Trajectory tracking of a bouncing ball in a triangular billiard by unfolding and folding the billiard table

In this paper, a feedback control law is proposed to solve the asymptotic tracking problem for a ball bouncing in a triangular billiard. This controller is designed by firstly 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.