Capability Mapping Fundamentals

• Capability mapping is a formal process linking system requirements to semantically rich, technology-agnostic capabilities, facilitating dynamic system integration.
• Methodologies employ structural analysis, pattern matching, and semantic instantiation with bidirectional transformations to ensure accurate, interoperable skill realization.
• Applications span industrial automation, multi-robot coordination, and cloud services, enabling real-time resource allocation, performance analysis, and adaptive orchestration.

Capability mapping is the formal process of relating system requirements, resources, or functional elements to an explicit, structured set of capabilities. In technical domains such as robotics, industrial automation, human-robot teaming, and cloud computing, capability mapping enables reasoning, orchestration, and automated integration by transforming domain-specific descriptions into semantically rich, machine-interpretable models. These mappings serve as a bridge between heterogeneous technologies and facilitate advanced functionalities such as dynamic allocation, interoperability, performance analysis, and adaptive coordination.

1. Formal Definitions and Mathematical Foundations

Across domains, "capability" is defined as a technology-independent abstraction capturing what a system or agent can do, while "skill" often identifies the concrete, technology-dependent realization of a capability. Ontologies in manufacturing and robotics typically align with this distinction: a capability is equivalent to an abstract function (e.g., VDI 3682's ProcessOperator or IEEE 1872's Function), modeled as a mapping from a set of typed inputs to outputs,

$$c : \{\text{Inputs}\} \longrightarrow \{\text{Outputs}\}, \quad c \in \textsf{Capability}.$$

A skill is the implementation-level execution of a capability and is closely tied to actual interfaces, protocols, or state machines (e.g., OPC UA, REST, MQTT), with relations such as

$$\textsf{isRealizedBy}(s, c), \quad s \in \textsf{Skill},\ c \in \textsf{Capability}.$$

In human-robot teaming, capabilities are formalized as multidimensional vectors. Let $n$ be the number of distinct capabilities, $Q \subseteq \mathbb{N}_0$ a discrete rating scale (e.g., $Q = \{0, 1, ..., 5\}$), and $p^H, p^A \in Q^n$ the human and autonomous agent capability profiles. A required task imposes a requirement vector $r^k \in Q^{|B^k|}$ over indices $B^k \subseteq \{1..n\}$, leading to a "capability delta"

$\Delta^k = r^k - c^T,$

where $c^T = (f_j(c_j^H, c_j^A))_{j\in B^k}$ captures the team's present capability via a control distribution function $f_j$ (Mandischer et al., 2024).

In the digital manufacturing domain, mapping functions between model sets are defined formally. If $M_{aas}$ is the set of Asset Administration Shell (AAS) submodels and $M_{onto}$ the set of ontology individuals/triples, two total transformation functions are specified:

• $f_{a-o}: M_{aas} \rightarrow M_{onto}$ (AAS to ontology)
• $g_{o-a}: M_{onto} \rightarrow M_{aas}$ (ontology to AAS) with compositional identity under consistent naming (Silva et al., 2023).

2. Methodologies and Transformation Algorithms

Methodologies for capability mapping are domain-specific but converge on a few key principles: explicit model structure, bidirectional transformation logic, and semantic consistency.

In robotics and automation, mapping proceeds in a staged manner:

1. Structural analysis: Decompose the resource into components or modules according to reference models (e.g., VDI 2206 for robot structure or AML/AutomationML for process equipment).
2. Pattern matching: Associate each component or configuration with the corresponding capability classes from a taxonomy or ontology.
3. Semantic instantiation: For each matched capability, instantiate inputs, outputs, and properties (e.g., using IEC 61360 for DataElements).
4. Skill realization: For each capability, instantiate one or more Skill individuals, each bound to a genuine technology (e.g., OPC UA, REST API).
5. Interface and state modeling: Skills are linked to interface descriptions and executable state machines (often modeled after industry standards such as ISA-88).
6. Final output: Encode mappings as RDF triples (OWL), JSON (AAS), or AutomationML (for MTPs), as appropriate (Köcher et al., 2022, Silva et al., 2022).

In cloud computing, the mapping is formalized as a set function $f: R \to 2^M$, with $R$ a set of requirements (e.g., for scalability, annotation, or ontology population) and $M$ a set of available cloud mechanisms (e.g., Resource Cluster, Automated Scaling Listener). Each requirement is mapped to a subset of mechanisms that fulfill the associated technical specification via fit analysis (Adedugbe et al., 2020).

For human-robot capability mapping, the procedure is grounded in quantification scales, delta calculation, and algorithmic compensation. The process involves:

• Collection of capability vectors via standardized assessment (IMBA or similar);
• Calculation of the team capability via canonical aggregation (summation or max-type functions);
• Computation of the delta vector and associated norm to characterize the gap;
• Application of compensation logic, potentially including resource substitution or control redistribution across capability dimensions (Mandischer et al., 2024).

3. Reference Ontologies and Data Model Interoperability

Several reference ontologies and semantic models underpin capability mapping:

• VDI 3682 / IEEE 1872 / SUMO: Define abstract “ProcessOperator” (capability) and “Function” with semantic alignment relations.
• AuR-Cap: Provides domain-specific taxonomies for heterogeneous autonomous robots with explicit is-a hierarchies and composition relations.
• CaSkMan Ontology: Supplies a layered OWL-DL structure for distinguishing between Capability, Skill, Property, Constraint, and SkillInterface classes, supporting full reasoning and query via SPARQL (Silva et al., 2023, Silva et al., 2022).
• AAS Submodels: Hierarchically structure capability and skill information as JSON-based collections, supporting both implementation-independent (capability) and instance-specific (skill) declarations, with explicit linkages via semantic identifiers to external ontological references.

Bidirectional interoperability is established via declarative transformation languages: RML for unidirectional extraction from AAS to OWL, and RDFex (SPARQL-based) for ontology-to-AAS roundtrips. Mappings are guaranteed up to identifier conventions (e.g., IRI versus idShort) (Silva et al., 2023).

In process industry applications, module descriptions in AML-based MTPs are semantically lifted into capability/skill ontologies, enabling integration, orchestration, and automatic control across previously model-incompatible equipment via formally defined mapping functions and Object/DataProperty assignments (Köcher et al., 2022).

4. Practical Applications and Case Studies

Capability mapping underpins advanced operational contexts:

• Industrial Automation: Automated conversion of MTPs to skill ontologies supports plug-and-produce paradigms, semantic querying (e.g., “which modules provide mixing with temperature $\geq 80^\circ$C?”), consistency reasoning, and runtime orchestration via uniform interfaces (Köcher et al., 2022).
• Heterogeneous Multi-Robot Systems: Ontology-driven mapping permits vendor-agnostic task allocation, failure-tolerant reconfiguration, and dynamic planner invocation at the level of abstract capability rather than concrete device, supporting large-scale, multi-robot coordination (Silva et al., 2022).
• Human–Robot Collaboration: Capability mapping via capability deltas quantitatively assesses the “gap” between human/robot abilities and task requirements, enabling dynamic adjustment of control distributions and algorithmic assignment of compensatory actions (e.g., shifting the robot's operational share in a composite team) (Mandischer et al., 2024).
• Cloud Services: In semantic annotation platforms, the mapping between holistic requirements and cloud capability mechanisms provides architectural blueprints, aligning performance, scalability, SLA, and security requirements against composable microservices and infrastructure primitives (Adedugbe et al., 2020).

Concrete validation studies include laboratory plants with four process modules successfully lifted from AML to semantic web graphs, with SPARQL-driven competency questions yielding 100% mapping completeness and round-trip skill invocation times under 200 ms (Köcher et al., 2022). In robotics, case studies demonstrate the mapping from physical modules to capability/skill triples and robustness in automated task-robot pairing (Silva et al., 2022).

5. Evaluation Criteria, Benefits, and Limitations

Capability mapping is evaluated by several technical criteria:

• Mapping completeness and correctness: Empirical validation via competency questions and reasoning with OWL-DL reasoners.
• Performance: Real-time generation of ontology fragments or mapping transformations, with observed timescales (e.g., $< 1$ s for full AML module, $<$200 ms for skill invocation loop) (Köcher et al., 2022).
• Interoperability and extensibility: Cross-domain and cross-standard transformation between AAS, MTPs, OWL ontologies, and JSON/RDF models enables integration with legacy infrastructure and third-party systems (Silva et al., 2023).
• Scalability, consistency, and governance: Addressed via explicit mapping to infrastructure, scaling, management, and security mechanisms in conceptual cloud models (Adedugbe et al., 2020).

The principal benefits are mechanized interoperability, technology-agnostic system description, automatic reasoning, and runtime adaptability. Notable limitations include:

• Partial representation (current AAS templates do not capture all ontology-level elements);
• Manual engineering overhead in domain-specific extension and taxonomy construction;
• Scaling challenges for combinatorial n×m team scenarios (noted in human–robot teaming);
• Granularity limitations when mapping continuous real-world capabilities onto discrete rating scales (Silva et al., 2023, Silva et al., 2022, Mandischer et al., 2024).

6. Future Directions and Extensions

Ongoing research trajectories in capability mapping include:

• Automated extraction: Enhanced toolchains for auto-generating model elements from CAD, PLC code, URDF, or direct hardware introspection.
• Enrichment of ontological taxonomies: Community-driven expansion of domain capability catalogues, particularly in robotics and human–machine collaboration, to include richer sets of functionalities and quality constraints.
• Continuous estimation and adaptation: Integration of online learning algorithms (e.g., Gaussian process models) for real-time, sensor-driven estimation of both human and robot capability vectors (Mandischer et al., 2024).
• Dynamic and distributed orchestration: Microservice architectures capable of online round-trip mapping between industrial digital twins (AAS) and semantic web ontologies, with embedded validation (e.g., SHACL, OWL constraints) and naming service alignment.
• Multi-agent reasoning: Scalable mapping frameworks for n-human–m-robot teams and their dynamic control distributions, with explicit safety, criticality weightings, and involvement bounds.

Capability mapping continues to evolve as a foundational methodology, enabling coherent, interoperable, and adaptive behavior in increasingly complex, heterogeneous, and collaborative systems (Köcher et al., 2022, Silva et al., 2022, Silva et al., 2023, Mandischer et al., 2024, Adedugbe et al., 2020).