For the first time, automakers will be able to test autonomous cars with no steering wheels, brake pedals or human drivers on some public roads in California, under legislation signed Thursday by Gov. Jerry Brown.

The law does not open California’s vast network of freeways, highways and streets to robot cars. Instead, it is tailored to allowing tests in two particular places — both in the East Bay.

AB1592 allows self-driving car tests on public roads in the former Concord Naval Weapons Station and Bishop Ranch business park in San Ramon. The old naval facility, which used to store munitions, has been converted by the county into a test bed for autonomous vehicles, dubbed GoMentum Station.

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The Contra Costa Transportation Authority recently acquired two self-driving shuttles made by French company EasyMile. The shuttles will first be tested at GoMentum Station, which the authority manages, before being sent to Bishop Ranch, a 585-acre business park along Bollinger Canyon Road that is home to offices for Pacific Gas and Electric Co. and AT&T as well as Chevron’s global headquarters.

The bill was written by Assemblywoman Susan Bonilla, D-Concord. She cast the rules as necessary to maintaining the Bay Area’s role as a center for research into autonomous cars.

“California has always been a global leader in innovation, and as transportation technologies evolve, so must our laws and regulations,” she said in a press release. “With the passage of AB1592 our state will prove to the federal government and the rest of the nation that California remains the leader, and that the deployment of autonomous vehicles without the presence of a driver can be done safely and successfully.”

California currently requires that any autonomous cars tested on public roads have a human in the driver’s seat — as well as the equipment to ensure that the human can take control if needed.

The new law allows for very specific exceptions.

For example, any company wishing to test cars without drivers or steering wheels on public roads within the designated areas must first prove to the county that the cars have successfully navigated similar roads on their own. The company must also give the county detailed plans for the test and obtain insurance worth $5 million.

David R. Baker is a San Francisco Chronicle staff writer. Email: dbaker@sfchronicle.com Twitter: @DavidBakerSF