In this paper, a position feedback controller is proposed to solve the tracking problem in rectangular billiards. Such a controller is obtained by transforming the billiard table into a surface on which the ball moves without experiencing any impact, i.e., by reflecting the billiard table rather than the ball trajectory, and designing a position feedback controller based on such an unfolded billiard table. Furthermore, it is shown how such an infinite billiard table can be mapped to the surface of a torus, thus leading to bounded trajectories of the ball.
Trajectory tracking in rectangular billiards by unfolding the billiard table
Possieri Corrado;
2020
Abstract
In this paper, a position feedback controller is proposed to solve the tracking problem in rectangular billiards. Such a controller is obtained by transforming the billiard table into a surface on which the ball moves without experiencing any impact, i.e., by reflecting the billiard table rather than the ball trajectory, and designing a position feedback controller based on such an unfolded billiard table. Furthermore, it is shown how such an infinite billiard table can be mapped to the surface of a torus, thus leading to bounded trajectories of the ball.File in questo prodotto:
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