# Topological Navigation and Localization in
## 3 Topological Navigation and Localization for LHD
### Topological Map and Physical Representation  
The main component of the representation of the mine is the \"Topological Map\" (TM). Two types of nodes are defined on this map: (i) tunnel nodes and (ii) intersection nodes. A tunnel node is a section of the mine that can be traversed back and forth, i.e., it corresponds to a single path or trajectory between two physical points. Topologically, a tunnel node has two edges, connecting it with two intersection nodes. An intersection node may have multiple edges that connect it to other nodes, and it can also traverse back and forth. An example would be a fork in the tunnel, where the vehicle must choose one of the possible path alternatives. Each topological node contains a number of access points (APs) and waypoints (WPs), which are represented by a 2D pose within the node's coordinate system. APs connect different topological nodes; they signal the transitions between map nodes. WPs, on the other hand, correspond to specific poses within the topological node, each one containing relevant information for the navigation system, such as maximum driving speed. Examples of waypoints can be a location for dumping ore, a place to park the vehicle, or a location the vehicle must go through when traversing the node. As an example, Figure 3 shows a portion of a real mine, where a TM has been created. In this scenario, four main tunnels, T6, T7, T9, and T10, and one intersection, I0 (in green), define the map. It can also be seen that T9 contains a number of waypoints throughout its path, shown by arrows. Besides their associated 2D pose, APs and WPs have a defined heading. APs always face the outer side of the node they are in, but WPs always face in the predefined direction of the node. Because of this, APs and WPs can be connected in 4 different ways: front-to-front, front-to-back, back-to-front, and back-to-back (see Figure 4, the orange arrow is the default direction of the node). In Figure 5, a TM with 2 tunnel nodes, 1 intersection node, and its AP, WP, and the connections between them, is shown. Figure 3: Example of a topological map of a real mine. One of the problems that articulated vehicles face while traversing an underground mine is that they sometimes need to change their direction of movement, using a maneuver known as _inversion_. (See Figure 2). To tackle this problem, a Topological Movement's Map (TMM) is built automatically from the TM. To do this, for each AP and each WP in the TM, 6 nodes are created in the TMM. These 6 nodes represent how the vehicle would move through an AP or WP in the TM:  
1. [label=()]
2. Vehicle going towards the AP/WP moving forward (bucket facing the AP/WP). 3. Vehicle going towards the AP/WP moving backwards (rear bumper facing the AP/WP). 4. Vehicle going away from the AP/WP moving forward. 5. Vehicle going away from the AP/WP moving backwards. 6. Vehicle standing on the AP/WP facing in its same direction. 7. Vehicle standing on the AP/WP facing in its opposite direction. These new nodes in the TMM are then connected using the information on the topological map and a predefined set of rules that reflect how a vehicle would move between two different pairs of nodes in the TM. These rules are presented on Tables 1 and 2. Rules are slightly different when considering the special case of connecting APs from different TM nodes (see Table 2), because as these APs connect different TM nodes, they have the same physical location, and then connections between \"stopped\" nodes must be allowed. Figure 4: Types of connection between AP and WP. Figure 5: TM example showing one intersection node (Intersection 1), two tunnel nodes (Tunnel 1 and Tunnel 2), and the corresponding APs, WPs and connections between them. It is important to note that these connections are directional, and it is required to go through a \"stopped\" node ((v) or (vi)) to change the vehicle's direction of movement. Therefore, these rules must be applied in both directions of each connection. Nodes (v) and (vi), with the same origin AP/WP, are always connected.