On the controllability of an air hockey puck

In this paper we investigate the controllability of an air hockey puck subject to impulsive inputs, which is a special case of the more general problem of impulsive manipulation of rigid objects. We first formulate the control problem on the three dimensional velocity space of the system and characterize the set of velocities reachable with arbitrary impulsive inputs. In reality, one cannot specify impulsive forces as inputs but rather only the velocities of a striker impacting the puck. Therefore, we refine the characterization to include the case that the impulsive forces act on the puck through an impact with a second object. This characterization then depends on the material properties of the impacting objects. We use the two-dimensional Routh impact model which allows us to characterize the reachable velocities in terms of the coefficients of friction and restitution of the objects.