Spatial and Temporal Considerations in Vehicle Path Tracking With an Emphasis on Spatial Robustness

This dissertation researches the task and path management of an autonomous vehicle with Ackerman-type steering. The task management problem was approached as a path training operation in which a human operator drives the desired path through an environment. A training trajectory is converted into a series of path segments that are driveable by the autonomous vehicle by first fitting a general path to the dataset. Next, transition segments are added to the general path to match the vehicle velocity and steering angle rate limit. The path management problem has been approached by first deriving a kine- matic model of the vehicle. The time domain model is expressed in the frequency domain and then converted into a spatial frequency domain. Next, a stability crite- rion is derived and used in the synthesis of a spatially-robust path controller

More on complexity of operators in quantum field theory

Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten $p$-norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as $k$-local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU($n$) groups.Comment: Modified the Sec. 4.1, where we offered a powerful proof: if (1) the ket vector and bra vector in quantum mechanics contain same physics, or (2) adding divergent terms to a Lagrangian will not change underlying physics, then complexity in quantum mechanics must be bi-invariant

A Survey of path following control strategies for UAVs focused on quadrotors

The trajectory control problem, defined as making a vehicle follow a pre-established path in space, can be solved by means of trajectory tracking or path following. In the trajectory tracking problem a timed reference position is tracked. The path following approach removes any time dependence of the problem, resulting in many advantages on the control performance and design. An exhaustive review of path following algorithms applied to quadrotor vehicles has been carried out, the most relevant are studied in this paper. Then, four of these algorithms have been implemented and compared in a quadrotor simulation platform: Backstepping and Feedback Linearisation control-oriented algorithms and NLGL and Carrot-Chasing geometric algorithms.Peer ReviewedPostprint (author's final draft

Manifold-valued Image Generation with Wasserstein Generative Adversarial Nets

Generative modeling over natural images is one of the most fundamental machine learning problems. However, few modern generative models, including Wasserstein Generative Adversarial Nets (WGANs), are studied on manifold-valued images that are frequently encountered in real-world applications. To fill the gap, this paper first formulates the problem of generating manifold-valued images and exploits three typical instances: hue-saturation-value (HSV) color image generation, chromaticity-brightness (CB) color image generation, and diffusion-tensor (DT) image generation. For the proposed generative modeling problem, we then introduce a theorem of optimal transport to derive a new Wasserstein distance of data distributions on complete manifolds, enabling us to achieve a tractable objective under the WGAN framework. In addition, we recommend three benchmark datasets that are CIFAR-10 HSV/CB color images, ImageNet HSV/CB color images, UCL DT image datasets. On the three datasets, we experimentally demonstrate the proposed manifold-aware WGAN model can generate more plausible manifold-valued images than its competitors.Comment: Accepted by AAAI 201

Development of Forward and Inversion Schemes for Cross-Borehole Ground Penetrating Radar

Tomography is an imaging technique to develop a representation of the internal features of material using a penetrating wave, such as an electromagnetic wave. The calculation method used is an example of an inverse problem, which is a system where the input and the output are known but the internal parameters are not. These parameters can be estimated by understanding the responses of a penetrating wave as it passes through the unknown media. A forward problem is just the opposite; the internal structure and input penetrating wave is known and the output is determined. For both forward and inverse problems, raytracing is needed to define the raypath through the medium and inversion techniques are used to minimize the error for a discretized matrix of material properties. To assess various inversion techniques for use in shallow karst conditions, three synthetic karst geology models, each with increasing complexity, were generated. Each model was analyzed using forward modeling techniques to compare the calculated tomograms from known geometry and material properties. Gaussian Raytracing with LSQR inversion technique performed the best. This technique, Gaussian Raytracing with LSQR, was then applied to an inversion problem; cross-borehole ground penetrating radar data was collected at a karst geology field site and tomograms were produced. The resulting tomography confirmed information detailed in the driller\u27s logs and features between boreholes were identified. This confirmed that cross-borehole ground penetrating radar is an applicable technique for use in geotechnical site characterization activities in karst areas