The robots that will be needed in the near future are human-friendly robots that are able to coexist with humans and support humans effectively. To realize this, humans and robots need to be in close proximity to each other as much as possible. Moreover, it is necessary for their interactions to occur naturally. It is desirable for a robot to carry out human following, as one of the human-affinitive movements. The human-following robot requires several techniques: the recognition of the moving objects, the feature extraction and visual tracking, and the trajectory generation for following a human stably. In this research, a predictable intelligent space is used in order to achieve these goals. An intelligent space is a 3-D environment in which many sensors and intelligent devices are distributed. Mobile robots exist in this space as physical agents providing humans with services. A mobile robot is controlled to follow a walking human using distributed intelligent sensors as stably and precisely as possible. The moving objects is assumed to be a point-object and projected onto an image plane to form a geometrical constraint equation that provides position data of the object based on the kinematics of the intelligent space. Uncertainties in the position estimation caused by the point-object assumption are compensated using the Kalman filter. To generate the shortest time trajectory to follow the walking human, the linear and angular velocities are estimated and utilized. The computer simulation and experimental results of estimating and following of the walking human with the mobile robot are presented.