inverted-pendulum model of walking
The inverted-pendulum model of walking is a deliberately simple picture of how a legged robot (or a person) stays upright while moving. A normal pendulum, like a clock's, is a weight hanging down from a pivot and swinging gently below it. An inverted pendulum is the same thing flipped over: a weight balanced up on top of a stiff, thin support, like a broom balanced on your palm. The model says: ignore the arms, the swinging leg, and all the body's complicated parts, and pretend the robot is just one heavy lump (its body) sitting on top of one stick (the leg that is currently on the ground), pivoting around the foot.
This is useful because the messy physics of walking suddenly becomes the well-understood physics of a balancing stick. As the lump teeters forward over the planted foot, gravity tries to topple it; the trick of walking is to swing the other leg out ahead and plant a fresh foot just in time, so the body falls onto a new support and the process repeats. Walking, in this view, is really a controlled series of forward falls, each one caught by the next step. The model lets engineers compute where to put the next foot and how fast the body will travel, using a single clean equation instead of a tangle of joints.
Because it is so stripped-down, the inverted-pendulum model is the starting sketch for most walking-robot controllers; the popular 'linear' version even holds the body at a constant height, which makes the math simple enough to solve on the fly. Real robots then add back the details the model left out, but the core intuition — keep catching your own fall with the next step — comes straight from this picture.
To plan a walk, a humanoid's controller models its body as an inverted pendulum balanced on the support leg. It calculates that if the body is falling forward at a certain speed, planting the next foot 40 centimetres ahead will catch the fall and carry the motion smoothly into the following step.
Walking, modeled as a stick balancing a weight and catching each fall.
The model treats the leg as a rigid, massless stick and the body as a single point, so it captures balance and step timing well but says nothing about flexing knees or springy tendons — real legged robots layer those back in.