Jan Bender and Alfred Schmitt, Fast Dynamic Simulation of Multi-Body Systems Using Impulses, Virtual Reality Interactions and Physical Simulations (VRIPhys), 2006

 

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Abstract:


A dynamic simulation method for multi-body systems is presented in this paper. The special feature of this method is that it satisfies all given constraints by computing impulses. In each simulation step the joint states after the step are predicted. In order to obtain valid states after the simulation step, impulses are computed and applied to the connected bodies. Since a valid joint state is targeted exactly, there is no drift as the simulation proceeds in time and so no additional stabilisation is required. In previous approaches the impulses for a multi-body system were computed iteratively. Since dependencies between joints were not taken into account, the simulation of complex models was slow. A novel method is presented that uses a system of linear equations to describe these dependencies. By solving this typically sparse system the required impulses are determined. This method allows a very fast simulation of complex multi-body systems.

Additional information:


The paper describes another impulse-based simulation method which uses systems of linear equations to determine the required impulses very fast. In my current research I determined a way to solve the system of linear equations in linear time and in linear space.

Car

Car (DivX, Mpeg)

Crash test

Crash test (DivX, Mpeg)

Office toy

Office toy (DivX, Mpeg)

Tree

Tree with 127 bodies and joints (DivX, Mpeg)

Walker

Walker (DivX, Mpeg)

 

Jan Bender and Alfred Schmitt, Constraint-based collision and contact handling using impulses, In Proceedings of the 19th international conference on computer animation & social agents, 2006

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Abstract:


In this paper a new method for handling collisions and permanent contacts between rigid bodies is presented. Constraint-based methods for computing contact forces with friction provide a high degree of accuracy. The computation is often transformed into an optimization problem and solved with techniques like linear or quadratic programming. Impulse-based methods compute impulses to prevent colliding bodies from interpenetrating. The determination of these impulses is simple and fast. The impulse-based methods are very efficient but they are less accurate than the constraint-based methods because they resolve only one contact between two colliding bodies at the same time. The presented method uses a constraint-based approach. It can handle multiple contacts between two colliding bodies at the same time. For every collision and contact a non-penetration constraint is defined. These constraints are satisfied by iteratively computing impulses. In the same iteration loop impulses for dynamic and static friction are determined. The new method provides the accuracy of a constraint-based method and is efficient and easy to implement like an impulse-based one.

Additional information:


The paper presents a method which combines the advantages of the constraint-based and the impulse-based approach for collision and contact handling with friction.

 

Rattleback

Rattleback (DivX, Mpeg)

Crash test

Crash test (DivX, Mpeg)

1000 cubes

1000 cubes falling through a funnel (DivX, Mpeg)

Tree

1000 cubes falling through a funnel (DivX, Mpeg)

Tippe top

Tippe top (DivX, Mpeg)

Office toy 3

Office toy 3 (DivX, Mpeg)

Dominos

More dominos (DivX, Mpeg)