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We construct "higher" motion planners for automated systems whose space ofstates are homotopy equivalent to a polyhedral product space$Z(K,\{(S^{k_i},\star)\})$, e.g. robot arms with restrictions on the possiblecombinations of simultaneously moving nodes. Our construction is shown to beoptimal by explicit cohomology calculations. The higher topological complexityof other families of polyhedral product spaces is also determined.

The higher topological complexity of subcomplexes of products of spheres---and related polyhedral product spaces