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We consider systems composed of an unbounded number of uniformly designedlinear hybrid automata, whose dynamic behavior is determined by their relationto neighboring systems. We present a class of such systems and a class ofsafety properties whose verification can be reduced to the verification of(small) families of neighbouring systems of bounded size, and identifysituations in which such verification problems are decidable, resp. fixedparameter tractable. We illustrate the approach with an example fromcoordinated vehicle guidance, and describe an implementation which allows us toperform such verification tasks automatically.

Decidability of Verification of Safety Properties of Spatial Families of Linear Hybrid Automata