The present invention discloses a moveable robot that includes a head, a main body, and a moving chassis. A transport mechanism is mounted on the lower part of the moving chassis. The head and the main body are carried by moving chassis. A moveable connection mechanism between the main body and the moving chassis enables relative movements between the two components. A sliding platform comprising a sliding mechanism between the head and the main body allows the head to move relative to the main body. A projection system can a display an image through a window in the head, and to project an interactive map on the ground. An optical sensing system can detect movements of users relative to the displayed map on the ground. The projection system and the optical sensing system in combination provides an interactive user interface for the users. The optical sensing system can also sense the environment to assist obstacle avoidance and route planning moveable robot.