TOKYO—Toyota Motor Corp. is pushing back against technology companies muscling in to the automotive business, outlining plans to spend at least $1 billion on a Silicon Valley research center to study autonomous driving and robotics.

The move shows that the world’s largest auto maker is shedding some of its caution and accelerating plans to develop “smart” cars. Auto makers are rushing to set up labs in the home of technology giants such as Google Inc. that are pouring money into research on self-driving technologies.

The...