Fascinating concept, the crowned wheel, and it certainly seems to work reliably. But in a fighting robot the stresses a belt comes under are from all angles and far greater than simply starting a little off alignment. Imagine being pushed sideways by another machine, without some sort of guide, the belts will come off almost undoubtedly.

Point is I don't think it's as simple as just having a crowned pulley for this application. Crowned pulley with guides sounds good. Or the slotted pulley style as Mouldy mentioned sounds as likely to work.