# Conflict Resolution in Mechatronic Collaborative Design Using Category Theory
## 4 Conflict Resolution Approach Based on Category Theory  
### Main Concepts  
Collaborative design process involves stakeholders from different backgrounds and areas aiming at reaching a common objective about product development [30]. These experts have different views on the system and make use of heterogeneous modeling languages and tools. However, interrelations between these models are inevitable. Consequently, conflicts may appear and have to be carefully considered to guarantee a high quality of the system under design. To tackle this challenge, we propose a new conflict resolution model, based on CT, aiming at diagnosing and handling the inconsistencies between the expert models involved in the collaborative process. On the one hand, our approach is based on rules and patterns, which makes it more flexible. This technique makes removing or adding new rules during the conflict resolution process possible, which in turn can reduce development time in mechatronic design. On the other hand, we use CT in our methodology as a formal framework to illustrate conflict detection and resolution. The motivation of using this theory is its powerful mathematical constructions. Using this theory, graphs will carry all the intuitions coming from the practice and have a formal meaning. Furthermore, the traceability of collaboration between the different stakeholders is ensured in a formal way by means of the different categories containing all the results of this exchange. Moreover, querying graphs in the conflict resolution process is based on category mapping through functors, which makes this action formal and easy at the same time. The architecture of our approach is illustrated in Figure 2. As a first step, the different parameters of the expert models have to be abstracted into parameters categorical graphs \(\mathrm{P_{m}CG}\) using CT constructions. This step provides a common formalism that makes the several expert models homogeneous despite their heterogeneity. Then, dependencies among the parameters are established by means of CT through the definition of morphisms representing the dependency coefficient among the different parameters (objects). At this level, the process of diagnosis and handling can start. A set of consistency rules (CRs) is established to identify the constraints to be respected. Then, the conflicts appeared during the collaboration between the EMs are detected through graph patterns matching against the parameters categorical graphs. If the conflicting parameter has some dependencies with another one, the related parameter has to be updated. Consequently, the corresponding parameters categorical graphs have also to be updated and the modified values will be saved in the updated Parameters Categorical Graphs UP\({}_{\text{m}}\)CG. Otherwise, one of the resolution actions (RA) is applied to the conflicting parameter in order to manage this contradiction. The final results of the conflict resolution process will be saved in the final parameters categorical graphs FP\({}_{\text{m}}\)CG to ensure the traceability of collaboration. Based on this architecture, a Conflict Resolution Problem (CRP) is defined as an 8-tuple: CRP = <EM, P\({}_{\text{m}}\)CG, UP\({}_{\text{m}}\)CG, FP\({}_{\text{m}}\)CG, DCG, CR, GP, RA>, which contains the following elements:  
* Expert Model (EM) refers to a set of models, EM\({}_{1}\), EM\({}_{2}\),..., EM\({}_{\text{n}}\), that are relative to different domains and involved in the collaborative process. Examples of expert models may be: a control model using for instance Simulink software [19], a multi-physical model using Modelica language within Dymola software [39], a 3D model with CATIA environment [40] in order to verify the integration of the whole mechanism, a Commercial off-the-shelf (COTS) model to select the appropriate components against the properties obtained from the simulation, etc. Figure 2: Architectural overview of the conflict resolution model.