We present nonlinear Model Predictive Contouring Control (MPCC) in all six degrees of freedom, using the holonomic actuation of an autonomous underwater vehicle (AUV) to track position and attitude references independently. To the best of our knowledge, this is the first real-time deployment of this scheme on a holonomic AUV. We augment the nominal model with Gaussian Process (GP) residual dynamics, embed them in MPCC using a zero-order robust optimization scheme, and show in simulation that the choice of residuals to learn is decisive for performance. In-water validation on the MOLA AUV shows improved attitude tracking over a well-tuned Proportional-Integral-Derivative (PID) controller in a lawnmower survey and a spiraling inspection maneuver.
Introduction
The controller uses the AUV’s holonomic actuation to track position and attitude references independently. The proposed approach augments a nominal model with GP residual dynamics and incorporates those dynamics into MPCC through a zero-order robust optimization scheme. A simulation ablation shows that the selection of learned residuals has a decisive effect on performance.
The controllers are validated in-water on the MOLA AUV against a well-tuned PID controller. The experiments demonstrate improved attitude tracking during a lawnmower survey and a spiraling inspection maneuver.
Related Work
This work builds on GP residual modeling, without restricting the learned residuals to damping terms, and embeds the model in the optimal control problem. It also uses full nonlinear MPCC in three dimensions and exploits the AUV’s holonomic properties to track an attitude reference in addition to position.
This allows the vehicle to orient independently of its direction of travel, which is important during surveys and inspections.
Gaussian Process-Augmented MPCC
The GP-augmented MPCC uses regression input variables.
Gaussian Processes
Given the training inputs the input data used to train the GP and targets the corresponding training outputs, the posterior mean and variance of a GP are evaluated at a query point.
The kernel matrix is evaluated between the respective inputs, and the model includes a noise variance. The kernel encodes prior assumptions about the residual, such as its smoothness. Its hyperparameters are optimized by maximizing the marginal likelihood of the training data.
Experiments
The proposed method is validated with the MOLA AUV, first in simulation and then in hardware experiments. The setup is kept the same in both cases, allowing a transition from simulation to the real vehicle: the controller, communication, and residual-learning pipeline are identical, and only the vehicle interface differs.
Simulation Study
The controllers are analyzed in the Stonefish simulator in two scenarios.
The first scenario is a constant-heading lawnmower pattern, similar to a common field survey. The nominal MPCC (nom) is compared with the angular-residual (gp-pqr) and full-state (gp-full) GP-MPCC over five runs each.
The second scenario is an upward spiral around a virtual object of interest. During the maneuver, the vehicle keeps pointing toward the center while gradually increasing its pitch angle, mimicking a close-range inspection. This maneuver requires continuous attitude changes and is repeated ten times with the nominal and angular-residual MPCC.
In-Water Experiments
In the test tank, both the nominal and angular-residual GP-MPCC follow the inspection spiral closely. The PID controller regulates each degree of freedom independently toward the next waypoint and resorts to piecewise motion that does not resemble the intended inspection path.
Because the PID controller does not follow the spline reference, a quantitative comparison is not meaningful for this maneuver.
Acknowledgment
In accordance with IEEE policy on AI-generated content, the authors disclose that Claude (Anthropic) was used for coding assistance during implementation and for language editing of the manuscript.
Frequently Asked Questions
What does the controller track? It tracks position and attitude references independently across all six degrees of freedom.
What role do Gaussian Processes play in the method? They model residual dynamics that augment the nominal vehicle model.
Which simulation scenarios were used? The study evaluates a constant-heading lawnmower survey and an upward spiral inspection maneuver in the Stonefish simulator.
How did the controllers perform in the test-tank inspection spiral? The nominal and angular-residual GP-MPCC followed the spiral closely, while the PID controller produced piecewise motion that did not resemble the intended path.