When the trial kicks off later this month, Walmart customers can have their groceries driven over by Udelv's second-generation vehicles (dubbed "The Newton") by placing orders online. The driverless vans are powered by Chinese internet giant Baidu's updated self-driving platform, Apollo 3.5.

Walmart claims it has a store within five miles of 70 percent of the US population. And, outside the realm of trials, it pushed to make deliveries to 100 cities by the end of 2018 -- with help from Postmates and DoorDash. That could be down to the Amazon Prime effect, but Walmart's brick-and-mortar empire means it has different challenges to overcome that its e-commerce rival. After halting its deliveries with Uber last year, and hiccups with its employee-based dispatches, it's clearly banking on self-driving cars as the future.