Efficient continuous collision detection for bounding boxes under rational motion

This paper presents a simple yet precise and efficient algorithm for collision prediction of two oriented bounding boxes under univariate (piecewise) rational motion. We present an analytic solution to the problem of finding the time of collision and the feature involved, or declaring that no collision should occur. Our solution can be applied to boxes of any size, under arbitrary rational rigid motion. The algorithm is based on the efficient examination of the Minkowski sum (MS) of the two boxes, using a spherical Gauss map dual representation, and a precise extraction of the collision time, if any, as a solution to a set of rational equations that are automatically derived. © 2006 IEEE.published_or_final_versio

CCQ: Efficient Local Planning Using Connection Collision Query

Abstract We introduce a novel proximity query, called connection collision query (CCQ), and use it for efficient and exact local planning in sampling-based motion planners. Given two collision-free configurations, CCQ checks whether these con-figurations can be connected by a given continuous path that either lies completely in the free space or penetrates any obstacle by at most ε, a given threshold. Our approach is general, robust, and can handle different continuous path formulations. We have integrated the CCQ algorithm with sampling-based motion planners and can perform reliable local planning queries with little performance degradation, as compared to prior methods. Moreover, the CCQ-based exact local planner is about an order of magnitude faster than prior exact local planning algorithms.

Uniform accelerated motions

An Affine matrix which maps an initial and final pose can be computed by solving a system of linear equations. Then there exists an interesting problem of finding a time varying affinity which maps the given set of poses and if it exists is always unique and should hold some interesting properites such as affine-invariant, reversible, preserve rigidity, similarities and volume. The Steady Affine Motions and Morphs (SAM) introduced by Jarek Rossignac and Alvar Vinacua solved this problem of time varying affinity and defines the quality of such affinity by the term steadiness. Until SAM, no mathematical definition of steadiness was available and intuitively SAM defined a steady animation to be continuous, to vary dimensions and angles monotonically and rather uniformly, and to move points along pleasing arcs that are free of unnecessary kinks or loops. The authors defined the term ”Steady” as a constant velocity motion in the local moving frame. SAM creates pleasing in-betweening motions that interpolates between an initial and final pose, B and C and the derived equation of beauty was At B with A = C B·-1. SAM is affine-invariant, reversible, preserves isometries (i.e., rigidity), similarities and volume. Previously proposed approaches came up with a solution for the time varying affinity problem, but there was no proper definition of how beautiful or how good the motion was. With the advent of SAM, the beauty of a motion can now be measured by the unsteadiness and Steady Affine motions and morphs is the one solution which comes to have a value of zero for the unsteadiness term. Uniform Accelerated Motions (UAM) carries forward the above definition of steadiness into a constant acceleration motion in the local moving frame. The time varying affinity At is computed using closed form expressions and some of its interesting properties are studied. The constant acceleration motion (in local frame) in UAM is then compared with the constant velocity motion (in local frame) of SAM and the resuls are discussed

Computing and Visualizing Pose-Interpolating 3D Motions

CAD and animation systems offer a variety of techniques for designing and animating arbitrary movements of rigid bodies. Such tools are essential for planning, analyzing, and demonstrating assembly and disassembly procedures of manufactured products. In this paper, we advocate the use of screw motions for such applications, because of their simplicity, flexibility, uniqueness, and computational advantages. Two arbitrary control-poses of an object are interpolated by a screw motion, which, in general, is unique and combines a minimum-angle rotation around an axis A with a translation by a vector parallel to A. We explain the advantages of screw motions for the intuitive design and local refinement of complex motions. We present a new, simple and efficient algorithm for computing the parameters of a screw motion that interpolates any two control-poses and explain how to use it to produce animations of the moving objects. Finally, we discuss a new and efficient variant of a known procedure for computing a set of faces which may be used to display the 3D region swept by a polyhedron that moves along a screw motion

Constructive Lattice Geometry

Lattice structures are widespread in product and architectural design. Recent work has demonstrated the printing of nano-scale lattices. However, an anticipated increase in product complexity will require the storage, processing, and design of lattices with orders of magnitude more elements than current Computer-Aided Design (CAD) software can manage. To address this, we propose a class of highly regular lattices called Steady Lattices, which due to their regularity, provide opportunities for highly compressed storage, accelerated processing, and intuitive design. Special cases of steady lattices are also presented, which provide varying degrees of compromise between design freedom and geometric regularity. For example, the commonly used regular lattices, which provide little design freedom but offer maximum regularity, are the least general form of steady lattice. We propose the 2-directional, Bent Corner-Operated Trans-Similar (BeCOTS) lattices as a useful compromise between regular lattices and fully general steady lattices. A BeCOTS lattice may be controlled by four non-coplanar points, which represent four corners of the lattice. The Trans-Similar property ensures that a BeCOTS lattice is composed of groups of beams such that each consecutive pair of groups of beams along a particular direction is related by the same similarity. Trans-Similarity also enables constant-time queries such as surface area calculation, volume calculation, and point-membership classification. We take advantage of the regularity in steady lattices to efficiently produce and query highly complex lattice structures that we call Constructive Lattice Geometry (CLG), where CLG is an extension of traditional Constructive Solid Geometry (CSG). CLG models are periodic CSG models for which regular patterns of primitives are combined into many repeating CSG microstructures that are ultimately combined into one CSG macrostructure. We provide strategies for designing and processing recursively defined CLG models to enable the creation of CLG models composed of smaller CLG models. Parameterized steady lattices and CLG models may be defined by a few lines of code, which facilitates lazy (on-demand) evaluation, massively parallel processing, interactive editing, and algorithmic optimization.Ph.D

Design and implementation of a modular controller for robotic machines

This research focused on the design and implementation of an Intelligent Modular Controller (IMC) architecture designed to be reconfigurable over a robust network. The design incorporates novel communication, hardware, and software architectures. This was motivated by current industrial needs for distributed control systems due to growing demand for less complexity, more processing power, flexibility, and greater fault tolerance. To this end, three main contributions were made. Most distributed control architectures depend on multi-tier heterogeneous communication networks requiring linking devices and/or complex middleware. In this study, first, a communication architecture was proposed and implemented with a homogenous network employing the ubiquitous Ethernet for both real-time and non real-time communication. This was achieved by a producer-consumer coordination model for real-time data communication over a segmented network, and a client-server model for point-to-point transactions. The protocols deployed use a Time-Triggered (TT) approach to schedule real-time tasks on the network. Unlike other TT approaches, the scheduling mechanism does not need to be configured explicitly when controller nodes are added or removed. An implicit clock synchronization technique was also developed to complement the architecture. Second, a reconfigurable mechanism based on an auto-configuration protocol was developed. Modules on the network use this protocol to automatically detect themselves, establish communication, and negotiate for a desired configuration. Third, the research demonstrated hardware/software co-design as a contribution to the growing discipline of mechatronics. The IMC consists of a motion controller board designed and prototyped in-house, and a Java microcontroller. An IMC is mapped to each machine/robot axis, and an additional IMC can be configured to serve as a real-time coordinator. The entire architecture was implemented in Java, thus reinforcing uniformity, simplicity, modularity, and openness. Evaluation results showed the potential of the flexible controller to meet medium to high performance machining requirements

Refinement of object-based segmentation

Automated object-based segmentation methods calculate the shape and pose of anatomical structures of interest. These methods require modeling both the geometry and object-relative image intensity patterns of target structures. Many object-based segmentation methods minimize a non-convex function and risk failure due to convergence to a local minimum. This dissertation presents three refinements to existing object-based segmentation methods. The first refinement mitigates the risk of local minima by initializing the segmentation closely to the correct answer. The initialization searches pose- and shape-spaces for the object that best matches user specified points on three designated image slices. Thus-initialized m-rep based segmentations of the bladder from CT are frequently better than segmentations reported elsewhere. The second refinement is a statistical test on object-relative intensity patterns that allows estimation of the local credibility of a segmentation. This test effectively identifies regions with local segmentation errors in m-rep based segmentations of the bladder and prostate from CT. The third refinement is a method for shape interpolation that is based on changes in the position and orientation of samples and that tends to be more shape-preserving than a competing linear method. This interpolation can be used with dynamic structures and to understand changes between segmentations of an object in atlas and target images. Together, these refinements aid in the segmentation of a dense collection of targets via a hybrid of object-based and atlas-based methods. The first refinement increases the probability of successful object-based segmentations of the subset of targets for which such methods are appropriate, the second increases the user's confidence that those object-based segmentations are correct, and the third is used to transfer the object-based segmentations to an atlas-based method that will be used to segment the remainder of the targets