 <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073451342/295036/ch11.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (22.0K)</a>]]> | RoboCup is the international championship of robot soccer. Unlike the remote-controlled destructive robots that you may have seen on television, the robots in this competition are engineered and programmed to respond automatically to the positions of the ball, goal and other players. Once play starts, the robots are completely on their own to analyze the field of play and use teamwork to outmaneuver their opponents and score goals. RoboCup is a challenge for robotics engineers and artificial intelligence researchers. The competitive aspect of RoboCup focuses teams of researchers, while the annual tournament provides invaluable opportunities for feedback and exchange of information.
The competition is divided into several categories, each with its own unique challenges. Overall, one of the greatest difficulties has been providing the robots with adequate vision. In the small size category, "vision" is provided by overhead cameras, with information relayed wirelessly to the robots. With the formidable sight problem removed, the focus is on effective movement of the robots and on providing artificial intelligence for teamwork. The remarkable abilities of these robots are demonstrated by the sequence of frames shown here, where a robot on the Cornell Big Red team of 2001 hits a wide-open teammate with a perfect pass that leads to a goal.
There is a considerable amount of mathematics behind this play. To tell whether a teammate is truly open or not, a robot needs to take into account the positions and velocities of each robot, since opponents and teammates could move into the way by the time a pass is executed. In the sequence of photos, notice that all the robots are in motion. Both position and velocity can be described using vectors, but a different vector may be required for each time. In this chapter, we introduce vector-valued functions, which assign a vector to each value of the time variable. The calculus introduced in this chapter is essential background knowledge for the programmers of RoboCup. |
