PYTHON · NUMPY

To act is to descend an energy

Control a pendulum by descending a shaped energy — the energy IS the controller, not a policy bolted to one.

01Challenge

Complete the energy-shaping law so the controller drives the pendulum upright by pushing its energy downhill.

02Model

The incumbent stack learns a policy that maps states to actions. Energy First inverts it: define one scalar energy whose minimum is the goal, and to act is simply to descend it. For a mechanical body that descent is a control law you can write in one line.

03Guided practice

The shaped energy V = ½ω² + ½·Kp·θ² has its minimum exactly at the upright goal (θ=0, ω=0). Descending it means: cancel gravity, then push the energy down with a spring (−Kp·θ) and damping (−Kd·ω).

04Feedback

PASS WHEN PASS when the energy-shaping control drives the pendulum to upright (|θ|,|ω| < 0.02).

If your run fails, check:

The bench passes when the control law descends V to its minimum — the pole stands up.
The control has three parts: cancel gravity (−g·sinθ), a spring toward the goal (−Kp·θ), and damping (−Kd·ω).

05Retrieve & space

What does it mean, mechanically, to 'descend' the energy?
Why is there no separate policy network here?

06Mastery & project

Acting is energy descent: the energy's minimum is the goal, and the control law pushes the state downhill.

Change the goal to a non-zero angle by shifting V's minimum, and confirm the same descent reaches it.

← Energy First Architecture The same energy is the proof →

PYTHON · NUMPY

To act is to descend an energy

A pendulum, θ measured from upright. Fill in the energy-shaping control law and run — it PASSes when the pole reaches upright.

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