Dynamics Simulation A Survey

1
Dynamics Simulation- A Survey -

• ???????/????
• 1997. 12.
• ? ? ?

2
Contents

• Introduction
• Preliminary
• Particle simulation
• Rigid body simulation
• Articulated figure
• Dynamics simulation in VR
• Conclusion

3
Introduction

• Dynamics
• describes real world simulations
• very large, complex description
• considers all environments variables such as
  gravity, friction and etc.
• Dynamics simulation
• object has force, torque and etc.
• generates realistic motion
• different from kinematic, behavior simulation

4
Preliminaries

• Physical simulations
• acceleration-based (penalty method)
• spring model, overlapping
• velocity-based (analytic method)
• contact force model (contact but not overlap)
• position-based
• potential energy function (lower energy)
• Representations
• particle - no mass
• polyhedra
• surface

5
Preliminary

• Solving methods
• Euler method
• Midpoint method

6
Particle simulation (1/5)

• The Planet Jupiter Yaeger86
• particle generation
• composites several images and converts to
  particle
• fluid dynamics
• atmosphere fixed velocity, incompressible, no
  vertical motion
• vorticity derived from the velocity of
  atmosphere
• the velocity of the particle bilinear
  interpolation of the velocity grid
• efficiency double-buffered I/O, vectoring
  operations(Cray)

7
Particle simulation (2/5)

• Data parallel computation Sims90
• particle
• position(head, tail), velocity, radius, color,
  opacity
• one particle is creating by allocating a new CM
  virtual processor
• particle behavior language
• an animator with levels of control
• operations position, velocity initialization,
  applied velocity(vortex, translate randomly),
  acceleration(gravity,spiral, etc.)
• particle rendering
• dicing into fragments parallel processors
• sorting fragments by pixel and depth

8
Particle simulation (3/5)

• Turbulent wind field Stam93
• model
• density distributions of particles
  (advection-diffusion eq.)
• wind field
• large scale simple wind field primitives
  (viscous fluid)
• small scale 3D random vector field varying over
  space and time (inverse FFT)
• rendering
• subdivide the ray into N disjoint intervals
• ray tracing for scattering effect

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Particle simulation (4/5)

• Diffusion process Stam95
• model density, temperature, velocity, radiative
• wind field
• advects(by velocity) and diffuses(by temperature)
  blobs of density over time
• diffusion
• blob warping method

10
Particle simulation (5/5)

• The motion of a hot, turbulent gas Foster97
• gas model
• interacts with solid objects
• volume representation (scalar temperature,scalar
  pressure,vector velocity)
• simulation
• due to convection(velocity), drag(each other),
  thermal buoyancy(temparature)
• subdivide the environment into regular voxels
• use boundary conditions for special effects
  close to object, gas cells next to boundary are
  heated

11
Rigid body simulation(1/5)

• Non-penetrating rigid bodies Baraff89-92,94
• analytical method for finding forces btw
  polyhedral bodies based on linear programming 89
• calculating correct contact forces
• non-penetration constraints
• linear programming (conditions are linear)
• heuristic solution methods
• guess contact points(vanishing) equal empty
• predicting a non-empty contact points
• finding approximations
• dealing with incorrect predictions
• calculating forces given contact points

12
Rigid body simulation(2/5)

• The contact forces btw curved surfaces 90
• surface twice-differential, without boundary
• body polyhedra convex curved surfaces
• collision detection contact points
  determination
• collision separating method
• contact points Newtons method (quadratic model)
• contact forces determination
• characteristic function - geometric constraint
• positive semidefinite linear complementary
  problem
• Lemkes algorithm

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Rigid body simulation(3/5)

• the motion of contacting bodies with friction 91
• the Coulomb model of friction static or dynamic
• dynamic friction Lemkes algorithm
• contact force determination for static friction
• approximation using the algorithm developed for
  simulating dynamic friction
• quadratic programming - the iterative technique
  for solution
• the dynamic simulation of flexible bodies 92
• first- and second-order polynomially deformable
  bodies
• collision detection some number of triangular
  patches
• fast contact force computation 94
• a mix of contact points with static and dynamic
  friction
• inequality-constrained nonlinear minimization
  problem

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Rigid body simulation (4/5)

• Placing curved surfaces Snyder95
• object patches parametric surface
• assumptions
• no velocity, only one body moves
• computing points of contact
• converging to a stable config.
• compute external pseudo-forces
• gravity, local, connect
• updating body placement
• external forces
• residual forces
• friction forces

15
Rigid body simulation (5/5)

• Spheres and polyhedra Milenkovic96
• generate piles or clumps of many objects
• linear programming
• smooth convex decompositions
• the union of a finite number of convex sets with
  smooth boundaries
• Minkowski sum
• computes the minimum energy configurations
• if energy function is linear, it can be
  accomplished using linear p/g
• eg)
• simplex method 80-90 optimal solution

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Articulated figure (1/6)

• Goal-directed, human walking Bruderlin89
• fundamental parameters for locomotion
• forward velocity, step length, step freq.
• KLAW(Keyframe-Less Animation of Walking)
• high-level step constraints (duration, final
  leg angles)
• normalization formula
• symmetry of steps - use step length, compute the
  final conditions
• state-phase timings - use step freq., the
  duration of stance and swing
• middle-level approximation forces and torques
• the coordination of motion
• states(double support, single support), phases
  (stance, swing)
• low-level generates actual motion
• lower body dynamics (lower body angles)
• upper body kinematics (arm swing, pelvic
  movement)

17
Articulated figure (2/6)

• Autonomous legged locomotion McKenna90
• CORPUS - A dynamic locomotion simulator
• gait(the sequence of the legs stepping and
  standing) controller
• coordinates the gait
• each leg is assigned an oscillator(rhythmically
  triggers the leg to step)
• reflexes(trigger or retard) are modeled as
  conditional units
• motor programs
• generate the forces required stepping and stance
• stepping program compute the forces to lift the
  leg up and forward
• stance program supplies the forces needed to
  support the body via legs and propel it forward
• dynamic simulator
• compute the accelerations of the joints

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Articulated figure (3/6)

• Dynamic legged locomotion Raibert91
• animation process
• desired behavior speed, gait, path, etc.
• control actuators
• hopping - altitude of the hop
• speed - find displacement and determine the joint
  angles
• posture - generate torques
• modeling
• a tree of rigid bodies connected to joints
• next state finite state machine
• the equations of motion were integrated
  using Eulers method

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Articulated figure (4/6)

• Sensor-actuator networks van de Panne 93
• configurations
• simple sensors and actuators
• sensors touch, angle, eye, length
• actuator angle, length
• SANs
• provide control by connecting sensors to
  actuators through a network of weighted
  conn.
• network synthesis
• Phase 1 random generation and evaluation
• Phase 2 fine tuning
• adjust weights

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Articulated figure (5/6)

• Lagrange Multipliers Baraff 96
• characteristics
• treat bodies, forces and constraints as
  anonymously as possible
• does not rely on matrix bandwidth
• bodies need not be rigid
• formulation
• primary constraints equality constraints btw
  bodies
• auxiliary constraints inequality constraints
• smaller, dense matrices block-matrix
• eg) bodys dimension - the number of d.o.f.
• solving sparse matrix O(n)

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Articulated figure (6/6)

• Human athletics adapting behavior
  Hodgins95,97
• human athletics
• dynamic behaviors
• state machine - determine the control actions
• transition event - by active leg
• higher-level behaviors group behaviors
• secondary motions
• simulated sweatpants and splashing water (elastic
  model)
• adapting behavior
• control system parameters are scaled
• size, mass, moment of inertia
• find-tuned using search process
• forward speed, flight duration, balance

22
Dynamics simulation in VR

• Difficulties
• object/environment representation
• simulation time-step
• Solutions
• preprocessing
• parallel computation
• special purpose hardware

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Conclusion

• Dynamics simulation
• particle
• rigid body
• articulated figure
• More advanced simulation techniques are needed
  for VR