Autonomous UAV Algorithm Handbook

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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 ​

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

Tuning and Failure Modes ​

  • 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

References ​