Global Mapping: Minimal Route Graphs Under Spatial Constraints
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The matching of AGVGs as described in the previous chapter works well as long as the annotated metric information is reliable. This makes the approach well suited for identifying correspondences in AGVGs perceived in short order. However, while the robot moves around, the uncertainty, for instance in the position estimates of the nodes, accumulates and can grow without bounds. As a result of this and due to the fact that our matching algorithm currently does not bridge between different parts of the map AGVG, correctly closing cycles in the graph which correspond to large loops in the environment becomes difficult.
Therefore, a global mapping framework has to be built on top of the AGVG matching, which is the topic of this chapter. Our approach is to deal with the global mapping and loop closing problem by focusing on determining the correct discrete graph topology, relying on coarse but dependable spatial information instead of relying on the uncertainty-afflicted concrete metric annotations. The idea is to first determine the correct high-level graph structure using a multi-hypothesis tracking approach to deal with the uncertainty at the topological level. A concrete (H)AGVG can then be derived from a specific hypothesis.
As a consequence of this idea, we here regard the global mapping problem as the problem of determining the correct topology of a graph-like environment from a sequence of observations and interpret it as the task of finding a minimal route graph model that is consistent with the observations. The minimal model finding formulation of the mapping problem directly leads to a multi-hypothesis approach in which multiple consistent route graph hypotheses are tracked simultaneously.
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