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arxiv: 2606.01397 · v1 · pith:E35MTTX3new · submitted 2026-05-31 · 💻 cs.RO · cs.LG· cs.SY· eess.SY

Autopilot-Preserving Residual Q-Learning with HJB-Inspired Finite-Action Risk Filtering for Fixed-Wing UAV Command Supervision

Mehmet Iscan , Batuhan Temiz This is my paper

Pith reviewed 2026-06-28 16:48 UTC · model grok-4.3

classification 💻 cs.RO cs.LGcs.SYeess.SY
keywords UAV command supervisionresidual reinforcement learningHJB residual scoringfixed-wing autopilotfinite-action filteringpath tracking errorHamiltonian advantagecontrol barrier shield
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The pith

A learned supervisor above an unchanged autopilot uses HJB residual scoring to cut fixed-wing UAV path error by 86 percent.

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 command supervisor can sit above a fixed autopilot and select bounded residuals on airspeed, altitude, and heading references to improve tracking under wind and turbulence. The supervisor scores candidate residuals with a semi-discrete value-iteration critic drawn from the Hamilton-Jacobi-Bellman equation, ranks them by no-op-relative Hamiltonian advantage, and applies a finite-action shield inspired by control Lyapunov and barrier functions that always preserves a no-op fallback. In a shared 12-state simulation that keeps the plant, autopilot, and actuator model identical across methods, the HJB residual approach reduces mean RMS path-tracking error to 44.809 m from the baseline autopilot's 338.617 m, an 86.77 percent reduction, and beats a tabular-Q residual by 49.54 percent. The largest gains occur where the baseline performs worst, though the method trades some airspeed accuracy for the path improvement.

Core claim

The paper claims that placing an HJB residual scorer with finite-action risk filtering above an unmodified autopilot lets the system choose safe command adjustments from a bounded set, yielding a mean RMS path-tracking error of 44.809 m against 338.617 m for the baseline autopilot and 88.809 m for tabular-Q residual on identical runtime models.

What carries the argument

The HJB residual scorer that evaluates finite command residuals via semi-discrete value-iteration critic and no-op-relative Hamiltonian advantage, then shields them with a control-Lyapunov and control-barrier inspired filter that always retains the no-op option.

If this is right

  • The autopilot and actuator interface remain untouched, so the method adds supervision without recertifying the inner loop.
  • The finite action set and no-op fallback keep the system from issuing unsafe commands even when the critic is uncertain.
  • Gains concentrate in the wind and turn regimes where the baseline autopilot deviates most from the path.
  • A measurable increase in airspeed error accompanies the path improvement, so the supervisor trades one metric for another.

Where Pith is reading between the lines

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

  • The same supervisor layer could be tested on other baseline autopilots to check whether the error reduction depends on the specific inner controller.
  • Hardware trials would need to measure how sensor noise affects the value-iteration critic's ranking of residuals.
  • The approach might extend to quadrotors or other vehicles where preserving an existing certified controller is required.

Load-bearing premise

The fixed simulation environment with the plant, autopilot, and actuator model held constant gives a fair comparison that will continue to hold when the same supervisor runs on physical hardware that includes unmodeled dynamics and sensor noise.

What would settle it

Running the HJB residual supervisor on physical fixed-wing UAV hardware in real wind and gust conditions and checking whether the reported reduction in mean RMS path-tracking error relative to the baseline autopilot still appears.

Figures

Figures reproduced from arXiv: 2606.01397 by Batuhan Temiz, Mehmet Iscan.

Figure 1
Figure 1. Figure 1: Layered command-supervision framework shared by all controller modes. The mission reference passes through an optional residual supervisor and the command-projection operator into the fixed gain-scheduled autopilot, the actuator model, and the plant. The learned intervention is the bounded command residual ∆r(ak) only; the autopilot is the sole actuator-facing controller. All controller modes share the sam… view at source ↗
Figure 2
Figure 2. Figure 2: HJB residual finite-candidate pipeline. The supervisor encodes state and context, enumerates the seven bounded residual candidates Ar = {a0, . . . , a6}, predicts one-step feature consequences, scores each candidate with the tabular Q term and the value-iteration guidance term, applies the finite-action shield, and dispatches the selected residual with no-op fallback. 3.7 Online learning loop Algorithm 1 s… view at source ↗
Figure 3
Figure 3. Figure 3: Mean RMS spatial reference/path error over the 20-scenario full-duration benchmark (N = 20 episodes per method, one episode per scenario), in metres. Lower is better. Bars rank baseline 338.617, Q residual 88.809, and HJB residual 44.809. Error bars are across-scenario descriptive 95% intervals. end in exact ties [PITH_FULL_IMAGE:figures/full_fig_p028_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Full-duration aggregate metrics normalized to the baseline (N = 20 episodes per method). A ratio below one is lower than the baseline. HJB residual is lowest for spatial reference/path and altitude error; both residual packages exceed the baseline for airspeed RMS and control-activity index. spatial reference/path RMS than the baseline in the orbit, racetrack, climb, and fight-mode profile groups; in the f… view at source ↗
Figure 5
Figure 5. Figure 5: Mean spatial reference/path RMS (m) versus mean airspeed RMS (m/s) over the full-duration benchmark (N = 20 episodes per method); bubble area scales with the control-activity index. The baseline holds the lowest airspeed error, and the residual packages hold lower spatial reference/path error at higher airspeed error [PITH_FULL_IMAGE:figures/full_fig_p030_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Per-scenario strict winner counts over the 20-scenario full-duration benchmark (N = 20 scenarios). Spatial reference/path and altitude wins favour the residual packages; airspeed and control-activity wins favour the baseline; safety-violation and load-factor metrics are tie-heavy [PITH_FULL_IMAGE:figures/full_fig_p030_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Per-scenario spatial reference/path RMS (m) for the three methods over the full-duration benchmark (N = 20 scenarios). Lower is better. Several high-disturbance scenarios carry large baseline errors that fall under residual supervision; a smaller set keeps the baseline or Q competitive. to under 1 m for both residual packages [PITH_FULL_IMAGE:figures/full_fig_p031_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Mean spatial reference/path RMS (m) by mission profile over the full-duration benchmark, with unequal scenario counts per profile group. Lower is better. The residual packages have lower mean spatial reference/path RMS than the baseline across several profile families [PITH_FULL_IMAGE:figures/full_fig_p032_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Residual-supervisor diagnostics over the full-duration benchmark (N = 20 episodes per method): residual-active fraction, hard-condition score, HJB value proxy, HJB advantage, and shield-active fraction. HJB columns are nonzero only for HJB residual. episodes per method. Here the ranking on mean spatial reference/path RMS inverts: the baseline is lowest at 0.866 m, HJB residual is 1.174 m, and Q is 1.183 m.… view at source ↗
Figure 10
Figure 10. Figure 10: Coarse 20 × 50 short-horizon sweep (N = 1000 episodes per method, 8 s each). Lower is better. On mean spatial reference/path RMS the baseline is lowest (0.866 m), ahead of HJB residual (1.174 m) and Q residual (1.183 m); altitude RMS falls under residual supervision and airspeed RMS rises [PITH_FULL_IMAGE:figures/full_fig_p033_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Fight-mode 60 s smoke run (N = 1 run per method). Lower is better. The baseline has the lowest spatial reference/path RMS (177.140 m), followed by Q residual (185.854 m) and HJB residual (189.378 m); HJB residual has the lowest altitude RMS [PITH_FULL_IMAGE:figures/full_fig_p034_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Representative time series for one low-altitude crosswind/turbulence orbit scenario, showing reference error, altitude error, airspeed error, load factor, residual activity, and shield activity against time for the three methods. This is a single trace, not an aggregate [PITH_FULL_IMAGE:figures/full_fig_p035_12.png] view at source ↗
read the original abstract

A fixed-wing UAV must hold airspeed, altitude, and heading references under wind, gusts, and turbulence, channels coupled so that correcting one can degrade another. Classical autopilots stabilize the airframe well but adapt poorly when a hard crosswind meets an aggressive turn, while reinforcement-learning (RL) policies acting directly on the surfaces concentrate exploration risk at the actuator interface. We place a learned supervisor above an unchanged autopilot rather than inside it: it selects a residual from a finite, bounded action set on the commanded airspeed, altitude, and heading; the modified reference is projected into an admissible command envelope before reaching the autopilot, which stays the only actuator-facing controller. What is new is how the residual is chosen. HJB residual scores candidates with a semi-discrete value-iteration critic in the spirit of the Hamilton-Jacobi-Bellman (HJB) equation, ranks them by a no-op-relative Hamiltonian advantage, and filters them through a control-Lyapunov- and control-barrier-inspired finite-action shield that always keeps a no-op fallback. On a shared 12-state runtime holding the plant, autopilot, and actuator model fixed, so the comparison is at the package level, HJB residual lowers mean RMS path-tracking error to 44.809 m, against 338.617 m for the baseline autopilot and 88.809 m for a tabular-Q residual, an 86.77% reduction over the baseline and 49.54% over Q-learning. The gain concentrates where the baseline fails worst and comes with a measured rise in airspeed error, so no method dominates every metric. We present this autopilot-preserving residual command-supervision design and benchmark with its trade-offs reported intact.

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 / 1 minor

Summary. The manuscript proposes an autopilot-preserving residual command-supervision architecture for fixed-wing UAVs. A learned supervisor selects bounded residuals on airspeed, altitude, and heading references using an HJB-inspired semi-discrete value-iteration critic, no-op-relative Hamiltonian ranking, and a control-Lyapunov/control-barrier finite-action shield that always retains a no-op fallback. The autopilot remains the sole actuator-facing controller. On a shared 12-state simulation with fixed plant, autopilot, and actuator models, the method reports mean RMS path-tracking error of 44.809 m versus 338.617 m (baseline) and 88.809 m (tabular Q-learning), corresponding to 86.77% and 49.54% reductions, while noting a rise in airspeed error.

Significance. If the simulation results hold, the work demonstrates a practical way to layer safe residual supervision atop an existing autopilot without actuator-level exploration risk. The explicit package-level comparison on a frozen model, the preservation of a no-op fallback, and the reporting of metric trade-offs are strengths. The integration of HJB residual scoring with a finite-action shield offers a concrete instance of risk-filtered RL for coupled reference tracking.

major comments (2)
  1. [Abstract / Results] Abstract and results section: the headline numerical claims are reported as single mean RMS values (44.809 m, 338.617 m, 88.809 m) with derived percentages but without error bars, trial counts, standard deviations, or any variability statistics. This directly affects the reliability of the 86.77% reduction claim.
  2. [Simulation setup / Results] The benchmark is performed on a single fixed 12-state model shared across all methods; no Monte-Carlo parameter sweeps or sensitivity analysis over aerodynamic coefficients, sensor noise, or gust spectra are described. Because the HJB critic and Hamiltonian ranking are constructed from the identical model, this omission is load-bearing for any claim of robustness in the UAV command-supervision setting.
minor comments (1)
  1. [Methods] The description of the 12-state runtime and the precise construction of the admissible command envelope could be expanded for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and results section: the headline numerical claims are reported as single mean RMS values (44.809 m, 338.617 m, 88.809 m) with derived percentages but without error bars, trial counts, standard deviations, or any variability statistics. This directly affects the reliability of the 86.77% reduction claim.

    Authors: We agree that variability statistics are needed to support the reliability of the reported means. The presented results reflect single-run means on the fixed simulation. In the revised manuscript we will conduct multiple independent trials (with varied random seeds for wind/gust realizations), report trial counts, standard deviations, and include error bars in the results section and, space permitting, the abstract. revision: yes

  2. Referee: [Simulation setup / Results] The benchmark is performed on a single fixed 12-state model shared across all methods; no Monte-Carlo parameter sweeps or sensitivity analysis over aerodynamic coefficients, sensor noise, or gust spectra are described. Because the HJB critic and Hamiltonian ranking are constructed from the identical model, this omission is load-bearing for any claim of robustness in the UAV command-supervision setting.

    Authors: The fixed-model benchmark is intentional to enable a controlled, package-level comparison of the residual supervisors under identical plant, autopilot, and actuator dynamics. The manuscript does not claim robustness to parameter variations or environmental changes; improvements are reported for this specific benchmark. We will add an explicit statement of scope and a limitations paragraph noting the absence of sensitivity analysis. revision: partial

Circularity Check

0 steps flagged

No significant circularity; empirical benchmark on fixed models is self-contained

full rationale

The paper introduces a residual command-supervision architecture using a semi-discrete value-iteration critic inspired by the HJB equation, a no-op-relative Hamiltonian ranking, and a finite-action shield, then reports package-level simulation results on a shared 12-state runtime with fixed plant/autopilot/actuator models. The headline metrics (44.809 m vs 338.617 m RMS) are generated by executing the three supervisors (baseline, tabular-Q, HJB-residual) under identical dynamics; they are not obtained by fitting a parameter to a subset and relabeling it a prediction, nor by any self-definitional loop in which the output is constructed from the input by the method's own equations. No load-bearing uniqueness theorem, ansatz, or self-citation chain is invoked to force the result. The comparison is therefore an external experimental evaluation rather than a tautological reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the central numerical claim rests on an unverified simulation model and on the assumption that the chosen finite action set and HJB critic produce the reported error reductions without post-hoc tuning details.

axioms (1)
  • domain assumption The shared 12-state simulation with fixed plant, autopilot, and actuator model is representative of real-world closed-loop behavior
    The comparison and error reductions are reported under this fixed-model runtime.

pith-pipeline@v0.9.1-grok · 5865 in / 1383 out tokens · 22690 ms · 2026-06-28T16:48:41.511899+00:00 · methodology

discussion (0)

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Reference graph

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