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Children worldwide are becoming increasingly inactive, leading to significant wellness challenges. Initial findings from our research team indicate that robots could potentially provide a more effective approach (compared to other age-appropriate toys) for encouraging physical activity in children. However, the basis of this past work relied on either interactions with groups of children (making it challenging to isolate specific factors that influenced activity levels) or a preliminary version of results of the present study (which centered on just a single more exploratory method for assessing child movement). This paper delves into more controlled interactions involving a single robot and a child participant, while also considering observations over an extended period to mitigate the influence of novelty on the study outcomes. We discuss the outcomes of a two-month-long deployment, during which $N=8$ participants engaged with our custom robot, GoBot, in weekly sessions. During each session, the children experienced three different conditions: a teleoperated robot mode, a semi-autonomous robot mode, and a control condition in which the robot was present but inactive. Compared to our past related work, the results expanded our findings by confirming with greater clout (based on multiple data streams, including one more robust measure compared to the past related work) that children tended to be more physically active when the robot was active, and interestingly, there were no significant differences between the teleoperated and semi-autonomous modes in terms of our study measures. These insights can inform future applications of assistive robots in child motor interventions, including the guiding of appropriate levels of autonomy for these systems. This study demonstrates that incorporating robotic systems into play environments can boost physical activity in young children, indicating potential implementation in settings crafted to enhance children’s physical movement.