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REVIEW 3 major objections 6 minor 34 references

Leveling the Playing Field: Carefully Comparing Classical and Learned Controllers for Quadrotor Trajectory Tracking

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read After equalizing the task objective, training data, and feedforward information, reinforcement-learned and geometric quadrotor controllers perform nearly on par, with geometric control winning on steady-state error and RL winning on fast…

desk verdict A genuinely useful benchmarking protocol for RL-vs-classical comparisons, with credible near-parity results in simulation, but the paper overclaims in a couple of places and lacks hardware validation. read the letter →

arxiv 2506.17832 v1 pith:DQ2JKXUT submitted 2025-06-21 cs.RO cs.LGcs.SYeess.SY

Pratik Kunapuli , Jake Welde , Dinesh Jayaraman , Vijay Kumar This is my paper · ORCID
classification cs.ROcs.LGcs.SYeess.SY
keywords quadrotorcontrolreinforcementlearninggeometrictrajectorytrackingbenchmarkingmethodologyaerialmanipulationfeedforwardinformationsimulation-to-realtransfer
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the widely reported superiority of reinforcement learning over classical geometric control for quadrotor trajectory tracking is largely a benchmarking artifact. It identifies three ways prior comparisons favored RL: RL was optimized on the exact task objective and data while the classical controller was hand-tuned or tuned on hover data, and only RL was given information about the future trajectory. After equalizing these three factors, the paper finds the two controller classes perform about on par, with geometric control reaching lower steady-state error and RL recovering faster from large perturbations. The authors argue this protocol should be the default for comparing learned and model-based controllers, because each asymmetry alone can shift the apparent winner. The practical stakes are concrete: for slow tracking, classical control is better, while for agile, transient-dominated tasks such as catching a thrown ball, RL wins.

What carries the argument

The mechanism is a symmetric benchmarking protocol that equalizes three previously asymmetric resources between controller classes: (1) the objective function, a single reward combining position, yaw, velocity, and angular-velocity error terms, used both to train RL and to automatically tune GC gains; (2) the data, with both classes optimized on rollouts from the same task distribution rather than a hand-tuned hover baseline; and (3) feedforward information, with both controllers receiving a horizon of $H=10$ future position and yaw waypoints, which GC uses to estimate high-order reference derivatives and RL simply appends to its policy observation. This protocol is what isolates differences in controller synthesis itself from differences in access to task information.

What would settle it

Run the paper's best-in-class RL and GC controllers, with the same reward, the same tracking data, and the same 10-step lookahead, on a physical quadrotor with a fixed arm from the same set of initial perturbations, and plot position and yaw error over time; if GC's steady-state error does not converge to zero while RL retains its offset, or if RL's early-time error reduction is not faster than GC's, the central near-parity claim is falsified on hardware.

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Extended reading notes

Core claim

The paper's central claim is that the performance gap between RL and geometric controllers shrinks to near-parity once the comparison is symmetric. The paper demonstrates this by isolating each asymmetry: optimizing GC gains with the same reward function used to train RL, tuning or training both controller classes on data from the same task distribution, and giving both controllers the same horizon of future waypoints ($H=10$). In the best-versus-best tracking comparison on a quadrotor, RL's position RMSE is $0.119$ m versus GC's $0.158$ m, but the time-series shows GC's error converging toward zero while RL retains a steady-state offset. The result is a regime split rather than a clear winner: GC has better steady-state behavior, while RL has better transient behavior, so conclusions about which class is superior depend on which phase of tracking the task emphasizes. This directly challenges the common literature claim that RL outperforms geometric control for agile trajectory tracking.

Load-bearing premise

The entire ranking comes from simulation, so the load-bearing assumption is that the simulated rigid-body-plus-motor-delay dynamics behave like a real quadrotor in the ways that separate the two controller classes; if hardware differs in a class-dependent way, the measured near-parity could vanish.

Editorial extensions

If this is right

  • Previous comparisons that pitted RL against hand-tuned, hover-tuned, or feedforward-less geometric controllers should be re-run under the symmetric protocol; the paper's asymmetry experiments show each of these choices alone widens the apparent gap.
  • For applications dominated by steady-state tracking, such as slow or less agile flight, geometric control is the better choice because its error converges to zero and it can match RL on the overall reward.
  • For applications dominated by transient response, such as recovering from a large perturbation or catching a thrown ball, RL is the better choice; in the paper's ball-catching test, the end-effector RL policy catches 65% of balls at the hardest time-to-catch setting versus 30% for GC.
  • Reporting only RMSE can mislead, because RMSE conflates a large initial transient with asymptotic offset; the paper shows two controllers can have close RMSE yet differ in which phase of tracking they handle well.
  • The open-source implementations give future studies a ready-made, equalized basis for measuring new learned or model-based controllers against strong baselines of both classes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension is to apply the same three-way equalization to other learned-versus-classical benchmarks, such as RL versus model predictive control, where the classical side is often hand-tuned; the protocol would separate 'better controller' from 'better baseline tuning' claims.
  • The feedforward-horizon manipulation offers a direct test of why RL has a transient advantage: varying $H$ for both classes should continuously trade transient recovery against steady-state offset, and if RL's advantage persists even at very large $H$, the advantage comes from the learned policy rather than from lookahead access.
  • Because the paper's evaluations are simulated, the protocol's conclusions about which class wins which regime are predictions for hardware; repeating the exact protocol on a real platform would show whether the steady-state/transient split survives motor delay, saturation, and estimation noise.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper addresses the methodology of comparing reinforcement-learned (RL) and geometric (GC) controllers for quadrotor trajectory tracking. It identifies three asymmetries in prior comparisons—access to the task objective, access to representative training data, and access to feedforward trajectory information—and proposes a symmetric protocol: optimizing both controllers on the same reward, tuning GC gains automatically (rather than by hand), and giving both controllers a horizon of future waypoints. Experiments in IsaacSim/IsaacLab on a quadrotor and a fixed-arm aerial manipulator show that correcting each asymmetry significantly improves GC performance and that, after leveling the playing field, RL and GC achieve near-parity in tracking quality. The paper further reports that GC has lower steady-state error while RL has better transient performance, and it demonstrates a ball-catching task where RL's transient advantage leads to higher catch rates. The authors open-source their simulator environments, controller implementations, and tuning code.

Significance. The paper makes a useful and timely contribution to the empirical comparison of learned and classical control methods. Its systematic isolation of three fairness asymmetries is a valuable methodological template: the experiments in Fig. 2 convincingly show that optimization objective, training data, and feedforward information each affect measured performance gaps. The open-source release of both controller implementations and the simulation environment is a practical contribution that should benefit the community. If the results hold, the finding that the RL/GC gap is much smaller than previously reported is an important corrective to a strongly held belief. However, the paper's directional claims about which controller class is better in which operating regime are not fully supported by its own data, and the simulation-only evidence limits the generality of the conclusions. The central protocol improvements are sound and independently valuable; the main weaknesses are in the interpretation and scoping of the results.

major comments (3)
  1. [Section V-C and Tables IV and IX] The conclusion in Section V-C and the abstract that 'GC performs better in relatively slow or less agile tasks' is contradicted by the paper's own numerical results. In the Hover task, which is the least agile task considered, Table IX reports that GC-Opt-Hover-None has a lower average reward (13.756 vs 13.918) and higher position RMSE (0.355 m vs 0.327 m) than RL-Opt-Hover-None, with only yaw RMSE favoring GC. In the Lissajous tracking task, Table IV shows that GC has higher average reward than RL only on the aerial manipulator (13.792 vs 13.621), while on the quadrotor RL has a higher reward (14.196 vs 13.447) and lower position RMSE on both morphologies. The text in Section V-C states 'GC outperforms RL on the reward objective' but this is not supported for the quadrotor, where RL's reward is larger. The authors should remove or substantially weaken the directional claim about less agile tasks, or re-analyze the data (e.g., by separating transient and steady-state error) to support it.
  2. [Section IV-C and Appendix B] The feedforward protocol for the GC is not implemented or reported in sufficient detail to support the claim that both controllers are 'best-in-class'. The paper states that a horizon of H=10 future positions and yaws is appended to the observation for both controllers and that this allows the GC to approximate high-order derivatives via finite differencing, but it does not specify the finite-difference scheme, the order/accuracy of the approximation, or how these approximate derivatives are substituted into the GC control law (Eqs. 6-9). This is a load-bearing detail because the standard geometric controller is designed to use exact reference derivatives. If the GC's derivatives are approximated from a relatively short horizon, the GC may be handicapped relative to its true best-in-class implementation. The manuscript should provide the finite-difference implementation and include an ablation comparing GC with exact derivatives versus the finite-difference version used here; without this, the measured near-parity could be an artifact of a suboptimal GC feedforward implementation.
  3. [Section VI and Abstract] The headline conclusions are stated as general properties of the two controller classes, but all evaluations are performed in IsaacSim with a specific simulated dynamics model: a rigid body with a first-order motor model and no controller delay (Appendix D). The authors do acknowledge in Section VI that the evaluations are 'in simulation as opposed to on real hardware' and list this as a limitation, and they do include domain randomization (Table VI) and realistic dynamics (Table VII) ablations. However, the abstract and conclusions do not carry this qualification, so readers may take the directional claims (e.g., 'GC performing better in relatively slow or less agile tasks') as established for real platforms. Since the relative ordering could plausibly change with real actuator lag, saturation, or model mismatch, the central claims should be explicitly scoped to the simulated setting, or at least accompanied by a clear statement that hardware validation is future work.
minor comments (6)
  1. [Throughout] Controller naming is inconsistent across tables and text: for example, 'RL-Opt-Liss.-FF' in Table IV and 'RL-Opt-Lissajous-FF' in Table IX refer to the same model, and Section V-F uses 'GC-Complex' while Table VII uses 'GC-Realistic'. Please standardize the names.
  2. [Table V] The caption says 'Results are shown as mean catch rate over 100 trials' but the text says '100 evaluations of 5 catch opportunities each'. Please clarify whether the reported success rates are per catch attempt or per 5-catch episode, and include confidence intervals or standard errors.
  3. [Eq. (3)] The reward function uses an exponential kernel for position error but an unweighted absolute-value term for yaw error; it is not stated whether the yaw error is wrapped to [-pi, pi] or computed as a geodesic distance, which affects the reward value and the GC tuning objective.
  4. [Section V-B (Fig. 2)] The 'Normalized Gap to Max Reward' metric is not defined precisely. Please specify the normalization (e.g., relative to the maximum reward of 15.0) and state whether the 1000 evaluations are sufficient for the median/inter-quartile comparisons to be statistically distinguishable.
  5. [Appendix B] Equations (6)-(9) rely on both position and orientation errors, but the observer that provides the state (position, orientation, velocities) to the GC is not described. If the GC is assumed to have perfect state feedback, this should be stated explicitly, along with the RL policy's observation assumptions, so that the comparison is transparent.
  6. [Section I] There is a typo in 'throughly benchmark' in Section I; also, the definition of the RL policy's action space and the scaling to thrust/moment limits (Section III-B) could be made more explicit by citing the platform's limits.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the comparison is a self-contained empirical benchmark; no prediction reduces to a fitted parameter or to a self-citation chain.

full rationale

The paper's central claim is an empirical comparison between RL and GC after symmetric access to objective, data, and feedforward information. The GC gains are tuned with Optuna on the same reward used for RL, but this is the proposed fairness protocol rather than a hidden fit: both controllers are optimized on the same objective and evaluated on fresh rollouts, so the reported parity and ordering are not forced by construction. The reward function and observation are inherited from the authors' prior work [29], a self-citation, but that citation provides a design choice rather than a theorem from which the conclusions are derived; the comparison would remain meaningful even if that design were changed. The simulation-only evaluation is acknowledged in Section VI as a limitation, and it affects generality but does not make the derivation circular. No equation in the paper reduces to its own input, and no fitted parameter is renamed as a prediction. Therefore no circular step meets the evidentiary bar for flagging.

Assumptions & free parameters 7 free parameters · 4 assumptions · 0 invented entities

The central comparison rests on the chosen reward hyperparameters, the Optuna-tuned GC gains, the feedforward horizon, and the simulation fidelity assumption. No new physical entities are introduced. The reward weights and delta_p schedule are hand-chosen; the GC gains are fitted to the reward, and the simulation-to-hardware transfer is assumed.

free parameters (7)
  • Reward weight lambda_p = 15.0/dt
    Position error weight in Eq (3); hand-chosen and defines the objective used for both RL training and GC tuning.
  • Reward weight lambda_R = 4.0/dt
    Yaw error weight in Eq (3); hand-chosen.
  • Reward weight lambda_v = 0.05/dt
    Velocity error weight in Eq (3); hand-chosen.
  • Reward weight lambda_omega = 0.01/dt
    Angular velocity error weight in Eq (3); hand-chosen.
  • Position tolerance delta_p annealing schedule = 0.8 to 0.1, halved every 50M timesteps
    Shaping term in phi(x, delta); the authors state annealing was 'key to enabling agile behavior', so it directly shapes the RL policy and the comparison.
  • GC PD gains (8 parameters) = not reported; optimized via Optuna
    The geometric controller's position and attitude gains are tuned on the same reward to form the 'best-in-class' GC baseline; the comparison depends on the tuning procedure converging to good gains.
  • Feedforward horizon H = 10 waypoints
    Chosen as sufficiently large for GC to approximate high-order derivatives via finite differencing; affects how much future information each controller receives.
assumptions (4)
  • domain assumption The simulated dynamics (rigid body plus first-order motor delay and saturation, Appendix D) faithfully represent the real platform, so the simulated performance ordering holds on hardware.
    The authors validate in simulation only and rely on domain randomization and motor dynamics to stand in for real-world effects (Sec VI limitations). If this assumption is false, the RL-vs-GC ordering on hardware could differ.
  • domain assumption The reward function of Eq (3) is an adequate objective for trajectory tracking for both controller classes.
    The task objective is used both for optimization and evaluation; the conclusions about which controller is better are with respect to this reward. A different user objective could change the ranking.
  • domain assumption The Lissajous and Hover task distributions, with the random ranges in Appendix A, are representative of agile trajectory tracking tasks.
    Conclusions are drawn on these specific distributions; the authors note generality to other tasks is future work (Sec VI).
  • domain assumption Both controllers receive the same future reference information via the H=10 horizon, and the GC finite-difference approximation of high-order derivatives is adequate.
    If the finite difference approximation is poor for agile trajectories, GC would be disadvantaged; the paper does not check the derivative approximation against analytic derivatives.

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Cite this review

Pith. "Pith review of Leveling the Playing Field: Carefully Comparing Classical and Learned Controllers for Quadrotor Trajectory Tracking." pith.science (2026). https://pith.science/paper/DQ2JKXUT

@misc{pith2026250617832,
  author       = {Pith},
  title        = {Pith review of: Leveling the Playing Field: Carefully Comparing Classical and Learned Controllers for Quadrotor Trajectory Tracking},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DQ2JKXUT}},
  note         = {Machine review of arXiv:2506.17832}
}
read the original abstract

Learning-based control approaches like reinforcement learning (RL) have recently produced a slew of impressive results for tasks like quadrotor trajectory tracking and drone racing. Naturally, it is common to demonstrate the advantages of these new controllers against established methods like analytical controllers. We observe, however, that reliably comparing the performance of such very different classes of controllers is more complicated than might appear at first sight. As a case study, we take up the problem of agile tracking of an end-effector for a quadrotor with a fixed arm. We develop a set of best practices for synthesizing the best-in-class RL and geometric controllers (GC) for benchmarking. In the process, we resolve widespread RL-favoring biases in prior studies that provide asymmetric access to: (1) the task definition, in the form of an objective function, (2) representative datasets, for parameter optimization, and (3) feedforward information, describing the desired future trajectory. The resulting findings are the following: our improvements to the experimental protocol for comparing learned and classical controllers are critical, and each of the above asymmetries can yield misleading conclusions. Prior works have claimed that RL outperforms GC, but we find the gaps between the two controller classes are much smaller than previously published when accounting for symmetric comparisons. Geometric control achieves lower steady-state error than RL, while RL has better transient performance, resulting in GC performing better in relatively slow or less agile tasks, but RL performing better when greater agility is required. Finally, we open-source implementations of geometric and RL controllers for these aerial vehicles, implementing best practices for future development. Website and code is available at https://pratikkunapuli.github.io/rl-vs-gc/

Figures

Figures reproduced from arXiv: 2506.17832 by the authors.

Figure 1
Figure 1. Trajectory Tracking for a Quadrotor. Rollouts of tra￾jectory tracking from an initial perturbation of a reinforcement learning controller (blue) and a geometric controller (orange) on a quadrotor. Robots are visualized at t = 1 and t = 5 to highlight transient and steady-state performance relative to the reference trajectory (grey). RL Controller has better transient performance (t = 1), but worse steady-state error… view at source ↗
Figure 2
Figure 2. The Impact of Each Type of Asymmetry in RL vs. GC Comparisons. Model comparisons in both Lissajous Tracking (top row) and Hover (bottom row) tasks for the aerial manipulator vehicle. Results are shown with median and inter-quartile range across 1000 evaluations per task. Controllers are measured on normalized gap to maximum reward to highlight improved performance by correcting asymmetries. Hatched bars represent co… view at source ↗
Figure 3
Figure 3. Trajectory Tracking Errors. Position and yaw errors over time for both the best-in-class RL and GC controllers evaluated on the Quadrotor and Aerial Manipulator morpholo￾gies. Results are shown as the median with inter-quartile range shaded from 1000 evaluations per morphology in Lissajous Tracking. all result in misguided comparisons since the baseline method is handicapped. This ultimately results in an over-estim… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Hover Errors. Position and yaw errors over time for the RL controller observing the end-effector (RL-EE), RL controller observing the COM (RL-COM), and the geometric controller (GC). Errors are shown as the median with inter￾quartile ranges across 1000 evaluations in t…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.