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arxiv: 2607.02474 · v1 · pith:4BLWIUYBnew · submitted 2026-07-02 · 💻 cs.RO · cs.SY· eess.SY

QuadRocket: An Aerial Robotic Testbed for Adaptive Thrust-Vector Control of Rocket-Like Vehicles

Pedro Santos , Joel Reis , Paulo Oliveira , Carlos Silvestre This is my paper

Pith reviewed 2026-07-03 10:42 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords QuadRocketthrust-vector controladaptive backstepping controllertrajectory trackingreduced-attitude representationaerial roboticsrocket prototypenon-minimum phase
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The pith

An adaptive backstepping controller on a reduced-attitude model achieves almost global trajectory tracking for a quadrotor rocket prototype despite unknown constant disturbances.

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

This paper introduces QuadRocket, a low-cost quadrotor-based prototype designed to test thrust-vector control strategies for rocket-like vehicles. It models the system as an axisymmetric rigid body and develops an adaptive controller that tracks trajectories almost globally while rejecting constant disturbances. A transformation addresses non-minimum-phase dynamics, and the quadrotor is used as the actuator with its own dynamic surface controller. If successful, this provides a safe platform to experiment with control methods that could later apply to actual launch vehicles.

Core claim

The central claim is that by modeling the QuadRocket as a single axisymmetric rigid body actuated by a vectored force and using a reduced-attitude representation, an adaptive backstepping controller can be derived to achieve almost global trajectory tracking in the presence of unknown constant disturbances, with a control-point transformation to mitigate non-minimum-phase behavior, and the quadrotor serving as a thrust vector actuator under a dynamic-surface attitude controller.

What carries the argument

Adaptive backstepping controller with control-point transformation on a reduced-attitude two-sphere representation of an axisymmetric rigid body

If this is right

  • The complete control architecture achieves accurate trajectory tracking in simulation and experiments.
  • Unknown constant disturbances are compensated by the adaptive controller.
  • The control-point transformation mitigates non-minimum-phase behavior of the system.
  • The quadrotor attitude controller tracks the desired thrust vector without explicit differentiation of virtual controls.

Where Pith is reading between the lines

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

  • This testbed could be scaled to validate controls for full-scale rocket launches.
  • The reduced-attitude approach might be applied to other axisymmetric vehicles like missiles or satellites.
  • Indoor validation suggests the method could be tested outdoors with different disturbance profiles.

Load-bearing premise

The coupled system can be modeled as a single axisymmetric rigid body actuated by a vectored force along its longitudinal axis.

What would settle it

An experiment where the prototype fails to track a trajectory or does not compensate for a constant disturbance would falsify the controller performance claim.

Figures

Figures reproduced from arXiv: 2607.02474 by Carlos Silvestre, Joel Reis, Paulo Oliveira, Pedro Santos.

Figure 1
Figure 1. Figure 1: The QuadRocket: representation of reference frames (red, green, and blue represent the x, y, and z axes, respectively). lenges. Besides its primary goal of serving as a low-cost and low-risk testbed for advanced thrust-vector control of rocket-like vehicles, we envision two additional appli￾cations which naturally emerge from the proposed aerial vehicle: i) autonomous cargo transportation, in which the cyl… view at source ↗
Figure 2
Figure 2. Figure 2: QuadRocket scheme. All dimensions in meters. The orange rectangle represents the battery, and the universal joint is shown in red. illustrated in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Diagram of control architecture. Hence, according to Barbalat’s Lemma [37, Lemma 4.2], it is possible to conclude that V˙ → 0, which implies that z converges to zero. In turn, the convergence of z to zero implies that z1 → 0, e → 0, z2 → 0, r3 → ±r3d, and zΩ → 0. The geometric ambiguity associated with the collinearity between r3 and r3d is inevitable for static feedback controllers and is caused by the to… view at source ↗
Figure 5
Figure 5. Figure 5: Representation of the bump function. to the numerical implementation of (1)-(4). The built￾in variable-step ode45 solver was used with a maximum allowed step size of 0.01 seconds1 . A. Bump function-based reference trajectories To ensure that reference trajectories have the nec￾essary smoothness, class C∞ bump functions [42] were used to directly define the time evolution of the desired inertial velocity. … view at source ↗
Figure 6
Figure 6. Figure 6: Reference inertial velocity profile. from which the desired inertial position can be integrated from a given initial condition, and the subsequent time derivatives can be explicitly derived. For this simulated scenario, the initial position of the vehicle was set to p(0) = [ 0.3 − 0.4 − 0.5 ]T m, while the desired initial position of the control point was set to pd(0) = [ 0 0 − 1 ]T m. An initial inclinati… view at source ↗
Figure 7
Figure 7. Figure 7: Simulated trajectory tracking visualization with accurate [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Top to bottom: time evolution of z1, z2, zr, zΩ, and eq. Left subplots: initial transient and convergence performance. Right subplots: steady-state performance. interconnected system. Note that, appropriate tuning of the quadrotor attitude gain, kq, leads to a comparatively faster convergence of the quadrotor attitude error, eq. The right-side plots show the residual errors throughout the remainder of the … view at source ↗
Figure 9
Figure 9. Figure 9: Top: evolution of bb1. Bottom: evolution of ||be1||, ||be2||, and ||be3||. The QuadRocket was able to track the desired trajec￾tory in the presence of an unknown constant disturbance [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Experimental setup. Blue arrows indicate RC [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Experimental trajectory tracking results. On the left, actual and reference trajectories with snapshots of the vehicle. Center-left column [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: Quadrotor attitude tracking performance. Top: [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 13
Figure 13. Figure 13: Time evolution of bb1, bb2, and bb3. disturbance value was estimated by the first adaptation layer, bb1, with emphasis on the y-axis, which is attributed to a possible misalignment between the quadrotor attach￾ment point and the center of mass of the vehicle. The increase on the z-axis value towards the end of the flight reflects the thrust performance loss with the decrease of the battery voltage. In fac… view at source ↗
read the original abstract

This paper presents QuadRocket, a quadrotor-based rocket prototype that provides a low-cost, low-risk platform for validating advanced thrust-vector control strategies for launch vehicle-type systems. The prototype consists of a cylindrical main body mounted on top of a quadrotor through a universal joint, forming a flying inverted pendulum with non-negligible inertia. For control design, the coupled system is modeled as a single axisymmetric rigid body actuated by a vectored force applied along its longitudinal axis. A reduced-attitude representation on the two sphere is adopted to explicitly exploit the vehicle's axial symmetry and to decouple yaw from the thrust-vector direction. On this model, we derive an adaptive backstepping controller that achieves almost global trajectory tracking in the presence of unknown constant disturbances, while a control-point transformation mitigates non minimum-phase behavior. The quadrotor is then treated as a thrust vector actuator, and a dynamic-surface-based attitude controller is designed to track the desired thrust-vector, accounting for actuation dynamics and avoiding explicit differentiation of virtual control signals. The complete architecture is evaluated in simulation and validated experimentally in an indoor motion-capture arena. Results demonstrate accurate trajectory tracking, effective disturbance compensation, and confirm the suitability of the QuadRocket as a versatile testbed for thrust-vector-controlled robotic vehicles.

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

1 major / 1 minor

Summary. The paper presents QuadRocket, a quadrotor-based rocket prototype consisting of a cylindrical body mounted on a quadrotor via a universal joint. For control design, it models the system as a single axisymmetric rigid body with vectored thrust along the longitudinal axis. It adopts a reduced-attitude representation on the two-sphere, derives an adaptive backstepping controller for almost-global trajectory tracking under unknown constant disturbances, uses a control-point transformation to mitigate non-minimum-phase behavior, designs a dynamic-surface attitude controller for the quadrotor, and validates the approach through simulation and indoor motion-capture experiments.

Significance. If the single rigid-body modeling assumption holds for the hardware, this work offers a low-cost, low-risk testbed for validating advanced thrust-vector control strategies with theoretical stability guarantees. The experimental validation in an indoor arena demonstrates practical feasibility for trajectory tracking and disturbance compensation.

major comments (1)
  1. [Abstract and control design section] Abstract and control design section: The central modeling assumption that the coupled system behaves as a single axisymmetric rigid body actuated by a vectored force applied along its longitudinal axis underpins the derivation of the adaptive backstepping controller and the almost-global tracking claims. However, the physical platform consists of two bodies joined by a universal joint that permits relative rotation, which could alter the composite inertia tensor, effective thrust application point, and introduce additional disturbance torques not captured in the monolithic model. This discrepancy risks invalidating the applicability of the stability arguments to the actual hardware.
minor comments (1)
  1. [Abstract] The abstract refers to 'the two sphere'; this should be clarified as the two-sphere S^2 for standard notation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract and control design section] Abstract and control design section: The central modeling assumption that the coupled system behaves as a single axisymmetric rigid body actuated by a vectored force applied along its longitudinal axis underpins the derivation of the adaptive backstepping controller and the almost-global tracking claims. However, the physical platform consists of two bodies joined by a universal joint that permits relative rotation, which could alter the composite inertia tensor, effective thrust application point, and introduce additional disturbance torques not captured in the monolithic model. This discrepancy risks invalidating the applicability of the stability arguments to the actual hardware.

    Authors: We acknowledge that the physical platform consists of two bodies connected by a universal joint, as described in the manuscript. The single rigid-body model is an explicit modeling choice made for control synthesis to exploit axial symmetry and enable the reduced-attitude representation and adaptive backstepping design with almost-global guarantees. This is an approximation whose validity depends on keeping relative motion small under closed-loop control. The indoor experiments demonstrate practical performance, but we agree that the link between the model and hardware merits further clarification. In the revised manuscript we will add a paragraph in the modeling section discussing the conditions under which the rigid-body assumption is reasonable, including the joint's limited range and observed relative angles from experiments. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained on adopted model; no reduction to fitted inputs or self-citations

full rationale

The paper models the system as a single axisymmetric rigid body for control design (abstract), then applies standard adaptive backstepping and dynamic-surface control on the reduced-attitude representation to derive the trajectory-tracking law. No equations show a result being fitted to data and then renamed as a prediction, no load-bearing self-citation chains, and no ansatz or uniqueness claim imported from prior author work. The modeling choice is an explicit assumption whose validity is separate from whether the subsequent derivation is circular; experimental validation is reported but does not retroactively make the controller equations tautological. This is the normal case of an independent derivation on a chosen model.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard rigid-body modeling assumptions and the choice to treat disturbances as constant; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption The coupled quadrotor and cylindrical body can be modeled as a single axisymmetric rigid body actuated by a vectored force along its longitudinal axis.
    Invoked for control design and reduced-attitude representation.
  • domain assumption Disturbances are unknown but constant.
    Required for the adaptive backstepping law to achieve compensation.

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