Jan Bender, Impulse-based dynamic simulation in linear time, In Journal of Computer Animation and Virtual Worlds, John Wiley & Sons Ltd, 2007
Â
Abstract:
This paper describes an impulse-based dynamic simulation method for articulated bodies which has a linear time complexity. Existing linear-time methods are either based on a reduced-coordinate formulation or on Lagrange multipliers. The impulse-based simulation has advantages over these well-known methods. Unlike reduced-coordinate methods, it handles nonholonomic constraints like velocity-dependent ones and is very easy to implement. In contrast to Lagrange multiplier methods the impulse-based approach has no drift problem and an additional stabilisation is not necessary. The presented method computes a simulation step in O(n) time for acyclic multi-body systems containing equality constraints. Closed kinematic chains can be handled by dividing the model into different acyclic parts. Each of these parts is solved independently from each other. The dependencies between the single parts are solved by an iterative method. In the same way inequality constraints can be integrated in the simulation process in order to handle collisions and permanent contacts with dynamic and static friction.
Additional information:
The paper describes an algorithm to compute the required impulses in linear time and linear space.
Jan Bender and Alfred Schmitt, Fast Dynamic Simulation of Multi-Body Systems Using Impulses, Virtual Reality Interactions and Physical Simulations (VRIPhys), 2006
Â
Â
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.
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
Â
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.
Â
|
|
|
1000 cubes falling through a funnel (DivX, Mpeg)
|
1000 cubes falling through a funnel (DivX, Mpeg)
|
|
|
|
|
|
 |
|
