1. Physics simulation and character motion generation for virtual reality
Advanced Topic in Intelligence Sciences
Physics simulation and character motion generation for virtual reality
Precision & Intelligence Lab
Shoichi Hasegawa

2. Virtual reality Measure input and motion of human
Simulate virtual world
Present stimulates to the five senses.
The stimulates imitate the real world.
Interface
Presentation
Virtual world
Input Measurements
Computer
Senses
Motion
Simulation

3. What is Reality ? Real world → physical world
Sensation of real world → A world sensed by a human
Brain in a vat. The world of “Matrix” cinema.
Human senses the world via “five senses” and the brain recognizes the world.
Reality exists in human mind
Visual/Auditory/Olfactory/Gustatory
Computer
Haptic
Somatic sensations

4. How can we create a good virtual reality
Humans perceive the world via their senses
Stimulus which satisfy human senses are enough.
This fact decreases difficulty of virtual reality.
Interface
Computer
senses
presentation
Simulation
motion
input measurement
Virtual world

5. Window of senses A ray of light is a physical phenomena.
Human perceives visible rays only.
We do not have to reproduce infrared or ultra violet rays

6. Window of senses Human vision Color and light
Absorption spectrum of visual substances
on cone cells（S,M,L）and rod cells（R）of human eyes.
Three primary colors
（Center of foveas have cone cells only. Retinas for peripheral vision have rod cells only.）

7. Window of senses Light of wave length λ=590nm, intensity I=1.0
Humans perceives yellow.
Light of λ=600nm, I=0.9 ＋ λ=546nm I=0.9
Humans can not distinguish them. They are virtually equal to human.
We do not have to reproduce wave length

8. Researches for perfect virtual reality
Reproduce all senses of human same as in the real world.
World of “The Matrix”
Is is possible? Do you like such worlds ?
Cabin at univ. Tokyo
Olfactory display by Nakamoto lab.
Tokyo tech.
Sensics piSight HMD
2200x °x 60°
computer
SPIDAR by
Makoto Sato lab.
Tokyo tech
TorusTreadmill by Iwata lab.
Tsukuba univ.

9. What is realtiy ?
Is reproducing of all senses same as in the real world reality ?
If so, what is reality of novel ?
Before thinking about this problem. Let see some virtual system (made by me).

10. 1993 My first force feedback experience
Large robot arm like UNC’s Grope
I wrote some part of haptic rendering code.
This system uses FES(functional electric stimuli) to present feed back force for each finger.
f=knd d n

12. 1994: non-contact tracking haptic interface
Our haptic interfaces are heavy to drag.
For free space: Tracking hand without contact.
Displaying object: Stop the tracking. Hand hit to the device.
Method to measure distance:
Attach an antenna to the seat.
Measure the impedance between hand (surface of hunan) and sensor.
I think this is new and submit a pattent
but…
MIT media lab Fish sensor 1995

14. 1995 jumping locomotion device
Locomotion device for all direction.
We named this device G.O.D Gravity On Demand

16. １９９６ Locomotion device by walking
Walking sensation presenting device

18. １９９６ Join to Makoto Sato’s lab
I won lots to join to Sato lab.
Sato&Koike Gp. P&I Lab, Tokyo Institute of Technology
They research SPIDAR since 1989

19. １９９７　Virtual Basket
My first SIGGRAPH

20. ２０００　Virtual Rubik's cube

21. ２００４ Both hand direct manipulation

22. ２００５ Virtual Canoe

23. ２００５ Virtual Canoe

24. Hardware 1993 ARMSII Link and ・Gimbal mechanism
1994 ARMSIII pantograph mechanism and ball screw
1995 G.O.D. Electro magnetic break, rubber cords
1996 ARMSV AC servo motors, linear rail
1997 Virtual Basket SPIDAR with 8 motors
2000 Virtual Rubik’s Cube SPDIAR with 24 motors
2004 Both Hand Direct Manip SPIDAR with 8 motors
2005 Virtual Canoe SPIDAR with 8 motors

25. Software 1993 ARMSII Sense8’s World Tool Kit
1994 ARMSIII Sense8’s World Tool Kit
1995 G.O.D. Super Scape’s VRT
1996 ARMSV Original software based on Rend386
1997 Virtual Basket Direct X with simple physics simulation
2000 Virtual Rubik’s Cube
Direct3D and simple physical simulation
2004 Both hand haptic interaction Original physics engine based on Volumetric Penalty Method
2005 Virtual Canoe Direct3D and Original Fluid simulation

26. Realities for content Levels of Realtiy Reality of sensation
Resolution, Field of view，Color fidelity …
Reality of image
picture： number of polygons，lighting models …
Moving picture：Mocap，animation …
Reality of movie
Performance of actors，lines
Setting of stage，reality on the story
Reality of manga (comics)
Reality of novels VR AI
Large distance

27. Level of cognition and model Level of sensation and interface
Levels of Reality
Interface
Presentation
Virtual world
Input Measurement
Computer
Recognition
Action/Behavior
Motor control
Sensors
Mind
Reality of content
Level of cognition and model
Reality of surface
Level of sensation and interface 27

28. Perfect simulation
Is perfect simulation of the real world possible ?

29. Perfect simulation Is perfect simulation of the real world possible ?
Perfect simulation of the real world is impossible.
Simulation of an atom requires some bytes of memories.
Numbers of bytes of memory for real simulation of the real world are larger than number of atom in the real world.
One bit of memory consists of a lot of atoms.
The scale of quark to universe is 1040
powers of 10
We must pick up essence of the world. But, what is essence? It depends on the purpose of the virtual reality system.

30. Purpose of virtual world system
Many applications
Communication, telepresence, teleconference, teleoperation
Education, training, computer aided engineerings
Evaluation of design
Media for art / entertainments.
Examples of essences of the real world
Evaluation on vistas of urban
designs
Training for peace keeping forces
Important
-People in the city
- cars
Negligible
- Color of sky
Important
- Color of sky
Negligible
- People in the city

31. Reality of virtual world
Reality of virtual object
Measurement and modeling
Motion and reaction
Physics simulation
Reality of characters
Motion of creatures
Simulation of creatures
Authoring of artist

32. Summary The reason why virtual reality is possible
Window of sensation
Reproduce essence of the real world
Realities on contents of virtual reality are important.
Simulation techniques realize reality of motions and reactions.

33. Reality of virtual object Physics simulation for Virtual world

34. Example of physics simulation for VR
They often called “Physics Engine”

35. Usual modeling of dynamics and simulation
What is physics engine ?
Usual modeling of dynamics and simulation
Manual formulation
ODE Solver q
Find this equation with mysterious algorithm in human brain.
Lagrangian also requires some human intelligence to find formulation of energy

36. What is physics engine ? Physics engine
Forward dynamics is automatically computed from the configuration of the scene with formal algorithm.
So, physics engine calculate constraint force fc with formal algorithm.
⇒ Human intelligence is no longer required. fc
Other than constraint force fc , Newton and Euler’s equation requires external force and it’s application point only. q

37. Finding the constraint forces
Algorithm for constraint force computation
Most VR and games employ Physics Engines of
Velocity based constraint representation
LCP based formulation with Iterative solver
(Springhead and Sprighead2 are physics engines we developed)
Multi body rigid body dynamics simulators
Impluse method
Analytic method
Penalty method
Full DOF method
Reduced DOF method
Moore &
Williams 89
Hahn 88
Sequential collision (J. J. Moreau ’s) method
Projection of relative velocity on
Contact surface
Harmon 08
LCP and iterative solver
Mirtich 96
Acceleration based
Velocity based
Springhead1
Stewart 96
Armstrong 79
ODE
Featherstone 83
Baraff 89
bullet
OpenTissue
Springhead2

38. Constraint force calculation
Penalty method
LCP based method e
ODE solver
To find constraint force fc,
solve these simultaneous equations. q q rc
v, w
I,m
Description of constraint by the velocity of the constraint point.

39. Constraint force calculationM u Jt fe J
Constraint
Equation of motion
Other than modeling of constraint, the algorithm is completely formal and no human intelligence is required.

40. General case M u fc fe Case of two objects Case of many objects
Constraint force
External force
Case of two objects
Case of many objects
velocity
vj wj rj ri
vi wi
mj Ij
mi Ii M u fc fe
mass 40

41. Constraint of Hinge joint
Axis e3 is free. ⇒ No torque
Other axes are fixed ⇒ No velocity
Relative velocity and angular velocity on the joint
Constraint force and torque on the joint w l j e1
w1, l1 i
w4, l4 e2
w6 , l6
w2,, l2
w5 , l5 e3
Velocity
w3, l3
Coordinate system for constraints
Force
Velocity
Force 41

42. Integration of constraints
Variable transformation of equation of motion
Integrate constraint into the equation of motion
Constraint (hinge’s case)：
Substitute constraint for the equation of motion
Now we got the constraint forces. 42 42

43. Whole process of the simulation
Find the constraint force
Update velocities of objects
Update positions of objects
Springhead employs Gauss-Seidel iterative solver to solve this equation for l.
Position
Position and Orientation of objects
Orientation
Quaternion
A matrix translating velocity into diff of quaternion 43

44. Constraint and LCP
Many kind of constraints can be modeled by Linear Complementary conditions.
Joints
Contacts
Normal forces and friction forces
Springs and dampers :
Finding of constraint forces to satisfy these conditions and equations of motion results in Linear Complementary Problem (LCP).

45. Contact point
No interferences ＝stopping by contact force or leaving without force：
Static or dynamic friction：
No torques：
Relative velocity between the contact
Contact force
velocity
force
velocity
force
velocity
force 45

46. Contact point Equation of motion Constarint
velocity
force
velocity
force
There looks two variables (l and w).
However, one of two variables is fixed because of linear complementarily.
So, this equation has a explicit solution. 46 46

47. Joint and contact
We modeled contact and joint. So, objects with joints and contacts can be simulated.