Bayesian models of human navigation behaviour in an augmented reality audiomaze

Abstract

We investigated Bayesian modelling of human whole-body motion capture data recorded during an exploratory real-space navigation task in an "Audiomaze" environment (see the companion paper by Miyakoshi et al. in the same volume) to study the effect of map learning on navigation behaviour. There were three models, a feedback-only model (no map learning), a map resetting model (single-trial limited map learning), and a map updating model (map learning accumulated across three trials). The estimated behavioural variables included step sizes and turning angles. Results showed that the estimated step sizes were constantly more accurate using the map learning models than the feedback-only model. The same effect was confirmed for turning angle estimates, but only for data from the third trial. We interpreted these results as Bayesian evidence of human map learning on navigation behaviour. Furthermore, separating the participants into groups of egocentric and allocentric navigators revealed an advantage for the map updating model in estimating step sizes, but only for the allocentric navigators. This interaction indicated that the allocentric navigators may take more advantage of map learning than do egocentric navigators. We discuss relationships of these results to simultaneous localization and mapping (SLAM) problem.

Keywords: allocentric navigator; egocentric navigator; map generation; real-space navigation.

FIGURE 1

(a) Experimental environment and set up for participants. The experimental room had 8 × 9 meter size, equipped with 12 + 8 speakers (on walls and ceilings, respectively), 20 motion capture cameras, and sound‐absorbing wall materials painted in black. (b) Configuration of the motional capture markers. Participants were in the special suit that had 32 LED markers on the head, torso, right arm including hand, and both legs. (c) The shapes of the mazes. Each shape of the maze was repeated three times in a row

FIGURE 2

Schematic representation of the feedback‐based model and map‐based models. (a) The motion vector V was defined as the change of the torso position every 500 ms, specified by angle and distance. (b) All models switch between two step/angle distrubutions based on a prediction of whether there is a wall ahead or not. (c) The feedback model simply predicts a wall ahead when a wall is detected by hand/head sensors (left). The yellow area shows the angular range used for the wall detection. The map‐based models (right) detect a wall ahead based on a mental wall‐probability map learned from previous navigation in the maze. The definition of wall ahead was that there is high probability of a wall in the green area ahead but not in the light blue areas to the sides. (d) The mental map consists of wall probability and no‐wall probability maps updated each step based on the presence or absence of sensory feedback. Here, the nowall probability is updated after a forward step

FIGURE 3

Movement trajectories and estimated mental models for two participants, an allocentric‐ (left) and egocentric‐ (right) style navigator. (a, b) Red and black traces indicate the measured and estimated trajectories, respectively. From left to right, Trial 1, 2, and 3. (c, d) Participants wrote down the maze shape they estimated and the trajectory they moved through it after each trial. (e, f) Estimated mental maps by the map reset model. (g, h) Estimated mental maps by the map update model. From left to right, Trial 1, 2 and 3. The wall probability was subtracted from the no‐wall probability for visualization, with yellow showing 'wall' probability and blue the 'no‐wall' probability

FIGURE 4

Prediction performance of estimated step sizes (a) and turning angles (b). The log‐likelihood (L) depends on the number of steps and so was normalized by dividing by the number of steps taken during the current exploration to correct the imbalance in the number of steps between participants and trials. There are significant differences between models' ability to predict step size in all trials and turning angle in Trial 3 (Friedman's test, p < .01, df = 2). All asterisks in (a) and (b) indicate significant differences between the two map‐based models and the feedback‐based model (post hoc two‐sided Wilcoxon signed rank test, p < .001, Bonferroni corrected for multiple comparisons). The bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. Gray dots indicate outliers which are greater than q3 + 1.5 × (q3 − q1) or less than q1 − 1.5 × (q3 − q1), where q1 and q3 are the 25th and 75th percentiles, respectively. A whisker extends to the most extreme data value that is not an outlier

FIGURE 5

Comparison between estimated probability of step size p(d) and measured step size. Each step was divided into no‐wall condition (left) and wall condition (right) based on the wall detection criterion of each model. Black bars indicate rate of the number of steps with each step size across all participants and all trials. Green, blue and red lines show probability distribution function of estimated Gamma distributions for the three models. In the lowest panels, the estimated probabilities drawn separately in the upper panels are overwritten for comparison

FIGURE 6

Differences in step‐size prediction between egocentric participants (filled boxes) and allocentric participants (open boxes). From left to right, Trial 1, 2 and 3. There are significant differences between models in all panels (Friedman test, p < .0001). Asterisks: significant differences (post hoc two‐sided Wilcoxon signed rank test, Bonferroni correction, p < .05)