physics-based dlo simulation and it’s application...

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Simon Fraser UniversityBurnaby, Canada

Hans Fuhan Shi and Shahram Payandeh


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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• 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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• 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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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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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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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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• Spring Force - acting on one node (15th in this example)

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• Spring Damper Forces

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• Torsional Spring Forces

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• Torsional Damper Forces

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• Swivel Damper Forces

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• Friction - sliding over itself (one contact point)

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• 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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• Friction

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• Friction

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• 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


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Simon Fraser UniversityBurnaby, CanadaKnotting Experiments –

cont.

– Model 3: Same as model 2 with added torsional damper


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Simon Fraser UniversityBurnaby, CanadaKnotting Experiments–

cont.

– Model 4: Same as model 3 with added swivel damper


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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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Thank you very much!Any questions?

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physics-based dlo simulation and it’s application...

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