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In this paper, we present the design, implementation, and user study evaluation of a socially assistive robot (SAR) system designed to engage elderly users in physical exercise aimed at achieving health benefits and improving quality of life. We discuss our design methodology, which incorporates insights from psychology research in the area of intrinsic motivation, and focuses on maintaining engagement through personalized social interaction. We describe two user studies conducted to test the motivation theory in practice with our system. The first study investigated the role of praise and relational discourse in the exercise system by comparing a relational robot coach to a nonrelational robot coach. The second study evaluated participant preferences regarding user choice in the task scenario. Both studies served to evaluate the feasibility and overall effectiveness of the robot exercise system. The results of both studies are presented; they show a strong user preference for the relational over the nonrelational robot in terms of enjoyableness, companionship, and as an exercise coach, varying user preferences regarding choice, and high user ratings of the system across multiple metrics. The outcomes of the presented user studies, brought together, support the motivational capabilities of the robot, and demonstrate the viability and usefulness of the system in motivating exercise in elderly users.