PYTHON · NUMPY

A CPG Gait: Physics Plus a Kiss of Control

A central pattern generator drives a rhythmic gait. How much of the walking does the controller actually do?

Build a central pattern generator that drives a rhythmic gait, letting the body's dynamics do most of the work while a small control signal moves it forward.

01Challenge

The gait oscillator swings the legs but the robot goes nowhere, because there is no propulsion. Add the rhythmic forward impulse during stance and watch it travel. This is the passive-dynamic-walker idea: let physics carry it, add a kiss of control.

Predict firstA central pattern generator drives a rhythmic gait. How much of the walking does the controller actually do?

02Model

Walking was long treated as a hard planning problem, until a simpler idea took hold: a body with the right dynamics almost walks on its own. Tedrake's toddler learned to walk in about twenty minutes by adding a little actuation to a passive walker rolling down a ramp. A central pattern generator is that idea in software, a small set of coupled oscillators that produce the rhythm of a gait, hip and knee cycling in phase. You are not scripting every footfall; you are setting a rhythm and a well-timed push, and letting the pendulum dynamics of the legs handle the rest.

03Guided practice

1. See the rhythm. hip and knee already cycle from the phase; the body just does not move. 2. Add propulsion. Set push = 0.6 * max(0.0, np.cos(phase)), a forward impulse during the stance half of each cycle. 3. Integrate. The push drives velocity against drag, and velocity moves x. 4. Travel. Reach more than 0.3 m in the 4-second window.

04Feedback

PASS WHEN PASS when the gait carries the body more than 0.3 m: a rhythm plus a timed push, not a scripted trajectory.

If your run fails, check:

Travels 0.00 m: `push` is still zero. Add the rhythmic stance impulse `0.6 * max(0.0, np.cos(phase))`.
Barely moves: make sure the push is rectified (only the positive half), so it pushes forward without cancelling.
Oscillates but drifts nowhere: the push must be phase-locked to the gait, tied to `phase`, not constant.

05Retrieve & space

What is a central pattern generator, and what does it produce? (coupled oscillators giving a gait rhythm).
What did passive dynamic walkers show about walking? (the body's dynamics do most of the work).
Why is 'a rhythm plus a timed push' easier to tune than scripting every footfall?

06Mastery & project

Produce forward walking from an oscillator and a well-timed push: locomotion as dynamics plus a little control.

The gait you then have to transfer to a real robot in the next lesson, and to learn on-device in Forge.

GO FURTHER · THE LIVE PLAYGROUND

Teach a generated robot to walk ↗ · Forge learns a gait with Evolution Strategies over a CPG, on-device
Drive a walking biped ↗ · steer the humanoid Pilot and feel the gait under your commands

← Stepping to Recover: the Capture Point Sim-to-Real by Domain Randomization →

PYTHON · NUMPY

A CPG Gait: Physics Plus a Kiss of Control

A CPG in NumPy drives a toy gait. Add the stance-phase push so the body moves forward.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you