1. A robot motion data processing apparatus, comprising: a data extractor configured to intermittently extract restoration motion data from an input motion trajectory of a robot; and a data restorer configured to generate an output motion trajectory corresponding to the input motion trajectory based on a hardware operation limit of the robot and the restoration motion data, wherein the output motion trajectory does not exceed the hardware operation limit of the robot, wherein the data restorer is further configured to: generate an estimated trajectory estimated based on a received first restoration motion data; and generate a tracking trajectory of a second restoration motion data based on the second restoration motion data and a current robot motion data indicated by an end point of the estimated trajectory to generate the output motion trajectory in real time, in response to the second restoration motion data being received, wherein the tracking trajectory is generated to track estimated motion data, and wherein the estimated motion data is an estimate of a motion of the robot after a time from a point when the second restoration motion data is received based on the second restoration motion data.