This paper is concerned with the navigation of personal robots in human-populated environments. The behavior of a person among its peers is governed by a number of unspoken social rules, e.g. maintaining an appropriate distance. The primary contribution of this paper is a navigation scheme that is anthropomorphic, i.e. that emulates human behaviors and seeks to adhere to these social rules. Unlike previous works in this area, the focus herein is on dynamic scenarios. The navigation scheme proposed explicitly reasons on the future behavior of the people involved so as to produce better socially acceptable trajectories (not to mention safer trajectories as well). The navigation scheme relies upon a novel cost function called the social costmap that captures in a unified way the different social rules imposed by the people populating the robot's workspace.