Robot was able to transform from walking to driving mode for a while (see this blog post) but I was looking how to do it autonomously without holding robot in the air. After a lot of experimentation and some hardware changes I figured out how to make robot to balance during transformation:

For balancing to work on hard surface I had to put rubber tires on wheels otherwise robot would slip too much with plastic wheels. Wheel design had to undergo few iterations to make sure tires themselves don't slip from wheels sideways during transformation. Even in the latest design tires do come off the wheels occasionally so more improvements are needed for a final design.