In this paper, we offer a novel AI planning representation, based on a Cartesian coordinate system, for enabling the autonomous operations of Multi-Robot Systems in 3D environments. Each robot in the system has to conform to unique actuation and connection constraints that create a complex set of valid configurations. Our approach allows Multi-Robot Systems to self-assemble themselves into larger structures via AI planning, with the overarching goal of providing structural capabilities in harsh and uncertain environments. In comparing four different PDDL (Planning Domain Definition Language) domain representations, we show that our novel formulation satisfies the practical requirements emerging from robot deployment in the real world, resulting in an AI planning system that is accurate and efficient. We scale up performance by implementing direct FDR (Finite Domain Representation) generation based on the best performing PDDL model, bypassing the PDDL-to-FDR translation used by the majority of modern planners. The proposed approach is general and can be applied to a broad range of AI problems involving reasoning in 3D spaces.