Abstract: According to ellipsoidal pressure vessels opening and cutting groove, a special four degrees of freedom cutting robot was developed. The mechanical structure and the working principle were introduced, and the intersecting line mathematic model of ellipsoidal shells opening in polar coordinates was established by using space analytic geometry. The groove angle calculation formula and four-axis motion control algorithm during groove cutting were derived, and ideal movement trajectory was obtained through linear interpolation algorithm. In order to eliminate the disturbances of location error and vessel distortion, teaching compensation algorithm based on theory calculation was proposed to correct robot motion trajectory. The practical application results illustrated that opening and groove cutting can be realized with the special cutting robot, and the cutting quality meets the technology requirements.