HighFidelity Haptic Synthesis of Contact with Deformable Bodies

1
High-Fidelity Haptic Synthesis of Contact with
Deformable Bodies

• Jaeyoung Cheon
• icejae02_at_postech.ac.kr
• VR Lab, POSTECH
• 2006. 6. 5

2
Outline

• Introduction
• Simulating Soft Objects
• Response Synthesis
• Local Force Field Continuum
• Passivity
• Conclusion

3
Introduction
4
Introduction Requirements of High-fidelity
Haptic Synthesis

• Resemblance of virtual force response with actual
  responses
• Force continuity under all allowed maneuvers
• Passivity of the virtual environment
• High-force update rate to combat the adverse
  effects of discretization

5
Simulating Soft Objects Considerations for
Haptic Rendering

• Rigid object
• Location, geometry, texture, frictional
  properties, etc.
• Deformable object
• Considerations of rigid object
• Materials, support, internal structure, etc.

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Simulating Soft Objects Previous approach

• Assume that contact occurs at one, or at a small
  number of points
• Localized deformation
• The force of contact and the feel depend
  critically on the details of the shape of the
  object in contact
• Localized deformation can be neglected.
• By St. Venants principle
• If a deformable body is loosely supported, one is
  permitted to ignore the contact details.
• If it is well supported, the contact details
  dominate.

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Simulating Soft Objects
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Simulating Soft Objects

• For deformable bodies, the point contact
  representation for realistic virtual interactions
  with deformable bodies is an idealization that is
  neither necessary nor sufficient.
• Key Aspects for High-fidelity Haptic Rendering
• The shape of the tool
• The way it makes contact with the body

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Response Synthesis

• Common Method
• To encode the virtual objects properties
• To predict the contact responses by solving the
  continuum equations of deformation
• The cost is heavy, thus it requires
  simplification.
• Two Types of Approach to Speed Up
• To represent high-order dynamic deformation
  models
• The contact problem can be over simplified.
• To precalculate a large number of responses
• Effective but cannot represent nonlinear aspects

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Response Synthesis The Proposed Method

• A precalculation method for non-linear contact
  problems
• Properties
• The number of precomputation steps is
  proportional to
• The number of possible cases of interaction
• The number of dimensions considered
• The precomputation burden can be reduced.
• The storage requirements are acceptable.

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Local Force Field Continuum Sticking State

• There is no need to compute its shape during
  deformation after sticking state until slipping
  occurs.
• Local force field at c for p
• c The initial contact point on the body surface
• p The corresponding point on the tool surface
• These are the only quantities required to
  determine the subsequent response

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Local Force Field Continuum Sticking State
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Local Force Field Continuum The Force at
Contact Point

• fc(d)fcx(dcx)ucxfcy(dcy)ucyfcz(dcz)ucz
• Ucucx, ucy, ucz Local coordinate system
• fcx(dcx), fcy(dcy), fcz(dcz) The
  force-deflection curves
• d(t)p(t)-c(t) Deflection
• p(t) p changes according to the movements of the
  tool
• c(t) c changes when the tool slides over the
  body

Instrument
c(t)
Deformable Body
d(t)
p(t)
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Local Force Field Continuum Sliding State

• fcr(dcr) µc(dcz) fcz(dcz)
• µ Coefficient of friction
• fcr, dcr The respective projections of fc and
  dc on the surface of the undeformed body
• c moves over the body surface such that dr lt
  dcr

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Local Force Field Continuum The Force at
Contact Point
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Local Force Field Continuum Reconstruction of
The Continuum

• It is required that an interpolation method to
  generate all possible responses from a finite
  set.
• Division of the surface into triangular patches
• Two-step process
• Interpolate the coordinate bases
• Interpolate the components
• Weight of interpolation is determined by
  barycentric coordinate.

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Local Force Field Continuum Reconstruction of
The Continuum
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Local Force Field Continuum Arbitrary Tool
Contacts

• Cartesian product of two sets of initial contact
  points
• One on the tool
• One on the body

Instrument patch
Body patch
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Passivity

• High update rate can resolve passivity problems.
• But attempting to run all haptic simulations at a
  high rate clearly is a great limitation.
• Multirate Design for Passivity
• High Rate Process
• To evaluate interpolation equations
• To supply forces to the device
• Lower Rate Process
• To supply local data to the high rate process
• i.e. Collision detection

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Passivity Multirate Design - Patch Update

• Aspect of Continuity
• Well preserved
• Aspect of Passivity
• Delayed collision detection causes
• Deflection inconsistency
• Tangential force inconsistency
• Frictionless sliding movement on the surface of a
  nonhomogeneous body with constant penetration

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Conclusion

• The continuum reconstruction approach enables
• To create high-fidelity haptic simulation
• To reproduce many nonlinear effects of interest
  to surgical simulation
• Limitations
• The simulation of contact conditions that have
  been precomputed is available.
• It can not simulate permanent changes.
• It does not consider introducing new surfaces at
  runtime.

22
References

• M. Mahvash and V. Hayward, "High-Fidelity Haptic
  Synthesis of Contact with Deformable Bodies,"
  IEEE Computer Graphics and Applications, vol. 24,
  pp. 48-55, 2004.

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Supplement St. Venants Principle

• Definitions
• The difference between the stresses caused by
  statically equivalent load systems is
  insignificant at distances greater than the
  largest dimension of the area over which the
  loads are acting.
• The localized effects caused by any load acting
  on the body will dissipate or smooth out within
  regions that are sufficiently away from the
  location of the load.
• Statically equivalent systems of forces produce
  the same stresses and strains within a body
  except in the immediate region where the loads
  are applied.