LEDAS Solutions for Mechanical System Modeling

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• LEDAS Solutions for Mechanical System Modeling
• and Related Problems

Egor Ermolin (LEDAS)
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Agenda

• LEDAS Company
• LEDAS Phoenix and Related Projects
• History
• Mechanical simulation engine
• Functionality
• Architecture Dynamic Engine, Collision
  Detection, Collision Resolution
• Impulse-based Collision Resolution
• Geometry
• Calculation of Dynamic Properties
• Effective Collision Detection
• Narrowing broad phase
• Demos
• Key Features
• Development Perspective

3
LEDAS Company

• Positioning
• Mission
• Competence
• Customers
• Isicad-2008

4
Positioning of LEDAS

• LEDAS Ltd. is an independent software development
  company founded in 1999 in Novosibirsk, Russia
• Using proprietary mathematical technologies,
  LEDAS provides computational components and
  services for software development companies in
  the fields of PLM (including CAD, CAM, CAE, PDM)
  and ERP
• The 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

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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
Development
Marketing
LEDAS
Deployment
Customization
Manufacturing enterprise
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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

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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
  translation
• Exigen (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 parts
• Purdue Unviversity (USA), Novosibirsk Technical
  University (Russia)
• Education research

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Isicad-2008

• Third international multi-vendor PLM forum
• June 4-6, Novosibirsk, Russia
• About 500 attendees representing large, medium
  and small manufacturing enterprises
• More than 30 CAD, CAM, CAE, PDM solution
  providers
• Autodesk, Siemens PLM, PTC and Dassault are
  traditional participants
• All leading Russian CAD/PLM RD companies
• Leading Russian mass media
• Multi-format
• Invited talks
• Plenary session talks
• Technical section talks
• Companys seminar
• Round table and press conference
• Rich social program
• More information at http//isicad.ru/2008

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We are here

• LEDAS Company
• LEDAS Phoenix and Related Projects
• History
• Mechanical simulation engine
• Functionality
• Architecture Dynamic Engine, Collision
  Detection, Collision Resolution
• Impulse-based Collision Resolution
• Geometry
• Calculation of Dynamic Properties
• Effective Collision Detection
• Narrowing broad phase
• Demos
• Key Features
• Development Perspective

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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 used for 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
2007 Convex Hull 3D and Minimal Bounding Box algorithms are implemented
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A Mechanical Simulation Engine

• Modeling of 2D/3D rigid bodies motion according
  to physical laws
• Modeling 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

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Architecture
Application
Rigid bodies data
Getting a geometrical data
Getting/updating coordinates and velocities
Getting a physical data Updating velocities
Collision Detection
Collision Resolution
Dynamic Engine
Passing list of colliding bodies
Passing list of moved bodies Getting list of
colliding bodies
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Dynamic Engine

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

• Manages Collision Detection and Collision
  Resolution modules

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Collision Resolution

• Collision Resolution is aimed to correct rigid
  bodies velocities in order to avoid
  interpenetrations
• Known approaches

Chosen approach
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Impulse-based approachInitial assumptions

• 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

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

• Relative velocity at the point is calculated from
  first body to second

• Normal at collision point is taken from first body

• Case scalar product
• lt 0 interpenetration point
• 0 contact point
• gt 0 leaving point

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Approach Overview

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

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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

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

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Impulse-based approachIterative scheme

• With known new velocities we should check other
  contact points for which initially no penetration
  occurred
• If there are points in which the bodies are
  penetrating we repeat impulses computation for
  these new set of points
• As practice showed this iterations are converged
  for e1

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Joints Handling

• This approach can be used for a modeling of
  joints
• Joint is modeled via three (or two for 2D)
  collision points with e0 considered on each time
  step
• On 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

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We are here

• LEDAS Company
• LEDAS Phoenix and Related Projects
• History
• Mechanical simulation engine
• Functionality and applications
• Architecture Dynamic Engine, Collision
  Detection, Collision Resolution
• Impulse-based Collision Resolution
• Geometry
• Calculation of Dynamic Properties
• Effective Collision Detection
• Narrowing broad phase
• Demos
• Key Features
• Development Perspective

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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 Greens theorems to reduce complex 3D
  integral to line integrals

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Collision Detection

• Broad phase test collision for only for bodies
  which have bounding primitives intersecting
• Solution encapsulate objects by simple shells
  with inexpensive intersection test
• Optimization of this phase dont check
  intersection for shells that obviously dont
  intersect (rule?)

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

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Collision Detection

• Narrow phase pair-wise element check test each
  geometry primitive of one body with each anothers

• 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

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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 objective
• Broad 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)
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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

• Which pattern better fits the broken window?

AABB OBB Minimal BB

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

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Finding Minimal Boxes LEDAS Implementations

• 2D case only requires body to be convex,
  algorithm is quite straightforward and can be
  described by rotating calipers model
• 3D 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

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Computational effectiveness of BB
2D 3D
AABB O(n) O(n)
OBB O(n) O(n)
Minimal BB O(n) convex O(nlogn) general O(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

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We are here

• LEDAS Company
• LEDAS Phoenix and Related Projects
• History
• Mechanical simulation engine
• Functionality and applications
• Architecture Dynamic Engine, Collision
  Detection, Collision Resolution
• Impulse-based Collision Resolution
• Geometry
• Calculation of Dynamic Properties
• Effective Collision Detection
• Narrowing broad phase
• Demos
• Key Features
• Development Perspective

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Demos
Unstable stack
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Demos
Domino effect
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Demos
Springs
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Demos
Telescopic mast
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Demos
Door latch
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Demos
Engine
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Demos
Jib
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Demos
3D Collision
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Industrial Application

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

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We are here

• LEDAS Company
• LEDAS Phoenix and Related Projects
• History
• Mechanical simulation engine
• Functionality and applications
• Architecture Dynamic Engine, Collision
  Detection, Collision Resolution
• Impulse-based Collision Resolution
• Geometry
• Calculation of Dynamic Properties
• Effective Collision Detection
• Narrowing broad phase
• Demos
• Key Features
• Development Perspective

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Key Features of Phoenix Project

• Approach doesnt need decomposition of bodies
  into convex parts
• Absolute elastic (energy-preserving) and
  inelastic adjustability
• Native support of geometrical constraints
• Collision detection in 3D with near-industrial
  characteristics is ready
• If preprocessing allowed, bounding volumes can be
  very tight

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Implementation Summary

• 2D dynamic engine with segment-arc geometry,
  resolves collision, supports springs and joints
• Computation of mass and inertia properties for
  triangular mesh
• 3D dynamic engine based on triangular meshes OBB
  collision detection
• 3D convex hull module (Preparatas
  divide-and-conquer)
• Module for calculating minimal bounding box for
  triangle mesh

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Development Perspective

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