There are a number of ways to make origami robots, but the basic principle is simple: You have a flat material that permits a certain set of folds. Along those folds there are actuators—a fancy word for a machine part that can move—that cause the fold to fold itself. The “paper” contains the circuitry to talk to a computer, so you can simply program the robot to bend along the right folds at the right times. Because the machine can continue to fold even after it reaches its desired form, it can do things regular origami can’t, like walking around or grabbing things.
“There are a number of ways to make origami robots, but the basic principle is simple: You have a flat material that permits a certain set of folds. Along those folds there are actuators—a fancy word for a machine part that can move—that cause the fold to fold itself. The “paper” contains the circuitry to talk to a computer, so you can simply program the robot to bend along the right folds at the right times. Because the machine can continue to fold even after it reaches its desired form, it can do things regular origami can’t, like walking around or grabbing things.”
Reference
Weinersmith, Kelly, & Zach Weinersmith (2017, Oct. 7). “Soonish: Ten Emerging Technologies That'll Improve and/or Ruin Everything.” Kindle Edition. Chapter 5 Programmable Matter: What If All of Your Stuff Could Be Any of Your Stuff? p. 105 of 358, 24%.

