In the process, the companies are increasingly treading on the other's turf: Amazon is opening physical stores and agreed to pay $13.7 billion for upscale grocer Whole Foods Market. Wal-Mart, meanwhile, has beefed up its e-commerce business through acquisitions and offers like free two-day shipping.
An unmanned airborne warehouse -- laden with drones -- could help retailers lower the costs of fulfilling online orders, particularly the so-called "last mile" to a customer's house, which is usually handled by a local or national logistics company.
To avoid that expense, Wal-Mart and other retailers often encourage shoppers to pick up those orders at the store, where they might grab a few additional items. Earlier this week, Target agreed to acquire a software company that coordinates local deliveries.
"The core challenge of traffic and driving distance in any major city or in a very rural location can be helped by a floating warehouse," said Brandon Fletcher, an analyst at Sanford C. Bernstein. "Movable warehouses are a really nice idea because any flexible part of a logistics system allows it to be more efficient when demand varies wildly. The e-commerce world suffers from highly variable demand and more creative solutions are needed."
A movable warehouse could serve a wider distribution area, Fletcher said, compared with a traditional warehouse that can only fill orders within a fixed driving distance. The airship could fly to one town and release a flock of drones to deliver packages, after which the drones would return to the vessel and restock while it flew to the next town.
Such a system would be more efficient than having the drones fly back to a central distribution hub, according to research firm CB Insights.
"There are numerous ways to distribute and deliver products," according to Wal-Mart's patent application. "Getting the product to a delivery location, however, can cause undesirable delays, can add cost and reduce revenue."
Wal-Mart's application stands a good chance of getting approved as it goes into more detail about the implementation of a gas-filled aircraft than Amazon's patent, which is a more general description of the concept of airborne-delivery systems, according to Khaled Fekih-Romdhane, managing partner at patent-licensing firm Longhorn IP.
This isn't the first time Wal-Mart has shadowed Amazon's intellectual property.
In October, it filed a patent application for a web-based system similar to Amazon's Dash buttons, which can quickly reorder household goods like paper towels or razor blades. The technology could also gather shopper data, such as how often a product is used and at what times of day.
In recent years, Wal-Mart has significantly stepped up its patent filings, many of which focus on web development and easing shoppers' journey through the store. The company has also filed a patent for in-store drones that would ferry products from the backroom to the sales floor.