# Angular Momentum about the Contact Point for Control of Bipedal Locomotion: Validation in a LIP-based Controller

arXiv: https://arxiv.org/abs/2008.10763 · HTML: https://mlsanity.com/paper/2008.10763/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2020.

## Built on by (most cited first, 4 of 4)

- [Adapting Rapid Motor Adaptation for Bipedal Robots](https://mlsanity.com/paper/2205.15299/) (2022)
- [GLiDE: Generalizable Quadrupedal Locomotion in Diverse Environments with a Centroidal Model](https://mlsanity.com/paper/2104.09771/) (2021)
- [Learning Linear Policies for Robust Bipedal Locomotion on Terrains with Varying Slopes](https://mlsanity.com/paper/2104.01662/) (2021)
- [Embedding Classical Balance Control Principles in Reinforcement Learning for Humanoid Recovery](https://mlsanity.com/paper/2603.08619/) (2026)

## Abstract (arXiv)

In the control of bipedal locomotion, linear velocity of the center of mass has been widely accepted as a primary variable for summarizing a robot's state vector. The ubiquitous massless-legged linear inverted pendulum (LIP) model is based on it. In this paper, we argue that angular momentum about the contact point has several properties that make it superior to linear velocity for feedback control. So as not to confuse the benefits of angular momentum with any other control design decisions, we first reformulate the standard LIP controller in terms of angular momentum. We then implement the resulting feedback controller on the 20 degree-of-freedom bipedal robot, Cassie Blue, where each leg accounts for nearly one-third of the robot's total mass of 35~Kg. Under this controller, the robot achieves fast walking, rapid turning while walking, large disturbance rejection, and locomotion on rough terrain. The reasoning developed in the paper is applicable to other control design philosophies, whether they be Hybrid Zero Dynamics or Reinforcement Learning.