Page 268 - Introduction to Autonomous Mobile Robots

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Mobile Robot Localization
a
where and define the learning and forgetting rate and n and n are the number of
b
s u
k
matched and unobserved predictions up to time , respectively. The update of the covari-
ance matrix Σ can be done similarly to the position update seen in the previous section. In
t
map-building the feature positions and the robot’s position are strongly correlated. This
forces us to use a stochastic map, in which all cross-correlations must be updated in each
cycle [55, 113, 136].
The stochastic map consists of a stacked system state vector:
T
X = x k() x k() x k() … x k() (5.71)
r
1
n
2
and a system state covariance matrix:

C C C … C
rr r1 r2 rn
C 1r C 11 …… C 1n
Σ = C …… … C (5.72)
2r 2n
…… ………
C nr C n1 C n2 … C nn

where the index r stands for the robot and the index i = 1 to n for the features in the map.
In contrast to localization based on an a priori accurate map, in the case of a stochastic
map the cross-correlations must be maintained and updated as the robot is performing auto-
matic map-building. During each localization cycle, the cross-correlations robot-to-feature
and feature-to-robot are also updated. In short, this optimal approach requires every value
in the map to depend on every other value, and therein lies the reason that such a complete
solution to the automatic mapping problem is beyond the reach of even today’s computa-
tional resources.

5.8.2 Other mapping techniques
The mobile robotics research community has spent significant research effort on the prob-
lem of automatic mapping, and has demonstrated working systems in many environments
without having solved the complete stochastic map problem described earlier. This field of
mobile robotics research is extremely large, and this text will not present a comprehensive
survey of the field. Instead, we present below two key considerations associated with auto-
matic mapping, together with brief discussions of the approaches taken by several auto-
matic mapping solutions to overcome these challenges.