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In the present study we investigated human-robot and robot-human approach distances. We found that subjects' personality profiles influence personal spatial zones in human-robot interaction experiments. We tested two hypotheses: first, we predicted that approach distances preferred by humans when interacting with a robot would be comparable to those preferred when humans interact socially with each other. Our experiments involving humans interacting with a mobile robot confirm this hypothesis. However, surprisingly, a large minority of subjects in the experiments took up positions which were significantly closer, suggesting that they were not treating the robot as a "social entity". We then tested the hypothesis that common personality factors exist which could be used to predict subjects' likely approach distance preferences. The subjects' personalities were assessed using several traits from the three-factor Eysenck personality model. Further analysis of the data identified four new factors, different from Eysenck's model, tentatively labeled "proactiveness", "social reluctance", "timidity" and "nervousness". When testing for correlations between approach distances and personality data, "proactiveness" correlates with social distance, i.e. subjects that score higher on this factor come less close to the robot. We discuss the potential suitability of personality factors to predict approach distances in human-robot interaction experiments.