Some Phoenix-area residents have been hailing rides in minivans with no drivers and no human safety operators inside. But that doesn’t mean they’re on their own if trouble arises.

From a command center, employees at Alphabet Inc.’s Waymo driverless-car unit monitor the test vehicles on computer screens, able to wirelessly peer in through the minivan’s cameras. If the robot brain maneuvering the vehicle gets confused by a situation—say, a car unexpectedly stalled in front of it or closed lanes of traffic—it will stop the vehicle...