This article establishes an Explicit Model Predictive Control (EMPC) scheme for controlling the adhesion of a climbing Vortex Robot (VR). The VR utilizes an Electric Ducted Fan (EDF) as the Vortex Actuator (VA), where the dynamics have been identified via an Autoregressive-Moving-Average with eXternal input (ARMAX) identification scheme. An explicit controller via the use of a Constraint Finite Time Optimal Control (CFTOC) approach is designed in an offline manner and implemented for the case of the VR, where the adhesion reference is provided by a static force model. The presented approach results in a lookup table realization that ensures overall system stability in all state transitions, while being able to accurately control the adhesion force for arbitrary setup orientations. The efficacy of the proposed control scheme is demonstrated through experimental results involving a moving test surface under random inclinations and robot orientations.