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Section: Scientific Foundations

Keywords : movement, animation, simulation, identification, hybrid systems, levels of detail.

Dynamic models of motion


Animation: 

Models and algorithms that produce motion accordingly to the animator specification.

Physically Based Animation: 

Animation models which take into account the physical laws in order to produce motion

Hybrid System: 

dynamic system resulting of the composition of a part which is differential and continuous and a part which is a discrete event system.

State Vector: 

data vector representing the system at time t, example: position and velocity.


As for realistic image synthesis, the physically based animation introduces physical laws in algorithms. Furthermore, natural motion synthesis (living beings) needs to take into account complex phenomena such as mechanics, biomechanics or neurophysiology in order to treat aspects like planning and neuro-musculo activation.

The generation of motion for 3D objects or virtual characters needs to implement dedicated dynamic models depending on different application contexts: natural motion simulation, animation for multimedia production or interactive animation.

The mathematical model of the motion equations and the algorithmic implementation are based on the theory of dynamic systems and use tools coming from mechanics, control and signal analysis. The general structure of the dynamic model of the motion is a hybrid one, where two parts interact. The first one is a differential part while the second one is a discrete event system:

Im1 $\mtable{...}$

In this equation, the state vector xis the concatenation of discrete and continuous state parameters, uis the command vector and tthe time.

For example, the contact and collision mechanical computation is performed using an hybrid system. Physically, a collision is a discontinuity in the state vector space (impulse = velocity discontinuity).

In the context, some emerging topics appear:

Automatic model generation: 

using a high level specification language, the challenge consists in producing both the hybrid dynamic model and the control algorithm.

Identification :

a synthetic model is always difficult to produce off-hand. A new method consists in observing real systems using structural and parametric identification tools in order to determine it.

Level of detail :

this tendency is essential in order to treat complex models and can be applied to solve geometric complexity but also mechanical complexity.


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