Real time 3D human capture system for mixed-reality art and entertainment

Master'sMASTER OF ENGINEERIN

On the Convergence of AdaGrad on Rd\R^{d}: Beyond Convexity, Non-Asymptotic Rate and Acceleration

Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an explicit constant factor that holds true for the entire function class. Furthermore, in the stochastic setting, only a modified version of AdaGrad, different from the one commonly used in practice, in which the latest gradient is not used to update the stepsize, has been analyzed. Our paper aims at bridging these gaps and developing a deeper understanding of AdaGrad and its variants in the standard setting of smooth convex functions as well as the more general setting of quasar convex functions. First, we demonstrate new techniques to explicitly bound the convergence rate of the vanilla AdaGrad for unconstrained problems in both deterministic and stochastic settings. Second, we propose a variant of AdaGrad for which we can show the convergence of the last iterate, instead of the average iterate. Finally, we give new accelerated adaptive algorithms and their convergence guarantee in the deterministic setting with explicit dependency on the problem parameters, improving upon the asymptotic rate shown in previous works.Comment: Updated manuscript from ICLR 202

The roles of allocentric representations in autonomous local navigation

In this thesis, I study the computational advantages of the allocentric represen- tation as compared to the egocentric representation for autonomous local navigation. Whereas in the allocentric framework, all variables of interest are represented with respect to a coordinate frame attached to an object in the scene, in the egocentric one, they are always represented with respect to the robot frame at each time step. In contrast with well-known results in the Simultaneous Localization and Mapping literature, I show that the amounts of nonlinearity of these two representations, where poses are elements of Lie-group manifolds, do not affect the accuracy of Gaussian- based filtering methods for perception at both the feature level and the object level. Furthermore, although these two representations are equivalent at the object level, the allocentric filtering framework is better than the egocentric one at the feature level due to its advantages in the marginalization process. Moreover, I show that the object- centric perspective, inspired by the allocentric representation, enables novel linear- time filtering algorithms, which significantly outperform state-of-the-art feature-based filtering methods with a small trade-off in accuracy due to a low-rank approximation. Finally, I show that the allocentric representation is also better than the egocentric representation in Model Predictive Control for local trajectory planning and obstacle avoidance tasks.Ph.D

Stochastic finite element analysis of the free vibration of non-uniform beams with uncertain material

This paper deal with the stochastic finite element method for investigating the eigenvalues of free vibration of non-uniform beams due to a random field of elastic modulus. The formulation of stochastic analysis of the non-uniform beam is established using perturbation method in conjunction with finite element method. Monte Carlo simulation (MCS) used for validation with stochastic finite element approach. The spectral representation was used to generate a random field to employ the Monte Carlo simulation. The performance of results of the uncertain eigenvalue problem of non-uniform beams with random field of elastic modulus by comparing the first-order perturbation technique with the same moments evaluated from the Monte Carlo simulation. The numerical results show that the response of coefficient of variation of eigenvalue increases when the ratio of correlation distance of random field increases

Stochastic finite element analysis of the free vibration of non-uniform beams with uncertain material

This paper deal with the stochastic finite element method for investigating the eigenvalues of free vibration of non-uniform beams due to a random field of elastic modulus. The formulation of stochastic analysis of the non-uniform beam is established using perturbation method in conjunction with finite element method. Monte Carlo simulation (MCS) used for validation with stochastic finite element approach. The spectral representation was used to generate a random field to employ the Monte Carlo simulation. The performance of results of the uncertain eigenvalue problem of non-uniform beams with random field of elastic modulus by comparing the first-order perturbation technique with the same moments evaluated from the Monte Carlo simulation. The numerical results show that the response of coefficient of variation of eigenvalue increases when the ratio of correlation distance of random field increases

Investigation of bond performance of reinforced fly ash-based Geopolymer concrete using experiments and numerical analysis

This study evaluates the bond performance of reinforced fly ash-based geopolymer concrete by using experiments and numerical analysis. Three types of mixture proportions along with two types of reinforcement diameter, (d12, ribbed bar) and (d14, smooth bar) mm, were selected for experimental work. The bond behaviour of reinforced geopolymer concrete is determined using the pullout test, and Finite Element Analysis (FEA). The test data indicated that the bond strength of reinforced fly ash-based geopolymer concrete increases with the increase in compressive strength. The concrete cover to diameter ratio (c/db) increases from 4.86 to 5.75 and the bond strength of all three groups of samples also increases. Besides, the bond stress-slip curves obtained by the ABAQUS software closely match the results from experimental works. Furthermore, the parametric analyses show that when the compressive strength of geopolymer concreteincreases, the bond strength of reinforced fly ash-based geopolymer concrete increases. These results are consistent with the test data

Monocular Parallel Tracking and Mapping with Odometry Fusion for MAV Navigation in Feature-Lacking Environments

©2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Presented at the IEEE/RSJ International Workshop on Vision-based Closed-Loop Control and Navigation of Micro Helicopters in GPS-denied Environments (IROS 2013), November 7, 2013, Tokyo, Japan.Despite recent progress, autonomous navigation on Micro Aerial Vehicles with a single frontal camera is still a challenging problem, especially in feature-lacking environ- ments. On a mobile robot with a frontal camera, monoSLAM can fail when there are not enough visual features in the scene, or when the robot, with rotationally dominant motions, yaws away from a known map toward unknown regions. To overcome such limitations and increase responsiveness, we present a novel parallel tracking and mapping framework that is suitable for robot navigation by fusing visual data with odometry measurements in a principled manner. Our framework can cope with a lack of visual features in the scene, and maintain robustness during pure camera rotations. We demonstrate our results on a dataset captured from the frontal camera of a quad- rotor flying in a typical feature-lacking indoor environment