How do dogs follow a scent, presumably the scent lingers on physical objects along the path?
RFID isn't directional enough either
Could the robot have a pair of ears able to detect ultrasound that would permit the robot to determine the direction of an ultasonic source carried by the person? The spacing of the ears would need have to be realistic but match the processing capability of the Arduino.
Otherwise the person could wear IR light sources, or feducials reflective of a light emitted by the robot.
Some of these would need to be visible to the robot whatever the person's orientation to the robot.
Ears fits in with the pet theme.