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 coursesThe Body: Morphology and Actuation
Design the physical robot: size a joint's actuator against gravity in real physics, and reason about how a body's degrees of freedom set what it can reach and do.
- L3Sizing a Joint ActuatorSize 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 WorkspaceSolve 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 BaseDesign 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 ControlWrite 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.→
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 PointCompute 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 ControlBuild 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 RandomizationChoose 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 ScratchShow 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 SystemsShow 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.→
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 BeatMake a robot's motion expressive by synchronizing its gait to a musical beat, the entrainment at the heart of choreorobotics.→
- L4Martial Arts: Forms and TimingCompose 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 BodyShow 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 RewardsShow 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 EfficiencyImplement 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 PlaceAnalyze 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 ReplaceDesign 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.