Autonomous UAV Algorithm Handbook

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LQR Hover ​

Problem Statement ​

LQR hover control optimizes stabilization around a hover equilibrium by balancing state error and control effort. It gives a principled gain matrix and clean performance trade-offs through weighting matrices.

Model and Formulation ​

Linearized dynamics around hover:

$$ \dot{x} = Ax + Bu $$

Objective:

$$ J = \int_0^\infty \left(x^\top Qx + u^\top Ru\right)dt $$

Optimal policy:

$$ u = -Kx,\quad K = R^{-1}B^\top P $$

where P solves the continuous-time algebraic Riccati equation.

Algorithm Procedure ​

  1. Linearize UAV dynamics around trim hover.
  2. Choose Q and R according to tracking vs effort priorities.
  3. Solve Riccati equation for P, then compute feedback gain K.
  4. Apply full-state feedback in the hover envelope.

Tuning Guidance ​

  • Increase position-state weights in Q for tighter hover.
  • Increase R to smooth actuation and reduce aggressive commands.
  • Re-linearize if operating point drifts far from hover assumptions.

Failure Modes and Diagnostics ​

  • Performance degrades in strongly nonlinear/aggressive regimes.
  • State-estimation latency can destabilize high-gain solutions.
  • Poorly scaled units in Q/R create unintuitive controller behavior.

Implementation and Execution ​

bash
python -m uav_sim.simulations.path_tracking.lqr_hover

Evidence ​

LQR Hover

References ​