Donald J. McTavish

Shock Response of a Damped Linear Structure Using GHM Finite Elements

The use of “GHM” finite-elements is a technique that can be used to incorporate general linear viscoelastic behaviour, i.e., general linear damping, into time-domain structural dynamics models. The original second-order form of the method has been published previously. This paper introduces the use of the first-order form of the GHM method. This first-order form and its second-order predecessor support and encourage the incorporation of measured material linear viscoelastic behaviour. The constant coecient form necessary for statespace methods is retained, while additional coordinates are added to represent the material properties. The use of a selectable number of modulus function terms allows arbitrarily good representation of general viscoelastic behaviour over a given spectrum of known material response. The method is applied to a prototype shock response problem. This class of problem is significant in that the excitation and therefore the dynamic response is “broadband”. A model that incorporates material damping must be similarly broadband in its representation of material behavior, otherwise the model will be incapable of producing a consistent prediction of structural response. In the sample problem, the GHM model is applied to actual viscoelastic material whose behaviour is neither simple viscous nor simple hysteretic. Damping in Finite-Element Analysis

Stability Improvement of Vision Algorithms

This paper presents and demonstrates an automated generic approach to improving the accuracy and stability of iterative pose estimation in computer vision applications. The class of problem involves the use of calibrated CCD camera video imagery to compute the pose of a slowly moving object based on an arrangement of visual targets on the surface of the object. The basis of stereo-vision algorithms is to minimize a re-projection error cost function. The proposed method estimates the optimal target locations within the area of interest. The optimal target configuration delivers the minimal condition number of the linear system associated with the iterative algorithm. The method is demonstrated for the case when targets are located within a 3D domain. Two pose estimation algorithms are compared: single camera and two-camera algorithms. A better accuracy in pose estimation can be achieved with a single camera algorithm with optimized target locations. Also, this method can be applied to perform optimization of target locations attached to a 2D surface.

Practical Large-Motion Modeling of Geometrically Complex Flexible Vehicles

This paper introduces a powerful convenience method for automatically building largemotion models of flexible bodies of general structural form (not just beams). The starting point is the assembled standard mass matrix of a small-motion finite-element model. The goal point is a fully-coupled, all-terms-included large motion model that incorporates the same arbitrarily detailed structural geometry as the source finite-element model. An explicit straightforward procedure is provided for constructing both full and reduced-order models of flexible bodies that are able to undergo arbitrary displacement and rotation. The body translational and angular velocities are allowed to be large. Within the context of small deformations, all terms of the equations of motion are included. A standard finite-element small (absolute) motion model is used as the base model from which the equations of motion of the unrestrained body are derived. A fully consistent inertia formulation is assumed and encouraged; rotational coordinates are naturally admitted; and no low-level knowledge of the finite-element nodal shape functions is required. Lumped-mass formulations are included as a special sub-class. Automatic generic approximation is used for certain shape function products that cannot be directly extracted from the mass matrix of the small motion model. The critical strategy used to produce the approximations is called the “LISA Method” (Localized Implicit Shape-Function Approximation). The LISA Method has been demonstrated to reproduce exact results for a number of practical element types.

CONTINUUM SHAPE CONSTRAINT ANALYSIS: A CLASS OF INTEGRAL SHAPE PROPERTIES APPLICABLE TO LIDAR/ICP-BASED POSE ESTIMATION

Surface registration involving the estimation of a rigid transformation (pose) which aligns a model provided as a triangulated mesh with a set of discrete points (range data) sampled from the actual object is a core task in computer vision. This paper refines and explores the previously introduced notion of Continuum Shape Constraint Analysis (CSCA) which allows the assessment of object shape towards predicting the performance of surface registration algorithms. Conceived for computer-vision assisted spacecraft rendezvous analysis, the approach was developed for blanket or localized scanning by LIDAR or similar range-finding scanner that samples non-specific points from the object across an area. Based on the use of Iterative Closest-Point Algorithm (ICP) for pose estimation, CSCA is applied to a surface-based self-registration cost function which takes into account the direction from which the surface is scanned. The continuum nature of the CSCA formulation generates a registration cost matrix and any derived metrics as pure shape properties of the object. For the context of directional scanning as considered in the paper, these properties also become functions of viewing direction and is directly applicable to the best view problem for LIDAR/ICP pose estimation. This paper introduces the Expectivity Index and uses it to illustrate the ability of the CSCA approach to identify productive views via the expected stability of the global minimum solution. Also demonstrated through the examples, CSCA can be used to produce visual maps of geometric constraint that facilitate human interpretation of the information about the shape. Like the ICP algorithm it supports, the CSCA approach processes shape information without the need for specific feature identification and is applicable to any type of object.

Development of Continuum Shape Constraint Analysis (CSCA) for Computer Vision Applications Using Range Data

This paper further presents continuum shape constraint analysis (CSCA) of surfaces. CSCA is a generalization of discrete-point based constraint analysis which can be used to predict performance of registration algorithms. A surface-based self-registration cost function to which constraint analysis can be applied is introduced. This cost function takes into account a direction the object is viewed at. A sample study is provided to illustrate this approach applied to the problem of pose estimation using range-data taken from a scanning instrument such as LIDAR. Specifically, CSCA is used to assess an object feature for suitability for local LIDAR scanning and subsequent application of the ICP (iterative closest-point) algorithm to determine pose. In this study, the constraint analysis uses noise amplification index (NAI) as an output measure. The continuum nature of the CSCA approach renders the registration cost matrix and the derived NAI as pure shape properties of the feature with a dependence on viewpoint.

Modeling of an Unconstrained Flexible Rocket Using Finite-Elements and the LISA Method

This paper describes the production of a finite-element based unconstrained motion model for a flexible rocket. The main contribution is a demonstration of the LISA Method, a procedure for transforming a detailed finite-element (small-motion) model directly into a large-motion model with all of its requisite inertia terms. The work is targeted at the problem of modeling flight vehicles, whether aircraft or spacecraft, but is applicable to any large-motion flexible structure modeling application. This methodology promotes a “model it as it is” approach that bypasses the traditional practice of structural simplification to beams or other degenerate structural forms when an unconstrained flexible model is required. The sample problem used to demonstrate the modeling methodology employs the SPHADS-1 rocket vehicle developed at Ryerson University. A source finite-element model of the vehicle was developed in ANSYS and the assembled mass and stiffness matrices exported. The LISA Method was applied to produce a full-detail, full-order large-motion model. To render it more amenable to simulation, a reduced-order dynamics model was then derived from the full-order model. The application of this model in a limited study of aeroelastic stability is described briefly.

A Dynamics Estimation Filter for Pose and Motion Estimation in Orbit

The fundamental task of a space vision system for rendezvous of satellites on-orbit is the real-time determination of the motion of the target satellite as observed from the chaser spacecraft. The usual task of a vision system is to return a snapshot and measurement of the targets position and orientation at a moment in time. Augmenting this architecture with an extended Kalman filter, incorporating a dynamic model and the ability to propagate motion, synthesizes a system that is more efficient and robust.