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