Path Tracking
Path tracking converts geometric references into feasible attitude and thrust commands. This chapter spans linear and nonlinear feedback structures used for hover and mission-level behavior.
Core Questions
- How should positional and attitude loops be decoupled?
- Which error-state definitions improve transient response?
- How do saturation and actuator limits affect stability margins?
Algorithms
- PID Hover
- LQR Hover
- LQR Path Tracking
- MPC Tracking
- Geometric Control on SE(3)
- Pure Pursuit 3D
- Fixed-Wing Mission Navigation
- Path Smoothing
- Flight Ops Demo
The One Thing That Separates Hovering From Tracking
Every controller in this chapter can hold a point. What distinguishes them on a moving reference is whether they are given its derivatives.
A pure feedback loop has to manufacture the reference's own acceleration out of tracking error, so it settles at whatever error does the job — error proportional to how hard the trajectory is. Feeding the reference acceleration forward removes that term from the error dynamics entirely. On the atlas figure-8 the difference is an order of magnitude for every controller here:
| Controller | Feedback only | With feed-forward |
|---|---|---|
| LQR | 0.158 m | 0.017 m |
| Geometric SO(3) | 0.388 m | 0.023 m |
| MPC (preview) | 0.395 m | 0.032 m |
| Feedback linearisation | 0.234 m | 0.014 m |
The symptom to recognise: tracking error that scales with reference speed, and an overshoot on the trajectory's fastest axis. That is not a gain that needs raising.
Prerequisites
- State-space control basics
- Hover linearization around trim
- Attitude representation in SO(3)/Euler form