Title: HighFidelity Haptic Synthesis of Contact with Deformable Bodies
1High-Fidelity Haptic Synthesis of Contact with
Deformable Bodies
- Jaeyoung Cheon
- icejae02_at_postech.ac.kr
- VR Lab, POSTECH
- 2006. 6. 5
2Outline
- Introduction
- Simulating Soft Objects
- Response Synthesis
- Local Force Field Continuum
- Passivity
- Conclusion
3Introduction
4Introduction 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
5Simulating 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.
6Simulating 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.
7Simulating Soft Objects
8Simulating 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
9Response 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
10Response 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.
11Local 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
12Local Force Field Continuum Sticking State
13Local 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)
14Local 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
15Local Force Field Continuum The Force at
Contact Point
16Local 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.
17Local Force Field Continuum Reconstruction of
The Continuum
18Local 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
19Passivity
- 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
20Passivity 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
21Conclusion
- 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.
22References
- 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.
23Supplement 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.