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Control synthesis (LQR)

Draft

This page is scaffolded. The outline below marks what it should cover.

LQR(world, …) synthesizes a state-feedback regulator about an operating point — the third sibling transform. It regulates a controllable subset and freezes the rest.

To cover

  • The operating point — x_ref / u_ref (trim), and why a free rigid body is underactuated so full-state LQR isn't stabilizable.
  • regulate= — selecting the controllable subspace (e.g. ["drone.position", "drone.velocity"]) and freezing the remainder at the operating point.
  • Q / R cost weights — distinct from the EKF's process/measurement noise; how they shape the gain.
  • The runtime surface — lqr.control(state_dict) → {input: u} and retarget(...) to move the setpoint.
  • Under-actuation through attitude — how a single-thruster craft regulates position via attitude (the quadcopter demo).

Source material