This page contains supplementary material for the following paper:

General Notes

This supplementary material includes multi-agent animations, CHARON output, and additional descriptions. For the animations, navigation systems and virtual worlds were modeled and simulated using CHARON, a general-purpose tool for the specification and simulation of hybrid systems.

In the rendered animations presented below, actors (white mice) navigate in a virtual world of targets (usually cheese or mouse holes), obstacles (usually toys one might find on the floor), and other actors.

In general, we present the animations in two formats: Quick Time (QT) .mov files, and MPEG .mpg files. The QT files are larger, with better resolution, but both formats show the same navigations.

Crowd simulation

Using CHARON, we created a simple crowd simulation animation as something of a proof of concept: This crowd simulation is similar to other animations used to demonstrate multi-agent low-level navigation systems, suggesting that a hybrid system approach is comparably expressive to standard methods. In this animation (QT, size: 33.9M) (MPEG, size: 2.6M), a crowd of mice move from the bottom of the screen to their mouse hole (home) at the top, navigating around a crowd of mice simultaneously crossing from the top of the screen to their home at the bottom.

System Architecture

In section 3.3 of our paper, we mention a straightforward system for navigation mode switching based on one variable, c (comfort). This mode switching system guides the behavior of the navigating agent as it passes by two rows of obstacles. Along the way, as it becomes more comfortable, it changes to other modes, changing aggressiveness, velocity, and the dynamic evolution of c, as discussed in our paper. This is a schematic diagram of that simple, very straightforward system. It merely shows the transitions we used; it does not include the continuous dynamics in the particular modes. For more details, see our example CHARON code.

We emphasize for readers that our mode switching system is but one simple example. The hybrid system framework we discuss can model far more sophisticated behavior. For this paper, however, our intent was not to present an optimal model of agent navigation but to demonstrate a general modeling framework.

Selective Repeller Response and Navigation Mode Switching

In section 4.2 of our paper, we mention a two-segment animation scenario in which an actor: uses non-selective, complex steering to avoid obstacles in segment 1; and either uses straight, linear navigation or selective repeller response in segment 2. Animations presented below demonstrate the effects of different choices for segment two.

Selective Repeller Response

To demonstrate selective repeller response, we used CHARON to generate animations that illustrate the various possible courses an actor might take. One animation (QT, size: 12.6M) (MPEG, size: 1.0M) shows the result of switching to a linear course for segment 2. (See paper Figure 4.)

Another, slightly different animation (QT, size: 12.2M) (MPEG, size: 1.0M) shows selective repeller response. In this one, there is no longer a dinosaur obstacle near the second target; instead, it is a familiar-looking brown toy mouse. Our white mouse protagonist responds to the toy mouse on its right as if it were significantly less threatening than a dinosaur or flying saucer. Such subjective, individualized treatment of obstacles and actors in the environment is the crux of selective repeller response.

We also generated an animation (QT, size: 12.4M) (MPEG, size: 1.0M) to demonstrate how the agent's course would differ if it did not switch to the straight, linear steering or selective repeller response in segment 2. (See paper Figure 6.)

Navigation Mode Switching

We present a simple animation (QT, size: 18.4M) (MPEG, size: 1.4M) that demonstrates navigation mode switching based on comfort, as discussed in the system architecture section above. Being the intelligent mouse that it is, our actor becomes much more comfortable after recognizing that the sneaker (first obstacle) isn't moving and the dinosaur (second obstacle) won't bite. (We use the word "recognizing" loosely. There is no higher order cognition, just a sense of increasing comfort.) In general, it grows more comfortable as it progresses. Noticeably, after passing the first row of obstacles and reaching the first target, it moves faster and stays closer to the second row of obstacles. Indeed, at the very end of the animation, when it must choose between linear navigation and selective repeller response according to the system in paper Figure 2, its comfort level is high enough that it chooses straight linear navigation.

As indicated in the transitions output file from CHARON, it actually changes modes twice before reaching its first objective (i.e., target) and once more before reaching its second objective. Had we chosen different coefficients for the CHARON system (as illustrated in our example CHARON code), we could have generated different mode switching behavior.

Eric Aaron, eaaron@cs.rutgers.edu