The goal of the current work was to develop an interaction management system for a mobile robot companion. In comparison to many desktop computer applications, such a robot poses a number of new scientific questions that need to be addressed by its interaction management system. More specifically, the interaction management system should fulfill the following 8 requirements of Human-Robot Interaction (HRI): (1) handle cooperative interaction, (2) enable mixed-initiative interaction style, (3) separate interaction from domain task execution, (4) account for multi-modality of embodied interaction, (5) facilitate recognition of interaction initiated by users, (6) make use of different modalities in a meaningful way, (7) enable social behaviors, and (8) contribute to the usability of the entire robot system. In the current work, a powerful computational model of multi-modal grounding, the MMPDA model, was proposed. This model improves the existing grounding models and naturally supports multi-modal embodied communication in HRI. For the robot BIRON, the MMPDA model was implemented within two Implementation-Evaluation-Cycles (IEC), in which users played an important role in the determination of implementation foci. In the course of the IECs, various functions and behaviors were realized and their benefits were also proven in the user studies of each cycle. The MMPDA model and the implemented system completely fulfill the above eight requirements of HRI.