Cruise Automation Inc., a Silicon Valley startup being snapped up by General Motors Co., is gearing up to spend some money and put its new owner in the driver’s seat on autonomous vehicles.

The San Francisco company largely has flown under the radar since its launch in 2013, gaining modest attention for a plan to sell a kit that would let Audi AG owners retrofit their cars with self-driving technology. Cruise Automation ditched that plan and is now touting grander ambitions.

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