A motorcyclist was injured in a collision with a Waymo self-driving car last month — but Waymo says the accident underscores the robot cars’ safety, as it was caused by the backup driver.

The Oct. 19 accident came days before Waymo, the self-driving unit of Google parent Alphabet, won approval from the California Department of Motor Vehicles to test cars without drivers on public roads — the first company in California allowed to do so. It has not yet begun those tests, although its cars have operated without backup drivers on Arizona roads for a year.

For Waymo, as for all of the carmakers, tech companies and startups rushing to develop robot cars, it’s important to manage public perception of the cars’ safety. People are much less accepting of robot-car accidents than they are of human-caused ones. Some consumer advocates charge that the companies are rushing unproven technology onto public roads too soon.

The motorcycle collision took place on El Camino Real near Waymo’s Mountain View headquarters, according to the required accident report Waymo filed with the DMV.

As the Waymo car — all of its cars are white Chrysler Pacifica minivans — drove at 21 mph in the middle of three lanes, a car in the left lane began to merge into that middle lane. The test driver “took manual control of the AV (autonomous vehicle) out of an abundance of caution, disengaged from self-driving mode, and began changing lanes into Lane 3” (the right-hand lane), the report said.

A motorcycle was in the right-hand lane traveling at 28 mph and beginning to overtake the Waymo car. Waymo’s car and the motorcycle collided at the car’s right rear bumper. The injured motorcyclist was transported to a hospital, the report said.

After each “disengagement” incident — an instance where humans take control of the car — Waymo runs software simulations of how the robot car would have responded if it had stayed in autonomous mode.

In this case, the simulation showed the car slowing down to avoid the car merging from the left and nudging slightly into its lane — avoiding a collision with either the other car or the motorcycle.

While humans sometimes make “a split-second decision with insufficient context,” the car had a 360-degree view of its environment, Waymo CEO John Krafcik wrote in a blog post about the incident.

“Our self-driving system was simultaneously tracking the position, direction and speed of every object around it,” Krafcik wrote. “Crucially, our technology correctly anticipated and predicted the future behavior of both the merging vehicle and the motorcyclist.”

Every single company working on autonomous cars says that safety is its top concern and that the vehicles will lower the nation’s current 36,000 annual deaths from car accidents.

However, especially while the cars are in their early days, it’s likely that there will continue to be crashes.

In the first known fatality caused by a self-driving car, an Uber vehicle in Arizona struck and killed a pedestrian in March. The car was in self-driving mode, with a backup driver who was watching a video (in violation of all rules for such drivers), and emergency braking features were disabled.

Uber shut down all autonomous drives on public roads after the fatality, but last week applied to resume testing in Pittsburgh, promising to take extra safety precautions, such as having two operators in the cars at all times.

Uber’s well-publicized incident, plus some fatal accidents with Tesla cars operating in Autodrive, a semi-autonomous mode, has caused public confidence in self-driving cars to fall in recent months, according to surveys.

Testing on public roads is crucial for self-driving cars, Waymo’s Krafcik wrote, and the company is sorry that someone sustained an injury.

“We recognize the impact this can have on community trust,” he wrote.

Carolyn Said is a San Francisco Chronicle staff writer. Email: csaid@sfchronicle.com Twitter: @csaid