Industrial robotic systems increasingly operate as heterogeneous ecosystems in which production, maintenance, quality assurance, safety, and human–machine interaction are coupled through shared data and cross-layer constraints. Existing modeling approaches remain structurally fragmented: hierarchical taxonomies support decomposition, graph-based models primarily encode pairwise relations, and analytical layers are commonly attached as external pipelines. This paper proposes a hypergraph-based framework for the multi-contextual state representation of industrial robotic systems. The framework combines a multi-layer problem taxonomy, a formal definition of context as an active semantic processing unit, and a directed hypergraph model with signed incidence for representing dependency, interpretative, compositional, and cross-layer constraint relations without binary decomposition. The model is instantiated on grasping and maintenance examples and translated into a numerical interface for downstream analytical processing. Quantitative results are also reported. Benchmarking shows near-linear compile-time and star-expansion scaling, while comparison with pairwise encodings confirms lower representational overhead for higher-order relations. In a canonical grasping scenario, one-cycle hypergraph-grounded inference remains in the microsecond range on CPU, with a median latency of 2.264 µs. These results indicate that the proposed framework is computationally tractable as a representational substrate for context-aware analysis. The contribution of the paper is not a new control algorithm, but a formal representation and numerical translation layer for future learning-based and rule-based analytical methods.
Szilágyi et al. (Sat,) studied this question.