Page 213 - Introduction to Autonomous Mobile Robots

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Path of the robot Belief states at positions 2, 3, and 4 Chapter 5
Figure 5.11
Example of multiple-hypothesis tracking (courtesy of W. Burgard [49]). The belief state that is
largely distributed becomes very certain after moving to position 4. Note that darker coloring repre-
sents higher probability.

µ
σ
mean plus a standard deviation parameter , thereby defining a Gaussian distribution.
The intended interpretation is that the distribution at each position represents the probabil-
ity assigned to the robot being at that location. This representation is particularly amenable
to mathematically defined tracking functions, such as the Kalman filter, that are designed
to operate efficiently on Gaussian distributions.
An alternative is to represent the set of possible robot positions, not using a single Gaus-
sian probability density function, but using discrete markers for each possible position. In
this case, each possible robot position is individually noted along with a confidence or
probability parameter (see figure 5.11). In the case of a highly tessellated map this can
result in thousands or even tens of thousands of possible robot positions in a single-belief
state.
The key advantage of the multiple-hypothesis representation is that the robot can explic-
itly maintain uncertainty regarding its position. If the robot only acquires partial informa-
tion regarding position from its sensors and effectors, that information can conceptually be
incorporated in an updated belief.
A more subtle advantage of this approach revolves around the robot’s ability to explic-
itly measure its own degree of uncertainty regarding position. This advantage is the key to
a class of localization and navigation solutions in which the robot not only reasons about
reaching a particular goal but reasons about the future trajectory of its own belief state. For
instance, a robot may choose paths that minimize its future position uncertainty. An exam-
A
B
ple of this approach is [141], in which the robot plans a path from point to point that
takes it near a series of landmarks in order to mitigate localization difficulties. This type of