We present a method for a mobile robot to follow a person autonomously where there is an interaction between the robot and human during following. The planner takes into account the predicted trajectory of the human and searches future trajectories of the robot for the path with the highest utility. Contrary to traditional motion planning, instead of determining goal points close to the person, we introduce a task dependent goal function which provides a map of desirable areas for the robot to be at, with respect to the person. The planning framework is flexible and allows encoding of different social situations with the help of the goal function. We implemented our approach on a telepresence robot and conducted a controlled user study to evaluate the experiences of the users on the remote end of the telepresence robot. The user study compares manual teleoperation to our autonomous method for following a person while having a conversation. By designing a behavior specific to a flat screen telepresence robot, we show that the person following behavior is perceived as safe and socially acceptable by remote users. All 10 participants preferred our autonomous following method over manual teleoperation.