1. A robot picking system, comprising: a robot that picks up a work in a stocker accommodating a plurality of works; a control device that controls an operation of the robot; and an image acquiring device that acquires image data including information related to the plurality of works, wherein the robot is secured on a base at a fixed location, the robot comprising a plurality of arm sections, and a ort ser mounted to an end of the arm sections, and wherein the control device comprises: a candidate data generating unit that generates candidate data including information of candidate works that are candidates of a picking-up target using the image data, a posture data generating unit that generates posture data including information of a posture and a position of the arm sections and the gripper of the robot, a trajectory data generating unit that generates trajectory data including information of trajectory to each of the candidate works using the posture data and the candidate data, and a target work selecting unit that selects a target work that is a picking-up target from the candidate works using the trajectory data, wherein the robot secured on the base has a movable range, and wherein the target work selecting unit includes a movable range checking unit configured to determine whether an operation according to the trajectory data can be performed without exceeding the movable range.