Here's how it works:

There are two main principles to get a ball rolling on its own - to rotate a mass inside the ball or to displace its centre of mass.

In order to move the pendulum is lifted in the direction of travel, the centre of mass gets displaced in front of contact point between the ball and the ground and the ball starts rolling.

Turning is accomplished by moving the pendulum to either side.
(From Rotundus technology)

(Rotundus internal diagram)

The finished version of the Rotundus robot will navigate using an internal GPS sensor and will be navigable by a remote operator. Ultimately, the goal is to make it an autonomous robot that can patrol a perimeter, or go practically anywhere a person could go. The robot operates equally well on sidewalks, sand or snow. On a hard surface, the robot can achieve speeds of up to 20 miles per hour.

Update 21-Jan-2009: Take a look at this Rotundus spherical robot video.

End update.

I saw this story about the Rotundus security robot prototype about a month ago, but I couldn't quite think of what it reminded me of. Thanks to an alert reader, I've got it! The Rovers from the late 1960's sci-fi television series The Prisoner were security balls of various sizes.

(The Rover seeks its prey)

In the television show, the Rovers were living creatures modeled to some extent on blowfish. They could alter their size and were equipped with toxins that could incapacitate prisoners who tried to escape (they would give chase to the fastest moving living creature). They could run faster than a man, just like the Rotundus robot. They also served as eyes and ears for the Village monitors. They were adapted for different environments, including undersea use.

Also, in the early 1980's supermacromation series The Terrahawks, spherical robots called Zeroids were used to fight the evil witch-like alien Zelda.

(Sargeant Major Zero and Zeroid 18)

The Rotundus robot could also be considered a land-based version of copseyes, a spherical security robot introduced by science fiction writer Larry Niven in his 1972 story Cloak of Anarchy. Copseyes were golden spheres that floated off the ground; they had security cameras and stunners to spot and stop rule-breakers (repectively). (Update 19-Nov-2006: See also the Robot Probes (Arr-twos) from Niven and Pournelle's 1981 novel Oath of Fealty End update.)

Update 04-Jun-2025: Compare this item with the Ruum robot from The Ruum by Arthur Porges.

Jim Irwin had once worked with mercury, and for a second it seemed to him that a half-filled leather sack of the liquid metal had rolled into the clearing. For the quasi-spherical object moved with just such a weighty, fluid motion. But it was not leather; and what appeared at first a disgusting wartiness, turned out on closer scrutiny to be more like the functional projections of some outlandish mechanism. Whatever the thing was, he had little time to study it, for after the spheroid had whipped out and retracted a number of metal rods with bulbous, lens-like structures at their tips, it rolled towards him at a speed of about five miles an hour.

End update.