Graph-Slam(一)
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GraphSLAM is a unifying algorithm for the offline
SLAM problem.It transforms the SLAM posterior into a graphical network,
representing the log-likelihood of the data. It then reduces this
graph using variable elimination techniques, arriving at a lowerdimensional
problems that is then solved using conventional optimization
techniques. As a result, GraphSLAM can generate maps
with
1 Mapping SLAM Problems into Graphs
1.1 The Offline SLAM Problem
In SLAM, time is usually discrete, and t labels the time index. The robot pose at time t is denoted
we will use
To acquire an environment map, the robot is able to sense. The measurement at time t is denoted
here
Some robotic systems are also are provided with a GPS system. Then the measurement is of the form
where
Finally, the robot changes its pose in SLAM by virtue of issuing control commands.The control asserted between time t−1 and time t is denoted
where
The offline SLAM posterior is now given by the following posterior probability over the robot path
This is the posterior probability over the entire path
We note that a key assumption in our problem formulation is the assumption of independent Gaussian noise.
1.2 GraphSLAM: Basic Idea
Figure 1 illustrates the GraphSLAM algorithm. Shown there is the graph that GraphSLAM extracts from four poses labeled
To compute a map posterior,GraphSLAM linearizes the set of constraints. The result of linearization is a sparse information matrix and an information vector. The sparseness of this matrix enables GraphSLAM to apply the variable elimination algorithm,thereby transforming the graph into a much smaller one only defined over robot poses. The path posterior map is then calculated using standard inference techniques. GraphSLAM also computes a map and certain marginal posteriors over the map; the full map posterior is of course quadratic in the size of the map and hence is usually not recovered.
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