A Framework for Reasoning About Animation Systems

Abstract

In this paper, we consider the potential for reasoning about animations in the language of hybrid dynamical systems (i.e., systems with both continuous and discrete dynamics). We begin by directly applying hybrid systems theory to animation, using a general-purpose hybrid system specification tool to generate multi-agent animations; this application also illustrates that hybrid system models can provide systematic modular ways to incorporate low-level behavior into a design for higher-level behavioral modeling. We then apply the logical framework of hybrid systems to animation: we formally state properties of animation systems that may not be readily expressed in other frameworks; and we mechanically check a collision-avoidance property for a simple race-like game. This hybrid systemsoriented approach could improve our ability to reason about virtual worlds, thus improving our ability to create intelligent virtual agents.

Scalable nonlinear dynamical systems for agent steering and crowd simulation

“…Nonetheless, theoretical models of hybrid systems allow us to rigorously specify a statetransition approach to global planning without sacrificing any aspect of our technique for local, continuous behavior. In the paper [48], our agent steering method was the basis for crowd simulation and agent navigation animations that were formally specified and generated using the general purpose hybrid system tool, charon [49]. That paper also presents a simple demonstration that, in some obstacle/target configurations, the ability to switch between continuous behaviors in a hybrid system may result in more effective global planning than if only one continuous behavior were possible.…”

“…(These results do not add to the foundations of our approach to agent navigation, so a full discussion of them is outside the scope of this paper. See [48] for more details.) Because our method for agent navigation is designed to accommodate a layered approach to planning, it is an excellent fit in a hybrid systems framework.…”

A hybrid dynamical systems approach to intelligent low-level navigation

“…This option represents a kind of control experiment, a straightforward continuation of the standard obstacle avoidance that guided it up until the first target; Figure 7 is a frame from the resulting animation, showing how much farther the white mouse goes if it does not consider navigation mode switching or selective repeller response. (See [4] and [5] for further discussion and other animations. )…”

“…Our present work is, in part, a first exploration of animation from a hybrid systems perspective, creating a connection so that modal logics for hybrid systems might be employed to reason about animation. (A discussion of the logical frameworks established for reasoning about hybrid systems is beyond the scope of this paper; see [4] for details.) Indeed, related work with robots (e.g., [19]) suggests that a hybrid systems framework could be appropriate for reasoning about animations without undue disregard for the dynamic nature of animation systems.…”

“…In particular, we hope to develop a hybrid system model of intelligent highlevel navigation in CHARON; we could then embed this lowlevel navigation system into the high-level system (exploiting the modularity mentioned in section 2.2), creating a full system for agent navigation. In addition, we are investigating the potential for reasoning about animation systems using logics for hybrid systems, as discussed in [4].…”