ledas solutions for mechanical system modeling and related problems egor ermolin (ledas)

LEDAS Solutions for Mechanical System Modelingand Related Problems

Egor Ermolin (LEDAS)

10 April 2008SBRAS/ Intel GeometrySeminar 22 | | 4242

Agenda

LEDAS CompanyLEDAS Phoenix and Related Projects:– History

Mechanical simulation engine– Functionality– Architecture: Dynamic Engine, Collision Detection, Collision

ResolutionImpulse-based Collision ResolutionGeometry:– Calculation of Dynamic Properties– Effective Collision Detection– Narrowing broad phase

DemosKey FeaturesDevelopment Perspective


LEDAS Company

PositioningMissionCompetenceCustomersIsicad-2008


Positioning of LEDAS

LEDAS Ltd. is an independent software development company founded in 1999 in Novosibirsk, RussiaUsing proprietary mathematical technologies, LEDAS provides computational components and services for software development companies in the fields of PLM (including CAD, CAM, CAE, PDM) and ERPThe company also provides services for manufacturers:– Custom application development, integration & localization– Creation of 3D models using different CAD systems– Consulting, reselling, trainings

Information on LEDAS is available at www.ledas.com


Mission

We at LEDAS perceive our mission as the automation of key industrial processes – design, simulation and planning– These are areas where system users

require a set of intelligent functions in order to accelerate product development and planning of related processes and resources

LEDAS does not develop end-user nor enterprise software, but it collaborates actively with both CAD/CAM/CAE/PDM software development companies andmanufacturing enterprises by offering them– Computational software components– Software development & 3D modeling– Consulting, reselling, training– Places where they can meet together

CAD/CAM/CAE/PDM development company

Manufacturing enterprise

LEDAS

Developm

ent

Marketing

Deploym

ent

Custom

ization


LEDAS Competence

Mathematics & Computer Science– Numerical analysis– Constraint satisfaction– Computational

geometry– Scheduling algorithms

Software Development– Development Processes– Quality Assurance– Available platforms– Programming skills– Software tools

CAD/CAM/CAE/PDM skills– Creation of 3D models– Custom application

development– Translation & localization– Certified training– Reselling– Consulting

Publishing & Conferencing– Web sites– Books– Conferences


LEDAS Customers

Dassault Systèmes (France)– Development of core computational components for CATIA V5 products– Software localization for Russian market– Total cost of development projects is about 80 person-years since 1999

Sukhoi Civil Aircrafts (Russia), AVTOVAZ (Russia), and others– Consulting & training on CATIA/CAA solutions– Custom software development (add-on applications for CATIA and NX) in the

field of computational geometry, data translation and CAD application integration

Proficiency (Israel), ADEM Technologies (Russia), AWV (Switzerland), Tecnos (Italy), Evo.Solutions (Japan), and others– Licensees of LEDAS Geometric Solver (LGS) software components– Cooperation on integration of LGS into different CAD applications: sketcher,

assembly design, data translationExigen (USA), CTRUE (Israel), and others– Development of advanced software packages based on LEDAS competence

in optimization algorithms, resource scheduling, and computational geometry

VirtualCAD (Canada)– Creation of libraries of parametric 3D models and web-catalogues of CAD

partsPurdue Unviversity (USA), Novosibirsk Technical University (Russia)– Education & research


Isicad-2008

Third international multi-vendor PLM forum– June 4-6, Novosibirsk, Russia

About 500 attendees representing large, medium and small manufacturing enterprisesMore than 30 CAD, CAM, CAE, PDM solution providers– Autodesk, Siemens PLM, PTC and

Dassault are traditional participants– All leading Russian CAD/PLM R&D

companiesLeading Russian mass mediaMulti-format– Invited talks– Plenary session talks– Technical section talks– Company’s seminar– Round table and press conference– Rich social program

More information at http://isicad.ru/2008


We are here


Mechanical simulation engine– Functionality– Architecture: Dynamic Engine, Collision Detection,

Collision ResolutionImpulse-based Collision ResolutionGeometry:– Calculation of Dynamic Properties– Effective Collision Detection– Narrowing broad phase



The Phoenix Project

The LEDAS Phoenix Project is oriented to a creation of competitive mechanical simulation engine with broad spectrum of applications

2003

2D prototype was implemented. Segments and circular arcs were usedfor a geometrical representation. Gravity, springs, user-defined forces,sliding friction.Collision detection and resolution.

2004

A full-scale 3D engine is under development. Simple 3D Collision detection.Scalable architecture

2005 3D Collision Detection is implemented

2007Convex Hull 3D and Minimal Bounding Box algorithms are implemented


A Mechanical Simulation Engine

Modeling of 2D/3D rigid bodies motion according to physical lawsModeling of forces with different nature– Gravity– Springs– Dynamically acting user-defined forces

Collision detection and resolution– Avoiding interpenetration

Motion modeling under geometrical constraints– Assembly constraints


Architecture

Application

Collision Resolution

DynamicEngine

Collision Detection

Rigid bodies data

Getting/updating coordinates and velocities

Getting a geometrical data

Getting a physical data

Updating velocities

Passing list of colliding bodies

Passing list of moved bodies

Getting list of colliding bodies


Dynamic Engine

Manages Collision Detection and Collision Resolution modules

Models motion of rigid bodies with account of external forces• Gravity• Springs• Dynamically acting user-defined forces

i

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Uses simple explicit difference scheme


Collision Resolution is aimed to correct rigid bodies velocities in order to avoid interpenetrationsKnown approaches

Collision Resolution

• Penalty method

• Constraints based techniques for contact resolution

• Impulse-based methods

Chosen approach


Basic assumptions– Collision time is infinitely small– Collision forces are infinitely large– Increments of impulses are finite

There are two phases of collision– Compression phase– Restitution phase

Total impulse obtained by a body during collision takes into account both phases:

Impulse-based approachInitial assumptions

Cp where is a coefficient of restitution, and impulse obtained during compression phase

CT pep )1( 10 e


Some definitions

Relative velocity at the point is calculated from first body to second: 12 vvvrel

Normal at collision point is taken from first body

Case scalar product :< 0 interpenetration point= 0 contact point> 0 leaving point

1nvrel


Approach Overview

Consider contact points with negative normal relative velocities, such that bodies are penetrating

mPP1

Assume that force acts in contact pointtpnF iii /iP

Express velocities of the bodies after a compression phase via unknown compression impulses

Consider contact points with negative normal relative velocities, such that bodies are penetrating

mPP1

Assume that force acts in contact pointtpnF iii /iP

With known expressions for velocities express relative normal velocities of the bodies in the contact point


Impulse-based approachLinear system

Condition of vanishing of the relative normal velocities at the end of the compression phase leads to the following linear mxm system of equations

bpA

We can obtain compression impulses via SVD-method and full impulses passed between bodies due to collision in i-th point is

iiT pep )1(,

ipiTp ,

After determination of the impulses we can compute new velocities of the bodies


Impulse-based approachIterative scheme

With known new velocities we should check other contact points for which initially no penetration occurredIf there are points in which the bodies are penetrating we repeat impulses computation for these new set of pointsAs practice showed this iterations are converged for e≤1


Joints Handling

This approach can be used for a modeling of jointsJoint is modeled via three (or two for 2D) collision points with e=0 considered on each time stepOn each time step relative velocities of the bodies in the joint point coincide

Impulses corrections have to be calculated from a condition of coordinates coincidence not velocities


We are here


Mechanical simulation engine– Functionality and applications– Architecture: Dynamic Engine, Collision Detection, Collision




From Dynamic to Geometry: Calculation Of Dynamic

Properties

Given a manifold 3D triangular mesh, we can compute mass and inertia tensor properties of encapsulated volume

Mirtich in 1996 proposed to use divergence and Green’s theorems to reduce complex 3D integral to line integrals:


Collision Detection

Broad phase: test collision for only for bodies which have bounding primitives intersectingSolution: encapsulate objects by simple shells with inexpensive intersection testOptimization of this phase: don’t check intersection for shells that obviously don’t intersect (rule?)

In 2D prototype implementation we use pair-wise check on broad phase using circles as bounding primitives


Collision Detection

Narrow phase: pair-wise element check – test each geometry primitive of one body with each another’s

Various space partitions can be applied to reduce number of pairs to check

In 2D prototype implementation we use direct check of all pairs

Detects collisions and returns coordinates of a contact points and normal vectors

It supports line segments and arcs as geometry primitives and uses direct collision detection with rejection of bodies which are situated far apart


Collision Detection 3D Implementation

Based on OBB-approach (inertia axis) in narrow phase, collision detection library OPCODE 1.3 is used for reference. Current implementation consumes less memory than OPCODE (about 10%), but is 1.7 times slower*. However, performance optimization was not the objectiveBroad phase uses O(n2) pairwise OBB-comparison. This stage can be optimized up-to O(nlogn) comparison (in practice O(n)), but even this is not top of high-performance…

* Data is based on LEDAS collision detection report (in Russian)


Collision Detection: narrowing broad phase

The problem is that OBB is usually better heuristics of bounding volume than AABB (in terms of volume), but it is not minimal bounding box for body in general case

The advantage is obvious: the less volume BB has, the less number of false narrow phase triggering will happen

AABB OBB Minimal BB

Which pattern better fits the broken window?


Finding Minimal Boxes: LEDAS Implementations

2D case only requires body to be convex, algorithm is quite straightforward and can be described by “rotating calipers” model3D case also operates on convex mesh and involves Gaussian sphere structure to test configuration. It requires polynomial trigonometric equation solver to find minimum of volume function


Computational effectiveness of BB

2D 3D

AABB O(n) O(n)

OBB O(n) O(n)

Minimal BBO(n) convex

O(nlogn) generalO(n3)

Minimal 3D BB with heuristics

- O(n2)

Conclusion: minimal BB can be used in applications which allow preprocessing and require maximum performance or have scenes with great number of objects


We are here






Demos

Unstable stack


Demos

Domino effect


Demos

Springs


Demos

Telescopic mast


Demos

Door latch


Demos

Engine


Demos

Jib


Demos

3D Collision


Industrial Application

Integration of Minimal Bound Box solution into CATIA (customer SCAC) is in processAt LEDAS convergence of BB code is performed


We are here






Key Features of Phoenix Project

Approach doesn’t need decomposition of bodies into convex partsAbsolute elastic (energy-preserving) and inelastic adjustabilityNative support of geometrical constraintsCollision detection in 3D with near-industrial characteristics is readyIf preprocessing allowed, bounding volumes can be very tight


Implementation Summary

2D dynamic engine with segment-arc geometry, resolves collision, supports springs and jointsComputation of mass and inertia properties for triangular mesh3D dynamic engine based on triangular meshes OBB collision detection3D convex hull module (Preparata’s divide-and-conquer)Module for calculating minimal bounding box for triangle mesh


Development Perspective

We have advanced results in mechanical modeling and computational geometry related problemsSome of our implementations already have applications, but our solutions have much greater potentialThus we are looking for partner/customer to bring our ideas to life

ledas solutions for mechanical system modeling and related problems egor ermolin (ledas)

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