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Consider a fibration \[p:E\to S^{p-1}\] with fiber $F$. We have the followingnatural question: Under what conditions does this fibration admit across-section? Our purpose is to discuss this problem when the fibration $p$ isthe Milnor fibration $f_{\mid}:f^{-1}(S^{p-1}_{\delta})\cap D^{n}_{\epsilon}\toS^{p-1}_{\delta}$ with Milnor fiber $F_f$ and the Milnor fibration ofarrangements $Q:\mathcal{M}(\mathcal{A})\to \mathbb{C}^\ast$ with fiber$F=F(\mathcal{A})$. Furthermore, we use our results to study the taskingplanning problem for the Milnor fibration as a work map and we give the taskingalgorithms.

Cross-sections of Milnor fibrations and Motion planning