To analyze how close the RCAP model of human motion matches the data collected from real-world experiments, the paths in the validation dataset where compared to those
(a) (b)
Figure 5.10: Comparison of the true collision response curve (Blue Line) to the one predicted by RCAP with generic constants (Green Line) and the prediction with constants tuned to the specific runs (Red Line).
predicted by the RCAP algorithm. For this comparison the mean values forTobs,amax, and rwere used as given in Table 5.2. The results are analyzed qualitatively and quantitatively along three dimensions: the collision response timing, a biomechanical energy consumption based analysis of the trajectories, and on the paths themselves. A five-fold cross validation was also performed to analyze error in the model while reducing over-fitting.
5.6.1 Collision Response Phases
In analyzing the results qualitatively, three distinct phases of RCAP agent motion are apparent. These phases can be clearly seen in the collision response curves such as those in Figures 5.5, 5.6(a) and 5.6(b). The first phase is the observation phase, which lasts a little under a second. Here the agents move along at their preferred velocities, without any changes. Secondly, is thereaction phase, where the agents have computed an appropriate velocity and take a second or two to achieve it (depending on how far it is from the observation phase velocity). Finally, there is themaintenance phasewhere the agents maintain their collision-free velocities.
Participants in the experiment often show a similar means of response to a collision as the three phase response predicted by RCAP. People would at first not react to avoid
the collision, then slowly adopt a correct velocity, and finally maintain velocities which generally result to collision-free trajectories. This is in stark contrast to ORCA agents as they instantaneously adopt and maintain a collision-free velocity.
In all cases, there is little change in velocity when there is no imminent collision to avoid, such as in the scenario reported in Figure 5.7.
5.6.2 Biomechanical Energy Consumption Analysis
A more quantitative way to measure how realistic the simulated paths are is to analyze the biomechanical effort implied by the trajectory. As humans move in the environment, they expend energy and turn chemical potential energy stored in their body into the physical kinetic energy of motion. Humans have been shown to walk at speeds which minimize the amount of energy spent walking (Inman et al., 1981). Given an agent’s weight, velocities, and path taken, it is possible to calculate how much much energy the agent must have spent walking along that path (Whittle, 2002). This calculation can be performed for both the real and virtual humans, which gives us a means to determine if the virtual agents choose similarly efficient paths as compared to real humans.
Assuming a weight of 70 Kg, over the course of all the runs, the average real human consumed 1,778 joules (J) walking to his or her goal (standard deviation 306 J). During the same runs, the virtual agents consumed 1,770 J (s.d. 307 J). On any given run, the average difference between the energy consumed by real and virtual humans was only 20 J.
5.6.3 Path Similarity
In addition to comparing manner and pacing of collision response as above, the absolute paths taken by virtual agents can be compared to those of the real humans. In general the paths taken are very similar. Figure 5.11 shows a run of the simulation (shown in red) overlaid with the paths that the actual participants took. On average, the simulated and real humans were only 0.168m apart at any time.
Figure 5.11: A comparison of paths Real Humans vs Virtual Humans. Agents are displayed as circles with their goal for this simulation run show in Xs. The redline shows the path that the simulated humans took, and the black line shows the path of the humans.
Figure 5.12 shows more paths from different initial conditions for the real humans and virtual agents. Even in just these three runs, the six participants invoke a variety of different techniques to avoid collisions with each other including slowing down, speeding up, veering left or right, and keeping the same path while the other person adjusts. Despite this variety, the virtual agents are still able to follow the trajectories of the real humans very closely. 5.6.4 Cross Validation
In order to reduce the effect of overfitting, the above experiments war re-ran using a five-fold cross validation. That is, the model was trained five separate times with a different fifth of the training data removed each time. For each fold, error statistics were computed with respect to the removed data set. In all cases the resulting models show a strong agreement between the predicted paths and the validation data. Averaged across the five folds, the model showed an average root-mean square error (RMSE) of 0.217m (8.5”).
Figure 5.12: Comparisons of paths Real Humans vs Virtual Humans from two additional runs. Black lines: Real humans’ paths,Red lines: Virtual Agents’ paths
Additionally, the positions of the modeled agents and actual humans physically overlapped 95.1% of the time.