E1 · A push that knocks it over
3 minRun the 40 N block and describe the motion by reading the CoP and pelvis columns.
Done when: python3 kit/equilibrio.py --empurrao 40 ends with CoM dentro do apoio: não · saiu em t = 0.73 s and queda: sim.
Lesson 6 · 15 min
Balance: center of mass and support polygon
A standing humanoid is an inverted pendulum on two small feet. In this lesson you calculate the G1's center of mass, support polygon, and center of pressure from the model itself, push the robot with different forces, and separate three things that usually get mixed up: leaving the support, swaying, and falling.
Start the lesson
In this lesson you will
- 1Center of mass, support polygon, and center of pressure (ZMP on flat ground)
- 2CoM margin in centimeters, every 0.25 s
- 3Why 25 N leaves the support and comes back, and 35 N knocks it down
- 4Where classical control (ZMP) and RL come in
Goal: push the G1 and say, from the simulation, when the center of mass leaves the support polygon and whether the robot falls.
01Four quantities, one question: does it fall?
Click each block.
Click each block in the diagram to see what it does.
Standing still, it is enough for the CoM to be inside the support. In motion, the CoP and the speed are what matter.
02What the push sweep shows
A 0.2 s forward push on the torso, with the G1 just holding the pose. Click each band.
1. Up to 15 N
The CoM never leaves the polygon: the margin never goes negative at any moment.
That is what any rigid pose can handle: the impulse is small (3 N·s).
2. 20 to 30 N
The robot rises onto its toes, the polygon becomes a line, and the CoM is outside it for a moment. Even so, it comes back and ends up standing.
Leaving the support is not falling: it is starting to rotate.
3. 35 to 40 N
At 40 N the CoM leaves at t = 0.73 s; the robot sways forward, comes back, overshoots, and falls backward, without moving a foot.
A balance controller would take a step or move the hip and ankle. Here there is no controller: it is the limit of the body alone.
4. Classical × RL
Classical controllers plan the ZMP to stay inside the support (centroidal models, MPC). Humanoid locomotion in research today is trained with RL in thousands of parallel simulations (course 1).
The training's research found, as of 10/2026, no independent comparison saying which one is better: the two coexist.
03Pushing the G1
The equilibrio.py applies the force on the torso at t = 0.5 s and prints, every 0.25 s, the CoM margin (positive = inside the support), the CoP forward, and the pelvis height.
Terminal · 40 N push
F=${FTH:-$HOME/fth}; cd $F/anatomia && . $F/.venv/bin/activate
python3 kit/equilibrio.py --empurrao 40Terminal · from 10 N to 40 N
F=${FTH:-$HOME/fth}; cd $F/anatomia && . $F/.venv/bin/activate
for n in 10 15 20 25 30 35 40; do
echo "$n N → $(python3 kit/equilibrio.py --empurrao $n | tail -2 | cut -d'(' -f1 | tr '\n' ' ')"
doneExample from the repository
empurrão de 40 N por 0.2 s no tronco (t = 0.5 s) · impulso 8 N·s t (s) margem do CoM (cm) CoP x (cm) pelve z (m) 0.00 5.3 0.1 0.79 0.25 5.3 0.4 0.79 0.50 5.3 0.3 0.79 0.75 -8.1 12.0 0.79 1.00 -5.8 12.1 0.79 1.25 -8.1 12.2 0.79 1.50 -3.4 -4.8 0.79 1.75 -1.2 -4.8 0.79 2.00 -6.7 -4.8 0.79 2.25 -17.4 -4.7 0.76 2.50 -39.6 -4.5 0.64 2.75 -68.4 -8.4 0.15 3.00 -68.9 -11.4 0.06 CoM dentro do apoio: não · saiu em t = 0.73 s queda: sim (pelve a 0.06 m em t = 3 s)
The CoP goes to 12 cm (toes), then to -4.8 cm (heel); the pelvis only drops after 2.25 s, when the robot falls backward.
10 N → CoM dentro do apoio: sim queda: não 15 N → CoM dentro do apoio: sim queda: não 20 N → CoM dentro do apoio: não · saiu em t = 1.40 s queda: não 25 N → CoM dentro do apoio: não · saiu em t = 1.35 s queda: não 30 N → CoM dentro do apoio: não · saiu em t = 0.81 s queda: não 35 N → CoM dentro do apoio: não · saiu em t = 0.76 s queda: sim 40 N → CoM dentro do apoio: não · saiu em t = 0.73 s queda: sim
From 20 to 30 N the CoM leaves the support and the robot does not fall. Anyone who measures balance only by the CoM position gets it wrong from 20 to 30 N; you also need to look at the speed and what happens afterward.
04Practice
Find the limit of the body without a controller.
E2 · A push it can handle
3 minRepeat with 15 N.
Done when: python3 kit/equilibrio.py --empurrao 15 | tail -2 → CoM dentro do apoio: sim (o tempo todo) and queda: não.
E3 · Impulse, not force
5 minRun 40 N for 0.1 s and 80 N for 0.1 s. Compare with 40 N for 0.2 s: what matters, the force or the product of force × time?
Done when: --empurrao 40 --duracao 0.1 ends with queda: não and --empurrao 80 --duracao 0.1 with queda: sim; you wrote down the three impulses (4, 8 and 8 N·s).
05Lesson quiz
The explanation appears after you answer.
Question 1 of 3
With 25 N the CoM left the support polygon, but the robot ended up standing. How do you explain that?skill
Correct
Outside the support, the body starts to rotate over the edge. If the speed is low, gravity brings it back. Leaving the support is not falling.Not that one
Outside the support, the body starts to rotate over the edge. If the speed is low, gravity brings it back. Leaving the support is not falling.Review: What the push sweep showsQuestion 2 of 3
On flat ground, what is the ZMP in classical controllers?
Correct
On flat ground, ZMP and center of pressure coincide. The CoM is something else: it can leave the polygon; the CoP cannot.Not that one
On flat ground, ZMP and center of pressure coincide. The CoM is something else: it can leave the polygon; the CoP cannot.Review: Four quantities, one question: does it fall?Question 3 of 3
40 N for 0.1 s does not knock it over; 40 N for 0.2 s does. What does this teach?
Correct
4 N·s does not knock it over, 8 N·s does, with 40 N or with 80 N. And none of this is the limit of the real G1: there is no balance controller here.Not that one
4 N·s does not knock it over, 8 N·s does, with 40 N or with 80 N. And none of this is the limit of the real G1: there is no balance controller here.Review: Pushing the G1Quiz complete
You got {a} of {n} right. Get them all right and the lesson is marked as complete.Pick an option. The explanation shows up after you answer.
06In three sentences
QuantitiesCoM, support polygon and CoP come out of the model at every step.
DynamicsLeaving the support is rotating; falling is rotating too fast to come back.
LimitWithout a controller, the G1 takes 15 N for 0.2 s and falls with 35 N.