A static robot is one that does not have an “active” weapon. Static robots are usually build to be very good at pushing other robot around, and that is how they win their fights. As they are weaponless, it is generally harder for them to win a fight by disabling the other robot because they must rely on features such as drop off zones and pits.
In Antweights, static robots are particularly common, as an Antweight Arena must have at least 50% of its edges open, creating a large drop off zone. In heavyweight battles, static robots must usually rely on a much smaller pit, or shear power to completely overwhelm the opponent.
There has been some controversy surrounding static robots in the past. In 2002/2003 for the 7th series of Robot Wars, the rules were changed to ban static robots from entering the competition unless they had an active weapon. As a result, many static robots had to alter their design, or just didn't enter.
This rule banning static robots has not been included in the Fighting Robot Association's rules as of 2008, meaning that static robots can still compete at live events.