Tracking Control

In order to follow a human, tracking control is performed. Many studies have been performed in the field of the tracking control. However, the trajectory which a mobile robot tracks is limited in most cases to continuous and smooth ones. A human-following robot should be able to track actual human walking trajectories, including abrupt changes in velocity and direction. Therefore, stable tracking may not be achieved when conventional tracking control is used. A special control method for the mobile robot to follow humans is required.

In the control of a non-holonomic mobile robot, Brockett's theorem proved that a smooth state feedback law for an asymptotically stable to one point of the state space does not exist[15]. However, it is necessary to construct a closed-loop control system in which the error between the reference point and the state vector of a mobile robot should become zero for the tracking control of a mobile robot. In recent years, various closed-loop control systems which can overcome the feedback stabilization impossibility of Brockett's theorem, have been proposed. [16] proposed piecewise continuous controllers which neglect the "smoothness" and [17] proposed tracking control in which a mobile robot follows the trajectory planned as a function of time. These techniques are very effective in tracking control.

In ISpace, since a human walking trajectory is newly generated in every step, it can be considered that it is a function of time. Therefore, the application of tracking control is effective. However, although the target trajectory of a mobile robot is continuous and smooth in the usual tracking control, a human-following robot tracks the actual human walking trajectory that is generally unstable. Stable human following may not be achieved when the usual tracking control is used. In the following subsection, a tracking control method in ISpace for following humans is proposed.