A robust controller for a two-layered approach applied to the game of billiards

Abstract

Planning issues in a continuous domain in the presence of noise lead to important modeling and computational difficulties. The game of billiards has offered many interesting challenges to both communities of AI and Optimization. We present a two-layered approach consisting in a high level planner and a low level controller. We propose here a refined controller for billiards based on robust optimization combined with specific adjustments to take advantage of the domain knowledge. A multi-objective formulation of a robust controller will be presented to provide the tools needed to execute any desired shot on the table, as part of a two-layered approach for the game of billiards. Some results will be then shown, followed by a short discussion on future work.

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

“…The controller presented in [16], while very effective in lownoise situations, was not as impressive when higher noise levels were used. Faced with the necessity to make more calls to the controller to allow the planner to work effectively, we studied the possibility of changing the model used for the single-shot optimization.…”

“…For this reason, only the first few (best ones) are considered. The idea we propose to use is in continuity with what was discussed in the Future Work Section of [16] with advanced methods for selecting shot sequences.…”

“…These heuristics are part of the planner depicted in Fig. 2, which fits into the previously proposed two-layered approach (see [16] for more details).…”

“…We proposed a novel approach in [16] under the form of a two-layered model, using a planner and a controller to establish the optimal shot sequence. This is the first time such an approach has been proposed for the game of Billiards.…”

“…Up to now, state-of-the-art approaches [4], [27] usually planned two to three shots in advance by discretizing the search space so as to try various angles and speeds at which to hit the cue ball, simulating the shot, and then continuing at the next ply from the position reached by the cue ball. What was proposed in [16], however, was to divide the problem into two layers, such that a robust controller may be guided by a high-level planner, taking advantage of possible knowledge that can be extracted from the domain. Although the controller described in that work proved to be robust, the downside was a necessity for many simulator calls for every single evaluation of the objective function.…”