WILMINGTON, Mass.—When Target Corp. decided to revamp one of its biggest California distribution centers, it had a choice. It could build a new warehouse, it could install established technologies for picking products off shelves or it could take a risk on a new breed of robots from a reclusive billionaire.

Target went with the billionaire’s bots.

Target’s new automatons are from Symbotic LLC, part of a grocery empire run by New England billionaire Rick Cohen. Mr. Cohen, through his own national distribution network, and deals with some of the nation’s biggest retailers, aims to show that robots can overturn the business of storing, handling and hauling the cases of goods that retailers truck to their stores by the millions each year.

His sales pitch to grocery chains and retailers, including Target, Coca-Cola Co. and Wal-Mart Stores Inc. is simple: Symbotic’s automation system includes autonomous robots that can travel untethered among storage racks in a distribution center. They can move up and down aisles to stack and retrieve cases. They coordinate with more-conventional robots that perform simpler tasks.

That is in contrast to many other warehouse-automation systems, in which the robots tend to be bolted down or limited to fixed routes or tracks and are less flexible in what they can do.