PITTSBURGH — A key piece of the Pentagon’s plan to beat China and Russia in the high-stakes artificial intelligence race lies inside a research facility along the Allegheny River here, where a small but select U.S. Army team has been tasked with creating the weapons, vehicles and sensors needed for 21st-century combat.

Inside, the U.S. military is feverishly working to incorporate AI into its operations in a myriad of ways, including drones and robots to ferry wounded soldiers away from the battlefield, software that can spot a hidden enemy force over a hill, AI programs that can give g...