Organizations collaborate with each other for resource sharing and task performing. To protect their resources from unauthorized access the organization domains adopt own access control models. The collaboration thus faces a problem that how a secure collaboration is built between the domains with distinct access control models. Currently there are approaches focusing on role based access control model (RBAC), where role mapping is considered to be the main technique. It assumes that all organizations adopt RBAC model, then builds a global access control policy on role mappings. However if the organization domains, also including collaboration domain, use distinct access control models, role mapping and global policy can not be built on these models. In this paper we propose an equivalent access based approach and introduce a mediator involved collaboration pattern, where access control model entities have corresponding mapping and linking sets on which the equivalent accesses are built. Collaboration also introduces the ”Inter Domain Role Mapping” (IDRM) problem and we thus propose new algorithms for IDRM problem based on flat and hierarchical role structures, in addition we also introduce the necessary constraints transforming between organization and collaboration domains. Finally we analyzes our algorithms and present the testing and comparison results with existed approaches.