Ivo Tedbury is a London-based architect who's focused on how robotics will intersect with his field. To that end, he's designed this Sembler Walking Construction Robot with "a full step-over bipedal gait":

I assume this video is stop-motion, but it would be pretty rad if this is really what it looked like in motion:

"The robot uses its legs and chassis to stabilise itself in each stage of motion," Tedbury writes. "While other robot morphologies can be more dynamically stable, this design was investigated to explore its capacity to transport heavy loads (greater than its own body weight) using inexpensive motors and gearboxes."

"Simulations show the same robot with a gripper mounted under its chassis to transport and place bricks:"

Here's the full simluation of how Tedbury envisions a Semblr or two laying a brick wall, with the help of a scaffolding:

Now that I'm doing design work for a contractor, including site visits, I can tell you that witnessing construction firsthand can be pretty boring. But I could watch these Semblrs all day; I especially like watching them ascend stairs. They're like Slinkies, but with more horizontal action.