# Linear Inverted Pendulum Model (LIPM)

It turns out that we can model a biped robot quite simply as a single point mass with two force vectors representing the feet. Modeling the robot this way allows for easy mathematical modeling as well as being easier to visualize than a multi-mass model with many joints.

One further simplification which is very popular at the moment is to restrict the robots motion to the X-Y plane and prevent motion in the up down direction. This is called the Linear Inverted pendulum model (LIPM) [1] and is used extensively in current biped robotics research.

The equation of motion for the LIPM is described as follows

where

and is the height of the COM which should be a constant.

Next: Trajectory Generation

Previous: Center Of Mass Jacobian

**References**

[1]. “The Linear Inverted Pendulum Model: A simple modeling for a biped walking pattern generation”, Shuuji Kajita, Fumio Kanehiro, Kenji Kaneko, Kazuhito Yokoi and Hirohisa Hirukawa. Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems Maui, Hawaii, USA, Oct. 29 – Nov. 03, 2001

Ehm, what is the t after w in the equations?

Also how does this can be applied in ZMP calculation?

I see a lot of interesting articles on your blog.

You have to spend a lot of time writing, i know how to save you a lot of time,

there is a tool that creates unique, SEO friendly posts in couple

of seconds, just type in google – k2 unlimited content