⚡ electrical engineering

Data-Enabled Predictive Control with Predictive Adaptive Line-of-Sight Guidance for 3-D Path Following of Autonomous Underwater Vehicles

This paper presents a fully data-driven 3-D path-following framework for autonomous underwater vehicles that combines Data-Enabled Predictive Control with a predictive adaptive line-of-sight guidance law to eliminate the need for explicit hydrodynamic modeling while significantly reducing cross-track errors compared to state-of-the-art benchmarks.

Original authors: Sebastian Zieglmeier, Mathias Hudoba de Badyn, Narada D. Warakagoda, Thomas R. Krogstad, Paal Engelstad

Published 2026-06-02

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sebastian Zieglmeier, Mathias Hudoba de Badyn, Narada D. Warakagoda, Thomas R. Krogstad, Paal Engelstad

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to teach a submarine (specifically, a small, autonomous one called the REMUS 100) how to swim through the ocean along a specific 3D path, like a wireframe tunnel in the water. The ocean is tricky: currents push the sub sideways, the water resists its movement in complex ways, and the sub's own body reacts differently depending on how fast it's going.

Traditionally, to control this sub, engineers have to build a massive, complicated mathematical "recipe" (a model) of exactly how the water and the sub interact. They have to measure every drag coefficient and mass property, which is like trying to write a recipe for a cake by measuring every single grain of flour and drop of milk before you even bake it. If the conditions change (like the water getting warmer or the sub carrying a heavier payload), that recipe often becomes wrong.

This paper proposes a different way: Stop writing the recipe. Just watch the sub swim.

Here is the breakdown of their new "data-driven" approach using simple analogies:

1. The "No-Recipe" Pilot (DeePC)

Instead of using a pre-written mathematical model, the authors use a method called Data-Enabled Predictive Control (DeePC).

The Analogy: Imagine you are learning to ride a bike. A traditional model-based approach is like reading a physics textbook on friction and balance before you ever touch a bike. The DeePC approach is like a coach who has watched thousands of hours of video of you riding. When you wobble, the coach doesn't calculate the physics; they simply say, "Last time you leaned left, you fell. This time, lean right."
How it works: The system records thousands of past movements (inputs like steering the rudder, outputs like where the sub went). When it needs to make a decision, it looks at its "memory bank" of past trips to predict what will happen next. It doesn't need to know why the water pushes the sub; it just knows that it pushes the sub, based on what it has seen before.

2. The "Slow and Steady" Problem (Cascaded Control)

The sub has two main jobs: turning left/right (heading) and going up/down (depth).

The Problem: Turning is fast (like snapping your head). Going up and down is slow (like a heavy elevator). If you try to control the slow elevator using the same fast-paced "memory" system used for turning, the system gets confused because the elevator hasn't moved enough to give it good data.
The Solution: The authors built a two-layer system (Cascaded DeePC).
- The Outer Layer (The Boss): This layer is slow. It decides, "We need to go deeper," and tells the inner layer, "Tilt the nose down a little."
- The Inner Layer (The Worker): This layer is fast. It takes the "tilt down" command and immediately moves the tail fins to make that happen.
The Magic: By separating them, the "Boss" can learn from the "Worker's" success without getting overwhelmed by the slow speed of the actual depth change. It's like a general giving orders to a sergeant, who then commands the soldiers. The general doesn't need to know how to march; they just need to know the goal.

3. The "Crystal Ball" Guide (PALOS)

To follow a path of floating buoys (waypoints) in 3D space, the sub needs a guide. The old guide (Adaptive Line-of-Sight or ALOS) was like a person walking behind you, pointing at the next buoy and saying, "Go there!" But it only pointed at the next step.

The Problem: The "No-Recipe" pilot (DeePC) needs to see the whole path ahead to plan its moves, not just the next step.
The Solution: They created Predictive ALOS (PALOS).
- The Analogy: Instead of just pointing at the next buoy, PALOS is like a crystal ball. It simulates the sub's future path step-by-step. It asks, "If I turn left now, where will I be in 5 seconds? Where will I be in 10?" It then calculates the best steering commands for the entire future journey, not just the immediate next second.
- This gives the "No-Recipe" pilot a clear, long-term roadmap to follow, allowing it to anticipate turns and currents before they happen.

4. The Results: How did it do?

The authors tested this system in a super-realistic computer simulation (a "digital twin") of the REMUS 100 sub. They pitted their new system against the old standard (a classic PI/PID controller, which is like a reactive thermostat that only fixes errors after they happen).

The Outcome: The new system was significantly better.
- It stayed on course much more accurately, reducing the "wobble" (cross-track error) by about 28% compared to the old method.
- It handled ocean currents and sudden changes in speed much better.
- It even worked when the sub was moving slower than the data it was trained on (a "beyond the data" test), whereas the old system got confused and overshot its targets.

Summary

The paper claims that by forgetting the complex math models and instead learning from past data, and by splitting the control into fast and slow layers with a crystal-ball guide that looks ahead, they created a smarter, more robust way to steer autonomous underwater vehicles. It's a shift from "calculating the physics" to "learning from experience."

Technical Summary: Data-Enabled Predictive Control with Predictive Adaptive Line-of-Sight Guidance for 3-D Path Following of Autonomous Underwater Vehicles

Problem Statement
Autonomous Underwater Vehicles (AUVs) require reliable path-following capabilities to execute marine exploration and inspection missions. Traditional control architectures typically employ a hierarchical structure: a high-level guidance system (e.g., Line-of-Sight or LOS) generates reference signals, which are tracked by intermediate and low-level controllers (often PI/PID). While effective, these reactive controllers struggle with strong nonlinearities, actuator saturation, and dynamic delays.

Alternative Model Predictive Control (MPC) strategies offer superior performance by anticipating future behavior and handling constraints. However, standard MPC relies on explicit parametric models of AUV hydrodynamics. Deriving these models is complex, time-consuming, and often limited to specific operating ranges due to the nonlinear, coupled nature of hydrodynamic coefficients (added mass, drag, lift). This dependency on accurate identification limits the applicability of model-based approaches across varying speeds, payloads, and environmental conditions.

Methodology
This paper proposes a fully data-driven 3-D path-following framework that eliminates the need for explicit hydrodynamic modeling. The approach integrates Data-Enabled Predictive Control (DeePC) with a novel Predictive Adaptive Line-of-Sight (PALOS) guidance law.

DeePC for Heading and Depth Control:
- Heading Control: A standard DeePC formulation is applied to the yaw dynamics. It utilizes offline input-output trajectories (rudder deflection and yaw angle) to solve a constrained optimization problem, predicting future system behavior without a parametric model.
- Cascaded Depth Control: Direct application of DeePC to depth regulation is impractical because the heave (depth) dynamics evolve significantly slower than the actuator bandwidth (stern-plane deflection), making it difficult to satisfy the persistency-of-excitation requirement within feasible data lengths. To address this, the authors propose a cascaded DeePC architecture with loop-frequency separation:
  - An inner loop regulates the pitch angle ( $\theta$ ) via stern-plane deflection ( $\delta_s$ ) at a high frequency.
  - An outer loop maps the desired heave position ( $z_p$ ) to a desired pitch reference ( $\theta_d$ ) at a lower frequency.
  - To enable data collection for the outer loop, a "unity-gain assumption" is applied to the inner loop (treating $\theta = \theta_d$ ), allowing the outer loop to view the pitch angle as its input. A two-stage data collection procedure ensures sufficient excitation for both loops.
Predictive Adaptive Line-of-Sight (PALOS):
- Classical Adaptive LOS (ALOS) generates a single-step heading and pitch command. This is incompatible with receding-horizon controllers like DeePC, which require a reference trajectory spanning the entire prediction horizon.
- The authors extend ALOS to a multistep predictive formulation (PALOS). This algorithm recursively propagates the vehicle's position forward across the prediction horizon using commanded attitudes. At each predicted step, the ALOS law is re-evaluated to generate a horizon-consistent reference trajectory. This allows the guidance layer to anticipate path transitions and integrate directly into the DeePC optimization.

Key Contributions

Cascaded DeePC Architecture: A novel data-driven control structure for depth regulation that decouples slow heave dynamics from fast actuator dynamics. This extends the applicability of DeePC to plants where the dominant output evolves significantly slower than the actuator bandwidth, a regime previously precluded by persistency-of-excitation constraints.
Predictive ALOS (PALOS): A guidance law extension that transforms the single-step ALOS output into a horizon-consistent multistep reference. This bridges the gap between geometric guidance and receding-horizon predictive control, enabling 3-D waypoint tracking without horizon-mismatch artifacts.
Integrated Framework Validation: The complete system is validated in a high-fidelity 6-DOF simulation of the REMUS 100 AUV, incorporating nonlinear hydrodynamics, ocean currents, and actuator constraints.

Results
The proposed framework was tested against state-of-the-art benchmarks (tuned PI/PID controllers and standard ALOS) across four scenarios:

Nominal Operation: The DeePC controller demonstrated superior tracking accuracy compared to PI/PID, particularly in heave control, due to its predictive nature reducing phase lag.
Ocean Current Disturbances: The framework maintained robust trajectory tracking under horizontal and vertical current disturbances, outperforming the PI/PID baseline in Root Mean Square Error (RMSE) for yaw, heave, and pitch.
Operation Beyond Data Regime: When tested with propeller speeds significantly lower than the data collection speed (700 rpm vs. 1000 rpm), the DeePC controller maintained stability and recovered tracking once the vehicle could catch up. In contrast, the PI/PID controller suffered from integral wind-up and large overshoots.
3-D Waypoint Path Following: The PALOS-DeePC system reduced the cross-track error by approximately 28% compared to the ALOS-PI/PID baseline. The inner-loop tracking errors (yaw and pitch) were reduced by roughly an order of magnitude, demonstrating the efficacy of the data-driven inner control layer.

Significance
The paper claims that this work establishes the architectural viability of a fully data-driven, predictive control solution for AUVs without the burden of hydrodynamic identification. By combining a cascaded DeePC structure with a predictive guidance law, the framework achieves high-performance 3-D path following that is robust to environmental disturbances and nonlinearities. The results suggest that this approach offers a practical alternative to model-based MPC, eliminating the need for complex system identification while consistently outperforming classical reactive control strategies in high-fidelity simulations. Future work is identified as extending these methods to full trajectory tracking and validating them on physical hardware.