Ball positioning in robotic billiards: a nonprehensile manipulation-based solution

The development and testing of a robotic system to play billiards is described in this paper. The last two decades have seen a number of developments in creating robots to play billiards. Although the designed systems have uccessfully incorporated the kinematics required for gameplay, a system level approach needed for accurate shot- making has not been realized. The current work considers the different aspects, like machine vision, dynamics, robot design and computational intelligence, and proposes, for the first time, a method based on robotic non-prehensile manipulation. High-speed video tracking is employed to determine the parameters of balls dynamics. Furthermore, three-dimensional impact models, involving ball spin and friction, are developed for different collisions. A three degree of freedom manipulator is designed and fabricated to execute shots. The design enables the manipulator to position the cue on the ball accurately and strike with controlled speeds. The manipulator is controlled from a PC via a microcontroller board. For a given table scenario, optimization is used to search the inverse dynamics space to find best parameters for the robotic shot maker. 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

Deep learning for video game playing

In this article, we review recent Deep Learning advances in the context of how they have been applied to play different types of video games such as first-person shooters, arcade games, and real-time strategy games. We analyze the unique requirements that different game genres pose to a deep learning system and highlight important open challenges in the context of applying these machine learning methods to video games, such as general game playing, dealing with extremely large decision spaces and sparse rewards

Trajectory solutions for a game-playing robot using nonprehensile manipulation methods and machine vision

The need for autonomous systems designed to play games, both strategy-based and physical, comes from the quest to model human behaviour under tough and competitive environments that require human skill at its best. In the last two decades, and especially after the 1996 defeat of the world chess champion by a chess-playing computer, physical games have been receiving greater attention. Robocup TM, i.e. robotic football, is a well-known example, with the participation of thousands of researchers all over the world. The robots created to play snooker/pool/billiards are placed in this context. Snooker, as well as being a game of strategy, also requires accurate physical manipulation skills from the player, and these two aspects qualify snooker as a potential game for autonomous system development research. Although research into playing strategy in snooker has made considerable progress using various artificial intelligence methods, the physical manipulation part of the game is not fully addressed by the robots created so far. This thesis looks at the different ball manipulation options snooker players use, like the shots that impart spin to the ball in order to accurately position the balls on the table, by trying to predict the ball trajectories under the action of various dynamic phenomena, such as impacts. A 3-degree of freedom robot, which can manipulate the snooker cue on a par with humans, at high velocities, using a servomotor, and position the snooker cue on the ball accurately with the help of a stepper drive, is designed and fabricated. [Continues.

A theoretical analysis of billiard ball dynamics under cushion impacts

The last two decades have seen a growing interest in research related to billiards. There have been a number of projects aimed at developing training systems, robots, and computer simulations for billiards. Determination of billiard ball trajectories is important for all of these systems. The ball’s collision with a cushion is often encountered in billiards and it drastically changes the ball trajectory, especially when the ball has spin. This work predicts ball bounce angles and bounce speeds for the ball’s collision with a cushion, under the assumption of insignificant cushion deformation. Differential equations are derived for the ball dynamics during the impact and these equations are solved numerically. The numerical solutions together with previous experimental work by the authors predict that for the ball–cushion collision, the values of the coefficient of restitution and the sliding coefficient of friction are 0.98 and 0.14, respectively. A comparison of the numerical and experimental results indicates that the limiting normal velocity under which the rigid cushion assumption is valid is 2.5 m/s. A number of plots that show the rebound characteristics for given ball velocity–spin conditions are also provided. The plots quantify various phenomena that have hitherto only been described in the billiards literature

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Planification optimale discrète et continue : un joueur de billard autonome optimisé

Le sujet de Thèse de ce doctorat consiste en l'élaboration de méthodes pour la planification dans les domaines avec aspects continus, discrets et stochastiques. Cette classe de problème, bien qu'assez générale, ne comporte pas pour l'instant de solution efficace et est souvent traitée de façon discrète plutôt que continue afin d'y appliquer les approches existantes. L'aspect stochastique apporte une difficulté supplémentaire à la recherche d'un plan optimal, et rend le problème d'autant plus intéressant. L'ensemble des approches et méthodes proposées dans cette Thèse sont avant tout appliquées au jeu du billard, tout en gardant dans l'esprit qu'une généralisation permettrait son application à d'autres problèmes similaires. En un premier lieu, une classification de ce type de problème par rapport aux recherches existantes sera effectuée, suivie d'une courte revue des approches actuelles possiblement applicables pour la recherche d'une solution acceptable. Un modèle général développé dans le contexte du jeu du billard sera présenté, ainsi que quelques indices sur la façon de le résoudre à l'aide de la programmation dynamique. Deuxièmement, un modèle pour une approche à deux-couches sera proposé, utilisant un contrôleur robuste profitant de la finesse qui peut être exploitée des techniques d'optimisation non-linéaire. Finalement, le modèle à deux-couches sera raffiné et quelques heuristiques de planifications seront proposée, afin de guider le contrôleur de façon à déterminer un plan efficace. On terminera à l'aide d'une synThèse des résultats et une discussion sur les perspectives futures

A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations

We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter which extend those proposed by Kohn and Serfaty (2010). These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution of the PDE as the parameter tends to zero. Moreover, our construction allows us to treat both the oblique and the mixed type Dirichlet-Neumann boundary conditions.Comment: 58 pages, 2 figure

Extending a Game Engine with Machine Learning and Artificial Intelligence

Since the early days of Artificial Intelligence (AI), video games have been a popular testbed for evaluating methods. However, not until a long time ago, this only included building AI agents for playing board games like chess. In the last decade, researchers have found out that games are also a rich source for other types of AI problems. At the same time, Machine Learning (ML) has entered its golden age with the advancements of deep learning. In games, this has led to a wide range of novel AI methods for solving various problems like playing games with super-human performance. Despite the significant advances, state-of-the-art AI methods are still far from being used in commercial games. One of the main reasons is that the tools used by researchers and game developers are different, which makes it difficult to use open-source codes in game projects. Furthermore, implementing these methods requires a moderate understanding of ML, which is not among the skill set of a regular game programmer. This calls for plug-and-play tools that enable game developers to deploy AI methods with minimum cost. In this thesis, we develop a library that enables game developers to use state-of-the-art ML methods in their commercial projects. This library integrates Tensorflow, a modern ML toolbox, into Unity, the most common game engine in the industry. This library uses C# with intuitive Keras-like API for building and training models. We have also implemented several state-of-the-art algorithms, including Proximal Policy Optimization (PPO), Matrix Adaptation Evolution Strategies (MA-ES), and Generative Adversarial Networks (GAN). This library can also be used along with Unity ML-Agents, the Unity plugin for building AI-training environments. Moreover, we provide various examples that demonstrate the library and the algorithms. One important example is a game called Calamachine Union, where the core game mechanic includes training the AI

The efficiency of top agents: An analysis through service strategy in tennis

We consider the question whether top tennis players in a top tournament (Wimbledon) employ an optimal (efficient) service strategy. While we show that top players do not, in general, follow an optimal strategy, our principal result is that the estimated inefficiencies are not large: the inefficiency regarding winning a point on service is on average 1.1% for men and 2.0% for women, implying that–by adopting an efficient service strategy–players can (on average) increase the probability of winning a match by 2.4%-points for men and 3.2%-points for women. While the inefficiencies may seem small, the financial consequences for the efficient player at Wimbledon can be substantial: the expected paycheck could rise by 18.7% for men and even by 32.8% for women. We use these findings to shed some light on the question of whether economic agents are successful optimizers