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arxiv: 2606.05709 · v1 · pith:EPIFJHWRnew · submitted 2026-06-04 · 📡 eess.SY · cs.SY

Tracking Control for a Dynamic Model of an Underwater Submersible

Matthew Hampsey , Pieter van Goor , Ravi Banavar , Robert Mahony This is my paper

Pith reviewed 2026-06-28 00:22 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords underwater vehiclesSE(3)Hamiltonian controltracking controlerror dynamicsrigid body dynamicsenergy-based controladded mass
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The pith

A novel error function on SE(3) produces Hamiltonian error dynamics, enabling energy-based tracking control for underwater submersibles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that a specific choice of error function on the special Euclidean group SE(3) causes the error dynamics of an underwater vehicle to retain the Hamiltonian structure of the original model. This preservation of structure permits the design of a tracking controller that exploits the passivity properties of the Hamiltonian system. Asymptotic convergence of the closed-loop tracking errors is then proved using Lyapunov methods for a fully coupled rigid-body model that incorporates added mass effects. The controller is tested in simulation on the BlueROV2 submersible. A reader would care because the approach extends energy-shaping control techniques from stabilization tasks to trajectory tracking while keeping the underlying geometric and energetic advantages intact.

Core claim

The paper claims that a novel choice of error function on SE(3) leads to error dynamics that are themselves Hamiltonian. From this property an energy-based tracking controller is derived for the fully coupled dynamic model of a submersible vehicle, and asymptotic convergence of the resulting closed-loop system is established.

What carries the argument

The novel error function defined on SE(3) that yields Hamiltonian error dynamics, allowing the passivity-based controller construction.

If this is right

  • An energy-based tracking controller can be constructed directly from the passivity of the Hamiltonian error system.
  • Asymptotic convergence of the vehicle pose and velocity tracking errors is guaranteed.
  • The controller applies to the fully coupled model including added mass without requiring decoupling assumptions.
  • The design is illustrated by simulation on the BlueROV2 vehicle dynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same error-function construction could be tested on other rigid-body tracking problems that evolve on SE(3).
  • Alternative geometrically defined error functions on SE(3) might also preserve the Hamiltonian property and yield different controller families.
  • Hardware experiments on a physical submersible would reveal whether the asymptotic guarantee survives unmodeled hydrodynamic effects.

Load-bearing premise

The chosen error function on SE(3) produces error dynamics that remain Hamiltonian.

What would settle it

Explicit computation of the closed-loop error equations under the proposed error function to verify whether they satisfy the defining conditions of a Hamiltonian system; failure of this verification or loss of asymptotic convergence in an extended simulation would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.05709 by Matthew Hampsey, Pieter van Goor, Ravi Banavar, Robert Mahony.

Figure 1
Figure 1. Figure 1: BlueROV2 Heavy. Image sourced from Blue Robotics [2025] [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a): The log Lyapunov function log L(t) for the helix tracking simulation. (b): Desired position xd (red) vs actual position x (blue-dashed) trajectories for SE(3) helix tracking simulation. The attitudes Rd and R are represented by the orthogonal frames superimposed on the trajectory. −0.50 −0.25 0.00 0.25 0.50 −0.50 −0.25 0.00 0.25 0.50 −0.30 −0.15 0.00 0.15 πd(t) π(t) (a) −50 −25 0 25 50 −50 −25 0 25 50… view at source ↗
Figure 3
Figure 3. Figure 3: (a): Desired angular momentum πd (red) vs actual angular momentum π (blue-dashed) trajectories for SE(3) helix tracking simulation. (b): Desired momentum pd (red) vs actual angular momentum p (blue-dashed) trajectories for SE(3) helix tracking simulation. 7 Discussion It is clear from Figures 2 and 3 that the control causes the perturbed system to correctly track the desired trajectory. The main benefit to… view at source ↗
read the original abstract

Underwater vehicles are naturally modelled as rigid bodies on SE(3) subjected to added mass effects. The passivity of the Hamiltonian structure of the system can be exploited to design energy-based stabilising controllers, however, the extension of these control designs to tracking control is not trivial since the error system for the classical error formulations is not itself Hamiltonian. In this paper, we show that a novel choice of error function leads to error dynamics that are Hamiltonian. We go on to derive an energy-based tracking control for a fully coupled model of a submersible vehicle. Asymptotic convergence of the control scheme is proved and the control is demonstrated in a simulation study of the Blue Robotics BlueROV2 Heavy submersible.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that a novel error function on SE(3) yields error dynamics that remain Hamiltonian for a fully coupled rigid-body model of an underwater vehicle with added mass. This property is used to construct an energy-based tracking controller whose asymptotic convergence is proved; the result is illustrated by simulation on the BlueROV2 Heavy.

Significance. If the claimed preservation of Hamiltonian structure under the proposed error function holds for the fully coupled added-mass dynamics, the work would provide a useful extension of passivity-based methods from regulation to tracking on SE(3). The explicit stability proof and the simulation on a realistic vehicle model are positive features.

major comments (2)
  1. [§3] The central claim rests on the assertion that the chosen error function produces Hamiltonian error dynamics (abstract and §3). Without the explicit form of the error function and the subsequent derivation of the error-system Hamiltonian, it is not possible to verify that the structure is preserved for the fully coupled inertia matrix; this step is load-bearing for both the controller design and the stability proof.
  2. [§4] The asymptotic convergence proof (abstract) is stated to follow from the Hamiltonian error dynamics and energy-based control. The manuscript should supply the explicit Lyapunov function or passivity argument used, together with the conditions under which the closed-loop error system is asymptotically stable.
minor comments (2)
  1. [§2] The abstract refers to 'a fully coupled model' but does not state whether the added-mass matrix is assumed constant or configuration-dependent; this should be clarified in the model section.
  2. [§5] Figure captions and simulation parameters (e.g., vehicle inertia values, controller gains) should be listed explicitly so that the numerical study can be reproduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight areas where the manuscript can be strengthened by making key derivations more explicit. We address each major comment below and will revise the paper accordingly.

read point-by-point responses

  1. Referee: [§3] The central claim rests on the assertion that the chosen error function produces Hamiltonian error dynamics (abstract and §3). Without the explicit form of the error function and the subsequent derivation of the error-system Hamiltonian, it is not possible to verify that the structure is preserved for the fully coupled inertia matrix; this step is load-bearing for both the controller design and the stability proof.

    Authors: We agree that the explicit error function and the step-by-step derivation of the Hamiltonian error dynamics are essential for independent verification, particularly for the fully coupled added-mass inertia matrix. The original manuscript states the result but does not expand the intermediate calculations sufficiently. In the revision we will insert the full expression for the SE(3) error function together with the complete derivation showing that the error dynamics remain Hamiltonian; this will be placed in a new subsection of §3. revision: yes

  2. Referee: [§4] The asymptotic convergence proof (abstract) is stated to follow from the Hamiltonian error dynamics and energy-based control. The manuscript should supply the explicit Lyapunov function or passivity argument used, together with the conditions under which the closed-loop error system is asymptotically stable.

    Authors: We accept that the stability argument must be stated explicitly rather than left implicit. The revised manuscript will include the candidate Lyapunov function (the total energy of the error system), the passivity-based dissipation term, and the LaSalle invariance argument establishing asymptotic convergence under the stated assumptions on the reference trajectory and the damping matrix. These additions will appear in §4 immediately after the controller derivation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper constructs a novel error function on SE(3) and derives that the resulting error dynamics remain Hamiltonian for the coupled rigid-body model with added mass. This property is shown via direct computation from the system equations rather than by definition or fitting. The energy-based tracking controller and asymptotic stability proof then follow from standard passivity and Hamiltonian structure on SE(3), which are external to the specific choice. No self-citations, fitted inputs renamed as predictions, or reductions of the central claim to its own inputs appear. The argument rests on independent geometric and dynamical properties.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the domain modeling assumption that the vehicle dynamics admit a Hamiltonian structure on SE(3) with added mass, plus the paper-specific construction of an error function whose properties are not independently verified outside the derivation.

axioms (1)
  • domain assumption Underwater vehicles are naturally modelled as rigid bodies on SE(3) subjected to added mass effects whose Hamiltonian structure is passive.
    Explicitly stated as the starting modeling premise in the abstract.
invented entities (1)
  • novel error function no independent evidence
    purpose: to produce Hamiltonian error dynamics for tracking
    Introduced as the key technical device enabling the controller; no external falsifiable evidence supplied.

pith-pipeline@v0.9.1-grok · 5653 in / 1315 out tokens · 32019 ms · 2026-06-28T00:22:10.647022+00:00 · methodology

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Reference graph

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