Embodied AI Design: Humanoids for Work and Play
Design an embodied AI end to end, the body and the behavior, for the two arenas pulling humanoids into the world: work and play. You size a joint in real MuJoCo, build a walking gait, transfer it from simulation with domain randomization, build the foundation-model stack that turns pixels into actions (the priors, not the guarantee, what makes each action safe is the certificate it commits under, and its economy is joules per viability-second), give motion style through dance and martial-arts form, and probe how a robot learns by playing. Grounded in the 2026 reality of humanoids on real lines and in real homes, it closes on the question the field is actually asking: how a robot amplifies people instead of replacing them.
▶ Start the course ← All coursesWhere this sits, and what moves it.
Binding constraint · Torque density and the energy budget it implies. A humanoid's behaviour is written by what its actuators can deliver at the joint, and every gait, catch, and dance step is a withdrawal against that.
Sizing an actuator against a gait meant hardware. You built the leg, discovered the joint saturated mid-stride, and rebuilt it -- a cycle measured in months, which is why bipedal walking stayed in a handful of labs.
Real physics in a browser collapses that cycle to a session, and sim-to-real with domain randomisation crosses a gap that used to swallow projects. The gap has not closed: randomisation buys robustness by paying in conservatism, and a policy tuned to survive every sampled world is not the best policy in the real one.
The lever is a body whose dynamics are identified well enough that randomisation can narrow rather than widen -- closing the loop from a real robot's telemetry back onto the simulator's parameters. Watch the width of the randomisation band a lab needs; it is a direct readout of how well anyone actually knows their machine.
Every hard thing was impossible until the constraint that made it impossible was named. How we read a frontier →
The Body: Morphology and Actuation
Design the physical robot: size a joint's actuator against gravity in real physics, reason about how a body's degrees of freedom set what it can reach and do, and then site the guard that has to stand back from it once the safe state is one the robot holds actively rather than one that survives the power being cut.
- L3Sizing a Joint ActuatorTo hold its arm straight out, a robot's shoulder needs the MOST torque when the arm is…Size a compliant joint's holding stiffness so it supports a leg segment at a target crouch, the balance a real series-elastic actuator must strike.→
- L3Reach: Kinematics and the WorkspaceYou have a 2-link arm and a target point. What decides whether the arm can reach it at all?Solve the inverse kinematics of a 2-link arm to show how a body's link lengths and joints set the space it can reach.→
- L3Standing Up: the Support BaseA standing biped stays balanced as long as its center of mass projects…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.→
- L4Active Stance: Coordinated Whole-Body ControlYou command a humanoid into a deep crouch by bending the knee. What happens?Write a controller that commands a real MuJoCo humanoid into a deep, coordinated stance and holds it upright, the active counterpart to the passive support base.→
- L4The fence a fall buysA protective stop on an industrial arm removes power. Apply the same stop to a balancing humanoid. What does the ISO 13855 calculation inherit?Site a light curtain for a balancing humanoid from ISO 13855, and measure how much of the required distance is bought by the one term in the formula that carries no certification.→
Learning to Move: Stepping, Gait, and Sim-to-Real
Make a humanoid keep its feet and cover ground: step to a capture point to catch a push, generate a walking gait, and transfer it to reality with domain randomization.
- L4Stepping to Recover: the Capture PointA hard shove sets a standing robot’s center of mass moving. Can a strong enough ankle stiffness ALONE bring it back to rest?Compute where a biped must step to arrest a push, using the capture point of the linear inverted pendulum, the reduced-order model roboticists design stepping balance with.→
- L4A CPG Gait: Physics Plus a Kiss of ControlA 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.→
- L4Sim-to-Real by Domain RandomizationYou train a walking policy in one perfectly-tuned simulator, then deploy it to the real robot. It most often…Choose a controller that survives the reality gap by optimizing worst-case behavior across a randomized ensemble of robot models, the recipe behind 84-93% zero-shot transfer.→
The Behavior: Foundation Models for Action
Understand the vision-language-action stack that turns pixels and instructions into robot actions, and the data strategy and architecture that make it learn efficiently.
- L4The Bridge, Not From ScratchHow many demonstrations does a modern robot policy need to learn a new reach task, when it STARTS from a pretrained base?Show why a robot policy learns from a handful of demonstrations when it starts from a pretrained backbone's features, versus needing far more data from scratch.→
- L4Action Chunking and the Two SystemsA policy that sees the target only every few steps lags behind a moving goal. What lets a chunked policy TRACK it instead of chasing it?Show why predicting a short horizon of actions from one observation tracks a moving goal better than a purely reactive policy, the idea behind pi-0 and Figure's Helix.→
- L4What reaches the robotOf a humanoid foundation model's 440.5 million parameters, reported as 'used for real tests', roughly how many does the robot's control loop run?Find out how much of a humanoid foundation model runs on the robot, reconcile a released checkpoint to the byte, and see a file-size argument confirm the wrong answer.→
Dance, Martial Arts, and Play
Design movement that carries style and meaning, not just a path: rhythm and expressiveness from choreorobotics, form and timing from martial arts, and play as the open-ended drive that expands what a body can do.
- L4Dance: Style and the BeatYou want a robot's gait to lock onto a musical beat. What is the mechanism?Make a robot's motion expressive by synchronizing its gait to a musical beat, the entrainment at the heart of choreorobotics.→
- L4Martial Arts: Forms and TimingYou compose a form from timed keyframe poses. What has to hold between the keyframes as well as on them?Compose a martial-arts form from timed keyframe poses, hitting each on time while keeping the center of mass over the support base.→
- L4Play: The Drive That Expands the BodyTo expand what an agent can do fastest, should it practice goals chosen RANDOMLY across its whole world, or goals just beyond its current ability?Show that an agent that plays at the edge of its competence expands what it can do far faster than one chasing random goals, play as a self-directed curriculum.→
Learning by Exploring: Curiosity and Agency
Study how an embodied agent acquires skills and goals by exploring, using curiosity and intrinsic motivation, and why efficient, goal-directed action is the real measure of embodied intelligence.
- L4Curiosity: Learning Before RewardsTwo agents explore the same world. One moves randomly, the other picks the least-visited neighbour. How much more of the world does the second one see?Show that an agent driven by novelty explores far more of its world than a random walk, the mechanism by which robots (and children) learn through play before any goal is set.→
- L4Agency and Action EfficiencyAn action-efficiency score compares a solution against a human baseline. Why is the ratio squared rather than used directly?Implement the action-efficiency score that measures goal-directed intelligence, and see why brute force scores near zero while an efficient, guided agent scores high.→
Work: Deployment and Amplification
Put a humanoid to work in a real line and design the human-robot division of labor that amplifies people instead of replacing them.
- L3Where the Robot Earns Its PlaceA production line runs at 5 units a minute. You add a humanoid work cell at the fastest station. What happens to throughput?Analyze a production line to find the bottleneck and deploy a humanoid work cell where it actually raises throughput, the deployment reality of 2026.→
- L4Amplify, Not ReplaceYou split work between a human and a humanoid to beat either working alone. Which tasks go to the robot?Design the division of labor between a human and a humanoid so the pair beats either working alone, while keeping high-value craft work with the person.→
Capstone: Design a Humanoid for Work and Play
Bring the whole course together: design a single humanoid for a named work-and-play role so that every requirement, one per module, is satisfied at once.
Anatomy demonstrations
The machines behind this course, taken apart three ways, the body, the one rule, and the small learned brain. Guess before you look; an open core proves every number on the page.
From the interactive textbook
The ideas under this course as live explorables, each runs the real Rust library and re-derives its own result.