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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Non-penetration modeling error in physical simulation time-steppers A more accurate and robust method Binh Nguyen, Jeff Trinkle Computer

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion

Non-penetration modeling error in physical simulation time-steppers

A more accurate and robust method Binh Nguyen, Jeff Trinkle

Computer Science Department,RPI

May 29, 2008

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion

Introduction Review of physical simulation Review of current physical simulation methods Error in non-penetration modeling Case study Active set in physical simulation New method to determine active set Constraints activation in physical simulation The algorithm Conclusion

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Review of physical simulation Review of current physical simulation methods

Building block of physical simulation

Common physical simulations follow the same set of rules (models)

◮ force = mass × acceleration. ◮ Non-penetration and rigid body

laws

◮ Friction law

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Review of physical simulation Review of current physical simulation methods

Current physical simulation methods

There are many physical simulation libraries available

◮ Havok (Intel), Ageia (NVIDIA), ODE (open source), Bullet

(open source),CHRONO (free for noncommercial), TrueAxis (free for noncommercial),...

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Review of physical simulation Review of current physical simulation methods

Current physical simulation methods

There are many physical simulation libraries available

◮ Havok (Intel), Ageia (NVIDIA), ODE (open source), Bullet

(open source),CHRONO (free for noncommercial), TrueAxis (free for noncommercial),...

◮ Most of them are created for games, virtual reality.

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Review of physical simulation Review of current physical simulation methods

Current physical simulation methods

There are many physical simulation libraries available

◮ Havok (Intel), Ageia (NVIDIA), ODE (open source), Bullet

(open source),CHRONO (free for noncommercial), TrueAxis (free for noncommercial),...

◮ Most of them are created for games, virtual reality. ◮ Many robotics researchers are using them and having great

difficulty to get satisfactory accuracy.

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Review of physical simulation Review of current physical simulation methods

Current physical simulation methods

There are many physical simulation libraries available

◮ Havok (Intel), Ageia (NVIDIA), ODE (open source), Bullet

(open source),CHRONO (free for noncommercial), TrueAxis (free for noncommercial),...

◮ Most of them are created for games, virtual reality. ◮ Many robotics researchers are using them and having great

difficulty to get satisfactory accuracy.

◮ Simulation quality depends heavily on collision detection.

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Review of physical simulation Review of current physical simulation methods

Normal simulation steps

Constraint in 2D consists of a pair of edge and vertex. In step two, we model the system as Linear Complimentarily Problem.

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Review of physical simulation Review of current physical simulation methods

Non-penetration constraint

There are two main types of method to model non-penetration constraint:

◮ Type 1: Correcting penetration (most current physics engines)

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Review of physical simulation Review of current physical simulation methods

Non-penetration constraint

There are two main types of method to model non-penetration constraint:

◮ Type 1: Correcting penetration (most current physics engines) ◮ Type 2: Preventing penetration (dvc2D, a 2D physics engine

developed by RPI and UPenn)

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Case study Active set in physical simulation

A case study: Disk - Line

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Case study Active set in physical simulation

Disk - Line

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Case study Active set in physical simulation

Disk - Line

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Case study Active set in physical simulation

Disk - Line

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Case study Active set in physical simulation

Disk - Line

ql

l

ql+1

2

ql+1

1 v

n p (p,n)

Error of method type 1

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Case study Active set in physical simulation

Constraints activation scheme

◮ Type 1 : Only activate when there is penetration. So the

active set A reported from collision detection in this method at time l is empty and at time l + 1 is {(circle, plane)}.

◮ Type 2 : Only activate if there could be a penetration in the

next time step. So the active set A reported from collision detection in this method is {(circle, plane)} at both time l and l + 1. A simple (and actual used in practice) heuristic to decide whether to activate a constraint is if their distance is less than a threshold ǫ then activate.

Lesson learnt

◮ Methods of type one always have a error proportion to relative

velocity and time step even in this simplest example.

◮ Methods of type two give expected result.

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Constraints activation in physical simulation The algorithm

Disk - Two lines

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Constraints activation in physical simulation The algorithm

Disk - Two lines

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Constraints activation in physical simulation The algorithm

Disk - Two lines

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Constraints activation in physical simulation The algorithm

The algorithm

Definition

A group of constraint corresponding to a pair of objects contains all possible constraints between them to make sure that there is no penetration. 2 3 4 5 6 7 Depend on the situation, we can choose the group of constraint differently.

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion Constraints activation in physical simulation The algorithm

The algorithm

◮ Step 1 (Exploratory step) : Formulate a complete system with

all possible constraints. Solve for it and determine which constraint is actually active in a group. (Active constraint is the one with distance value equals zero)

◮ Step 2 : If there is no active constraint then go to step 4. ◮ Step 3 : Now reformulate with the correct active constraint

determined in step 1 then solve for it.

◮ Step 4 : Update then go to step 1.

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion

Conclusion

◮ The three types of methods to model non-penetration

constraints have different errors and activation schemes.

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion

Conclusion

◮ The three types of methods to model non-penetration

constraints have different errors and activation schemes.

◮ The new method is more flexible and robust.

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp

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Outline Introduction Error in non-penetration modeling New method to determine active set Conclusion

Conclusion

◮ The three types of methods to model non-penetration

constraints have different errors and activation schemes.

◮ The new method is more flexible and robust. ◮ It can also remove the need for a sophisticated collision

detection (with the price of having to solve larger LCP system).

Binh Nguyen, Jeff Trinkle Non-penetration modeling error in physical simulation time-stepp