5. RESULTS AND DISCUSSION

Results reported elsewhere indicate that these navigation controllers are robust to group size and character type. The controllers generate groups of human bicyclists as they avoid obstacles and ride along a path. The results verify that distributed navigation controllers can be used with the locomotion controllers of physically simulated characters to generate goal-oriented behavior. However, the unique dynamic abilities of each character impose limitations on the character's ability to react to the environment. The navigation controllers described in this paper partially account for these variations by performing simulated annealing tuning experiments for the herding gains and the path following look-ahead time. Additional manual adjustments must be made to prevent the navigation controllers from specifying unreasonable desired velocities to the locomotion controllers.

The tuning procedures described in this paper automatically adjust to many of the unique qualities of the different characters, but they provide indirect parameterizations and fail to capture the variety of mobility constraints that result from a character's dynamic state. The tuned values of kp and kd reflect how the characters compute desired velocities from errors in position with respect to visible neighbors. The ratio between the spring and damper gains demonstrates significant differences between the human and alien characters' mobility constraints. The human bicyclist has values of 0.297 and 0.339, which indicate a very high damping coefficient. Subjective analysis of the bicyclist reveals that these gain settings compensate for the character's relatively high degree of lateral momentum. Once the bicyclist begins to lean and turn, it has difficulty returning to an upright posture. Alternatively, the alien bicyclist has a higher value of kp , 0.467, and a low value for kd , 0.0598. The relatively low damping term indicates that the character is able to quickly correct orientation errors without the risk of reaching a high yaw velocity. Indeed, qualitative observation of the alien bicyclist reveals that the character can quickly initiate and eliminate lateral velocities. Although these parameters are tuned automatically, they provide only a superficial connection between the navigation controller and the mobility constraints of the character. The computed k p and kd values are tied to the exercises used to tune them, rather than being absolute and related only to the character. In our experiments, for example, the tuned parameters allowed the bicyclist to quickly shift its position 4.0 m to the right, but these parameters may be ineffective for smaller transitions. By selecting an appropriate set of tuning exercises, a family of tuned parameters can be created for use in many scenarios. Gain scheduling allows the run-time selection of the most appropriate gains from this set, but successful scheduling algorithms require a good set of optimized gains.

The amount of time in the future, t, that the bicyclists use to evaluate the look-ahead point is also a very important parameter. A large value of t smoothes out the effects of variations in the path's trajectory and provides the opportunity to anticipate and initiate changes in riding direction. Due to the trigonometric relationship between an observed shift in the path position and the magnitude of t, turns in the path result in smaller changes in desired riding direction when t is large. Large t values allow characters to transition into corners more gradually, but it also risks eliminating some curves entirely, thus causing bicyclists to ride off the path (figure 8). The t value of 4.1 s for the human bicyclist reflects its inability to initiate a turn quickly. This high look-ahead value provides ample time to begin a gradual cornering maneuver, but it also reduces the effect of smaller turns in the path. The alien bicyclist utilizes a much smaller look-ahead value, 1.1 s, which generates a navigation controller that is more responsive to changes in the path's direction. As was the case with the herding gains, the value of t mirrors subjective observations of the two bicyclist's mobility constraints. Unfortunately, the look-ahead parameter is tuned on a particular set of curves, which might not accurately reflect the type of curves encountered at run time. Furthermore, we cannot precompute a set of optimal t look-ahead values that cover the wide range of curvatures present on the bicycle's path.

The herding and look-ahead parameters reflect differences between the mobility constraints of two characters, but additional variations occur within each individual character's range of state configurations. For example, the turning ability of the bicyclists is nonlinear with respect to their roll angle. A perfectly upright bicyclist requires a significant amount of time to complete even a small change in riding direction. Attempts to quickly execute large changes in riding direction result in the character losing balance and falling. A bicyclist already leaning to one side, however, can easily complete more aggressive maneuvers if the turn is in the direction of the lean. The navigation controller ignores how the bicyclist's dynamic abilities change as a result of roll when computing a desired velocity. Instead, the navigation controller heavily clamps the changes in riding direction attempted by the bicyclist. This conservative approach prevents failures when the bicyclist is upright, but it also retards achievable actions when the character is already leaning to one side. An improved navigation controller would adjust its actions based on the dynamic state of the character.

In our future work, we will develop simplified versions of characters that will serve to support navigation controllers and other high-level behaviors. We propose that by reducing the accuracy of some degrees of freedom and eliminating others entirely, the simplified character will be fast to compute while preserving the mobility constraints present in the original simulation. In this way, the simplified character will support the navigation controller to better adapt to different types of characters and changing run-time mobility constraints.