This paper proposes an autonomous-robot following controller that can integrate information provided from behavioral cues of the leader to increase the reliability and the performance of following. The controller continuously estimates the future predicted position of the leader as it moves, and then directs the follower robot to this position. A Kalman filter is employed for an estimation that uses vision-based measurements of leader position, a dynamic model of the leader, and a behavioral-cue model of the leader. The behavioral-cue model serves to either tune the dynamic model and/or create pseudomeasurements to further help the Kalman filter estimate the leader's future position. Once the leader's future position is estimated, a trajectory planner plans a path to the future position, and a motor controller implements the required control signals to the robot wheels. It is suggested that this controller may have particular importance for human following by autonomous robots in future human-robot interaction environments.