physics-based dlo simulation and it’s application...
TRANSCRIPT
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Simon Fraser UniversityBurnaby, Canada
Hans Fuhan Shi and Shahram Payandeh
Simon Fraser UniversityBurnaby, Canada
Physics-based DLO Simulation and It’s Application in Suturing
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Simon Fraser UniversityBurnaby, CanadaOutline
• DLO Model description– External forces– Internal forces– Force propagation
• Real-time knotting and unknotting– Collision detection– Collision management
• Knotting and unknotting case study and result– Force study– Knotting– Unknotting
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Simon Fraser UniversityBurnaby, CanadaModel Description
• Mass Points - physics– A sequence of mass points laying on
the centre line of the suture• Cylinder - geometry
– During graphic rendering, we use cylinder as segment to connect two successive points
• Forces - Haptic– To computer the configuration of the
suture, we need to obtain the net force acting on each point, and then use Euler method to get the positions.
Rope model
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Simon Fraser UniversityBurnaby, CanadaModel Description
- External Forces• Input forces
– by the user with the grippers• Friction forces
– during knotting or unknotting• Contact forces
– Self contact – Obstacle– Used to computer friction forces
• Gravitational force
- Mass of one mass point
Where
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Simon Fraser UniversityBurnaby, CanadaUser Input Force
• Virtual coupling technique – introduces a spring-
damper between a simulated body and the device end effecter
– we can use different constants for computing the output force for the device versus the input force for the simulated body Virtual Coupling
Reference: J.E. Colgate, M.C. Stanley, J.M. Brown, Issues in the haptic display of tool use, Intelligent Robots and Systems 95
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Simon Fraser UniversityBurnaby, CanadaFriction
• Friction force – Static Friction (not implemented in this
project)– Kinematic Friction– Relative velocity of contact points
Two sliding segmentsSuppose F is a point along segment
E is a point along segmentThen, the velocities of point E and F are:
- the fraction of point F along segment- the fraction of point E along segment
The relative velocity of point E and F is: Intersection of two segments in contact
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Simon Fraser UniversityBurnaby, CanadaFriction – cont.
• Friction force – Direction of Friction
- Relative velocity- Unit vector from point E to F
– Normal Force
- Spring constant
- Rope radius
- Distance between center lines of two segments
- Damper constant- Relative velocity- Unit vector of normal force
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ˆ ˆ( (2 ) ( ))rs rdk r d k= − −n rf v n ni
ˆ ˆ( )ˆ .ˆ ˆ|| ( ) ||
−= −−
r rf
r r
v v n nev v n n
i
i
E
F
rv
ˆ ˆ( )−r rv v n ni
n̂
ˆ ˆ( )rv n ni
ˆ feDirection of Friction
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Simon Fraser UniversityBurnaby, CanadaFriction – cont.
• Friction force – Kinematic Friction
- Friction constant
- Normal force- Friction direction vector
Where
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Simon Fraser UniversityBurnaby, CanadaInternal Forces
• Linear spring force
Where
where
• Linear damper
- Rest length of rope segment
- Linear spring constant
- Current length of rope segmentLinear Spring
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1 ˆ ,iv + = ⋅i+1 iv e ˆiv = ⋅i iv e
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Simon Fraser UniversityBurnaby, CanadaInternal Forces - cont.
• Torsional spring
- unit vectors of directions of
Where
Torsional spring
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ˆ ˆ ˆ ˆarcsin(|| ||) 0ˆ ˆ ˆ ˆarcsin(|| ||) 0
ifif
απ
⋅ ⋅ >⎧= ⎨ − ⋅ ⋅ <⎩
i-1 i i-1 i
i-1 i i-1 i
e e e ee e e e
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Simon Fraser UniversityBurnaby, CanadaInternal Forces - cont.
• Torsional damper
where
- Torsional damper constant
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1ˆ ,iv − = ⋅i-1 i-1v t ˆ ,ibv = ⋅i i-1v t ˆ ,iav += ⋅i i 1v t 1
ˆ .iv + + += ⋅i 1 i 1v t
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Simon Fraser UniversityBurnaby, CanadaInternal Forces - cont.
• Swivel damper
Where
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Simon Fraser UniversityBurnaby, CanadaForce Propagation
- Maximum length
- Minimum length
• Consideration:Prevent suture from being stretched too long or
compressed too short:
• Condition A – No propagation of user input force
if
All the user input forces have been converted to internal forces
Suturing segment model
Pulling with one hand
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Simon Fraser UniversityBurnaby, Canada
Force Propagation – cont.
Pulling with one hand
where
- Expected length of the segment
– Force computation
where- User input force,
- Force component which creates motion
- Force component which propagated,
- the segment direction vector
• Condition B– Pulling with one hand
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ˆ ˆ( )= ⋅p h i if f e eˆ ˆ( )m m m= ⋅hf f e e
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Simon Fraser UniversityBurnaby, CanadaForce Propagation –
cont.• Condition C (Pulling two points)
– Force computation method is same as in condition B.– Starting from point to – Second compute from to
Pulling with two hands
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Simon Fraser UniversityBurnaby, Canada
Collision Detection and Management
– Bounding-Volume Hierarchy( BVH )• Self-collisions• Collision with other objects
BVH of a suture with five segments
– Collision Management• If segment distance each segment
move away with Where,is safety margin.
• Velocity calculation – applying impulses to segment end points
- Impulse
- Normal force
- Time interval
Where,
Two sliding segments
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Simon Fraser UniversityBurnaby, Canada
Collision Management – cont.
– Collision Management• Velocity calculation
- Fraction of point F along Where,
- Fraction of point E along - Mass of one point- Unit vector of normal force
Reference: R. Bridson, R. Fedkiw, J. Anderson, Robust treatment of collisions,contact and friction for cloth animation 2002
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Condition - rope swings freely
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Spring Force - acting on one node (15th in this example)
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Spring Damper Forces
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Torsional Spring Forces
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Torsional Damper Forces
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Swivel Damper Forces
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Friction - sliding over itself (one contact point)
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Friction
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ˆ ˆ( )ˆ .ˆ ˆ|| ( ) ||
−= −−
r rf
r r
v v n nev v n n
i
iˆ ˆ( (2 ) ( ))rs rdk r d k= − −n rf v n ni
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Friction
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Friction
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Simon Fraser UniversityBurnaby, CanadaForce Study
• Friction
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Simon Fraser UniversityBurnaby, CanadaCase Study and Result –
cont.• Knotting Experiments
– We build several different models with various combinations of component forces
– Model 1• Linear spring• Linear damper
Fig.1 of Model 1 Fig.2 of Model 1
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Simon Fraser UniversityBurnaby, CanadaKnotting Experiments –
cont.
– Model 2: Same as model 1 with added torsional spring
Fig.1 of Model 2 Fig.2 of Model 2
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Simon Fraser UniversityBurnaby, CanadaKnotting Experiments –
cont.
– Model 3: Same as model 2 with added torsional damper
Fig.1 of Model 3 Fig.2 of Model 3
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Simon Fraser UniversityBurnaby, CanadaKnotting Experiments–
cont.
– Model 4: Same as model 3 with added swivel damper
Fig.1 of Model 4 Fig.2 of Model 4
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Simon Fraser UniversityBurnaby, Canada
Knotting Experiments–
• Conclusion: – model 4 is the most realistic model– We take model 4 for the following experiments
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Simon Fraser UniversityBurnaby, CanadaCase Study and Result –
cont.• Force propagation Experiments
– Take model 4 as example– Plot the output forces which feed the haptic device in each
haptic update frame during pulling– One Hand Pulling
Screen shot of one hand pulling Force plot of one hand pulling
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Simon Fraser UniversityBurnaby, CanadaForce propagation Experiments–
cont.
– Two-Hand Pulling
Screen shot of two-hand pulling
Force plot of two-hand pulling
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Simon Fraser UniversityBurnaby, CanadaCase Study and Result – cont.
• Unknotting Experiments– Successful unknotting
• Over hand knot
Over hand knot
Unknotting 1
Unknotting 2
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Simon Fraser UniversityBurnaby, CanadaUnknotting Experiments –
cont.
– Successful unknotting• Figure of eight knot
Figure of eight knot
Unknotting 1
Unknotting 1
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Simon Fraser UniversityBurnaby, CanadaUnknotting Experiments –
cont.
– Unsuccessful unknotting• Figure of eight knot
Unsuccessful unknotting 1 Unsuccessful unknotting 2
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Simon Fraser UniversityBurnaby, Canada
Thank you very much!Any questions?
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