Mechanical Engineering Design, March 2005 -- "Turning on a Dime," Feature Article

mechanical engineering design

turning on a dime

Making robotic soccer players more agile proved to be a matter of direction for a group of fledgling engineers.

by Michael Sherback

No one will ever mistake them for Pelé, but Cornell's robotic soccer players have gotten more efficient and agile, thanks to developments in omnidirectional drive.

RoboCup is an international research and education initiative whose goal is to foster research into artificial intelligence, robotics, and related fields by providing a standard problem where a wide range of technologies can be examined and integrated. RoboCup chose to use soccer as a central topic of research, aiming at innovations to be applied for socially significant problems and industries. The ultimate goal of the RoboCup project is to develop, by 2050, a team of fully autonomous robots that can win against the human world champion soccer team.

Cornell University, in Ithaca, N.Y., has been competing for the past six years in the Small Size League, which uses cantaloupe-size robots. We've won the championship in four of those years.

In the Small Size League, two teams of five vehicles play soccer on a field measuring 2.5 by 4.5 meters, or about the size of two Ping-Pong tables. A golf ball takes the place of a soccer ball. A video camera mounted above the field provides feedback to an external computer on the location of the ball and every robot. Another computer determines strategy and sends commands wirelessly to each robot on the team. Relevant objects are distinguished by color.

Cornell's 2003 RoboCup model puts free rollers around the wheel edges.

The robotic teams are completely autonomous, meaning that during the games they execute programmed strategies, and the students can only sit back and watch. (Recently, Cornell has developed a way to eliminate the off-field, decision-making computer and put the intelligence on board the robots. This is a phase in a move toward fully autonomous individual robots, as opposed to a team that is autonomous as a whole.)

The competition also includes leagues with larger rolling robots, robots that play on four legs instead of wheels, and a simulation league in which games are played entirely inside a computer, as a pure test of artificial intelligence.

Having the fastest and most agile robots has been a trademark of the Cornell team. But, up until 2000, RoboCup robots weren't as nimble as they might be. At that point, they were designed with two wheels and operated like standard wheelchairs. To move the robot sideways, it was necessary to perform a maneuver similar to parallel parking. When receiving a pass, jockeying for position near a ball, or cutting down angles as a goalie, this imposed a great limitation on agility.

I became convinced that a reasonably simple mechanism was possible that would solve the problem—an omnidirectional design. This would allow the robots to move in any direction at any time. This is analogous to being able to parallel park your car by just sliding it sideways. Since then, the Cornell team has refined the concept and developed algorithms that take full advantage of this new freedom.

As I researched it, I found that I was far from the first person to see it this way, and that both theory and practice of omnidirectional drive had been developed. It turned out that omnidirectionality is a special case of a more general concept, holonomicity. Put as simply as possible, a vehicle is holonomic if it can move to change its velocity instantaneously in all available directions. In more technical terms, a holonomic vehicle has as many velocity degrees of freedom as it has position degrees of freedom at any instant. For example, a hovercraft is holonomic, because it can go from moving forward to sliding sideways without first having to stop and change direction.

Cars, conversely, like the vast majority of vehicles, are not holonomic, since regular wheels force the lateral velocity at the point of contact to be zero. People have built omnidirectional vehicles by building something analogous to an office chair with powered casters, but this is not holonomic because it takes some time to swivel the casters. Non-holonomic systems are more difficult to control.

I based my design on the Omnidirectional Holonomic Platform from Oak Ridge National Laboratory, developed by Francois Pin and Stephen Killough. That platform was used as part of a new battery-powered wheelchair design. The wheelchair has unrestricted, resistance-free, 360-degree movement. The chair can spin freely in a circle, move sideways, move at any angle without turning, and change directions without having to first stop and then restart.

There is a need for a special kind of wheel for holonomic drive in order to eliminate the constraint of zero velocity perpendicular to the wheel's path. The problem of lateral constraint at the point of wheel contact is solved by using truncated spherical wheels, whose axles are held by rotating forks. The free rotation of the wheels about the axles means that each pair of wheels constrains velocity only in one direction, eliminating the lateral constraint seen with regular wheels.

Two wheels held 90 degrees out of phase are used at each contact point so that when the fork holding one wheel needs to clear the ground, the other wheel is supporting the robot. By controlling the rotation rate of the forks, one component of velocity at the point of contact is controlled. By having three of these modules, the robot can be driven in any direction and rotated at any time.

In 2000, Cornell's Big Red team, our first to use omnidirectional drive, won the world championship. Other teams have almost universally adopted this technology, and have refined the design.

Patrick Dingle and Len Evansic, members of Cornell's 2003 RoboCup team, adapted a design from the Free University in Berlin to create the current standard for RoboCup robots. This model takes a more direct approach to eliminating the lateral constraint of normal wheels by putting free rollers around the edge of the wheel.

Adopting a holonomic system meant refining the control systems to ensure that the robot utilized all its newfound maneuverability.

The 2000 soccer robot was the first with omni- directional drive.

Tamas Kalmar-Nagy, a professor in Cornell's Department of Theoretical and Applied Mechanics; Raffaello D'Andrea, associate professor of Cornell's Sibley School of Mechanical and Aerospace Engineering and RoboCup faculty advisor since 1999; and Oliver Purwin, a doctoral student in mechanical engineering at Cornell and fellow RoboCupper, all worked to develop trajectory generation algorithms for controlling and maneuvering the robots. A closed form method developed in Matlab is used to determine a trajectory that minimizes either the time or energy used for a desired motion. Matlab, a technical computing language and environment for algorithm development, data visualization, and data analysis from The MathWorks of Natick, Mass., is our team's main analysis tool.

Omnidirectional drive principles have been used in other applications besides RoboCup robots. The battery-powered wheelchair based on Oak Ridge's Omnidirectional Holonomic Platform was commercialized by CyberTrax Innovative Technologies of Tampa, Fla. Omnidirectional forklifts have been made by Airtrax of Hammonton, N.J.

Omnidirectional drive demonstrates the importance of kinematics in machine design. Advancing the mechanisms themselves by applying kinematic principles has proven very rewarding for the Cornell RoboCup team.

Michael Sherback is a graduate student in dynamics and control in the mechanical engineering program at Cornell University. He is also an active member of Cornell's RoboCup team.