Google Inc., which has been working on software to help major automakers build self-driving cars, also is quietly going around them by designing and developing a full-fledged self-driving car, according to people familiar with the matter. In recent months, Google has held talks with contract manufacturers to build new cars to Google’s specifications, said the people familiar with the matter. The move came after Google’s talks with big car brands about incorporating its technology into their vehicles failed to yield a partnership, one of these people said. Google also has a novel idea for what it could do with these cars. The company has considered ways to sell self-driving vehicles to individuals. But it also has focused on the potential for an autonomous car it designs to become part of “robo-taxi” services that pick up passengers on demand, these people said.