The motion synthesis approach to physics-based control bears greater resemblance to how real animals move. It synthesizes the muscles in natural animals as a set of actuators that are capable of driving the dynamic model of a character to produce locomotion. Unlike inverse dynamics, the motion synthesis approach can take into account the limitations of natural muscles, and unlike constrained optimization, it guarantees that the laws of physics are never violated. It also allows sensors to be incorporated into the animate models which establishes sensorimotor coupling or closed-loop control. This in turn enables an animated character to automatically cope with the richness of its physical environment. Since this approach can emulate natural muscles as actuators, it is able to synthesize various locomotion modes found in real animals by emulating their muscle control patterns. The quality of the results will of course depend upon the fidelity with which the relevant biomechanical structures are modeled. The motion synthesis approach offers less direct animator control than the constraint-based approach. For example, it is almost impossible to produce motions of an animate body that exactly follow some given trajectory, especially for multi-body models, such as human bodies (though humans do experience difficulty when attempting to produce specific trajectories).
Several researchers have successfully applied the motion synthesis approach to animation [Miller1988, Terzopoulos and Waters1990, Lee, Terzopoulos and Waters1993, van de Panne and Fiume1993, Ngo and Marks1993]. The artificial fish model that we develop is inspired by the surprisingly effective model of snake and worm dynamics proposed by Miller Miller88 and the face model proposed by Terzopoulos and Waters Terzopoulos90.
An essential physical feature of the bodies of snakes and worms and of human faces is that they are deformable. In both Miller's and Terzopoulos and Waters' works, this feature is efficiently modeled by mass-spring systems. The springs are used to simulate simple muscles that are able to contract by varying their rest lengths. Like these previous models, our fish model is a dynamic mass-spring-damper system with internal contractile muscles that are activated to produce the desired motions. Unlike these previous models, however, we simulate the system using a semi-implicit Euler method which, although computationally more expensive than simple explicit methods, maintains the stability of the simulation over the large dynamic range of forces produced in our simulated aquatic world. Using mass-spring-damper systems, we also model the passive dynamic plants found in the artificial fish habitat.
The major task in motion synthesis is to derive suitable actuator control functions, in particular the time-varying muscle actuator activation functions for different modes of locomotion, such as hopping or flying. When activated according to the corresponding function, each muscle generates forces and torques causing motion of the actuated body parts. The aggregate motion of all body parts forms the particular locomotion pattern. The derivation of actuator control functions becomes increasingly difficult as the number of muscles involved in controlling the locomotion increases. There are two approaches to deriving control functions: the manual construction of controllers and optimization-based controller synthesis, also known as optimal control or learning.
|Xiaoyuan Tu||January 1996|