How will the robot age transform warfare? What geopolitical futures are being imagined by the US military? This article constructs a robotic futurology to examine these crucial questions. Its central concern is how robots - driven by leaps in artificial intelligence and swarming - are rewiring the spaces and logics of US empire, warfare, and geopolitics. The article begins by building a more-than-human geopolitics to de-center the role of humans in conflict and foreground a worldly understanding of robots. The article then analyzes the idea of US empire, before speculating upon how and why robots are materializing new forms of proxy war. A three-part examination of the shifting spaces of US empire then follows: (1) Swarm Wars explores the implications of miniaturized drone swarming; (2) Roboworld investigates how robots are changing US military basing strategy and producing new topological spaces of violence; and (3) The Autogenic Battle-Site reveals how autonomous robots will produce emergent, technologically event-ful sites of security and violence - revolutionizing the battlespace. The conclusion reflects on the rise of a robotic US empire and its consequences for democracy.