Specification and Synthesis of Hybrid Automata for Physics-Based Animation

Abstract

Physics-based animation programs can often be modeled in terms of hybrid automata. A hybrid automaton includes both discrete and continuous dynamical variables. The discrete variables define the automaton's modes of behavior. The continuous variables are governed by mode-dependent differential equations. This paper describes a system for specifying and automatically synthesizing physics-based animation programs based on hybrid automata. The system presents a program developer with a family of parameterized specification schemata. Each scheme describes a pattern of behavior as a hybrid automaton passes through a sequence of modes. The developer specifies a program by selecting one or more schemata and supplying application-specific instantiation parameters for each of them. Each scheme is associated with a set of axioms in a logic of hybrid automata. The axioms serve to document the semantics of the specification scheme. Each scheme is also associated with a set of implementation rules. The rules synthesize program components implementing the specification in a general physics-based animation architecture. The system allows animation programs to be developed and tested in an incremental manner. The system itself can be extended to incorporate additional schemata for specifying new patterns of behavior, along with new sets of axioms and implementation rules. It has been implemented and tested on over a dozen examples. We believe this research is a significant step toward a specification and synthesis system that is flexible enough to handle a wide variety of animation programs, yet restricted enough to permit programs to be synthesized automatically.

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