Can an Underwater Robot Learn How the Water Pushes It? Agile AUVs Explained

SAM, a slim underwater robot about 1.5 m long, can tip its nose 60° up or down by sliding its own battery. At angles that steep, it's hard to predict how the water pushes back. Researchers at KTH in Stockholm and MBARI in California kept the physics they trust and let a model learn the rest, mostly drag, from a few seconds of the robot's own data. They compared three ways to learn it, on two very different robots. With heavy noise added in simulation, one of them still got through 50 runs in a row on both robots without failing.

In this video

• Hydrobatics: why weight and buoyancy are easy to model, and why drag at steep angles is not
• The two robots: SAM, a slim torpedo that steers with a swiveling nozzle and a sliding battery, and MOLA, an eight-thruster hybrid AUV/ROV built by Boxfish Research for MBARI
• Planning ahead: a controller that tries out moves a short way ahead, makes only the first, then measures and plans again
• The key idea: learn only what the physics gets wrong, and refit as new measurements come in
• Three ways to learn it: least squares, a sparse method that keeps the simplest formula that fits, and a Gaussian process that also says how uncertain it is
• Simulation: all three learned from a few seconds of data and trained in under half a second. As noise was added, the other two broke down well before the Gaussian process
• Test-tank recordings: SAM in a 10 m round tank in Motala, Sweden, and MOLA in MBARI's saltwater tank. Overall, the Gaussian process had the lowest error and drifted the least
• Agile maneuvers, in simulation: with the Gaussian process, SAM pitched to 60° and settled in 15 s, and MOLA pitched to 80° and settled in 25 s, the same as planners given the true model. SAM ended a little further off its target. Every version ran faster than real time
• Robustness, also in simulation: with the model made 20% wrong on purpose and heavy noise, SAM's worst miss was 3% of the distance it traveled, MOLA's 8%
• Neural networks for comparison: with this little data, about three times the other methods' error, on average. Physics first more than halved it
• What's next: field tests of the learning controller in open water. The authors also suggest learning waves and currents separately, and leave a formal convergence proof to future work

For engineers

The model is the known rigid-body physics plus a learned residual (residual learning) in 6 DOF. The learners are nonlinear least squares for a 6×6 damping matrix; a Gaussian process with a Matern kernel; and GreySINDy, the authors' name for SINDy (sparse regression over a library of candidate terms, solved with LASSO) applied only to the residual.

The controller is a linear time-varying MPC that periodically re-linearizes and refits the model on a window of recent measurements, with an LQR terminal cost. Simulation training times were 0.059–0.48 s (Table 1). The noise test counts consecutive runs before the first failure, capped at 50, from SNR 100 to 0.1 dB (Table 2). Tank-data RMS error, LSQ/GP/GreySINDy: SAM 1.1856/0.9304/2.0282, MOLA 0.3484/0.2095/0.2355 (Table 3). Table 4 gives rise time, overshoot and steady-state error per model; real-time ratios were 0.35–0.74 in Matlab.

The paper

"Online learning for agile underwater maneuvering: Gaussian processes and sparse regression for data-driven model predictive control"
Sriharsha Bhat, Giancarlo Troni, Ivan Stenius
KTH Royal Institute of Technology, Stockholm; Monterey Bay Aquarium Research Institute (MBARI), Moss Landing, CA
Robotics and Autonomous Systems 195, 105211, January 2026 (online 3 October 2025), doi:10.1016/j.robot.2025.105211. Open access, CC BY 4.0.

Read the paper

This work was supported by the Swedish Foundation for Strategic Research (SSF) through the Swedish Maritime Robotics Center (SMaRC). G. Troni is funded by the David and Lucile Packard Foundation.

If you work on AUV modeling or control, the paper is worth reading in full.

This is an independent explainer. I'm not affiliated with or endorsed by the authors, KTH or MBARI, and the research is all theirs. The animations are my own drawings, not footage from the experiments, and charts marked schematic are sketches. Any mistakes are mine.

I'm Bora Celik from Piccard. I explain new research in ocean science and robotics.