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 E: Updating the ULM

Under the supervision of the control system, different blocks are activated to update the ULM. Let's assume that the region represented in Figure C6 is region E, located in the environment as indicated in Figure E1.

Figure E1. Accessibility: Discontinuous region. Places E1 and E4 are examined. Places E2 and E5 (shown in gray) contain obstacles. After exploration the initial region is divided in two. One that contains places E1, E4, E2, and E5 and another that contains places E3 and E6.

By using place-region connections place E1 (see 1 in Figure E2) activates region E (see 2 in Figure E2) and the activation spreads in the network using the region-place connections (see 3 in Figure E2). Thus, places E1, E2, E4, and E5 become active. Next, the activation spreads from places E1 and E4, using the place-place connections in the LLM, to places D6, D3, A6, B4, and B5 (see 4 in Figure E2). Then, the activation spreads back at the ULM using the place-region connections, and regions D, A, and B become active (see 2 in Figure E2). The connections between the activated regions (D, A and B) and the current region E are reinforced in the ULM. Because region F is not active the connection between region E and region F is weakened. The connections for the new region E' are updated in a similar fashion. Region E' activates places E3 and E6 at the LLM (see 3 Figure E2). Next, places B6, C4, F1, and F4 become active (see 4 in Figure E2). Next, regions B, C and F are activated in the ULM (see 2 in Figure E2). The activated regions and the new region E' are connected.

Figure E2. Update of region-region connections. Under the supervision of the control system, the current place  activates the following representations: current region , all places in current region , places in neighboring regions  and through the place-region connections the neighboring regions . Thick lines represent flow of information.


 

Figure E3. Region division. The obstacle that occupies places 2 and 5 divides the region in two subregions E and E'.

In sum, as a result of the ULM update, region E is connected to regions D, A and B, and region E' is connected to regions B, C, and F. Figure E3 shows how region E is split in two subregions.

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