GPU-based proximity query processing on unstructured triangular mesh model

This paper presents a novel proximity query (PQ) approach capable to detect the collision and calculate the minimal Euclidean distance between two non-convex objects in 3D, namely the robot and the environment. Such approaches are often considered as computationally demanding problems, but are of importance to many applications such as online simulation of haptic feedback and robot collision-free trajectory. Our approach enables to preserve the representation of unstructured environment in the form of triangular meshes. The proposed PQ algorithm is computationally parallel so that it can be effectively implemented on graphics processing units (GPUs). A GPU-based computation scheme is also developed and customized, which shows >200 times faster than an optimized CPU with single core. Comprehensive validation is also conducted on two simulated scenarios in order to demonstrate the practical values of its potential application in image-guided surgical robotics and humanoid robotic control.published_or_final_versio

Proximity Queries for Absolutely Continuous Parametric Curves

In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is generally non-convex and serves as a significant computational bottleneck for motion planning algorithms. In this paper, we present methods for a general class of absolutely continuous parametric curves to compute: (i) the minimum separating distance, (ii) tolerance verification, and (iii) collision detection. Our methods efficiently compute bounds on obstacle proximity by bounding the curve in a convex region. This bound is based on an upper bound on the curve arc length that can be expressed in closed form for a useful class of parametric curves including curves with trigonometric or polynomial bases. We demonstrate the computational efficiency and accuracy of our approach through numerical simulations of several proximity problems.Comment: Proceedings of Robotics: Science and System

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

Collision Detection and Part Interaction Modeling to Facilitate Immersive Virtual Assembly Methods

Realistic part interaction is an important component of an effective virtual assembly application. Both collision detection and part interaction modeling are needed to simulate part-to-part and hand-to-part interactions. This paper examines several polygonal-based collision detection packages and compares their usage for virtual assembly applications with the Voxmap PointShell (VPS) software developed by the Boeing Company. VPS is a software developer’s toolkit for real-time collision and proximity detection, swept-volume generation, dynamic animation, and 6 degree-of-freedom haptics which is based on volumetric collision detection and physically based modeling. VPS works by detecting interactions between two parts: a dynamic object moving in the virtual environment, and a static object defined as a collection of all other objects in the environment. The method was found to provide realistic collision detection and physically-based modeling interaction, with good performance at the expense of contact accuracy. Results from several performance tests on VPS are presented. This paper concludes by presenting how VPS has been implemented to handle multiple dynamic part collisions and two-handed assembly using the 5DT dataglove in a projection screen virtual environment