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This paper aims to find an objects representation scheme with high precision and to compute the objects’ separation distance effectively in final analysis. Proximity queries have been used widely in robot trajectory planning, automatic assembly planning, virtual surgery and many other applications. The core of proximity query is the precise computation of (minimum) separation distance in narrow phase, and specific object representation scheme corresponds to different methods of separation distance computation.

In this paper, a second-order cone programming (SOCP)-based (minimum) separation distance computation algorithm was proposed. It treats convex superquadrics, descriptive primitives of complex object as the study objects. The separation distance between two convex superquadrics was written as a general nonlinear programming (NLP) problem with superquadric constraints and then transformed into an SOCP problem with the method of conic formulation of superquadric constraints. Finally, a primal-dual interior point method embedded in MOSEK was used for solving the SOCP problem.

The proposed algorithm achieved exact separation distance computation between convex superquadrics, with a relative error of 10-6. It is particularly suitable for proximity queries in narrow phase of static collision detection algorithms. Further, the proposed algorithm achieved continuous collision detection between rectilinear translation superquadrics.

The proposed algorithm in narrow phase of static collision detection algorithms makes objects’ separation distance effectively computed. Proximity queries are easy and more accurate to perform in this way.

This paper discusses advances in interactive discrete element simulation for use in computer‐aided concurrent design. We highlight the computational problems of creating a ‘virtual world’ populated by objects which behave much as real world objects and propose a system based on a new class of volumetric models, called superquadrics. These functions have significant advantages for calculating multibody interactions, and by coupling volumetric representation to a modal decomposition method for the physical dynamics we have been able to gain up to two orders of magnitude in efficiency. The modal method allows us to trade off high order modes for improved stability, time step magnitude, temporal aliasing and speed of response, and so provide almost real time feedback to the designer. We believe that virtual manufacturing systems will be especially useful in conceptual design, in design for manufacture and in the new thrust in concurrent design.

This paper describes an imaging system that was developed to aid industrial bin picking tasks. The purpose of this system was to provide accurate 3D models of parts and objects in the bin, so that precise grasping operations could be performed. The technology described here is based on two types of sensors: range mapping scanners and video cameras. The geometry of bin contents was reconstructed from range maps and modeled using superquadric representations, providing location and parts surface information that can be employed to guide the robotic arm. Texture was also provided by the video streams and applied to the recovered models. The system is expected to improve the accuracy and efficiency of bin sorting and represents a step toward full automation.

When simulating the behaviour of granular assemblies and multi‐body systems using a discrete element analysis, the shape representation of the bodies and the contact detection algorithm greatly influence the flexibility, accuracy and efficiency of the simulation. Several geometrical shape descriptors of two and three dimensional arbitrary rigid bodies are reviewed and a flexible 3‐D descriptor introduced. The aim is to identify appropriate shape descriptors which allow a variety of types of bodies to be investigated while ensuring accurate and efficient detection of inter‐particle contacts. Polygons/polyhedrons, and continuous and discrete function representations are examined. The investigation favours discrete representations due to their efficiency and flexibility, but illustrates the elegance and efficiency of using a continuous function representation, e.g. a superquadric, to generate the discrete representation and simplify the contact detection process.

A new method of representing non‐spherical, smooth‐surfaced, axi‐symmetrical particles in discrete element (DE) simulation using model particles comprising overlapping spheres of arbitrary size whose centres are fixed in position relative to each other along the major axis of symmetry of the particle is presented. Contact detection and calculation of force‐deformation and particle movement is achieved using standard DE techniques modified to integrate the behaviour of each element sphere with that of the multi‐element particle to which it belongs. The method enables the dynamic behaviour of particles of high aspect ratio and irregular curvature (in two dimensions) to be modelled. The use of spheres to represent a particle takes advantage of the computational speed and accuracy of contact detection for spheres, which should make the method comparable in computational efficiency to alternative schemes for representing non‐spherical particles.

We present an algorithm for contact resolution that is valid for a wide variety of polygonal two dimensional shapes and is of linear computational complexity. The algorithm is designed for use in discrete element analysis of granular and multibody systems exhibiting discontinuous behaviour. Contact detection usually consists of a spatial sorting phase and a contact resolution phase. The spatial sorting phase seeks to avoid an all‐to‐all body comparison by culling the number of objects which are potential contactors of a given object. The contact resolution phase resolves the details of the contact between two given objects. The algorithm presented here (called DFR) addresses the contact resolution phase and is applicable to convex geometries and to a restricted set of concave geometries. Examination of the algorithm establishes an upper bound linear computational complexity, of order O(N), with respect to the number of points (N) used to define the object boundary. The DFR algorithm is combined with a modified heapsort algorithm for spatial sorting of M bodies which has complexity O(M log M) and is applied to a baseline granular simulation problem to test its efficiency.

Application of the discrete element method (DEM) to real scale engineering problems involving three‐dimensional modelling of large, non‐spherical particles must consider the inertia tensor and temporal change in the orientation of the particles when calculating the rotational motion. This factor has commonly been neglected in discrete element modelling although it will significantly influence the dynamic behaviour of non‐spherical particles. In this paper two methods, vector transformation and tensor transformation, for calculation of the rotational motion of particles in response to applied moments are presented. The methods consider the inertia tensor and the local object frame of arbitrary shaped particles and suggest solutions for the non‐linear Euler equations for calculation of their rotational motion. They are discussed with respect to implementation into a discrete element code and assessed in terms of their accuracy and computational efficiency.

This paper presents the results of a Discrete Element Method study on the influence of particle shape on the strength and deformation behaviour of two dimensional assemblages of ellipse‐shaped particles. Assemblages of particles with varying individual particle aspect ratio were formed with a preferred bedding plane, isotropically compressed with varying isotropic confining stresses and then sheared with biaxial compression. The results indicate that Discrete Element analysis using two dimensional ellipse‐shaped particles produces mechanical behaviour which is similar both quantitatively and qualitatively to the behaviour of real granular materials. Even small particle out‐of‐roundness increases the observed macroscopic strength significantly. In systems composed of flatter particles, particle rotations are greatly inhibited. Decomposing relative contact displacements into contributions due to particle rotation and translation demonstrates that most of the displacements in round particle systems are due to individual particle rotation.

Robotic hands are still a long way from matching the grasping and manipulation capability of their human counterparts, but computer simulation may help us understand this disparity. We present our publicly available simulator, and describe our research projects involving the system including the development of a human hand model derived from experimental measurements.

Unlike other simulation systems, our system was built specifically to analyze grasps. It can import a wide variety of robot designs by using standard descriptions of the kinematics and link geometries. Various components support the analysis of grasps, visualization of results, dynamic simulation of grasping tasks, and grasp planning.

The simulator has been used in several grasping research problems and can be used to plan grasps for an actual robot. With the aid of a vision system, we have shown that these grasps can be executed by a robot.

We are currently developing methods to handle deformable surfaces, tendon driven models, and non‐ideal joints in order to better model human grasping.

This work is part of our current project to create a biomechanically realistic human hand model to better understand what features are most important to mimic in the designs of robotic hands. Such a model will also help clinicians better plan reconstructive hand surgeries.

We describe our publicly available grasping simulator and review experiments performed with it. The paper demonstrates the usefulness of this system as a tool for grasping research.

To use distinct element simulation (PFC2D) to investigate the relationships between microparameters and macroproperties of the specimens that are modeled by bonded particles. To determine quantitative relationships between particle level parameters and mechanical properties of the specimens.

A combined theoretical and numerical approach is used to achieve the objectives. First, theoretical formulations are proposed for the relationships between microparameters and macroproperties. Then numerical simulations are conducted to quantify the relationships.

The Young's modulus is mainly determined by particle contact modulus and affected by particle stiffness ratio and slightly affected by particle size. The Poisson's ratio is mainly determined by particle stiffness ratio and slightly affected by particle size. The compressive strength can be scaled by either the bond shear strength or the bond normal strength depending on the ratio of the two quantities.

The quantitative relationships between microparameters and macroproperties for parallel‐bonded PFC2D specimens are empirical in nature. Some modifications may be needed to model a specific material. The effects of the particle distribution and bond strength distribution of a PFC2D specimen are very important aspects that deserve further investigation.

The results will provide guidance for people who use distinct element method, especially the PFC2D, to model brittle materials such as rocks and ceramics.

This paper offers some new quantitative relationships between microparameters and macroproperties of a synthetic specimen created using bonded particle model.