In this paper, a real-time trajectory planning method which is effective for a robot to track a moving object is derived. This method generates the optimal trajectory based on the minimum acceleration criterion whose position and velocity are coincident with those of a moving object at predefined time. Therefore, this method is effective for reliable capture of a moving object. First, the optimal trajectory for a moving object with constant velocity is derived. The problem is formulated as an inhomogeneous regulator problem, and the optimal trajectory to minimize a cost function is solved analytically. Next, the way to generate the trajectory when the maximum speed or acceleration is limited is discussed. Optimal trajectory planning for a moving object with acceleration or rotation is developed also. Finally, results of experiments to capture moving objects are presented. The experimental system consists of a 3-DOF manipulator, a dummy object, a CCD hand-eye camera and a vision processing system. The manipulator and dummy object are floating on a plate base using air bearings. The vision system can detect the position/direction of the dummy object every 17 [msec] .
