Exploration and Navigation Using Hierarchical Cognitive Maps

Nestor Schmajuk1 and  Horatiu Voicu 2
 1 Department of Psychological and Brain Sciences, Duke University
2 Institute for Intelligent Systems, University of Memphis

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Appendix A: Cognitive Map Memory Size

Appendix B: Decision Time

Appendix C: Description of the Associative Network

Appendix D: Basic Procedures

Appendix E: Updating the Upper Level Map

Appendix C: Description of the Associative Networks

In the associative network shown in Figure 3, the connections Vi,j and Vj,i between the neuron representing place (or region) i (where the agent is located) and each neuron representing neighboring places (or regions) j are updated as follows

Vi,j  = Vj,i  = 1 if place  or region j can be accessed from place or region i,

Vi,j  = Vj,i  = 0 otherwise                                                                           [1]

At each location, the Motivation System activates the desired goal (e.g., unvisited places or regions), and the goal activates Place (Region) j where it is found,

pi = Wi,h Goal h                                                                                       [2]

This activation spreads through the network by using the following equation

pj = η Σi Vi,j pi                                                                                        [3]

When the location (Place or Region) of the agent is activated or the number of iterations is greater than R, the maximum number of iterations the spreading of activation stops. The activation of all neurons represents a gradient that is used for planning a path to the closest goal. For each place m, this is accomplished by choosing

Next Place (Region) = Maxn pn                                                                            [4]

where n denotes a neighbor of place (region) m.

Equation 4 ensures that the agent will move in the direction of the nearest goal if all goals are of the same magnitude. When several neighboring places i have an identical Goal value, priorities are used to decide the next place. Priorities are given in the following order: North, West, East, North-West, North-East, South,  South-West, and  South-East.

Parameter η, (η = .5) which controls the attenuation at each reinjection in the network, was chosen to obtain an adequate signal at the neurons representing the goal(s). R, the maximum number of reinjections, (R= 625) was selected to ensure that the representation of the location of the agent is activated from any place in the environment where the goal can be found.

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