Page 215 - Introduction to Autonomous Mobile Robots

Chapter 5
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information to navigate robustly in an array of environments, as we shall see in the case
studies below.

5.5 Map Representation

The problem of representing the environment in which the robot moves is a dual of the
problem of representing the robot’s possible position or positions. Decisions made regard-
ing the environmental representation can have impact on the choices available for robot
position representation. Often the fidelity of the position representation is bounded by the
fidelity of the map.
Three fundamental relationships must be understood when choosing a particular map
representation:

1. The precision of the map must appropriately match the precision with which the robot
needs to achieve its goals.
2. The precision of the map and the type of features represented must match the precision
and data types returned by the robot’s sensors.
3. The complexity of the map representation has direct impact on the computational com-
plexity of reasoning about mapping, localization, and navigation.
In the following sections, we identify and discuss critical design choices in creating a
map representation. Each such choice has great impact on the relationships listed above and
on the resulting robot localization architecture. As we shall see, the choice of possible map
representations is broad. Selecting an appropriate representation requires understanding all
of the trade-offs inherent in that choice as well as understanding the specific context in
which a particular mobile robot implementation must perform localization. In general, the
environmental representation and model can be roughly classified as presented in chapter
4, section 4.3.

5.5.1 Continuous representations
A continuous-valued map is one method for exact decomposition of the environment. The
position of environmental features can be annotated precisely in continuous space. Mobile
robot implementations to date use continuous maps only in 2D representations, as further
dimensionality can result in computational explosion.
A common approach is to combine the exactness of a continuous representation with the
compactness of the closed-world assumption. This means that one assumes that the repre-
sentation will specify all environmental objects in the map, and that any area in the map
that is devoid of objects has no objects in the corresponding portion of the environment.
Thus, the total storage needed in the map is proportional to the density of objects in the
environment, and a sparse environment can be represented by a low-memory map.