Graph-Based Maps¶

How warehouse topology is represented.

Graph Structure¶

A warehouse map is a weighted graph G = (V, E):

V: Set of nodes (vertices)
E: Set of edges connecting nodes
w: Edge weights (lengths)

Why Graphs?¶

Flexibility¶

Any layout can be represented
Non-rectangular warehouses
Multiple floors (separate graphs)

Efficiency¶

Standard graph algorithms
Fast pathfinding
Compact representation

Realism¶

Actual travel paths
Accurate distances
Physical constraints

Map Components¶

Nodes (Vertices)¶

{
  "id": 0,
  "name": "N0",
  "x": 0.0,
  "y": 0.0,
  "type": "aisle"
}

Properties:

Unique identifier
Position coordinates
Type classification

Edges¶

{
  "id": 0,
  "from": 0,
  "to": 1,
  "length": 3.0,
  "bidirectional": true
}

Properties:

Source and destination nodes
Physical length
Directionality

Map Topology¶

Connected Graph¶

All nodes must be reachable:

No isolated nodes
No disconnected regions
Robots can reach any location

Bidirectional vs One-Way¶

Bidirectional (default):

Robots can travel both directions
Most flexible

One-way:

Traffic flow control
Reduces congestion
More complex routing

Pathfinding¶

Shortest Path¶

Default routing finds shortest path by distance.

A* Algorithm¶

Uses heuristic for faster long-distance routing:

f(n) = g(n) + h(n)

Where:

g(n): Actual cost from start
h(n): Estimated cost to goal (Euclidean distance)

Congestion-Aware¶

Optional weighting by current congestion:

cost = distance + congestion_weight × congestion_score

Example Layouts¶

Simple Grid¶

5x5 grid with 3m spacing:

[N0]--[N1]--[N2]--[N3]--[N4]
 |     |     |     |     |
[N5]--[N6]--[N7]--[N8]--[N9]
 |     |     |     |     |
...

Zone-Based¶

Zone A          Zone B
[A1]--[A2]  |  [B1]--[B2]
 |     |    |   |     |
[A3]--[A4]--+--[B3]--[B4]
            |
        Main Aisle

Best Practices¶

Node Density¶

More nodes = finer granularity
Fewer nodes = simpler routing
Balance accuracy vs. complexity

Edge Lengths¶

Use actual physical distances
Consistent units (meters)
Account for corners/turns

Capacity Planning¶

Identify bottleneck paths
Add parallel routes if needed
Consider traffic flow