The Average Landmark Vector (ALV) method is a biologically inspired navigation strategy used by insects (like desert ants) and mobile robots to return to a "Home" location without complex maps.
1. The Concept
Instead of memorizing a full picture (snapshot) of the home location, the agent simply calculates the average direction of all visible landmarks. This average direction is a single vector called the ALV.
2. Calculating the ALV
For a set of \(n\) landmarks, if the vector pointing from the robot to the \(i\)-th landmark is \(\vec{v}_i\), the Average Landmark Vector is:
$$ \vec{ALV} = \frac{1}{n} \sum_{i=1}^{n} \vec{v}_i $$
Vectors: Typically, standard ALV uses Unit Vectors (magnitude = 1), meaning it only cares about direction. However, some variations use the full distance vector. You can toggle this using the checkbox in the simulation.
3. Homing
To return home, the robot compares its current ALV (\(\vec{A}_{curr}\)) with the stored ALV at home (\(\vec{A}_{home}\)). The difference between these two vectors gives the homing direction \(\vec{H}\):
$$ \vec{H} = \vec{A}_{curr} - \vec{A}_{home} $$
By moving in the direction of \(\vec{H}\), the robot reduces the discrepancy between the current view and the home view.
Reference: Goldhoorn, A., et al. (2007). "Using the Average Landmark Vector Method for Robot Homing". CCIA.