In the provision of robot‐assisted personal services, the ergonomic design of the phase when a robot approaches a human being is important for the efficacy, efficiency, and safety of human‐robot interaction. For this reason, an empirical user study was conducted, using a repeated measures fractional factorial design. The participants (n  =  30) were approached 30 times by the 1.45‐m‐tall service robot Care‐O‐bot® 3 under different conditions to investigate what influences the distances that humans will accept between themselves and an approaching robot. The results show that participant body position, robot speed, and speed profile significantly influence the accepted distances. Furthermore, an effect of habituation was found for the repeated approaches. Significant effects of participant age and gender as well as robot appearance on the accepted distance were not found.