Occupancy Mapping

Problem Statement

Occupancy mapping converts range observations into a probabilistic spatial model for collision checking and navigation. It underpins path planning and local obstacle avoidance.

Model and Formulation

Log-odds update for each cell:

L_{t} (m_{i}) = L_{t - 1} (m_{i}) + \log \frac{p (m_{i} | z_{t})}{1 - p (m_{i} | z_{t})} - L_{0}

Probability recovery:

p (m_{i}) = 1 - \frac{1}{1 + \exp (L_{t} (m_{i}))}

Algorithm Procedure

Ray-cast each lidar measurement through the grid.
Mark traversed cells as free and endpoint as occupied.
Update log-odds with inverse sensor model.
Export occupancy map to planning modules.

Tuning and Failure Modes

Beam angles are body-referenced; the vehicle heading has to go in too. Integrating every scan as though the vehicle pointed along +x produces a map that is correct only while it flies straight and smears progressively as it turns.
Treat a range near the sensor maximum as a no-return. Range noise pushes a genuine miss just under the limit, and marking that cell occupied paints a phantom obstacle at the edge of every scan — a ring of false wall around the vehicle. Gate the occupied update with a margin.
Log-odds must be clipped, or the sigmoid overflows once a cell has been seen enough times.
Incorrect sensor model causes inflated false positives/negatives.
Dynamic obstacles can leave ghost occupancy without decay logic.
Grid resolution too coarse obscures narrow passages.

Implementation and Execution

bash

python -m uav_sim.simulations.perception.occupancy_mapping

Evidence

Occupancy Mapping

Occupancy Mapping ​

Problem Statement ​

Model and Formulation ​

Algorithm Procedure ​

Tuning and Failure Modes ​

Implementation and Execution ​

Evidence ​

References ​

Related Algorithms ​

Occupancy Mapping

Problem Statement

Model and Formulation

Algorithm Procedure

Tuning and Failure Modes

Implementation and Execution

Evidence

References

Related Algorithms