<p>Structural controllability challenges arise from imprecise system modeling and system interconnections in large-scale systems. In this paper, we study structural control of bilinear systems on the special Euclidean group. We employ graph-theoretic methods to analyze the structural controllability problem for driftless bilinear systems and structural accessibility for bilinear systems with drift. This facilitates the identification of a sparsest pattern necessary for achieving structural controllability and discerning redundant connections. To obtain a graph-theoretic characterization of structural controllability and accessibility on the special Euclidean group, we introduce a novel idea of solid and broken edges on graphs; subsequently, we use the notion of transitive closure of graphs.</p>