It will be up to franchisees whether to deploy the labor-saving technology, but Wendy's President Todd Penegor did note that some franchise locations have been raising prices to offset wage hikes.

McDonald's (MCD) has been testing self-service kiosks. But Wendy's, which has been vocal about embracing labor-saving technology, is launching the biggest potential expansion.

Wendy's Penegor said company-operated stores, only about 10% of the total, are seeing wage inflation of 5% to 6%, driven both by the minimum wage and some by the need to offer a competitive wage "to access good labor."

It's not surprising that some franchisees might face more of a labor-cost squeeze than company restaurants. All 258 Wendy's restaurants in California, where the minimum wage rose to $10 an hour this year and will gradually rise to $15, are franchise-operated. Likewise, about 75% of 200-plus restaurants in New York are run by franchisees. New York's fast-food industry wage rose to $10.50 in New York City and $9.75 in the rest of the state at the start of 2016, also on the way to $15.