Trust evaluation and trust establishment play crucial roles in the management of trust within a multi-agent system. When it comes to collaboration systems, trust becomes directly linked to the specific roles performed by agents. The Role-Based Collaboration (RBC) methodology serves as a framework for assigning roles that facilitate agent collaboration. Within this context, the behavior of an agent with respect to a role is referred to as a process role. This research paper introduces a role engine that incorporates a trust establishment algorithm aimed at identifying optimal and reliable process roles. In our study, we define trust as a continuous value ranging from 0 to 1. To optimize trustworthy process roles, we have developed a consensus-based Gaussian Process Factor Graph (GPFG) tool. Our simulations and experiments validate the feasibility and efficiency of our proposed approach with autonomous robots in unsignalized intersections and narrow hallways.