicles need to follow each other at shorter headways than in typical driving scenarios. The reduced separation distance between the lead and follow vehicle reduces visibility and the reaction time available for the follow vehicle; this renders most modern Active Driver Assist Systems (ADAS) ineffective since they are not designed for operation in such short headway conditions. The focus of this work is related to understanding and improving the failures of Lane Keep Assist (LKA) systems in the follow vehicles of a platoon. In this work, the source of lane detection degradation when using a monocular forward facing camera in short headway platooning is identified. Furthermore, a novel lane augmentation algorithm is proposed to improve the lane detection capability of follow vehicles in a platoon. The lane augmentation process utilizes a longitudinal transformation of lane parameters from the lead to the follow vehicles. The transformation utilizes an accurate understanding of the relative spatial position and orientation of the two vehicles. The transformation also requires a reliable communication system between the two vehicles such as a Vehicle-to-Vehicle (V2V) module. The work presented in this thesis develops theory, simulation and verification using real world data of the proposed cooperative lane augmentation. The results of this work indicate that it is possible to improve vehicle platooning performance by distributing the required sensing across multiple agents of the platoon. / Master of Science / Vehicle platooning is an advanced vehicle maneuver that allows for the simultaneous control of several vehicles traveling on the roadway cite{al2010experimental}. Automated platoons, when activated in tractor trailer convoys, have a high potential of increasing the fuel efficiency and improving the utilization of our roadways by allowing more vehicles to share the road at the same time. The increased fuel efficiency translates to lower cost on goods and motivates a more environmentally friendly and sustainable economy. In order to achieve the promised fuel savings from vehicle platooning, the vehicles need to follow each other at closer distances (headway) than in typical driving scenarios. The reduced separation distance between the lead and follow vehicle reduces visibility and the reaction time available for the follow vehicle; this renders most modern Active Driver Assist Systems (ADAS) ineffective since they are not designed for operation in such short headway conditions. The focus of this work is related to understanding and improving the failures of Lane Keep Assist (LKA) systems - the automated system used to keep the vehicle in the center of the lane - in the follow vehicles of a platoon. In the proposed scenario, the LKA uses a single forward facing camera to detect the lane lines ahead of the vehicle. The detected lanes serve as inputs to the lateral position (steering) controller in order to keep the vehicle in the center of the lane. In this work, the source of lane detection degradation in a follow vehicle of a short headway platoon is identified. Furthermore, a novel cooperative lane detection algorithm is proposed to improve the lane detection capability of the follow vehicles. The proposed algorithm utilizes lane information transformed from the lead to follow vehicle frame. The transformation utilizes the relative spatial position and orientation of the two vehicles. Additionally, a reliable communication protocol between the vehicles is required to transport the lane information. The work presented in this thesis develops theory, simulation and verification using real world data of the proposed algorithm. The results of this work indicate that lane keeping performance in a platoon can be improved using cooperative lane detection.

The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.

Il est intéressant d'observer qu'une grande partie des objets déformables qui nous entourent sont caractérisés par une forme élancée : soit filiforme, comme les cheveux, les plantes, les fils ; soit surfacique, comme le papier, les feuilles d'arbres, les vêtements ou la plupart des emballages. Simuler (numériquement) la mécanique de telles structures présente alors un intérêt certain : cela permet de prédire leur comportement dynamique, leur forme statique ou encore les efforts qu'elles subissent. Cependant, pour pouvoir réaliser correctement ces simulations, plusieurs problèmes se posent. Les modèles (mécaniques, numériques) utilisés doivent être adaptés aux phénomènes que l'on souhaite reproduire ; le modèle mécanique choisi doit pouvoir être traité numériquement ; enfin, il est nécessaire de connaître les paramètres du modèle qui permettront de reproduire l'instance du phénomène souhaitée. Dans cette thèse nous abordons ces trois points, dans le cadre de la simulation de structures élancées.Dans la première partie, nous proposons un modèle discret de tiges de Kirchhoff dynamiques, de haut degré, basé sur des éléments en courbures et torsion affines par morceaux : les Super-Clothoïdes 3D. Cette discrétisation spatiale est calculée de manière précise grâce à une méthode dédiée, adaptée à l'arithmétique flottante, utilisant des développements en séries entières. L'utilisation des courbures et de la torsion comme degrés de liberté permet d'aboutir à un schéma d'intégration stable grâce à une implicitation, à moindres frais, des forces élastiques. Le modèle a été utilisé avec succès pour simuler la croissance de plantes grimpantes ou le mouvement d'une chevelure. Nos comparaisons avec deux modèles de référence de la littérature ont montré que pour des tiges bouclées, notre approche offre un meilleur compromis en termes de précision spatiale, de richesse de mouvements générés et d'efficacité en temps de calcul.Dans la seconde partie, nous nous intéressons à l'élaboration d'un algorithme capable de retrouver la géométrie au repos (non déformée) d'une coque en contact frottant, connaissant sa forme à l'équilibre et les paramètres physiques du matériau qui la compose. Un tel algorithme trouve son intérêt lorsque l'on souhaite simuler un objet pour lequel on dispose d'une géométrie (numérisée) « à l'équilibre » mais dont on ne connaît pas la forme au repos. En informatique graphique, un exemple d'application est la modélisation de vêtements virtuels sous la gravité et en contact avec d'autres objets : simplement à partir de la forme objectif et d'un simulateur de vêtement, le but consiste à identifier automatiquement les paramètres du simulateur tels que la forme d'entrée corresponde à un équilibre mécanique stable. La formulation d'un tel problème inverse comme un problème aux moindres carrés nous permet de l'attaquer avec la méthode de l'adjoint. Cependant, la multiplicité des équilibres, donnant au problème direct son caractère mal posé, nous conduit à « guider » la méthode en pénalisant les équilibres éloignés de la forme objectif. On montre enfin qu'il est possible de considérer du contact et du frottement solide dans l'inversion, en reformulant le calcul d'équilibres en un problème d'optimisation sous contraintes coniques, et en adaptant la méthode de l'adjoint à ce cas non-régulier. Les résultats que nous avons obtenus sont très encourageants et nous ont permis de résoudre des cas complexes où l'algorithme se comportait de manière intuitive. / It is interesting to observe that many of the deformable objects around us are characterized by a slender structure: either in one dimension, like hair, plants, strands, or in two dimensions, such as paper, the leaves of trees or clothes. Simulating the mechanical behavior of such structures numerically is useful to predict their static shape, their dynamics, or the stress they undergo. However, to perform these simulations, several problems need to be addressed. First, the model (mechanical, numerical) should be adapted to the phenomena which it is aimed at reproducing. Then, the chosen mechanical model should be discretized consistently. Finally, it is necessary to identify the parameters of the model in order to reproduce a specific instance of the phenomenon. In this thesis we shall discuss these three points, in the context of the simulation of slender structures.In the first part, we propose a discrete dynamic Kirchhoff rod model of high degree, based on elements with piecewise affine curvature and twist: the Super-Space-Clothoids. This spatial discretization is computed accurately through a dedicated method, adapted to floating-point arithmetic, using power series expansions. The use of curvature and twist as degrees of freedom allows us to make elastic forces implicit in the integration scheme. The model has been used successfully to simulate the growth of climbing plants or hair motion. Our comparisons with two reference models have shown that in the case of curly rods, our approach offers the best trade-off in terms of spatial accuracy, richness of motion and computational efficiency.In the second part, we focus on identifying the undeformed configuration of a shell in the presence of frictional contact forces, knowing its shape at equilibrium and the physical parameters of the material. Such a method is of utmost interest in Computer Graphics when, for example, a user often wishes to model a virtual garment under gravity and contact with other objects regardless of physics. The goal is then to interpret the shape and provide the right ingredients to the cloth simulator, so that the cloth is actually at equilibrium when matching the input shape. To tackle such an inverse problem, we propose a least squares formulation which can be optimized using the adjoint method. However, the multiplicity of equilibria, which makes our problem ill-posed, leads us to "guide" the optimization by penalizing shapes that are far from the target shape. Finally, we show how it is possible to consider frictional contact in the inversion process by reformulating the computation of equilibrium as an optimization problem subject to conical constraints. The adjoint method is also adjusted to this non-regular case. The results we obtain are very encouraging andhave allowed us to solve complex cases where the algorithm behaves intuitively.