toni first_draft
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@@ -53,7 +53,7 @@
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to the simple transition \refeq{eq:transSimple} addresses only minor local errors
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% like not sticking too close to walls. In most cases this lead only to slight improvements
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and is therefore not further evaluated.
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To examine the contribution our approach is able to provided, we will have a closer look
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To examine the contribution our approach is able to provide, we will have a closer look
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at a long walk with many stairs, intentionally leaving the shortest path several times,
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named path 4 (see fig. \ref{fig:paths}).
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%
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