This thesis treats the subject of applying human motion models to create estimators for the input signals of human operators controlling a telerobotic system.In telerobotic systems, the control signal input by the operator is often treated as a known quantity. However, there are instances where this is not the case. For example, a well-studied problem is teleoperation under time delay, where the robot at the remote site does not have access to current operator input due to time delays in the communication channel. Another is where the hardware sensors in the input device have low accuracy. Both these cases are studied in this thesis. A solution to these types of problems is to apply an estimator to the input signal. There exist several models that describe human hand motion, and these can be used to create a model-based estimator. In the present work, we propose the use of the minimum jerk (MJ) model. This choice of model is based mainly on the simplicity of the MJ model, which can be described as a fifth degree polynomial in the cartesian space of the position of the subject's hand. Estimators incorporating the MJ model are implemented and inserted into control systems for a teleoperatedrobot arm. We perform experiments where we show that these estimators can be used for predictors increasing task performance in the presence of time delays. We also show how similar estimators can be used to implement direct position control using a handheld device equipped only with accelerometers. / QC 20100810

The problem of dynamic autonomous agent placement for tracking moving targets arises in many real-life applications, such as rescue operations, security, surveillance, and reconnaissance. The objective of this thesis is to develop a distributed hierarchical approach to address this problem. After the approach is developed, it is tested on a number of urban surveillance scenarios. The proposed approach views the placement problem as a multi-tiered architecture entailing modules for low-level sensor data preprocessing and fusion, decentralized decision support, knowledge building, and centralized decision support. This thesis focuses upon the modules of decentralized decision support and knowledge building. The decentralized decision support module requires a great deal of coordination among agents to achieve the mission objectives. The module entails two classes of distributed algorithms: non-model-based algorithms and model-based algorithms. The first class is used as a place holder while a model is built to describe agents knowledge about target behaviors. After the model is built and evaluated, agents switch to the model-based algorithms. To apply the approach to urban environments, urban terrain zones are classified, and the problem is mathematically formulated for two different types of urban terrain, namely low-rise, widely spaced and high-rise, closely spaced zones. An instance of each class of algorithms is developed for each of the two types of urban terrain. The algorithms are designed to run in a distributed fashion to address scalability and fault tolerance issues. The class of model-based algorithms includes a distributed model-based algorithm for dealing with evasive targets. The algorithm is designed to improve its performance over time as it learns from past experience how to deal with evasive targets. Apart from the algorithms, a model estimation module is developed to build motion models online from sensor observations. The approach is evaluated through a set of simulation experiments inspired from real-life scenarios. Experimental results reveal the superiority of the developed algorithms over existing ones and the applicability of the online model-building method. Therefore, it is concluded that the overall distributed approach is capable of handling agent placement or surveillance applications in urban environments among other applications.

Movité par des questions posées par F. Santambrogio, cette thèse est dédiée à l'étude de jeux à champ moyen et des modèles impliquant le transport optimal avec contraintes de densité. A fin d'étudier des modèles de MFG d'ordre deux dans l'esprit des travaux de F. Santambrogio, on introduit en tant que brique élementaire un modèle diffusif de mouvement de foule avec contraintes de densité (en généralisant dans une sense les travaux de Maury et al.). Le modèle est décrit par l'évolutions de la densité de la foule, qui peut être vu comme une courbe dans l'espace de Wasserstein. Du point de vu EDP, ça correspond à une équation de Fokker-Planck modifiée, avec un terme supplémentaire, le gradient d'une pression (seulement dans la zone saturée) dans le drift. En passant par l'équation duale et en utilisant des estimations paraboliques bien connues, on démontre l'unicité du pair densité et pression. Motivé initialement par l'algorithm de splitting (utilisé dans le résultat d'existence ci-dessus), on étudie des propriétés fines de la projection de Wasserstein en dessous d'un seuil donné. Intégrant cette question dans une classe plus grande de problèmes impliquant le transport optimal, on démontre des estimations BV pour les optimiseurs. D'autres applications possibles (en transport partiel, optimisation de forme et problèmes paraboliques dégénérés) de ces estimations BV sont également discutées.En changeant le point de vu, on étudie également des modèles de MFG variationnels avec contraintes de densité. Dans ce sens, les systèmes de MFG sont obtenus comme conditions d'optimalité de premier ordre pour deux problèmes convexes en dualité. Dans ces systèmes un terme additionnel apparaît, interpreté comme un prix à payer quand les agents passent dans des zones saturées. Premièrement, en profitant des résultats de régularité elliptique, on montre l'existence et la caractérisation de solutions des MFG de deuxième ordre stationnaires avec contraintes de densité. Comme résultat additionnel, on caractérise le sous-différentiel d'une fonctionnelle introduite par Benamou-Brenier pour donner une formulation dynamique du problème de transport optimal. Deuxièmement, (basé sur une technique de pénalisation) on montre qu'une classe de systèmes de MFG de premier ordre avec contraintes de densité est bien posée. Une connexion inattendu avec les équations d'Euler incompressible à la Brenier est égalment donnée. / Motivated by some questions raised by F. Santambrogio, this thesis is devoted to the study of Mean Field Games and models involving optimal transport with density constraints. To study second order MFG models in the spirit of the work of F. Santambrogio, as a possible first step we introduce and show the well-posedness of a diffusive crowd motion model with density constraints (generalizing in some sense the works by B. Maury et al.). The model is described by the evolution of the people's density, that can be seen as a curve in the Wasserstein space. From the PDE point of view, this corresponds to a modified Fokker-Planck equation, with an additional gradient of a pressure (only living in the saturated zone) in the drift. We provide a uniqueness result for the pair density and pressure by passing through the dual equation and using some well-known parabolic estimates. Initially motivated by the splitting algorithm (used for the above existence result), we study some fine properties of the Wasserstein projection below a given threshold. Embedding this question into a larger class of variational problems involving optimal transport, we show BV estimates for the optimizers. Other possible applications (for partial optimal transport, shape optimization and degenerate parabolic problems) of these BV estimates are also discussed.Changing the point of view, we also study variational Mean Field Game models with density constraints. In this sense, the MFG systems are obtained as first order optimality conditions of two convex problems in duality. In these systems an additional term appears, interpreted as a price to be paid when agents pass through saturated zones. Firstly, profiting from the regularity results of elliptic PDEs, we give the existence and characterization of the solutions of stationary second order MFGs with density constraints. As a byproduct we characterize the subdifferential of a convex functional introduced initially by Benamou-Brenier to give a dynamic formulation of the optimal transport problem. Secondly, (based on a penalization technique) we prove the well-posedness of a class of first order evolutive MFG systems with density constraints. An unexpected connection with the incompressible Euler's equations à la Brenier is also given

Occlusion is a frequently occuring challenge in vision systems for autonomous driving. The density of objects in the field-of-view of the vehicle may be so high that some objects are only visible intermittently. It is therefore beneficial to investigate ways to predict the paths of objects under occlusion. In this thesis, we investigate whether trajectory prediction methods can be used to solve the occlusion prediction problem. We investigate two different types of approaches, one based on motion models, and one based on machine learning models. Furthermore, we investigate whether these two approaches can be fused to produce an even more reliable model. We evaluate our models on a pedestrian trajectory prediction dataset, an autonomous driving dataset, and a subset of the autonomous driving dataset that only includes validation examples of occlusion. The comparison of our different approaches shows that pure motion model-based methods perform the worst out of the three. On the other hand, machine learning-based models perform better, yet they require additional computing resources for training. Finally, the fused method performs the best on both the driving dataset and the occlusion data. Our results also indicate that trajectory prediction methods, both motion model-based and learning-based ones, can indeed accurately predict the path of occluded objects up to at least 3 seconds in the autonomous driving scenario.