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Over the last decade, eye tracking systems have been developed and used in many fields, mostly to identify targets on a screen, i.e. a plane. For novel applications such as the control of robotic devices by the user vision, there is a great interest in developing methods base on eye tracking to identify target points in free three dimensional environments. The objective of this paper is to characterise the accuracy the eye tracking and computer vision combination that was designed recently to overcome many limitations of eye tracking in 3D space. We propose a characterization protocol to assess the behavior of the accuracy of the system over the workspace of a robotic manipulator assistant. Applying this protocol to 33 subjects, we estimated the behavior of the error of the system relatively to the target position on a cylindrical workspace and to the acquisition time. Over our workspace, targets are located on average at 0.84 m and our method shows an accuracy 12.65 times better than the calculation of the 3D point of gaze. With the current accuracy, many potential applications become possible, such as visually controlled robotic assistants in the field of rehabilitation and adaptation engineering.