Southeast Asia's leading ride-hailing firm Grab on Friday teamed up with a US-based software developer to run a limited public trial of a self-driving car service in Singapore.

Applications for free rides on the "robo-cars" opened on Friday, with the service expected to kick off next week, Grab Singapore head Lim Kell Jay told journalists.

The revolutionary technology will be used to ferry passengers as well as a safety driver and an engineer around One North, a research campus with limited traffic.

"If a trip requires travel on roads outside of One North, the safety driver will take control of the vehicle for that portion of the trip," a joint statement by Grab and software company nuTonomy said.

The partnership follows the September 15 launch of a groundbreaking driverless car service in the US city of Pittsburgh by Uber, the world's leading car-hailing company.

The trial will run for the next two months, and may be extended for as long as it continues to yield useful feedback and data that can feed into the roll-out of driverless taxis across Singapore in 2018.

The announcement came three days after Singapore-based Grab said it had raised $750 million in funding from investors, taking its total capital to more than $1.0 billion, as it looks to expand in the lucrative Southeast Asian market and bolster its lead over Uber.

But Uber's launch of a driverless car service last week catapulted it ahead of Detroit auto giants and Silicon Valley rivals with technology that could revolutionise transportation.

In an ambitious experiment, a fleet of cars laden with lasers, cameras and other sensors -- but with no hands on the wheel -- were deployed on Pittsburgh's challenging roads, steering themselves to pick up passengers.

In addition to Uber and Grab, Google's parent company Alphabet is also working on getting self-driving vehicles to market.

Grab's Singapore trials are backed by the wealthy city-state's government.

But Karl Iagnemma, chief executive and co-founder of nuTonomy, brushed off suggestions that the launch was timed to take the shine off Uber's Pittsburgh success.

"My strong belief of what we're going to see is the emergence of multiple regional winners," Iagnemma said.

Competition between Uber and local startups has grown fierce in Southeast Asia, home to more than 600 million people and a rising middle class.

Grab operates in Singapore, Indonesia, the Philippines, Malaysia, Thailand and Vietnam.