Learning Terrain Dynamics: A Gaussian Process Modeling and Optimal Control Adaptation Framework Applied to Robotic Jumping

The complex dynamics characterizing deformable terrain presents significant impediments toward the real-world viability of locomotive robotics, particularly for legged machines. We explore vertical, robotic jumping as a model task for legged locomotion on presumed-uncharacterized, nonrigid terrain. By integrating Gaussian process (GP)-based regression and evaluation to estimate ground reaction forces as a function of the state, a 1-D jumper acquires the capability to learn forcing profiles exerted by its environment in tandem with achieving its control objective. The GP-based dynamical model initially assumes a baseline rigid, noncompliant surface. As part of an iterative procedure, the optimizer employing this model generates an optimal control strategy to achieve a target jump height. Experiential data recovered from execution on the true surface model are applied to train the GP, in turn, providing the optimizer a more richly informed dynamical model of the environment. The iterative control-learning procedure was rigorously evaluated in experiment, over different surface types, whereby a robotic hopper was challenged to jump to several different target heights. Each task was achieved within ten attempts, over which the terrain's dynamics were learned. With each iteration, GP predictions of ground forcing became incrementally refined, rapidly matching experimental force measurements. The few-iteration convergence demonstrates a fundamental capacity to both estimate and adapt to unknown terrain dynamics in application-realistic time scales, all with control tools amenable to robotic legged locomotion

Optimisation of blade type spreaders for powder bed preparation in additive manufacturing using DEM simulations

Powders used in the Particle Bed Fusion process are spread onto compact layers and then are fused to generate a layer of the final part. This process is repeated layer-upon-layer to form the final products. It has recently been demon- strated [Powder Technology, 306 (2017) 45–54] that spreading the particles with a counter-rotating roller produces a bed with a higher quality (i.e. a lower void fraction) compared to a blade type spreader. This is related to the geometry of the two spreaders which directly changes the bed-spreader contact dynamic and consequently affects the bed's quality. Based on this rationale, here, it is postulated that changing the blade profile at the blade bed contact region can significantly enhance the bed's quality and improve the effectiveness of a blade as a spreading device. A set of Discrete Element Method (DEM) simulations is performed at device-scale to optimise the geometry of blade spreaders to yield the lowest void fraction using simple rod-shaped grains to control the computational costs. The blade profile is parametrised using a super-ellipse with three geometrical parameters. Firstly, it is demonstrated that geometric optimisation of a blade profile is an effective alternative to using more complex spreading devices. Secondly, for the proposed parametrisation, the optimum values are found using computer simulations and it is shown that bed volume fractions close to critical values are achievable. Finally, a new technique for multi-sphere approximation (MSA) is developed and applied to 3D models of real powder grains to generate realistic particle shapes for the DEM simulations. Then using these grains it is shown that the proposed optimum blade profile is capable of producing a bed with qualities comparable (and even better) to a roller at the actual operating conditions and with realistic grain characteristics

Structure Preserving and Scalable Simulation of Colliding Systems

Predictive computational tools to study granular materials are important in fields ranging from the geosciences and civil engineering to computer graphics. The simulation of granular materials, however, presents many challenges. The behavior of a granular medium is fundamentally multi-scale, with pair-wise interactions between discrete granules able to influence the continuum-scale evolution of a bulk material. Computational techniques for studying granular materials must therefore contend with this multi-scale nature. This research first addresses both the question of how to accurately model interactions between grains and the question of how to achieve multi-scale simulations of granular materials. We propose a novel rigid body contact model and a time integration technique that, for the first time, are able to simultaneously capture five key features of rigid body impact. We further validate this new model and time integration method by reproducing computationally challenging phenomena from granular physics. We next propose a technique to couple discrete and continuum models of granular materials to one another. This hybrid model reveals a family of possible discretizations suitable for simulation. We derive an explicit integration technique from this framework that is able to capture phenomena previously reserved for discrete treatments, including frictional jamming, while treating bulk regions of the material with a continuum model. To effectively handle the large plastic deformations inherent in the evolution of a granular medium, we further propose a method to dynamically update which regions are treated with a discrete model and which regions are treated with a continuum model. We demonstrate that hybrid simulations of a dynamically evolving granular material are possible and practical, and lay the foundation for further algorithmic development in this space. Finally, as the the tools used in computational science and engineering become progressively more complex, the ability to effectively train students in the field becomes increasingly important. We address the question of how to train students from a computer science background in numerical computation techniques by proposing a new system to automatically vet and identify problems in numerical simulations. This system has been deployed at the undergraduate and graduate level in a course on physical simulation at Columbia University, and has increased both student retention and student satisfaction with the course

The Foundational Model of Anatomy Ontology

Anatomy is the structure of biological organisms. The term also denotes the scientific discipline devoted to the study of anatomical entities and the structural and developmental relations that obtain among these entities during the lifespan of an organism. Anatomical entities are the independent continuants of biomedical reality on which physiological and disease processes depend, and which, in response to etiological agents, can transform themselves into pathological entities. For these reasons, hard copy and in silico information resources in virtually all fields of biology and medicine, as a rule, make extensive reference to anatomical entities. Because of the lack of a generalizable, computable representation of anatomy, developers of computable terminologies and ontologies in clinical medicine and biomedical research represented anatomy from their own more or less divergent viewpoints. The resulting heterogeneity presents a formidable impediment to correlating human anatomy not only across computational resources but also with the anatomy of model organisms used in biomedical experimentation. The Foundational Model of Anatomy (FMA) is being developed to fill the need for a generalizable anatomy ontology, which can be used and adapted by any computer-based application that requires anatomical information. Moreover it is evolving into a standard reference for divergent views of anatomy and a template for representing the anatomy of animals. A distinction is made between the FMA ontology as a theory of anatomy and the implementation of this theory as the FMA artifact. In either sense of the term, the FMA is a spatial-structural ontology of the entities and relations which together form the phenotypic structure of the human organism at all biologically salient levels of granularity. Making use of explicit ontological principles and sound methods, it is designed to be understandable by human beings and navigable by computers. The FMA’s ontological structure provides for machine-based inference, enabling powerful computational tools of the future to reason with biomedical data

A framework for local terrain deformation based on diffusion theory

Terrains have a key role in making outdoor virtual scenes believable and immersive as they form the support for every other natural element in the scene. Although important, terrains are often given limited interactivity in real-time applications. However, in nature, terrains are dynamic and interact with the rest of the environment changing shape on different levels, from tracks left by a person running on a gravel soil (micro-scale), to avalanches on the side of a mountain (macro-scale). The challenge in representing dynamic terrains correctly is that the soil that forms them is vastly heterogeneous and behaves differently depending on its composition. This heterogeneity introduces difficulties at different levels in dynamic terrains simulations, from modelling the large amount of different elements that compose the oil to simulating their dynamic behaviour. This work presents a novel framework to simulate multi-material dynamic terrains by taking into account the soil composition and its heterogeneity. In the proposed framework soil information is obtained from a material description map applied to the terrain mesh. This information is used to compute deformations in the area of interaction using a novel mathematical model based on diffusion theory. The deformations are applied to the terrain mesh in different ways depending on the distance of the area of interaction from the camera and the soil material. Deformations away from the camera are simulated by dynamically displacing normals. While deformations in a neighbourhood of the camera are represented by displacing the terrain mesh, which is locally tessellated to better fit the displacement. For gravel based soils the terrain details are added near the camera by reconstructing the meshes of the small rocks from the texture image, thus simulating both micro and macro-structure of the terrain. The outcome of the framework is a realistic interactive dynamic terrain animation in real-time

Efficient From-Point Visibility for Global Illumination in Virtual Scenes with Participating Media

Sichtbarkeitsbestimmung ist einer der fundamentalen Bausteine fotorealistischer Bildsynthese. Da die Berechnung der Sichtbarkeit allerdings äußerst kostspielig zu berechnen ist, wird nahezu die gesamte Berechnungszeit darauf verwendet. In dieser Arbeit stellen wir neue Methoden zur Speicherung, Berechnung und Approximation von Sichtbarkeit in Szenen mit streuenden Medien vor, die die Berechnung erheblich beschleunigen, dabei trotzdem qualitativ hochwertige und artefaktfreie Ergebnisse liefern

Synthesis of Spatially Extended Sources in Virtual Reality Audio

This thesis details a real-time implementation of spatial extent synthesis for virtual sound source objects made from mono sound signals and source object geometries. Techniques for distributing components of sound across basic and mesh-like geometry surfaces are discussed. A virtual-world audio environment supporting a listener avatar and various spatially extensive sound sources is described, and forms of source-to-listener distance attenuation are outlined with their roles in sound localization of spatially extensive sound sources. The implementation described herein takes form as an audio plug-in, of which the behavior, usage details, and compatible host applications are mentioned

Is the Sun Lighter than the Earth? Isotopic CO in the Photosphere, Viewed through the Lens of 3D Spectrum Synthesis

We consider the formation of solar infrared (2-6 micron) rovibrational bands of carbon monoxide (CO) in CO5BOLD 3D convection models, with the aim to refine abundances of the heavy isotopes of carbon (13C) and oxygen (18O,17O), to compare with direct capture measurements of solar wind light ions by the Genesis Discovery Mission. We find that previous, mainly 1D, analyses were systematically biased toward lower isotopic ratios (e.g., R23= 12C/13C), suggesting an isotopically "heavy" Sun contrary to accepted fractionation processes thought to have operated in the primitive solar nebula. The new 3D ratios for 13C and 18O are: R23= 91.4 +/- 1.3 (Rsun= 89.2); and R68= 511 +/- 10 (Rsun= 499), where the uncertainties are 1 sigma and "optimistic." We also obtained R67= 2738 +/- 118 (Rsun= 2632), but we caution that the observed 12C17O features are extremely weak. The new solar ratios for the oxygen isotopes fall between the terrestrial values and those reported by Genesis (R68= 530, R6= 2798), although including both within 2 sigma error flags, and go in the direction favoring recent theories for the oxygen isotope composition of Ca-Al inclusions (CAI) in primitive meteorites. While not a major focus of this work, we derive an oxygen abundance of 603 +/- 9 ppm (relative to hydrogen; 8.78 on the logarithmic H= 12 scale). That the Sun likely is lighter than the Earth, isotopically speaking, removes the necessity to invoke exotic fractionation processes during the early construction of the inner solar system

Aeolian Simulations: A Comparison of Numerical and Experimental Results, with Projections for Titan.

Aeolian processes are major determinants of geomorphology on bodies in the Solar System possessing an atmosphere-surface interface and transportable sediment, including Earth, Mars, Venus, and Titan. Substantial efforts have been made over the last few decades to understand these processes using specialized wind tunnels, field studies, and, more recently, numerical simulations. This thesis describes a model of aeolian sediment transport using computational fluid dynamics (CFD), and compares the results with those obtained in the Martian Surface Wind Tunnel (MARSWIT) testing conducted in the Planetary Aeolian Laboratory at NASA Ames Research Center. The ultimate goal of the thesis was to develop an experimentally validated computational approach for modeling aeolian sediment saltation on Titan and other planetary bodies. In this thesis, sieved walnut shell particles with diameters of 175-250 microns were placed on the test section floor of the MARSWIT tunnel, the tunnel was started, and the free stream airspeed was raised to ~2.5 to 7.5 m/s. A Phantom v12 high-speed camera was used to image the resulting particle motion at 1000 frames per second, and the open source software, ImageJ, was used to evaluate particle motion. Airflow in the MARSWIT facility was modeled with Ansys FLUENT, a commercial CFD program. Surface properties for roughness height (Ks) and roughness constant (Cs) were determined through computation of a dimensionless roughness height parameter, , while using von Kármán\u27s constant. The turbulent scheme used in FLUENT to obtain closed-form solutions to the Navier-Stokes equations was a 1st Order Discretization, k-epsilon (two-equation) model. These methods produced computational velocity profiles that agreed with experimental data to within 10-15%. Once satisfactory modeling of the flow field had been achieved, a Discrete Phase Model (DPM) was utilized to simulate particle trajectories numerically. A Euler-Lagrangian scheme was employed, treating the particles as spheres and tracking each particle at its center. Calculated particle trajectories agreed closely with experimental results, within error bounds. Projections of Titan trajectories for specific conditions are among the major results presented and discussed and show higher and longer lofts than currently estimated

Controls on Erosion and Transport of Mass by Debris Flows

Debris flows and sediment-rich floods are common transport processes in steep valleys that dissect mountainous terrain. Rapid movement, high discharges, and the transport of large quantities of coarse-grained sediment characterize these hydrologically-driven processes. Despite the importance of debris flows for landscape evolution and natural hazards, there is not an agreed upon mechanical framework to describe how debris flows entrain sediment, erode bedrock, and transport mass. As a result, large uncertainties remain pertaining to the potential for a debris flow to grow through entrainment of loose sediment, the rate at which bedrock is eroded, and the manner in which changes in climate, tectonics, or land-use might affect steep landscapes. I use a combination of in situ measurements of debris-flow dynamics from a natural laboratory located in the headwaters of a debris-flow dominated catchment, grain-scale numerical modeling of granular flows, and digital elevation model data to constrain the mechanics controlling erosion and transport of mass by debris flows. In particular, I quantify: (1) the characteristic flow properties of natural debris-flow surges and how they relate to total travel distance; (2) the mechanics controlling the rate of bed-sediment entrainment and growth of flow volume; (3) the degree to which debris flows erode the bedrock channel floor; and (4) how changes to channel or flow properties influence the erosive potential of a flow. Monitored debris-flow events were composed of multiple surges, each with clear variation of flow properties along the length of the surge. Relatively fine-grained and water-rich tails that had a wide range of pore-fluid pressures pushed along steep, highly resistant, visually unsaturated surge fronts of coarse-grained material. Surges with large excess pore-fluid pressures, and thus lower frictional resistance, had longer travel distances. The dominant control of non-equilibrium pore pressure on flow resistance makes the prediction of travel distance based solely on channel properties problematic. During passage of dense granular-fronts as well as water-rich, inter-surge flow, bed sediment was entrained from the sediment-surface downward in a progressive fashion. Despite similar flow properties and thicknesses of bed sediment entrained across all events, time-averaged entrainment rates for bed sediment that was saturated prior to flow arrival could exceed entrainment rates for dry sediment by over an order of magnitude. As a result, a debris flow over wet bed sediment will be larger than the same flow over dry bed sediment. Once all shielding bed sediment was entrained, flow particles could directly impact the bedrock channel floor. Average bedrock erosion rates that resulted were ~1 cm yr--1. Variability in impact-stress magnitude increased linearly with the mean basal stress and measured probability density functions were generally best fit by Pareto or power law distributions with well-defined means and variances. Using the grain-scale numerical modeling, I observed a nonlinear increase in particle-bed impact forces and impact energy as a function of slope. In contrast, particle impact flux increased at small slopes, but then decreased linearly as slope increased beyond a threshold value. Predicted erosion rate, which scales as the product of impact energy and impact flux, increased as a nonlinear function of slope. Steep landscapes in which millennial scale erosion rates have been quantified display a similar nonlinear relationship between erosion rate and channel gradient. This suggests that the grain-scale mechanics quantified here place strong controls on steepland morphology that evolves over thousands to millions of years