Human-Like Sequential Learning of Escape Routes for Virtual Reality Agents

Abstract

The Piper Alpha disaster (1988) witnessed 167 casualties. The offshore safety guidelines developed afterward highlighted the need for effective and regular training to overcome the problems in evacuation procedures. Today, virtual environments are effective training platforms due to high-end audio/visual and interactive capabilities. These virtual environments exploit agents with human-like steering capabilities, but with limited or no capacity to learn routes. This work proposes a sequential route learning methodology for agents that resembles the way people learn routes. The methodology developed here exploits a generalized stochastic Petri-net based route learning model iteratively. The simulated results are compared with the route learning strategies of human participants. The data on human participants were collected by the authors from an earlier study in a virtual environment. The main contribution lies in modeling people’s route learning behavior over the course of successive exposures. It is found that the proposed methodology models human-like sequential route learning if there are no easy detours from the original escape route. Although the model does not accurately capture individual learning strategies for all decision nodes, it can be used as a model of compliant, rule-following training guides for a virtual environment.

Appendix A: The GSPNRL Model

GSPN stands for generalized stochastic Petri net. The RL stands for route learning and hence the acronym GSPNRL is a model of route learning that exploits the stochastic Petri nets for representation of the phenomenon a human being undergoes when there is a need to learn a new route in an environment.

The model has thirty places, ten stochastic transition, and twenty-three immediate transitions. The stochastic transitions are depicted in Fig. 2 as simple rectangles, and solid rectangles show the immediate transitions. Circles show the places. A circle with one dot shows a single token on the place, and a circle with a number inside shows the number of tokens that are present in that place. The place A₂₂ is of integer type. The type integer is referred to as NUM in the model. The place A₂₁ and A₂₃ are of type NUMLEVELS, where NUMLEVELS is a product type in which the first member is NUM and the second member is an enumerated datatype D = {LOW, LOWEST, MEDIUM, HIGH, HIGHEST}, which represents the difficulty levels associated with a landmark. The remaining places do not associate any type and, therefore, represent only simple tokens in the model.

The GSPNRL model is 1-bounded. Thus, if any of the transitions from t₂₈ to t₃₂ are enabled, the others will be disabled and cannot execute allowing only one landmark to be processed at a single time. This resembles a real-life situation where people avoid getting confused dealing with more than one landmarks at a time, rather every landmark is processed in a sequential way. The net N3 is the only net in the model that uses colored tokens—tokens with custom datatypes such as the type NUMLEVELS. Colored Petri-net allows the development of compact and parameterized models, which otherwise require a difficult to read and understand, and lengthy models.

The net N2 is the main component of the model. It integrates the information coming from N1 and N3 by using a semi-Markov process [2] such that the firing rates of the stochastic transitions are kept higher for inputs with higher difficulty level landmarks. Table 2 describes the range of stochastic transition rates assigned to the GSPNRL model. The rate ranges in Table 2 are selected, so that: (i) at the lowest difficulty possible, the rate of forgetting is at the minimum, (ii) at the highest difficulty possible, the rate of remembering is at the minimum. The boundaries of the rate ranges are defined to produce results close to the empirical values. The stochastic transitions t₈, t₁₀, t₁₂, t₁₄, and t₁₆ can be assigned randomly picked values from the ranges defined in Table 2. A particular assignment of stochastic transition rates is dependent on the application. If a rate λ is to be used, the average time to fire (execute) will be 1/λ, because the model uses exponentially distributed firing delays. The distribution of firing time of transition t_i is given by the rule:

$$ F\left( x \right) = 1 - e^{{ - \lambda_{i} x}} . $$

Transitions t₈ and t₉ are conflicting transitions: if t₈ fires, then t₉ will become disabled and vice versa. Firing of t₈ means that the model will not retain the navigation command, whereas firing of t₉ will save the navigation command along with the landmark information. The pairs of stochastic transitions (t₈, t₉), (t₁₀, t₁₁), (t₁₂, t₁₃), (t₁₄, t₁₅), and (t₁₆, t₁₇) are developed so that the first transition in each pair, if fired, is responsible for showing the behavior of forgetting, say by not saving any of its input data. The second transition in each pair shows the remembering behavior by saving its inputs into the memory of an agent that uses the GSPNRL model.