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Occupancy Grids


Occupancy grids are used to represent a robot workspace as a discrete grid. Information about the environment can be collected from sensors in real time or be loaded from prior knowledge. Laser range finders, bump sensors, cameras, and depth sensors are commonly used to find obstacles in your robot’s environment.

Occupancy grids are used in robotics algorithms such as path planning (see robotics.PRM). They are used in mapping applications for integrating sensor information in a discrete map, in path planning for finding collision-free paths, and for localizing robots in a known environment (see robotics.MonteCarloLocalization). You can create maps with different sizes and resolutions to fit your specific application.

2-D occupancy grids have two representations:

A binary occupancy grid uses true values to represent the occupied workspace (obstacles) and false values to represent the free workspace. This grid shows where obstacles are and whether a robot can move through that space. Use a binary occupancy grid if memory size is a factor in your application.

A probability occupancy grid uses probability values to create a more detailed map representation. This representation is the preferred method for using occupancy grids. This grid is commonly referred to as simply an occupancy grid. Each cell in the occupancy grid has a value representing the probability of the occupancy of that cell. Values close to 1 represent a high certainty that the cell contains an obstacle. Values close to 0 represent certainty that the cell is not occupied and obstacle free. The probabilistic values can give better fidelity of objects and improve performance of certain algorithm applications.

Binary and probability occupancy grids share several properties and algorithm details. Grid and word coordinates apply to both types of occupancy grids. The inflation method also applies to both grids, but each grid implements it differently. The effects of the log-odds representation and probability saturation apply to probability occupancy grids only.

World and Grid Coordinates

When working with occupancy grids in MATLAB®, you can use either world or grid coordinates.

The absolute reference frame in which the robot operates is referred to as the world frame in the occupancy grid. Most Robotics System Toolbox™ operations are performed in the world frame, and it is the default selection when using MATLAB functions in this toolbox. World coordinates are used as an absolute coordinate frame with a fixed origin, and points can be specified with any resolution. However, all locations are converted to grid locations because of data storage and resolution limits on the map itself.

Grid coordinates define the actual resolution of the occupancy grid and the finite locations of obstacles. The origin of grid coordinates is in the top-left corner of the grid, with the first location having an index of (1,1). However, the GridLocationInWorld property of the occupancy grid in MATLAB defines the bottom-left corner of the grid in world coordinates. When creating an occupancy grid object, properties such as XWorldLimits and YWorldLimits are defined by the input width, height, and resolution. This figure shows a visual representation of these properties and the relation between world and grid coordinates.

Grid Coordinates from World Coordinate Inputs

When setting occupancy locations, you can input the locations in either grid or world coordinates. However, based on the limits of the grid, the locations are set to the closest grid locations. Edges of the grid belong to the lower-left grid location.

Show how locations are interpreted on the grid by creating an occupancy grid and setting points as occupied by obstacles. Then, plot the original input points over the map to show how they are interpreted. If any point within the grid cell is set as occupied, the entire grid cell is set as occupied.

Create an occupancy grid map and set obstacle locations.

map = robotics.BinaryOccupancyGrid(10,10,5);
xy = [5 5; 4.3 4.4; 5.6 5.3];

Display the map, original points, and set the axes limits to zoom in. You can see how the edge points affect the entire grid location status.

hold on
plot(xy(:,1),xy(:,2),'xr','MarkerSize', 20)
grid on
xlim([4 6])
ylim([4 6])

Inflation of Coordinates

Both the binary and normal occupancy grids have an option for inflating obstacles. This inflation is used to add a factor of safety on obstacles and create buffer zones between the robot and obstacle in the environment. The inflate method of an occupancy grid object converts the specified radius to the number of cells rounded up from the resolution*radius value. Each algorithm uses this cell value separately to modify values around obstacles.

Binary Occupancy Grid

The robotics.BinaryOccupancyGrid.inflate method takes each occupied cell and directly inflates it by adding occupied space around each point. This basic inflation example illustrates how the radius value is used.

Inflate Obstacles in a Binary Occupancy Grid

This example shows how to create the map, set the obstacle locations and inflate it by a radius of 1m. Extra plots on the figure help illustrate the inflation and shifting due to conversion to grid locations.

Create binary occupancy grid. Set occupancy of position [5,5].

map = robotics.BinaryOccupancyGrid(10,10,5);
setOccupancy(map,[5 5], 1);

Inflate occupied spaces on map by 1m.


Plot original location, converted grid position and draw the original circle. You can see from this plot, that the grid center is [4.9 4.9], which is shifted from the [5 5] location. A 1m circle is drawn from there and notice that any cells that touch this circle are marked as occupied. The figure is zoomed in to the relevant area.

hold on
theta = linspace(0,2*pi);
x = 4.9+cos(theta); % x circle coordinates
y = 4.9+sin(theta); % y circle coordinates
plot(5,5,'*b','MarkerSize',10) % Original location
plot(4.9,4.9,'xr','MarkerSize',10) % Grid location center
plot(x,y,'-r','LineWidth',2); % Circle of radius 1m.
axis([3.6 6 3.6 6])
ax = gca;
ax.XTick = [3.6:0.2:6];
ax.YTick = [3.6:0.2:6];
grid on
legend('Original Location','Grid Center','Inflation')

As you can see from the above figure, even cells that barely overlap with the inflation radius are labeled as occupied.

Occupancy Grids

The robotics.OccupancyGrid.inflate method uses the inflation radius to perform probabilistic inflation. Probabilistic inflation acts as a local maximum operator and finds the highest probability values for nearby cells. The inflate method uses this definition to inflate the higher probability values throughout the grid. This inflation increases the size of any occupied locations and creates a buffer zone for robots to navigate around obstacles. This example shows how the inflation works with a range of probability values.

Inflate Obstacles in an Occupancy Grid

This example shows how the inflate method performs probabilistic inflation on obstacles to inflate their size and create a buffer zone for areas with a higher probability of obstacles.

Create a 10m x 10m empty map.

map = robotics.OccupancyGrid(10,10,10);

Update occupancy of world locations with specific values in pvalues.

map = robotics.OccupancyGrid(10,10,10);
x = [1.2; 2.3; 3.4; 4.5; 5.6];
y = [5.0; 4.0; 3.0; 2.0; 1.0];

pvalues = [0.2 0.4 0.6 0.8 1];

updateOccupancy(map,[x y],pvalues)

Inflate occupied areas by a given radius. Larger occupancy values are written over smaller values. You can copy your map beforehand to revert any unwanted changes.

savedMap = copy(map);

Log-Odds Representation of Probability Values

When using occupancy grids with probability values, the goal is to estimate the probability of obstacle locations for use in real-time robotics applications. The OccupancyGrid class uses a log-odds representation of the probability values for each cell. Each probability value is converted to a corresponding log-odds value for internal storage. The value is converted back to probability when accessed. This representation efficiently updates probability values with the fewest operations. Therefore, you can quickly integrate sensor data into the map.

The log-odds representation uses the following equation:


Log-odds values are stored as int16 values. This data type limits the resolution of probability values to ±0.001 but greatly improves memory size and allows for creation of larger maps.

Probability Saturation

When updating an occupancy grid with observations using the log-odds representation, the values have a range of –∞ to ∞. This range means if a robot observes a location such as a closed door multiple times, the log-odds value for this location becomes unnecessarily high, or the value probability gets saturated. If the door then opens, the robot needs to observe the door open many times before the probability changes from occupied to free. In dynamic environments, you want the map to react to changes to more accurately track dynamic objects.

To prevent this saturation, update the ProbabilitySaturation property, which limits the minimum and maximum probability values allowed when incorporating multiple observations. This property is an upper and lower bound on the log-odds values and enables the map to update quickly to changes in the environment. The default minimum and maximum values of the saturation limits are [0.001 0.999]. For dynamic environments, the suggested values are at least [0.12 0.97]. Consider modifying this range if the map does not update rapidly enough for multiple observations.

See Also

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