Minkowski Sum Construction and other Applications of Arrangements of Geodesic Arcs on the Sphere

We present two exact implementations of efficient output-sensitive algorithms that compute Minkowski sums of two convex polyhedra in 3D. We do not assume general position. Namely, we handle degenerate input, and produce exact results. We provide a tight bound on the exact maximum complexity of Minkowski sums of polytopes in 3D in terms of the number of facets of the summand polytopes. The algorithms employ variants of a data structure that represents arrangements embedded on two-dimensional parametric surfaces in 3D, and they make use of many operations applied to arrangements in these representations. We have developed software components that support the arrangement data-structure variants and the operations applied to them. These software components are generic, as they can be instantiated with any number type. However, our algorithms require only (exact) rational arithmetic. These software components together with exact rational-arithmetic enable a robust, efficient, and elegant implementation of the Minkowski-sum constructions and the related applications. These software components are provided through a package of the Computational Geometry Algorithm Library (CGAL) called Arrangement_on_surface_2. We also present exact implementations of other applications that exploit arrangements of arcs of great circles embedded on the sphere. We use them as basic blocks in an exact implementation of an efficient algorithm that partitions an assembly of polyhedra in 3D with two hands using infinite translations. This application distinctly shows the importance of exact computation, as imprecise computation might result with dismissal of valid partitioning-motions.Comment: A Ph.D. thesis carried out at the Tel-Aviv university. 134 pages long. The advisor was Prof. Dan Halperi

Computer Aided Design of Side Actions for Injection Molding of Complex Parts

Often complex molded parts include undercuts, patches on the part boundaries that are not accessible along the main mold opening directions. Undercuts are molded by incorporating side actions in the molds. Side actions are mold pieces that are removed from the part using translation directions different than the main mold opening direction. However, side actions contribute to mold cost by resulting in an additional manufacturing and assembly cost as well as by increasing the molding cycle time. Therefore, generating shapes of side actions requires solving a complex geometric optimization problem. Different objective functions may be needed depending upon different molding scenarios (e.g., prototyping versus large production runs). Manually designing side actions is a challenging task and requires considerable expertise. Automated design of side actions will significantly reduce mold design lead times. This thesis describes algorithms for generating shapes of side actions to minimize a customizable molding cost function. Given a set of undercut facets on a polyhedral part and the main parting direction, the approach works in the following manner. First, candidate retraction space is computed for every undercut facet. This space represents the candidate set of translation vectors that can be used by the side action to completely disengage from the undercut facet. As the next step, a discrete set of feasible, non-dominated retractions is generated. Then the undercut facets are grouped into undercut regions by performing state space search over such retractions. This search step is performed by minimizing the customizable molding cost function. After identifying the undercut regions that can share a side action, the shapes of individual side actions are computed. The approach presented in this work leads to practically an optimal solution if every connected undercut region on the part requires three or fewer side actions. Results of computational experiments that have been conducted to assess the performance of the algorithms described in the thesis have also been presented. Computational results indicate that the algorithms have acceptable computational performance, are robust enough to handle complex part geometries, and are easy to implement. It is anticipated that the results shown here will provide the foundations for developing fully automated software for designing side actions in injection molding

Minimum time kinematic trajectories for self-propelled rigid bodies in the unobstructed plane

The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit from precise knowledge of optimal trajectories for a set of permitted controls. In this work, we present a general solution to the problem of finding minimum time trajectories for an arbitrary self-propelled, velocity-bounded rigid body in the obstacle-free plane. Such minimum-time trajectories depend on the vehicle’s capabilities and on and the start and goal configurations. For example, the fastest way to move a car sideways might be to execute a parallel-parking motion. The fastest longdistance trajectories for a wheelchair-like vehicle might be of a turn-drive-turn variety. Our analysis reveals a wide variety of types of optimal trajectories. We determine an exhaustive taxonomy of optimal trajectory types, presented as a branching tree. For each of the necessary leaf nodes, we develop a specific algorithm to find the fastest trajectory in that node. The fastest trajectory overall is drawn from this set

Verified lifting of stencil computations

This paper demonstrates a novel combination of program synthesis and verification to lift stencil computations from low-level Fortran code to a high-level summary expressed using a predicate language. The technique is sound and mostly automated, and leverages counter-example guided inductive synthesis (CEGIS) to find provably correct translations. Lifting existing code to a high-performance description language has a number of benefits, including maintainability and performance portability. For example, our experiments show that the lifted summaries can enable domain specific compilers to do a better job of parallelization as compared to an off-the-shelf compiler working on the original code, and can even support fully automatic migration to hardware accelerators such as GPUs. We have implemented verified lifting in a system called STNG and have evaluated it using microbenchmarks, mini-apps, and real-world applications. We demonstrate the benefits of verified lifting by first automatically summarizing Fortran source code into a high-level predicate language, and subsequently translating the lifted summaries into Halide, with the translated code achieving median performance speedups of 4.1X and up to 24X for non-trivial stencils as compared to the original implementation.United States. Department of Energy. Office of Science (Award DE-SC0008923)United States. Department of Energy. Office of Science (Award DE-SC0005288

Planning in constraint space for multi-body manipulation tasks

Robots are inherently limited by physical constraints on their link lengths, motor torques, battery power and structural rigidity. To thrive in circumstances that push these limits, such as in search and rescue scenarios, intelligent agents can use the available objects in their environment as tools. Reasoning about arbitrary objects and how they can be placed together to create useful structures such as ramps, bridges or simple machines is critical to push beyond one's physical limitations. Unfortunately, the solution space is combinatorial in the number of available objects and the configuration space of the chosen objects and the robot that uses the structure is high dimensional. To address these challenges, we propose using constraint satisfaction as a means to test the feasibility of candidate structures and adopt search algorithms in the classical planning literature to find sufficient designs. The key idea is that the interactions between the components of a structure can be encoded as equality and inequality constraints on the configuration spaces of the respective objects. Furthermore, constraints that are induced by a broadly defined action, such as placing an object on another, can be grouped together using logical representations such as Planning Domain Definition Language (PDDL). Then, a classical planning search algorithm can reason about which set of constraints to impose on the available objects, iteratively creating a structure that satisfies the task goals and the robot constraints. To demonstrate the effectiveness of this framework, we present both simulation and real robot results with static structures such as ramps, bridges and stairs, and quasi-static structures such as lever-fulcrum simple machines.Ph.D

Research in Structures, Structural Dynamics and Materials, 1990

The Structural Dynamics and Materials (SDM) Conference was held on April 2 to 4, 1990 in Long Beach, California. This publication is a compilation of presentations of the work-in-progress sessions and does not contain papers from the regular sessions since those papers are published by AIAA in the conference proceedings

Cloud geometry for passive remote sensing

An important cause for disagreements between current climate models is lack of understanding of cloud processes. In order to test and improve the assumptions of such models, detailed and large scale observations of clouds are necessary. Passive remote sensing methods are well-established to obtain cloud properties over a large observation area in a short period of time. In case of the visible to near infrared part of the electromagnetic spectrum, a quick measurement process is achieved by using the sun as high-intensity light source to illuminate a cloud scene and by taking simultaneous measurements on all pixels of an imaging sensor. As the sun as light source can not be controlled, it is not possible to measure the time light travels from source to cloud to sensor, which is how active remote sensing determines distance information. But active light sources do not provide enough radiant energy to illuminate a large scene, which would be required to observe it in an instance. Thus passive imaging remains an important remote sensing method. Distance information and accordingly cloud surface location information is nonetheless crucial information: cloud fraction and cloud optical thickness largely determines the cloud radiative effect and cloud height primarily influences a cloud's influence on the Earth's thermal radiation budget. In combination with ever increasing spatial resolution of passive remote sensing methods, accurate cloud surface location information becomes more important, as the largest source of retrieval uncertainties at this spatial scale, influences of 3D radiative transfer effects, can be reduced using this information. This work shows how the missing location information is derived from passive remote sensing. Using all sensors of the improved hyperspectral and polarization resolving imaging system specMACS, a unified dataset, including classical hyperspectral measurements as well as cloud surface location information and derived properties, is created. This thesis shows how RGB cameras are used to accurately derive cloud surface geometry using stereo techniques, complementing the passive remote sensing of cloud microphysics on board the German High-Altitude Long-Range research aircraft (HALO). Measured surface locations are processed into a connected surface representation, which in turn is used to assign height and location to other passive remote sensing observations. Furthermore, cloud surface orientation and a geometric shadow mask are derived, supplementing microphysical retrieval methods. The final system is able to accurately map visible cloud surfaces while flying above cloud fields. The impact of the new geometry information on microphysical retrieval uncertainty is studied using theoretical radiative transfer simulations and measurements. It is found that in some cases, information about surface orientation allows to improve classical cloud microphysical retrieval methods. Furthermore, surface information helps to identify measurement regions where a good microphysical retrieval quality is expected. By excluding likely biased regions, the overall microphysical retrieval uncertainty can be reduced. Additionally, using the same instrument payload and based on knowledge of the 3D cloud surface, new approaches for the retrieval of cloud droplet radius exploiting measurements of parts of the polarized angular scattering phase function become possible. The necessary setup and improvements of the hyperspectral and polarization resolving measurement system specMACS, which have been developed throughout four airborne field campaigns using the HALO research aircraft are introduced in this thesis.Ein wichtiger Grund für Unterschiede zwischen aktuellen Klimamodellen sind nicht ausreichend verstandene Wolkenprozesse. Um die zugrundeliegenden Annahmen dieser Modelle zu testen und zu verbessern ist es notwendig detaillierte und großskalige Beobachtungen von Wolken durch zu führen. Methoden der passiven Fernerkundung haben sich für die schnelle Erfassung von Wolkeneigenschaften in einem großen Beobachtungsgebiet etabliert. Für den sichtbaren bis nahinfraroten Bereich des elektromagnetischen Spektrums kann eine schnelle Messung erreicht werden, in dem die Sonne als starke Lichtquelle genutzt wird und die Wolkenszene durch simultane Messung über alle Pixel eines Bildsensors erfasst wird. Da die Sonne als Lichtquelle nicht gesteuert werden kann, ist es nicht möglich die Zeit zu messen die von einem Lichtstrahl für den Weg von der Quelle zur Wolke und zum Sensor benötigt wird, so wie es bei aktiven Verfahren zur Distanzbestimmung üblich ist. Allerdings können aktive Lichtquellen nicht genügend Energie bereitstellen um eine große Szene gut genug zu beleuchten um diese Szene in einem kurzen Augenblick vollständig zu erfassen. Aus diesem Grund werden passive bildgebende Verfahren weiterhin eine wichtige Methode zur Fernerkundung bleiben. Trotzdem ist der Abstand zur beobachteten Wolke und damit der Ort der Wolke eine entscheidende Information: Wolkenbedeckungsgrad und die optische Dicke einer Wolke bestimmen einen Großteil des Strahlungseffektes von Wolken und die Höhe der Wolken ist der Haupteinflussfaktor von Wolken auf die thermische Strahlungsbilanz der Erde. Einhergehend mit der weiterhin zunehmenden Auflösung von passiven Fernerkundungsmethoden werden genaue Informationen über den Ort von Wolkenoberflächen immer wichtiger. Dreidimensionale Strahlungstransporteffekte werden auf kleineren räumlichen Skalen zum dominierenden Faktor für Fehler in Messverfahren für Wolkenmikrophysik. Dieser Einfluss auf die Messverfahren kann durch die Nutzung von Informationen über die Lage der Wolken reduziert und die Ergebnisse somit verbessert werden. Diese Arbeit zeigt, wie die fehlenden Ortsinformationen aus passiven Fernerkundungsmethoden gewonnen werden können. Damit kann ein vereinheitlichter Datensatz aller Sensoren des verbesserten specMACS-Systems für hyperspektrale und polarisationsaufgelöste Bilderfassung erstellt werden, in dem außer den gemessenen Strahlungsdichten auch die Positionen der beobachteten Wolkenoberflächen und daraus abgeleitete Größen enthalten sind. In dieser Arbeit wird gezeigt, wie RGB-Kameras genutzt werden, um mit Hilfe stereographischer Techniken die Geometrie der beobachteten Wolken ab zu leiten und so die Möglichkeiten zur passiven Fernerkundung auf dem Forschungsflugzeug HALO zu erweitern. Aus den so gemessenen Positionen der Wolkenoberflächen wird eine geschlossene Darstellung der Wolkenoberflächen berechnet. Dies ermöglicht es die Daten aus anderen passiven Fernerkundungsmethoden um Höhe und Ort der Messung zu erweitern. Außerdem ist es so möglich die Orientierung der Wolkenoberflächen und eine Schattenmaske auf Grund der nun bekannten Beobachtungsgeometrie zu berechnen. Das fertige System ist in der Lage, die sichtbaren Wolkenoberflächen aus Daten von einem Überflug zu rekonstruieren. Mit Hilfe theoretischer Strahlungstransportsimulationen und Messungen wird der Einfluss der neu gewonnenen Informationen auf bestehende Rekonstruktionsmethoden für Wolkenmikrophysik untersucht. In manchen Fällen helfen die neu gewonnenen Informationen direkt die Ergebnisse dieser Methoden zu verbessern und in jedem Fall ermöglichen es die Positionsdaten Bereiche zu identifizieren für die bekannt ist, dass bisherige Rekonstruktionsmethoden nicht funktionieren. Durch Ausschluss solcher Bereiche wird der Gesamtfehler von Mirkophysikrekonstruktionen weiterhin reduziert. Das aktuelle specMACS System ermöglicht auch polarisationsaufgelöste Messungen, wodurch eine sehr genaue Bestimmung der Wolkentropfengrößen möglich wird. Die nun verfügbaren Positionsdaten der Wolkenoberflächen helfen die Genauigkeit dieses Verfahrens deutlich zu verbessern. Die notwendigen Auf- und Umbauten des hyperspektralen und polarisationsauflösenden Messsystems specMACS, die während vier Flugzeuggestützer Messkampagnen auf dem Forschungsflugzeug HALO entwickelt wurden sind in dieser Arbeit beschrieben