Design of Dynamical Stability Properties in Character Animation

Abstract

Human movements and the collective behavior of interacting characters in crowds can be described by nonlinear dynamical systems. The design of stability properties of dynamical systems has been a core topic in control theory and robotics, but has rarely been addressed in the context of computer animation. One potential reason is the enormous complexity of the dynamical systems that are required for the accurate modeling of human body movements, and even more for the interaction between multiple interacting agents. We present an approach for the online simulation of realistic coordinated human movements that exploits dynamical systems that are simple enough in order to permit a systematic treatment of their stability. We introduce contraction theory as a novel framework that permits a systematic treatment of stability problems for systems in character animation. It yields tractable global stability conditions, even for systems that consist of many nonlinear interacting modules or characters. We show some first simple applications of this framework for the animation of coordinated behavior in groups of interacting human characters.