Impact controllability of an air hockey puck

in this paper, we investigate the controllability of an air hockey puck sli ding on a frictionless table and subject to impacts from a mallet. This pro blem is a special case of the more general problem of impulsive manipulatio n. We first characterize the set of velocities reachable with arbitrary imp ulsive inputs. In reality, one cannot specify impulsive forces as inputs bu t rather only the velocity of a mallet impacting the puck. Therefore, we re fine the characterization to the case that the impulsive forces arise throu gh impacts with a mallet whose velocity can be arbitrarily controlled. The characterization of the reachable puck velocities then depends on the mater ial properties of the impacting objects. We use the two-dimensional Routh i mpact model to determine these reachable velocities in terms of the coeffic ients of friction and restitution. We show that the system satisfies an acc essibility-like property as long as the coefficient of friction is nonzero. (C) 2001 Elsevier Science B.V. All rights reserved.