Ball Positioning in Robotic Billiards: A Nonprehensile Manipulation-Based Solution

Abstract

The last two decades have seen a number of developments in creating robots to play billiards. The designed robotic systems have successfully incorporated the kinematics required and have had appropriate machine vision elements for a decent gameplay. Independently, computer scientists have also developed the artificial intelligence programs needed for the strategy to play billiards. Despite these developments, the accurate ball manipulation aspect of the game, needed for good performance, has not been addressed enough; two important parameters are the potting accuracy and advantageous cue ball positioning for next shot. In this regard, robotic ball manipulation by predicting the ball trajectories under the action of various dynamic phenomena, such as ball spin, impacts and friction, is the key consideration of this research. By establishing a connection to the methods used in nonprehensile robotic manipulation, a forward model is developed for the rolling, sliding, and two distinct types of frictional impacts of billiards balls are developed. High-speed camera-based tracking is performed to determine the physical parameters required for the developed dynamic models. To solve the inverse manipulation problem, i.e., the decision on shot parameters, for accurate ball positioning, an optimization based solution is proposed. A simplistic ball manipulator is designed and used to test the theoretical developments. Experimental results show that a 90% potting accuracy and a 100–200 mm post-shot cue ball positioning accuracy has been achieved by the autonomous system within a table area of $6 \times 5$ ft2.