WUZHEN, China—The engineer chaperoning our driverless car has the anxious look of a parent seated next to a teenage student driver. Perched behind the wheel, he floats his hands at the three- and nine-o’clock positions, just in case.

And then, we’re off.

I’m passenger No. 139 in a series of test drives Wednesday to showcase Baidu Inc.’s new autonomous-driving technology, which the internet search giant hopes to make commercially viable in about three years.

My car, a blue BYD Qin, has been tricked out with a spinny hat, a lidar that sees the surroundings with the help of 64 laser beams spinning 360 degrees. There are three smaller 16-laser lidars to cover blind spots and a millimeter-wave radar under the front bumper to catch anything the lidars may miss in poor visibility. There is a supercomputer in the trunk.

“They look kind of like Smurfs,” a Baidu employee says of the cars, and I can’t disagree.