ELSEVIER.PLAN.ACTIVITY.AND.INTENT.RECOGNITION.THEORY.AND.PRACTICE.1ST.EDITION.2014 by Unknown

Author:Unknown
Format: epub
Published: 0101-01-01T00:00:00+00:00

7.2.2 Formal Modeling

This section provides mathematical details of the BToM framework sketched previously; this can be skipped by the casual reader. First, we describe the construction of the state space, action space, state-transition distribution, observation space, and observation distribution used for POMDP planning. We then derive the formation and dynamics of the BToM representation of agents’ beliefs and desires. Finally, we derive the Bayesian computations that support joint belief and desire inference, then explain how model predictions are generated for our experiment.

In the food-truck domain, the agent occupies a discrete state space of points in a 2D grid. The world state space is the set of possible assignments of the K, L, and M trucks to parking spots (consisting of 13 configurations in total). For simplicity, we assume that the world is static (i.e., that the locations of the trucks do not change over the course of a episode), although the extension to dynamic worlds is straigntforward (e.g., allowing trucks to arrive, depart, or move). The action space includes actions North, South, East, West, Stay, and Eat. The state-transition distribution represents the conditional probability of transitioning to agent state at time , given the world , the agent state , and action at time . Valid movement actions are assumed to yield their intended transition with probability and to do nothing otherwise; invalid actions (e.g., moving into walls) have no effect on the state. The Eat action is assumed to lead to a special “Finished” state if selected when the agent is at the location of a food truck and to have no effect on the state otherwise.

The agent’s visual observations are represented by the isovist from its present location: a polygonal region containing all points of the environment within a 360-degree field of view [36,94]. Example isovists from different locations in one environment are shown in Figure 7.2. The observation distribution is constructed by first computing the isovist for every agent and world state pair in . Then, for each agent state , the isovists for all worlds are compared to establish which sets of worlds are perceptually distinguishable from that agent state. In the food-truck domain, worlds are distinguished by the locations of the food trucks.

We assume that the probability of observing which truck is in a parking spot is proportional to the area of that grid cell contained within the isovist. We model observation noise with the simple assumption that with probability , the agent can fail to notice a truck’s presence in a parking spot, mistakenly observing the symbol that “nothing” is there instead. From a given agent state, all perceptually distinguishable worlds are assumed to generate different observation symbols; worlds that are indistinguishable will emit the same observation symbol. For example, in Figure 7.2, Frames 5 and 15, the observation symbol will be consistent with only worlds containing the Korean truck in the Southwest parking spot and either the Lebanese truck, Mexican truck, or nothing in the Northeast parking spot. The observation symbol in Frame 10 will uniquely identify the state of the world.

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