Depth & pitch control near the surface
Track a commanded depth while reducing unnecessary actuator activity in waves.
Visual description
The published studies use numerical simulations. This detailed explainer introduces the near-surface problem, separates slow tracking error from wave-frequency actuator activity, explains the architecture, and compares the roles of nominal LQR, frequency shaping and L1 reference augmentation. Its motion and traces are illustrative, not paper data.
Video chapters
Read the narration
The mission
An underwater vehicle must follow a depth command close to the surface. Waves disturb its motion, while uncertain hydrodynamics can shift its average depth. The aim is accurate mean tracking without asking the actuators to fight every wave.
Two different problems
With a nominal regulator, the vehicle can remain offset from the commanded depth. At the same time, the control surfaces may react repeatedly to wave-driven motion. The two plots distinguish a persistent tracking error from unnecessary high-frequency control activity.
A layered solution
The commanded depth enters an adaptive reference layer. The LQR autopilot follows that adjusted reference and manages the actuators. Measurements return to both layers. The adaptive layer addresses slow uncertainty, while the regulator shapes the vehicle response.
Do not chase every wave
The regulator is designed using an augmented model with frequency weighting. Control activity around the wave frequency receives an additional penalty. This is built into the LQR design. It is not simply a filter added after an already designed controller.
Correct the mean tracking error
The adaptive layer estimates the effect of uncertainty and changes the reference supplied to the autopilot. The original command stays fixed. As the internal reference adjusts, the mean vehicle depth approaches the command, while residual wave-driven motion may remain.
The actuators tell the other half
A new depth command requires a real maneuver. Tail planes, the sail plane, and the hover tank contribute according to the control allocation. The desired outcome is reduced rapid actuator motion, not motionless actuators: they still respond to slower changes.
Compare the contributions
Compare the same maneuver in three configurations. Nominal LQR can exhibit offset and wave-frequency activity. Frequency shaping reduces the rapid control oscillations. Adding adaptive reference management addresses the remaining mean error. These animation traces explain the mechanisms; they are not numerical results.
What the published study establishes
The published work evaluates the approach with a Joubert BB2 simulation model. Its central idea is a division of responsibilities: frequency-shaped regulation manages wave-related actuator activity, and adaptive augmentation addresses slow disturbances and uncertainty. Quantitative results are available in the linked papers.
The problem
Near the surface, waves and slower hydrodynamic disturbances affect both depth and pitch. Correcting every wave can make the actuators work unnecessarily.
My work
I developed and evaluated an L1-augmented LQR autopilot for the Joubert BB2 underwater vehicle. The design addresses persistent depth errors and reduces actuator response at wave frequency.
Context & evidence
The published studies use numerical simulations. This detailed explainer introduces the near-surface problem, separates slow tracking error from wave-frequency actuator activity, explains the architecture, and compares the roles of nominal LQR, frequency shaping and L1 reference augmentation. Its motion and traces are illustrative, not paper data.