Sheepdogs herd farm animals using laws of mathematics, which could be used to design a new generation of robots.

Swansea University researchers discovered the mathematical formula that canines follow when guiding sheep.

A GPS unit was attached to each of a number of sheep in a herd, in order to accurately track their positions. A similar unit, contained in a small backpack, was fitted to sheepdogs. A total of 46 female merino sheep dogs were tested, as they herded sheep over 12 acres of land. Their behavior was recorded using the highly-sensitive positioning devices, and computer models were developed from the data.

Just two simple rules appear to dictate patterns covered by sheepdogs when they are herding sheep. When the farm animals disperse over an area, dogs will herd them into a single group. Then, when the sheep are gathered together, the canine will begin to drive the animals toward a desired location.

Robots based on the newly-discovered rules of herding could find uses beyond simply controlling animals. Similar devices could also assist in cleaning up the environment or controlling large crowds during civil unrest.

A single dog is capable of herding 100 or more sheep, just by following those two simple rules, according to the investigation. To do this, the animal moves up and down, outside the flock of sheep, driving the crowd together.

"We had to think about what the dog could see to develop our model. It basically sees white, fluffy things in front of it. If the dog sees gaps between the sheep, or the gaps are getting bigger, the dog needs to bring them together," Andrew King of Swansea University said.

When large crowds of humans start to become unruly, a few individuals tend to lead the charge, while most people stay with others. Researchers believe that robots could be used to herd the human leaders, driving them back to the main mass of people.

Border collie, the most common breed of dog used by shepherds to assist in herding sheep. The animals were specially-bred for their intelligence and willingness to take orders. Animal researchers have long wondered how the canines carried out the process, and which rules they follow while directing their charges.

Computer models suggest that when 50 or more sheep are present in a group of the animals, herding is most efficient with two or more canine guides.

Study of sheepdogs and how their herding behavior could be adapted to robots was profiled in the Journal of the Royal Society Interface.

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