Reaction Mass Pendulum

I came across Ambarish Goswami's website while trolling the internet for related research. He has a nice page on what he calls the "Reaction Mass Pendulum" (RMP):

http://www.ambarish.com/simple_model.html

This model is the 3D generalization of an inverted pendulum with a flywheel. I used a linear inverted pendulum with flywheel model in my Humanoids '07 paper. Others have used similar models before as well.

The benefit of this model is that it provides a mapping from the robot to a reduced model that considers the 3D instantaneous centroidal inertia, which is a very important term when analyzing or controlling balance.

The interesting part of their work using this model is an "inertia shaping" controller, which is basically an inverse kinematics controller that drives the robot pose to a configuration that represents the desired centroidal inertia of the RMP.

For more information, see their ICRA paper:

S-H. Lee and A. Goswami, Reaction Mass Pendulum (RMP): An explicit model for centroidal angular momentum of humanoid robots, IEEE Int. Conf. on Robotics and Automation, Rome, Italy, April 2007. (pdf).