# Ivars Peterson's MathTrek

June 28, 2004

## Dogs Catching Frisbees

Some dogs are highly adept not only at retrieving but also at catching in midair a tossed ball or Frisbee. To do so requires the dog to be in the right place at the right time. How does a dog navigate to snatch a Frisbee out of the air?

To find out, researchers attached a tiny video camera to the head of each of two dogs to capture what the dogs could see as they hunted, then intercepted Frisbees. They concluded that dogs appear to use the same geometric strategy that a baseball fielder employs to snag a fly ball hit into the outfield.

Dennis M. Shaffer of Arizona State University West, Michael K. McBeath of Arizona State University, and Scott M. Krauchunas and Marianna Eddy of Saint Anselm College describe their experiments and results in the July Psychological Science.

In earlier studies, McBeath and other researchers had posited that baseball fielders typically use a fairly simple optical strategy for catching fly balls. Basically, an outfielder selects a running path that allows him or her to keep the image of the moving ball on the same part of the retina.

In effect, from the fielder's point of view, the ball appears to move in a straight line and at a constant speed relative to home plate and the background scenery. To get the desired result for a ball hit off to one side, for example, the fielder would run along a curved path to cancel out the curvature of the ball's trajectory.

This fielding approach is known as the Linear Optical Trajectory (LOT) model.

A Frisbee's trajectory and speed can change dramatically as it swoops through the air. Hence, catching an airborne Frisbee is probably a bit more complicated than catching a baseball.

Shaffer and his colleagues worked with two dogs, both experienced in catching Frisbees. One was a springer spaniel named Romeo, and the other was a border collie named Lilly.

After equipping the dogs with video cameras, the researchers launched Frisbees toward each dog at a variety of angles, all off to the side of the dog's initial position, and at varying forces from distances of between 9 and 19 meters. The dogs ran between 2 and 14 meters to catch the Frisbees.

The results supported the hypothesis that the dogs appeared to run as if they were keeping the image of the Frisbee moving at a constant rate in the vertical direction.

Even when a Frisbee's direction changed dramatically, the dogs continued to rely on the LOT strategy. They simply adopted one LOT strategy before the abrupt perturbation, then quickly switched to a new LOT strategy after the change in direction.

"This work demonstrates the use of simple control mechanisms that utilize invariant geometric properties to accomplish interceptive tasks," the researchers conclude. "It confirms a common interception strategy that extends across species and to complex target trajectories."

References:

Hodgens, M. 2003. Visual tracking strategies used by humans to optically track and catch moving objects. Saint Anselm College Department of Psychology senior thesis. Available at http://www.anselm.edu/internet/psych/sr2003/hodgens/webpage.html.

Peterson, I. 2003. A dog, a ball, and calculus. MAA Online (June 9).

______. 2002. Catching flies. MAA Online (Oct. 14).

Shaffer, D.M., S.M. Krauchunas, M. Eddy, and M.K. McBeath. 2004. How dogs navigate to catch Frisbees. Psychological Science 15(July):437-441. Abstract. Preprint available at http://www.psychologicalscience.org/members/journal_issues/psinpress/Shaffer.pdf.