Contact detection between a small ellipsoid and another quadric

[Abstract] We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient condition for an efficient method to detect contact. This condition, named smallness condition, is a feature on the size and the shape of the quadrics and can be checked directly from their parameters. Under this hypothesis, contact can be noticed by means of the expressions in a discriminant system of the characteristic polynomial. Furthermore, relative positions can be classified through the sign of the coefficients of this polynomial. As an application of these results, a method to detect contact between a small ellipsoid and a combination of quadrics is given

Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties

The shape of irregular particles has significant influence on micro- and macro-scopic behavior of granular systems. This paper presents a combined 3D thinning and greedy set-covering algorithm to approximate realistic particles with a clump of overlapping spheres for discrete element method (DEM) simulations. First, the particle medial surface (or surface skeleton), from which all candidate (maximal inscribed) spheres can be generated, is computed by the topological 3D thinning. Then, the clump generation procedure is converted into a greedy set-covering (SCP) problem. To correct the mass distribution due to highly overlapped spheres inside the clump, linear programming (LP) is used to adjust the density of each component sphere, such that the aggregate properties mass, center of mass and inertia tensor are identical or close enough to the prototypical particle. In order to find the optimal approximation accuracy (volume coverage: ratio of clump's volume to the original particle's volume), particle flow of 3 different shapes in a rotating drum are conducted. It was observed that the dynamic angle of repose starts to converge for all particle shapes at 85% volume coverage (spheres per clump < 30), which implies the possible optimal resolution to capture the mechanical behavior of the system.Comment: 34 pages, 13 figure

Continuous collision detection for ellipsoids

We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then we derive a time-dependent characteristic equation for two moving ellipsoids, which enables us to develop a real-time algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with several practical examples. © 2006 IEEE.published_or_final_versio

Contact force models for non-spherical particles with different surface properties : a review

This paper reviews the state-of-the-art contact force models for non-spherical particles, which describe the relationship between the contact force and the geometrical, material, and mechanical properties of the contacting particles. The review aims to select better contact force models to improve the current simplified contact force models used in discrete element method (DEM) simulations. First, the contact force models based on the extension of the classical Hertz theory are reviewed, in which a recent accurate geometrical contact force model is highlighted. Secondly, the research on the effects of different variables such as elastoplasticity, viscoelasticity, adhesion and surface roughness on contact force are reviewed respectively and then incorporated into the accurate geometrical contact force model. Thirdly, tangential force models for non-spherical particles in contact under various loading regimes are reviewed as well. Based on the review, a full set of improved contact force models for DEM is recommended. These contact force models can more accurately predict the contact force and contact area for non-spherical particles, which can be beneficial to the DEM simulation in emerging areas, such as nanoparticles and additive manufacturing

Discrete element modelling of the dynamic behaviour of non-spherical particulate materials

PhD ThesisA numerical model based on the discrete element (DE) method, for modelling the flow of irregularly shaped, smooth-surfaced particles in a 3-D system is presented. An existing DE program for modelling the contact between spherical particles in periodic space (without real walls or boundaries) was modified to model non-spherical particles in a system with containing walls. The new model was validated against analytical calculations of single particle movements and also experimentally against data from physical experiments using synthetic non-spherical particles at both a particle and bulk scale. It was then used to study the effect of particle shape on the flow behaviour of assemblies of particles with various aspect ratios discharging from a flat-bottomed hopper. The particles were modelled using the Multi-Sphere Method (MSM) which is based on the CSG (Constructive Solid Geometry) technique for construction of complex solids by combining primitive shapes. In this method particle geometry is approximated using overlapping spheres of arbitrary diameter which are fixed in position relative to each other. The contact mechanics and contact detection method are the same as those used for spheres, except that translation and rotation of element spheres are calculated with respect to the motion of the whole particle....Numerical simulations of packing and flow of particles from a flat-bottomed hopper with a range of aspect ratios were performed to investigate the effect of particle shape on packing and flow behaviour of a particulate assembly. It was found that the particle shape influenced both bed structure and flow characteristics such as flow pattern, shear band strength and the occurrence of bridging. The flow of the bed of spherical particles was smoother than the flow of beds of elongated particles in which flow was fluctuating and there was more resistance to shear.Ministry of Culture and Higher Education of IRAN: University of Mashhad

PHYSICS-AWARE MODEL SIMPLIFICATION FOR INTERACTIVE VIRTUAL ENVIRONMENTS

Rigid body simulation is an integral part of Virtual Environments (VE) for autonomous planning, training, and design tasks. The underlying physics-based simulation of VE must be accurate and computationally fast enough for the intended application, which unfortunately are conflicting requirements. Two ways to perform fast and high fidelity physics-based simulation are: (1) model simplification, and (2) parallel computation. Model simplification can be used to allow simulation at an interactive rate while introducing an acceptable level of error. Currently, manual model simplification is the most common way of performing simulation speedup but it is time consuming. Hence, in order to reduce the development time of VEs, automated model simplification is needed. The dissertation presents an automated model simplification approach based on geometric reasoning, spatial decomposition, and temporal coherence. Geometric reasoning is used to develop an accessibility based algorithm for removing portions of geometric models that do not play any role in rigid body to rigid body interaction simulation. Removing such inaccessible portions of the interacting rigid body models has no influence on the simulation accuracy but reduces computation time significantly. Spatial decomposition is used to develop a clustering algorithm that reduces the number of fluid pressure computations resulting in significant speedup of rigid body and fluid interaction simulation. Temporal coherence algorithm reuses the computed force values from rigid body to fluid interaction based on the coherence of fluid surrounding the rigid body. The simulations are further sped up by performing computing on graphics processing unit (GPU). The dissertation also presents the issues pertaining to the development of parallel algorithms for rigid body simulations both on multi-core processors and GPU. The developed algorithms have enabled real-time, high fidelity, six degrees of freedom, and time domain simulation of unmanned sea surface vehicles (USSV) and can be used for autonomous motion planning, tele-operation, and learning from demonstration applications

Electromagnetic Scattering Characteristics of Composite Targets and Software Development Based on PO Algorithm

Physical optics (PO) algorithm is a high-frequency electromagnetic (EM) algorithm, which is widely used to solve the EM scattering problems of electrically large composite targets. Due to the PO algorithm only considers the induced current in the bright region irradiated by EM wave, the computational memory and time consumption are superior than other high-frequency algorithms, and the calculation accuracy is pretty fine. Based on the PO algorithm, this thesis focuses on the occlusion judgement of PO algorithm and its application in composite targets. The main contents of this thesis are as follows: 1. The occlusion judgement software system for PO algorithm is developed. The main function of this software is to judge the bright region of the target under the irradiation of EM wave. This software uses two judgement methods: ray tracing method based on CPU and Z-Buffer method based on CPU and GPU. Moreover, due to the compromise between patch size and patch number, both methods have errors at the edge of bright and shadow regions. This thesis discusses the error and reduces it. 2. Based on PO algorithm, the EM scattering characteristics of targets covered by plasma sheath are discussed. We simulate the plasma sheath flow field data of hypersonic vehicle by FASTRAN software, compare and analyze the plasma sheath electron number density at different flight heights and speeds. On this basis, the bistatic RCS of hypersonic vehicle head-on irradiation under different flight heights and speeds is calculated by using the PO algorithm of layered medium. 3. SAR image simulation of tree ground composite target is carried out based on PO algorithm and Non-Uniform Fast Fourier Transform (NUFFT) method. Firstly, we introduce the geometric modeling and EM parameter modeling of tree ground composite target, and the scattering characteristics of tree ground composite target are obtained by using PO algorithm. Finally, the scattering field of the target is processed by NUFFT method, and the SAR simulation images of multiple trees scene are obtained

Numerical Modelling of Tidal Notch Sequences on Rocky Coasts of the Mediterranean Basin

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Objekt-Manipulation und Steuerung der Greifkraft durch Verwendung von Taktilen Sensoren

This dissertation describes a new type of tactile sensor and an improved version of the dynamic tactile sensing approach that can provide a regularly updated and accurate estimate of minimum applied forces for use in the control of gripper manipulation. The pre-slip sensing algorithm is proposed and implemented into two-finger robot gripper. An algorithm that can discriminate between types of contact surface and recognize objects at the contact stage is also proposed. A technique for recognizing objects using tactile sensor arrays, and a method based on the quadric surface parameter for classifying grasped objects is described. Tactile arrays can recognize surface types on contact, making it possible for a tactile system to recognize translation, rotation, and scaling of an object independently.Diese Dissertation beschreibt eine neue Art von taktilen Sensoren und einen verbesserten Ansatz zur dynamischen Erfassung von taktilen daten, der in regelmäßigen Zeitabständen eine genaue Bewertung der minimalen Greifkraft liefert, die zur Steuerung des Greifers nötig ist. Ein Berechnungsverfahren zur Voraussage des Schlupfs, das in einen Zwei-Finger-Greifarm eines Roboters eingebaut wurde, wird vorgestellt. Auch ein Algorithmus zur Unterscheidung von verschiedenen Oberflächenarten und zur Erkennung von Objektformen bei der Berührung wird vorgestellt. Ein Verfahren zur Objekterkennung mit Hilfe einer Matrix aus taktilen Sensoren und eine Methode zur Klassifikation ergriffener Objekte, basierend auf den Daten einer rechteckigen Oberfläche, werden beschrieben. Mit Hilfe dieser Matrix können unter schiedliche Arten von Oberflächen bei Berührung erkannt werden, was es für das Tastsystem möglich macht, Verschiebung, Drehung und Größe eines Objektes unabhängig voneinander zu erkennen