Determining Shot Accuracy of a Robotic Pool System

A process is described to determine the shot accuracy of an automatic robotic pool playing system. The system comprises a ceiling-mounted gantry robot, a special purpose cue end-effector, a ceiling-mounted camera, and a standard bar pool table. Two methods are compared for extracting the homography between the camera and the table plane. A challenge was the relatively large area of the table surface, which required a similarly large chessboard pattern to determine the point homography. In contrast, the Dual Conic method required only a set of orthogonal lines as a calibration target, which was more convenient to manipulate, and could be calculated from the integration of multiple images with multiple target locations. The Dual Conic method was shown experimentally to recover the homography with a similar, and sometimes greater accuracy than the Chessboard method. An experimental procedure was devised to measure the accuracy of an automatic shot using a sequence of images acquired from the overhead camera. For a set of 10 shots, the average absolute angular error in placing a shot was determined to be 0.74^0, with a standard deviation of 0.96^0.