Never mind the reindeer and elves. This year, robots are helping deliver the holidays.

Gap Inc. GPS 2.70% is using automated arms and artificial intelligence to sort the retailer’s clothing orders. Walmart Inc. WMT -0.22% is testing robots that roam store aisles to check inventory and tell workers where to find goods. And logistics providers are sending mobile step-stools mounted with shelves through fulfillment centers to help pull online orders for toys, apparel and Walt Disney Co. products.

With the busy holiday peak looming, retailers and logistics companies are ramping up automation as surging demand for labor outstrips the number of available workers. Much of the technology is being used in distribution operations, where workers pulling carts or driving forklifts are increasingly working alongside machines built to keep goods moving at a rapid pace.

“It’s a fight for talent…It’s like ‘Game of Thrones’ out there,” Erik Caldwell, chief operating officer for supply chain in the Americas and Asia Pacific at XPO Logistics Inc., XPO 2.25% said at an industry conference earlier this year, discussing the company’s use of robots to fulfill online orders.

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The use of robotics and other automation technology in industrial operations is growing, although the vast majority of warehouse work remains largely manual. About 16.5% of organizations across several industries including warehousing are now using commercial service robots, and 21.5% have them in pilot programs, according to a 2018 survey of 600 respondents by research firm IDC.

The holiday shopping season highlights a warehouse-worker squeeze that is driving more logistics operators to embrace automation, as the growth of online commerce pushes more retail sales from storefronts to distribution centers.

Online fulfillment centers—where companies like Amazon.com Inc. AMZN -2.32% pick, pack and ship consumer orders—require two to three times as many workers as traditional warehouses. Payrolls in the sector have nearly doubled over the past five years, and companies are competing for workers amid low unemployment. Deloitte forecasts online sales will grow by between 17% to 22% this holiday season over last year, reaching up to $134 billion.

“ It’s a fight for talent…It’s like ‘Game of Thrones’ out there. ” — Erik Caldwell of XPO Logistics.

Greenwich, Conn.-based XPO said this week it is deploying 5,000 autonomous mobile units from Singapore-based GreyOrange Pte. at logistics sites across North America and Europe. The robots, which resemble Roomba autonomous vacuum cleaners, sync up with XPO’s warehouse-management software to help workers fulfill up to 48 orders at a time, the company said.

The robots more than doubled the speed at which orders are processed and help the company keep better tabs on inventory, said XPO Chief Executive Brad Jacobs. They also “give our customers some protection against fluctuation in labor costs,” he said.

The technology resembles shelf-moving robots developed in the 2000s by Kiva Systems, which Amazon bought in 2012. XPO, whose clients include IKEA and Inditex SA’s Zara, uses up to 79 different types of robotic equipment, including more than 100 “Chuck” units from 6 River Systems Inc. that guide workers through warehouse aisles, lighting up when they reach the next item to pick.

At Gap’s distribution center complex in Gallatin, Tenn., yellow mechanical arms mounted inside six cylindrical sorting machines pick up poly-bagged items of clothing from the company’s Athleta, Banana Republic and Old Navy brands. The robots scan the bar code, then stow items in cubbies corresponding to individual orders.

Kindred robots sort garments at the Gap distribution center in Gallatin, Tenn. Photo: Kyle Dean Reinford for The Wall Street Journal.

The SORT robot, designed by startup Kindred, uses artificial intelligence to decide which object would be best to pick, avoiding overlapping items and dropping those whose bar codes can’t be read on the first round. When the robot can’t figure out how to grasp an item, it calls workers at Kindred’s Toronto office who take over and do it remotely.

The number of completely autonomous “picks” has increased fourfold since the second phase of the pilot began in April. The SORT now works at about the same pace as human workers on average, and has peak speeds that outperform humans—without taking breaks.

“When you see a machine sitting here, this would be four people working across four shifts,” said Kevin Kuntz, Gap’s senior vice president of global logistics fulfillment. “That’s the benefit. It works all the time.”

Gap still doubles or triples its usual workforce during its busy sales season, but automation including the SORT robot means it no longer has to hire six times as many workers, Mr. Kuntz said.

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Logistics-industry interest in robotics is spreading as the technology gets cheaper and easier to adopt. So-called collaborative robots for example, can work safely alongside humans and be added quickly to existing sites without disrupting operations.

Supply-chain contractor Geodis is using more than 150 collaborative robots from Locus Robotics Corp. at three U.S. warehouses to handle peak season e-commerce toy and apparel orders.

The “swarming” robots operate in groups, navigating warehouse aisles and parking themselves next to items that need to be picked. Workers wear Bluetooth badges linked to the robots, which display instructions on a touchpad in the picker’s preferred language.

The robots have reduced training time for new workers and doubled productivity over manually picking orders, the company said.

“We’re at basically full employment,” said Eric Douglas, the company’s executive vice president for technology and engineering. “We do have customers with high peak-season demand, we’re looking for the most efficient way…to get their products out the door.”

Write to Jennifer Smith at jennifer.smith@wsj.com