Optimal Initial Conditions for a Goal Kick in Rugby

Abstract

This paper describes the optimal initial conditions for the goal kick in rugby by using an elitist non-dominated sorting genetic algorithm. What is the best way to achieve a satisfactory kick for goal? The primary objective of this paper is to provide the answer. Two objective functions are considered. One is the height difference between the ball position and the crossbar, and the other is the lateral deviation of the distance of the ball position and the center of both goalposts. Seven initial conditions concerning the velocity vector and the angular velocity vector were defined as control parameters. The results are in order to satisfy the Pareto-optimal solutions, the angular velocity vector should be perpendicular to the velocity vector and the longitudinal axis of the ball.