Kyuhwan Yeon

Kyuhwan Yeon

I enjoy researching Physical AI

Occupancy Grid

Published:

Occupancy Grid

Definition

  • Discretized fine grain grid map

    • which can be 2D or 3D

  • Each grid square of the occupancy grid indicates if a static or stationary object is present in that grid location.

    • Example
      • Trees and buildings
      • Curbs and other non drivable surfaces

  • Each cell is a binary value

Assumption of Occupancy Grid

  • Static environment
  • Independence of each cell
  • Known vehicle state at each time step

Sensor

  • Example
    • Lidar
  • Data filtering
    • Ground plane should be filtered (Drivable road surface)
    • Objects above car height
    • Dynamic objects
      • All vehicles, bicycles, pedestrians..
  • Noise
    • There are noise –> we need probabilistic occupancy grid!

Probabilistic occupancy grid

In order to handle the sensor noise, we can use probabilistic occupancy grid

  • Probability of occupancy will be stored
\[m^i\in {0,1}\]
  • A belief map is built
\[bel_tm^i=p(m^i|y,x)\\ m^i = current\space map\space cell \\ y,x = Sensor \space measurement \space for \space given \space cell\]
  • Threshold of certainty will be used to establish occupancy

Bayesian update of the occupancy grid

  • To improve robustness multiple time steps are used to produce the current map
\[bel_tm^i=p(m^i|(y,x)_{1:t})\\\]
  • Bayes’theroem applied for at each update step for each cell! \(bel_tm^i=\eta p(y_t|m^i)bel_{t-1}(m^i)\\ p(y_t|m^i) = current\space measurement\\ bel_{t-1}(m^i) = previous \space belief \space map \\ \eta =normalizer \space constant\)