MUJOCO · DEVICE PHYSICS

Standing Up: the Support Base

Design a humanoid's feet so its center of mass stays over the support base and it does not topple, the most basic stability constraint of any legged body.

01Challenge

The biped starts with a small forward lean and short feet, so its center of mass falls past the front edge of its base and it topples to the floor. Lengthen the feet until the support base contains the center of mass and the robot stays standing. Real MuJoCo, the full biped.

Predict firstA standing biped stays balanced as long as its center of mass projects…

02Model

A legged robot stays up for one reason: its center of mass sits over its support base, the polygon enclosed by whatever is touching the ground. Step the mass past the edge of that polygon and gravity takes over; the body rotates about the edge and falls. This is why humanoid feet are the size they are, and why a wider stance feels stabler: both enlarge the support base. Here the robot leans forward with feet too short to catch it. You are not adding a controller; you are giving the body a base wide enough that statics alone keep it upright. It is the passive half of balance, the foundation the active controllers in Forge build on.

03Guided practice

1. Why it falls. The forward lean puts the center of mass ahead of the short foot's front edge, outside the support base, so it topples. 2. The fix. Enlarge the base: lengthen the feet fore-aft. 3. Edit. Find the two foot_l/foot_r geoms and change the first size number from 0.06 toward about 0.13. 4. Verdict. The torso must stay above 0.5 m (it holds upright) instead of dropping to the floor.

04Feedback

PASS WHEN PASS when the torso stays above 0.5 m: the enlarged feet put the support base under the center of mass and the leaning biped holds its stand. Real MuJoCo on the full biped.

If your run fails, check:

Still toppling (torso near the floor): the feet are still too short, so the center of mass is past the front edge. Grow the foot `size` x toward ~0.13.
Changed only one foot: lengthen BOTH `foot_l` and `foot_r`, or it still tips.
Edited the wrong number: the FIRST of the three size values is the fore-aft half-length; that is the one to grow.

05Retrieve & space

What is the support base (support polygon), and what keeps a legged body upright? (the CoM staying over it).
Why does a wider stance or longer foot feel more stable? (it enlarges the support base).
This lesson uses no controller; what does that make it? (passive/static balance, the foundation active control builds on).

06Mastery & project

Design a foot geometry whose support base contains the center of mass so a leaning biped stands: passive static stability in real physics.

The static-stability floor under every walking controller; the active balance that recovers from bigger disturbances is what Forge and the pilot islands add on top.

← Reach: Kinematics and the Workspace Active Stance: Coordinated Whole-Body Control →

MUJOCO · DEVICE PHYSICS

Standing Up: the Support Base

Edit the humanoid MJCF and run real MuJoCo. Lengthen the feet so the leaning biped's support base contains its center of mass and it stays standing.

You read

the body's mass, the spring and gravity forces, and its deflection each step

You change

the mass, stiffness, and damping you set on the device

Fixed

the MuJoCo solver, the device, and the settle check