Le travail présenté dans cette thèse est consacré à la modélisation de la dynamique de locomotion des "soft robots", i.e. les systèmes multi-corps mobiles compliants. Ces compliances peuvent être localisées et considérées comme des liaisons passives du système,ou bien introduites par des flexibilités distribuées le long des corps. La dynamique de ces systèmes est modélisée en adoptant une approche Lagrangienne basée sur les outils mathématiques développés par l’école américaine de mécanique géométrique. Du point de vue algorithmique, le calcul de ces modèles dynamiques s’appuie sur un algorithme récursif et efficace de type Newton-Euler, ici étendu aux robots locomoteurs munis d’organes compliants. Poursuivant des objectifs de commande et de simulation rapide pour la robotique, l’algorithme proposé est capable de résoudre la dynamique externe directe ainsi que la dynamique inverse des couples internes. Afin de mettre en pratique l’ensemble de ces outils de modélisation, nous avons pris le vol battant des insectes comme exemple illustratif. Les équations non-linéaires qui régissent les déformations passives de l’aile sont établies en appliquant deux méthodes différentes. La première consiste à séparer le mouvement de l’aile en une composante rigide dite de "repère flottant" et une composante de déformation. Cette dernière est paramétrée dans le repère flottant par la méthode des modes supposés ici appliquée à l’aile vue comme une poutre d’Euler-Bernoulli soumise à la flexion et à la torsion. Quant à la seconde approche, les mouvements de l’aile n’y sont pas séparés mais directement paramétrés par les transformations finies rigides et absolues d’une poutre Cosserat. Cette approche est dite Galiléenne ou "géométriquement exacte" en raison du fait qu’elle ne requiert aucune approximation en dehors des inévitables discrétisations spatiale et temporelle imposées parla résolution numérique de la dynamique du vol. Dans les deux cas,les forces aérodynamiques sont prises en compte via un modèle analytique simplifié de type Dickinson. Les modèles et algorithmes résultants sont appliqués à la conception d’un simulateur du vol, ainsi qu’à la conception d’un prototype d’aile, dans le contexte du projet coopératif (ANR) EVA. / The objective of the present work is to model the locomotion dynamics of "soft robots", i.e. compliant mobile multi-body systems. These compliances can be either localized and treated as passive joints of the system, or introduced by distributed flexibilities along the bodies. The dynamics of these systems is modeled in a Lagrangian approach based on the mathematical tools developed by the American school of geometric mechanics. From the algorithmic viewpoint, the computation of these dynamic models is based on a recursive and efficient Newton-Euler algorithm which is extended here to the case of robots equipped with compliant organs. The proposed algorithm is compatible with control, fast simulation and real time robotic applications. It is able to solve the direct external dynamics as well as the inverse internal torque dynamics. The modeling tools and algorithms developed in this thesis are applied to one of the most advanced cases of compliante locomotion i.e. the flapping flight MAVs bio-inspired by insects. The nonlinear equations governing the passive deformations of the wing are derived using two different methods. In the first method, we separate the wing movement into a rigid component (which corresponds to the movements of a "floating frame"), and a deformation component. The latter one is parameterized in the floating frame using the assumed modes approach where the wing is considered as an Euler-Bernoulli beam undergoing flexion and torsion deformations. Regarding the second method, the wing movements are no longer separated but directly parameterize dusing rigid finite absolute transformations of a Cosserat beam. This method is called Galilean or "geometrically exact" because it does not require any approximation apart from the unavoidable spatial and temporal discretizations imposed by numerical resolution of the flight dynamics. In both cases, the aerodynamic forces are taken into account through a simplified analytical model. The resulting models and algorithms are used in the context of the collaborative project (ANR) EVA to develop a flight simulator, and to design wing prototype.

Cette étude se propose d’analyser le comportement du double rotor contra-rotatif caréné dans lecadre des échelles réduites des microdrones, pour exploiter le potentiel d’amélioration desperformances stationnaires des rotors libres. La demande d’une performance propulsive de hautniveau, alors que les échelles sont très réduites constitue un véritable défi scientifique. De façongénérale, par rapport au rotor libre, l’ajout de la carène permet de piloter la contraction del’écoulement et offre un potentiel de poussée de carène. La tuyère par sa condition d’adaptationpilote le débit entrant à puissance donnée. L’augmentation du débit massique, par comparaison ausystème de rotor libre, amplifie la poussée à travers la dépression distribuée sur toute la surface decaptation. Pour comprendre les lois de fonctionnement d’un système propulsif caréné, il a d’abord été proposé un modèle théorique simplifié basé sur une extension de la théorie de Froude pour les rotors libres: le système rotor est assimilé à un disque actuateur, générateur de débit dans une conduite à section variable. Une simulation Navier Stokes 2D axisymétrique a permis d’optimiser les paramètres de forme du carénage. Les simulations ont confirmé l’influence déterminante des sections d’entrée et de sortie, et relativisé l’impact des formes possibles, pourvu que les variations de sections limitent le décollement de la couche limite. Après conception d’un banc d’essai utilisant un doublet de rotor coaxial placé dans cette carène optimisée, l’étude expérimentale complète et confirme les performances globales du système et qualifie l’écoulement méridien. Enfin, une simulation 3D instationnaire a été entreprise pour compléter l’analyse de l’écoulement autour des rotors. / This study aims to analyze the behavior of shrouded, contrarotating coaxial rotor in the reducedMAVs’ scale in order to exploit its potential to improve the free rotor steady performance. The highhover ability under low operational Reynolds number is therefore, a scientific challenge. Generally,comparing with free rotor, the addition of the shroud decreases the flow contraction and gives thepotential to generate an extra thrust. A suitable nozzle can control the mass flow for a given power.The increased mass flow, comparing with free rotor, amplifies the thrust offered by the lowpressure formed at the air entrance. To understand the principals of shrouded propulsion system, a simplified theory model was first proposed through the extension of Froude theory for free rotors: the double rotor is initially treated as an actuator disk, generating the flow at varied sections through the shroud passage. A 2D simulation which accounts for an axial flow of viscous effects within the actual shroud profile, confirmed effects of all defined geometrical parameters. It further demonstrated that within the non-stalling region of the different crosssections, shroud shape and inlet shape do not have asignificant impact on performance. The experimental study, carried out with coaxial rotor, contributed to the confirmation of the overall performance and the approximation of the flow field through the shroud. Meanwhile, the 3D simulation, developed to better model the actual coaxial rotor in counter rotation, was validated to well solve the steady performance. It was applied to complement the analysis of the flow around the coaxial rotor.

This thesis focuses on the design and development of a fixed wing micro air vehicle (MAV) and on the development of randomized sampling based motion planning and control algorithms for path planning and stabilization of the MAV. In addition, the thesis also contains probabilis-tic analyses of the algorithmic properties of randomized sampling based algorithms, such as completeness and asymptotic optimality. The thesis begins with a detailed discussion on aerodynamic design, computational fluid dy-namic simulations of propeller wake, wind tunnel tests of a 150mm fixed wing micro air ve-hicle. The vehicle is designed in such a way that in spite of the various adverse effects of low Reynolds number aerodynamics and the complex propeller wake interactions with the airframe, the vehicle shows a balance of external forces and moments at most of the operating conditions. This is supported by various CFD analysis and wind tunnel tests and is shown in this thesis. The thesis also contains a reasonably accurate longitudinal and lateral dynamical model of the MAV, which are verified by numerous flight trials. However, there still exists a considerable amount of model uncertainties in the system descrip-tion of the MAV. A robust feedback stabilized close loop flight control law, is designed to attenuate the effects of modelling uncertainties, discrete vertical and head-on wind gusts, and to maintain flight stability and performance requirements at all allowable operating conditions. The controller is implemented in the MAV autopilot hardware with successful close loop flight trials. The flight controller is designed based on the probabilistic robust control approach. The approach is based on statistical average case analysis and synthesis techniques. It removes the conservatism present in the classical robust feedback design (which is based the worst case de-sign techniques) and associated sluggish system response characteristics. Instead of minimizing the effect of the worst case disturbance, a randomized techniques synthesizes a controller for which some performance index is minimized in an empirical average sense. In this thesis it is shown that the degree of conservatism in the design and the number of samples used to by the randomized sampling based techniques has a direct relationship. In particular, it is shown that, as the lower bound on the number of samples reduces, the degree of conservatism increases in the design. Classical motion planning and obstacle avoidance methodologies are computationally expen-sive with the number of degrees of freedom of the vehicle, and therefore, these methodologies are largely inapplicable for MAVs with 6 degrees of freedom. The problem of computational complexity can be avoided using randomized sampling based motion planning algorithms such as probabilistic roadmap method or PRM. However, as a pay-off these algorithms lack algorith-mic completeness properties. In this thesis, it is established that the algorithmic completeness properties are dependent on the choice of the sampling sequences. The thesis contains analy-sis of algorithmic features such as probabilistic completeness and asymptotic optimality of the PRM algorithm and its many variants, under the incremental and independent problem model framework. It is shown in this thesis that the structure of the random sample sequence affects the solution of the sampling based algorithms. The problem of capturing the connectivity of the configuration space in the presence of ob-stacles, which is a central problem in randomized motion planning, is also discussed in this thesis. In particular, the success probability of one such randomized algorithm, named Obsta-cle based Probabilistic Roadmap Method or OBPRM is estimated using geometric probability theory. A direct relationship between the weak upper bound of the success probability and the obstacle geometric features is established. The thesis also contains a new sampling based algorithm which is based on geometric random walk theory, which addresses the problem of capturing the connectivity of the configuration space. The algorithm shows better performance when compared with other similar algorithm such as the Randomized Bridge Builder method for identical benchmark problems. Numerical simulation shows that the algorithm shows en-hanced performance as the dimension of the motion planning problem increases. As one of the central objectives, the thesis proposes a pre-processing technique of the state space of the system to enhance the performance of sampling based kino-dynamic motion plan-ner such as rapidly exploring random tree or RRT. This pre-processing technique can not only be applied for the motion planning of the MAV, but can also be applied for a wide class of vehicle and complex systems with large number of degrees of freedom. The pre-processing techniques identifies the sequence of regions, to be searched for a solution, in order to do mo-tion planning and obstacle avoidance for an MAV, by an RRT planner. Numerical simulation shows significant improvement over the basic RRT planner with a small additional computa-tional overhead. The probabilistic analysis of RRT algorithm and an approximate asymptotic optimality analysis of the solution returned by the algorithm, is also presented in this thesis. In particular, it is shown that the RRT algorithm is not asymptotically optimal. An integral part of the motion planning algorithm is the capability of fast collision detection between various geometric objects. Image space based methods, which uses Graphics Pro-cessing Unit or GPU hardware, and do not use object geometry explicitly, are found to be fast and accurate for this purpose. In this thesis, a new collision detection method between two convex/non-convex objects using GPU, is provided. The performance of the algorithm, which is an extension of an existing algorithm, is verified with numerous collision detection scenarios.