A Heuristic-Based Planner and Improved Controller for a Two-Layered Approach for the Game of Billiards

Abstract

In the past , we have proposed a two-layered approach to compute a winning strategy for the game of Billiards. AI tools as well as robust optimization routines for noisy environments were combined to plan the sequence of shots. We complete the modeling here by introducing significant developments for the highlevel planner which guides the precise optimal controller to generate a plan given at any random initial state. We will first resume the general model for this particular class of problems and then propose several domain-specific heuristics to guide our search and render the problem tractable. Several improvements to the optimal robust controller, including refinements in the objective function, will also be presented in order to improve single-shot optimization. Results are presented demonstrating the full potential of the methods proposed making it the state of the art in regards to the game of Billiards.

Intelligent Carom Billiards Assistive System for automatic solution path generation and actual path prediction with principal component analysis-based ball motion detection

“…With these means, the center position of the n ball positions is determined as P c ðX ; Y Þ. Next, the covariance between two dimensions for X and Y can be obtained based on Bessel's correction as in equation (25).…”

The economics–engineering nexus: response to the commentaries

“…In fact, the challenge of creating a robot accurate enough to compete and win against top professional players has always been a strong motivator for the robotics field. Many projects have been developed since the mid-1990s, and engineers are agonizing over finding the right solution to the problem (Landry et al, 2013 ). Engineers quickly discovered that «[t]he game of billiards is a game of skill, tactics, and ingenuity» (Landry et al, 2013 , p. 325).…”

“…Many projects have been developed since the mid-1990s, and engineers are agonizing over finding the right solution to the problem (Landry et al, 2013 ). Engineers quickly discovered that «[t]he game of billiards is a game of skill, tactics, and ingenuity» (Landry et al, 2013 , p. 325). The outcome of the game depends not only on the capacity of the players to approximate the laws of physics, but primarily on the attack or defense strategies that are adopted, 2 the perceptions of their own limits and external risks, the ability to interpret the opponent’s behavior and psychology, in order to counteract in an adequate manner.…”

A Straight Approach to Planning for 14.1 Billiards

“…We work around this problem by introducing a new penalty parameter, which will penalize the distance between the ball that has traveled the farthest after collision, and the closest rail: Figure 3 shows graphically how the difficulty coefficient is estimated for a given cue ball target-ball and pocket combination. We refer to [8] for more details on the evaluation of position values. It is mandatory that early on in the game, one or preferably two balls are left near to where the re-rack will be done such that the last shot will allow a re-break of the cluster.…”

“…PlanningPlanning for the game of Straight, as for other variants of billiards, demands a careful analysis of the table. For the game of eight-ball, we have previously explored a shortest-path approach in[8] to select a preferred shot-order on the table, such as to constrain the cue ball to travel as little as possible. This works well since distance (combined with cut angle) is a great indicator of shot difficulty.…”