Feb 1 (Reuters) - Self-driving tech firm Cruise on Tuesday said SoftBank Group Corp’s (9984.T) Vision Fund has agreed to invest an additional $1.35 billion through a second tranche, as it works to launch a commercial ride-hailing service in San Francisco. Cruise, majority owned by General Motors (GM.N), has strong financial support from its investors including Honda and Microsoft and is not planning to raise more funds from the capital markets in the near term, GM chief executive Mary Barra said. Dan Ammann, the previous chief executive of Cruise, said he hoped to get a regulatory permit to charge for driverless rides from California Public Utilities Commission early this year. Softbanks investment will help Cruise "quickly scale this technology" across San Francisco and into more communities, Vogt said in a blog posting. Cruise also said that as of Tuesday it would open up the waiting list to the general public to sign up for free rides in San Francisco.