Haptic interaction with rigid bodies by SPIDAR

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Haptic interaction with rigid bodies by SPIDAR

• Shoichi Hasegawa
• Makoto Satos group
• Precision and Intelligence Lab.
• Tokyo Institute of Technology

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Contents

• Control of SPIDAR
• Characteristics of SPIDAR
• Position measuring, Force displaying
• Update rate of haptic rendering
• Rigid body simulation
• Contact force modeling
• Haptic rendering for 6DOF
• Simulation of articulated body
• Demo
• For demonstration, please visit our booth.

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Hardware of SPIDAR
Motor and encoder Present force to
user. Measure length of string.
SPIDAR
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Hardware performance

• SPIDAR is the best device in performance
• Stiff and light

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Reconfigurable hardware

• Any DOF and arrangements are designable.
• Same control algorithm can be used

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Position measurement

• r posture vector (x,y,z,qx , qy , qz )
• pi tied point of string on the grip
• qi position of a motor
• li length of string

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Position measurement
Solve r by iterative method
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Displaying force

• Simple solution

t2
f2
t1
f1
tensions
f
t3
Directions of strings
f3
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Displaying force

• Discontinuous problem

Tension
Present the same force and move the pointer.
Position
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Displaying force

• Simple solution
• Use smaller tension
• Limitation
• Finally

Quadratic programming problem
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Displaying force
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Full presentation area
Partial presentation area
?
0.1
Calculated tension N
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?
0.2
?
1.0
0
(0,0,0)
(-0.2,-0.2,-0.2)
(0.2,0.2,0.2)
Position of end effecter m
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Displaying force
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Haptic rendering and update rate
Force display
Virtual World
1
2
3
Fkx

• Measure finger position
• Collision detection and force calculation
• Display the force

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Haptic rendering and update rate

• Problem on slow update rate

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Haptic rendering and update rate

• Solution by fast update rate

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Effect of fast update

• Advantage of stiffness
• Display of friction disturbs display of shapes.
  But, enough stiffness realizes both.

Virtual object (gear)
Virtual object (gear)
2N/mm, 1kHz
20N/mm, 10kHz
Trajectory of the haptic pointer on surfaces with
friction (m0.5)
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Real-time Rigid Body Simulationfor Haptic
Interactions
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Haptic interaction

• Touch the virtual world
• User feels contact force from haptic interface

Virtual
Real
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Haptic interaction

• Touch the virtual world
• User feels contact force from haptic interface
• The touched object receives force from the user.
• The response Dynamics

Virtual
Real
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Video Darumaw
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Contact force
Fmv NIw v(tD t) v(t) F/mDt w(tD t)w(t)
I-1NDt
Haptic pointer
Contact force fordynamics simulation
Contact forceto feedback user
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Contact model
Normal force

• Normal force
• Prevent penetration
• Friction force (coulombs model)
• Static friction
• Prevent sliding motion
• Dynamic friction
• Proportional to normal force

Friction force
ff lt m0fn
ff mfn
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Solving constraints(1)

• Analytical method
• David Baraff SIGGRAPH 89

• Advantages
• Object motions are stable.Wide time steps are
  affordable.
• Solves constraints accurately.Completely rigid.

• Drawbacks
• Much computation time for one step. O(n3 )
• A virtual coupling is needed to connect a haptic
  interface.
• Coulomb's friction model comes to NP complete
  problem.

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Solving constraints(2)

• Penalty method

.
penetration d,penetrating velocity d
Spring
Damper
.
slide l,sliding velocity l
Spring
Damper

• Advantages
• Very fast for one step. O(n)
• Direct connection to haptic interfaces.
• Coulombs friction model is easily realized.
• Integration of other models are easy. (e.g.
  Featherstones method)

• Drawbacks
• Stability and rigidity requires small time
  steps.(Haptic interfaces also need this.)
• Treatment of large contact area makes instability
  or takes a lot of computation time.

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Problem on large contact area

• Where should we put spring-damper model?

On the most penetrating point
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Problem on large contact area

• Where should we put spring-damper model?

?
On vertices
Top view
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Problem on large contact area

• Where should we put spring-damper model?

Will works well. But, it will takes
muchcomputation time and memory.
?
Many points
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Proposal for the problem

• Integrate forces from distributed model for each
  triangle.

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Steps

• Finding Contact force
• Find contact point and normal.
• Find the shape of the contact volume.
• Integrate forces over the contact area.

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Contact detection

• Gilbert, Johnson, and Keerthi (GJK) algorithm.
• Find closest points of two convex shapes.
• A complex shape can be represented by a set of
  convex shapes.
• After the contact, GJK cant find closest points,
  So

tt0
tt1
New closest points
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Contact Analysis

• Contact part Intersection of two convexes.
• D. E. Muller and F.P.PreparataFinding the
  intersection of two convex (1978)
• For given two convex and a point in the
  intersection.
• Find the intersection.

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Contact Analysis(2)

• Finding the intersection of two convex

Half space representation
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Contact Analysis(3)

• Finding the intersection of two convex(2)

Half space representation
Dual transform
Vertex of intersection
Dual transform
Quick hull
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Integration of force

• Penalty force
• Dynamic friction force
• Maximum static friction force

Integrate forces from distributed model for each
triangle.
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Integration for a triangle
p3
Force from spring model
Torque from from spring model
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Static friction force

• Spring-damper model for sliding constraint.

Two (translation and rotation) models
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Evaluation

• Compare three simulators
• Proposed
• Penalty method
• distributed model.
• Point based
• Penalty method
• A model on the most penetrating point.
• Analytic
• Analytical method
• Open Dynamics Engine (Smith R. 2000)

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Computation time
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Stability on normal force

• A cube on a floor.
• Measure angular momentum.

1
Proposed method
Point based penalty method
Analytical method
Angular momentum Nms
0
-1
0
1
2
times
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Motion of top
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Stick-slip motion

• State transition between static and dynamic
  friction makes stick-slip motion.

m00.265 m 0.160
2kg
0.0642m/s
Spring 400N/m
friction force
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Result
Real world
Analytical simulator
0.1
0.1
5
5
ForceN
Positionm
Positionm
ForceN
0
0
-5
-5
0
0
0
1
2
0
1
2
Times
Times
Proposed simulator
Point based simulator
0.1
0.1
5
5
ForceN
Positionm
ForceN
Positionm
0
0
-5
-5
0
0
0
1
2
0
1
2
Times
Times
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Both hand 6DOF haptic interaction
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Update rate of the simulation

• Update rate gt 300Hz

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Articulated body

• Constraints of joints should strictly be kept.
• Small errors can be magnified by mechanisms.
• To solve generic constraints, we need much
  computation time. But,
• Efficient computation method is affordable under
  some restriction of structure.
• Restriction Tree structure without ring

many rings
one ring
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Generic method
As eq of motion
Constraint of 1
Bs
So, we can write
Many 0,sparse matrix There can be fast
calculation method.
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Featherstones method

• Suppose whole rigid bodies are one rigid body.
  Then find the acceleration. Find the
  acceleration of A
• Suppose two rigid bodies of A and others.
• Find the force applied to the joint 1
• Find the acceleration of B
• Suppose three rigid bodies of A and B and
  others.

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Featherstones method

• Look the method from a viewpoint of the sparse
  matrix

1. From the leaves to the root we merge M
2.Find acceleration .
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Featherstones method
3.Find from the root to the leaves.
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Demo
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Our booth
We are here
Our booth (1F)
5 minutes walk