Hey friend
We have talked about balance a lot in this series from the Center of Mass and Base of Support to ZMP and Model Predictive Control.. There is a more advanced part that makes the difference between just standing or walking and really dynamic balance.
Today we are going to talk about three ideas that are used in advanced humanoid robots: Center of Mass, Angular Momentum and Capture Point Theory.
These ideas are what help robots like Boston Dynamics Atlas, Tesla Optimus and Figure 01 to get back up after being pushed to run, jump and walk with confidence on ground.
1. Center of Mass Revisited
Like we said before the Center of Mass is the position of all the robots mass. When the robot is moving the main goal is to control the motion of the Center of Mass.
When the robot is moving fast or something is pushing it just controlling the Center of Mass is not enough. We also need to control Angular Momentum.
2. Angular Momentum: The Spin Factor
Angular Momentum measures how much the robot is turning or twisting.
Even if the Center of Mass is in a position if the robot is turning or twisting too much it can still fall. The robot can also use Angular Momentum to help it get back up. For example it can swing its arms. Turn its body to get its balance back.
The people who make the balance controllers for these robots try to keep the Angular Momentum small when the robot is walking normally.. They allow the robot to use more Angular Momentum when it needs to get back up or make a big move.
That is why you often see humanoid robots swinging their arms when they are losing their balance. They are using their arm motion to stop the Angular Momentum.
3. Capture Point Theory: The Where Should I Step Concept
This is one of the powerful ideas in dynamic humanoid balance.
The Capture Point is the spot on the ground where the robot should put its foot to stop completely without falling if it can use the amount of force.
In words:
“If I step exactly here I can get my balance back and stop safely.”
There are two kinds:
- Instantaneous Capture Point: The spot where the robot should step right now to stabilize.
- Divergent Component of Motion: A related idea that is used in many modern controllers.
Simple idea:
When you are pushed while walking your bodys Center of Mass starts moving fast in one direction. Your brain automatically figures out where you should step to catch that motion and get your balance back. Humanoid robots do the thing using Capture Point theory.
Math idea:
The Capture Point can be thought of as:
Where the natural frequency is like the speed at which the robot would swing back and forth if it were a pendulum.
If the robot can put its foot at or beyond the Capture Point in time it can get back up. If the Capture Point is far away the robot will fall.
How Real Robots Use These Concepts
- Boston Dynamics Atlas: Uses Angular Momentum and Capture Point ideas to do parkour and get back up after being pushed.
- Tesla Optimus: Uses a Capture Point and ZMP control to walk and deal with small disturbances.
- Figure 01. Unitree G1: Use Capture Point planning and learning to get really good at balance.
Modern controllers often think about:
- The path of the Center of Mass
- Angular Momentum
- Capture Point and foot placement
- ZMP constraints
My Personal Take
Capture Point Theory was a moment for me. It answers the question: “Where should the robot step next?” in a simple way. This is something that feels natural for humans. Is hard to make robots do.
The Center of Mass, Angular Momentum and Capture Point give us a way to think about dynamic balance. They help us understand how to go from standing to really moving around.
The best humanoid robots are not just good at keeping their Center of Mass over their feet. They are also good, at controlling Angular Momentum and using Capture Points when they move fast.
This way of thinking about physics, combined with learning methods is what is making humanoid robots get better so quickly.