San Francisco has a new approach for addressing the hundreds of people living in vehicles on its streets: Instead of treating them as an annoyance, officials will offer shelter and social services — or enough gas money to get home.

Mayor London Breed will announce a plan Tuesday to clear the inhabited cars and RVs that line curbs and clot roadways, which have become more obvious now that the big tent encampments are gone. Workers from the Department of Homelessness and Supportive Housing counted 432 such vehicles in October — more than half in the Bayview and Mission neighborhoods — and now plan to methodically assess the needs of each.

Some car- and van-dwellers may be truly destitute, while others may be workers from outlying areas who use their vehicles as de facto hotels during the week. Still others may be travelers marooned by a broken engine or an empty gas tank. In at least two instances, people have bought RV trailers, parked them on a street and rented them out to homeless people, said Jeff Kositsky, director of the Department of Homelessness.

“We’re working to understand the problem and come up with a meaningful solution,” Kositsky said, characterizing San Francisco’s approach as more cautious and nuanced than the sanctioned parking lots that have failed in other cities.

To that end, Breed and two supervisors, Ahsha Safai and Vallie Brown, have laid out a multi-pronged strategy. First, they will direct the city’s Department of Homelessness to form a new team in January to disband clusters of vehicles and offer services to people living inside. Then they will set up a triage system, diverting some people into shelters and providing fuel or repairs for others.

Officials may open a temporary RV storage facility for people who accept shelter — because it’s easier to coax them out of their vehicles if they can retrieve them later, Kositsky said.

“Our belief is that people shouldn’t be sleeping in vehicles, but we also understand why they would be very reluctant to give up their most valuable possession,” he said, noting that a car or van can feel like home in ways that a tent does not. He said San Francisco lacks enough shelter beds to serve everyone living in a car or van, which is why his department hopes to identify those who just need help leaving the city.

Breed agreed that allowing people to live in RVs is not sustainable: Many vans lack running water or sewage disposal, and neighbors complain that they commandeer scarce parking. Even so, Breed acknowledged the need for “practical solutions” while the city works to build more affordable housing.

Traditionally, city officials have treated RVs and car dwellers as a nuisance.

And in past years, addressing that nuisance largely fell on the doorstep of the San Francisco Municipal Transportation Agency, which regulates parking. Its tools were blunt: a hard-to-enforce 1971 ordinance barring people from living in vehicles, and another prohibiting parking in one place for more than 72 hours.

The SFMTA board also banned trailers and large commercial trucks from certain streets in response to pressure from residents. Those bans effectively shunted the problem from one neighborhood to the next.

Safai drew attention to RV encampments in August, when he called for an overnight RV parking ban on De Wolf Street — a block of the Outer Mission neighborhood he represents that is flanked by houses on one side, and Interstate 280 on the other.

After a protracted debate, the SFMTA board approved the ban this month. By then, RVs had become a heated topic. Fed-up residents in the southeast neighborhoods circulated petitions to get the vehicles out, while homeless activists and van dwellers showed up at City Hall hearings to beg for empathy. The conflict provoked several politicians, including Safai, to search for a better solution.

“When I heard about what Safai was doing, I reached out to him,” Brown said. “I told him, ‘Look, you just never know who is living in those RVs. Sure, some people do it by choice, but for others, it’s housing of last resort.’”

Brown’s district spreads through the Haight, Fillmore, Western Addition and Cole Valley — an area with just a few RVs and trailers dispersed around soccer fields and community centers. But Brown said the issue is personal for her because she lived in vans off and on, growing up poor in Utah.

“This is a complicated issue that affects a lot of different groups,” Brown said. “You have families living in these vehicles that need help. You have college students who can’t afford rent. You have elderly people with disabilities, or people with substance-abuse issues. You have Uber and Lyft drivers who come from far away and sleep in their cars, because they don’t want to drive back and forth.”

As plans for RV triage inched along in the mayor’s office, Supervisor Hillary Ronen held community meetings to address the prevalence of trailers and camper vans in the Portola, particularly along the long, uninterrupted curbs around University Mound Reservoir and McLaren Park. Last month, Ronen crafted legislation to require the Department of Homelessness, SFMTA and the Real Estate Division to solve the problem in six months — by finding RV dwellers a safe place to park overnight with showers, bathrooms, waste receptacles and resources to find more stable living arrangements.

Ronen calls her concept a “vehicular Navigation Center,” referring to the elaborate homeless shelters that the late Mayor Ed Lee created for inhabitants of large tent encampments. She will introduce her ordinance at Tuesday’s Board of Supervisors meeting.

Of the 432 inhabited vehicles counted in San Francisco between Oct. 22 and Oct. 30, 313 were RVs and 119 were cars or trucks. Nearly a third were in the Bayview district, and a quarter were in the Mission. A fifth were in Taraval on the southwest side of Golden Gate Park, and the rest were scattered throughout the park and the Richmond and Ingleside neighborhoods, with a few speckling the northern and eastern waterfront.

Rachel Swan is a San Francisco Chronicle staff writer. Email: rswan@sfchronicle.com Twitter: @rachelswan