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Week 1: Classical Foundations
Week 1 -
Classical Foundations
Rigid transforms, forward and inverse kinematics, dynamics, and control.
Rigid transforms, frames, and your first MuJoCo sim
Glossary primer (10 min) Pose — A 6 DoF position + orientation. A point in SE(3) (Special Euclidean group in 3D). Rotation matrix R — A 3×3...
Forward kinematics (Product of Exponentials) and DH parameters
Glossary primer (10 min) Forward kinematics (FK) — Mapping from joint angles q to end effector pose T(q) . Product of Exponentials (PoE) — M...
Inverse kinematics, Jacobians, singularities
Glossary primer (12 min) Inverse kinematics (IK) — Given a desired EE pose T des , find joint angles q such that FK(q) = T des . Jacobian J(...
Dynamics: Lagrangian, mass matrix, gravity compensation
Glossary primer (10 min) Equation of motion (EOM) — M(q) q̈ + C(q, q̇) q̇ + g(q) = τ . Newton's law for an articulated body. Mass matrix M(q...
Control I: PID, LQR, feedforward (cart-pole stabilization)
Glossary primer (12 min) PID controller — τ = Kp · e + Kd · ė + Ki · ∫e dt . Three knobs. Surprisingly hard to beat in practice. LQR (Linear...
Control II: operational-space, impedance, contact
Glossary primer (12 min) Operational space control (OSC) — Compute desired task space (Cartesian) acceleration, then map to joint torques: τ...
Trajectory generation + Week 1 integration + fresh-clone test
Glossary primer (10 min) Trajectory — A time parameterized configuration: q(t), q̇(t), q̈(t) satisfying physical and kinematic constraints....
What you will know by end of Week 1
- Read the week's source papers without drowning in undefined terms.
- Run the week's core software stack from a fresh clone.
- Explain the week's systems in terms of data, control, and learning loops.