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arxiv: 2605.24301 · v1 · pith:WVNNMK56new · submitted 2026-05-23 · 💻 cs.RO

AcroRL: Learning Aggressive Quadrotor Inversion using Bidirectional Thrust

Gabriel Rodriguez , Henri Sayag , Abhishek Rathod , John Stecklein , Siddharth Saha , Christopher Barngrover , Wennie Tabib This is my paper

Pith reviewed 2026-06-30 13:53 UTC · model grok-4.3

classification 💻 cs.RO
keywords bidirectional thrustquadrotor inversionreinforcement learningaggressive maneuverstrajectory modulationflight regime transitionhardware validation
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The pith

Reinforcement learning policies enable compact quadrotor inversions with bidirectional thrust that outperform optimization baselines.

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

The paper establishes that separate reinforcement learning policies can be trained to manage the transitions between normal and inverted flight by modulating a constant reference trajectory. This approach addresses actuator saturation and motor reversal delays without the heuristic scheduling needed in prior geometric control methods. A sympathetic reader would care because bidirectional thrust expands the range of possible maneuvers such as inverted flight and perching, but only if the transitions remain reliable and compatible with existing trajectory planners. The framework claims lower position deviation and faster settling in simulation plus direct transfer to hardware experiments.

Core claim

The central claim is that two reinforcement learning policies, trained separately for nominal-to-inverted and inverted-to-nominal transitions, modulate a constant reference trajectory to achieve the lowest position root mean square error and shortest settling time among evaluated baselines in JAX simulation, with a 32 percent reduction in position RMSE and 57 percent reduction in settling time relative to the strongest optimization baseline, while hardware tests confirm successful inversions across yaw configurations with position RMSE below 0.35 meters and compatibility with circular flight in both regimes.

What carries the argument

The central mechanism is the pair of reinforcement learning policies for the two transition directions that modulate a constant reference trajectory to handle actuator saturation and motor reversal.

If this is right

  • The policies integrate directly with traditional trajectory generation and tracking controllers across both flight regimes.
  • Hardware demonstrations succeed for multiple yaw configurations without additional tuning.
  • The method supports downstream tasks such as circular flight after the inversion is complete.
  • An open-source implementation is provided to allow reproduction and extension.

Where Pith is reading between the lines

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

  • The same policy structure could be applied to other aggressive maneuvers that require bidirectional thrust, such as perching, if similar reference modulation is used.
  • Improved simulation fidelity for motor dynamics could further reduce the gap between simulation and hardware performance.
  • The approach suggests that learning-based modulation of reference trajectories may generalize to other vehicles that switch between multiple equilibrium conditions.

Load-bearing premise

The JAX simulation captures real-world effects such as motor reversal delays and actuator saturation accurately enough for the trained policies to transfer to hardware without further tuning.

What would settle it

A hardware experiment in which the quadrotor either fails to complete the inversion or records position RMSE above 0.35 meters would falsify the transfer claim.

Figures

Figures reproduced from arXiv: 2605.24301 by Abhishek Rathod, Christopher Barngrover, Gabriel Rodriguez, Henri Sayag, John Stecklein, Siddharth Saha, Wennie Tabib.

Figure 1
Figure 1. Figure 1: Overview of the proposed method. A reference modulation policy [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Still-frame visualizations of the learned quadrotor inversion trajectories in simulation. The [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Method comparison in simulation. Our approach consistently outperforms classical base [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A visualization of the settling cone for an NTI transition. The learned policy consistently outperforms both baselines in ev￾ery performance metric across all test cases. We attribute this to learning and optimizing over the true closed-loop system dynam￾ics, specifically the non-linearities and stochasticity of our transient thrust model. In contrast, the step command relies on heuristically tuned gains, … view at source ↗
Figure 5
Figure 5. Figure 5: Hardware experiments demonstrating the proposed method. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of the HFCA coordinate charts through stereographic projection. Modeling a quadrotor as a differentially flat hybrid system with flat variables η ∈ {±1},(r, ψ), is possible because thrust is aligned with ηbˆ 3, the product of thrust posture and the body z-axis. This alignment allows the attitude to be decomposed into a thrust direc￾tion s = ηbˆ 3 ∈ S 2 and a residual rotation about this axis,… view at source ↗
Figure 7
Figure 7. Figure 7: Custom quadrotor platform developed for the hardware experiments. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Thrust and torque model fit to experimental data collected using the Tyto Robotics Series [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
read the original abstract

Bidirectional thrust grants quadrotors a second equilibrium condition and increased control authority, expanding the envelope of possible aggressive maneuvers and enabling inverted flight, perching, and sensing. Prior geometric control approaches extend differential flatness through Hopf fibration-based attitude representations to support bidirectional thrust, but struggle with actuator saturation and motor reversal delay during inversions, requiring heuristic thrust posture scheduling and waypoint tuning. We propose a learning-based framework that modulates a constant reference trajectory to perform compact, position-constrained quadrotor inversions while remaining compatible with traditional trajectory generation and tracking across flight regimes. Separate policies are trained via reinforcement learning for nominal-to-inverted and inverted-to-nominal transitions. In JAX-based simulation, the proposed method achieves the lowest position deviation and settling time across all evaluated baselines, reducing position root mean square error (RMSE) by 32% and settling time by 57% relative to the strongest optimization-based baseline. Hardware experiments demonstrate successful inversion across multiple yaw configurations with position RMSE below 0.35m, and compatibility with downstream trajectory generation and control through circular flight in both regimes. Additionally, we provide an open-source implementation of the proposed framework.

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

3 major / 2 minor

Summary. The manuscript introduces AcroRL, a reinforcement learning framework for aggressive quadrotor inversions under bidirectional thrust. Separate policies are trained to modulate a constant reference trajectory for nominal-to-inverted and inverted-to-nominal transitions. In JAX simulation the method reports the lowest position deviation and settling time, with 32% RMSE reduction and 57% settling-time reduction versus the strongest optimization baseline; hardware trials show successful inversions across yaw angles with position RMSE below 0.35 m and continued compatibility with standard trajectory tracking and circular flight.

Significance. If the simulation-to-hardware transfer is reliable, the work provides a practical learning-based route to compact inversions that avoids heuristic scheduling required by prior geometric controllers. The open-source implementation is a clear strength that supports reproducibility and follow-on research in aggressive quadrotor flight.

major comments (3)
  1. [Simulation Experiments] Simulation Experiments: the headline 32% RMSE and 57% settling-time improvements are stated without reporting the number of random seeds, training trials, variance across runs, or statistical tests, making it impossible to assess whether the gains are robust or merely point estimates.
  2. [Hardware Experiments] Hardware Experiments: quantitative baseline comparisons are supplied only in simulation; the hardware section reports only qualitative success (RMSE < 0.35 m) with no side-by-side metrics against the optimization-based controllers, so the practical advantage on the physical platform remains unquantified.
  3. [Modeling and Simulation] Actuator Modeling: the JAX simulation incorporates motor-reversal delays and saturation, yet no step-response, reversal-timing, or frequency-response plots comparing the model to measured hardware data are provided; without this validation the sim-to-real transfer of the learned modulation policies rests on an unverified modeling assumption.
minor comments (2)
  1. [Method] The reward-function weights and policy-network architecture are listed as free parameters but their specific values and sensitivity analysis are not tabulated, which would aid readers attempting to reproduce the training.
  2. Figure captions for the hardware trajectories could explicitly state the yaw angles tested and whether the plotted reference is the constant or the modulated trajectory.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below, indicating where revisions will be made to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Simulation Experiments] Simulation Experiments: the headline 32% RMSE and 57% settling-time improvements are stated without reporting the number of random seeds, training trials, variance across runs, or statistical tests, making it impossible to assess whether the gains are robust or merely point estimates.

    Authors: We agree that statistical reporting is required to substantiate the claims. In the revised manuscript we will rerun all simulation experiments across multiple random seeds, report mean and standard deviation for position RMSE and settling time, and include statistical significance tests (e.g., paired t-tests) comparing against the optimization baseline. revision: yes

  2. Referee: [Hardware Experiments] Hardware Experiments: quantitative baseline comparisons are supplied only in simulation; the hardware section reports only qualitative success (RMSE < 0.35 m) with no side-by-side metrics against the optimization-based controllers, so the practical advantage on the physical platform remains unquantified.

    Authors: Direct quantitative hardware comparisons with the optimization baseline were not performed because safely executing those controllers on the physical platform requires extensive additional tuning and safety protocols beyond the scope of the current validation. The hardware results demonstrate successful sim-to-real transfer and compatibility with standard tracking. In the revision we will expand the discussion to explicitly state these experimental constraints and the practical advantages of the learned policies. revision: partial

  3. Referee: [Modeling and Simulation] Actuator Modeling: the JAX simulation incorporates motor-reversal delays and saturation, yet no step-response, reversal-timing, or frequency-response plots comparing the model to measured hardware data are provided; without this validation the sim-to-real transfer of the learned modulation policies rests on an unverified modeling assumption.

    Authors: The actuator model parameters were identified from hardware data. We will add step-response and motor-reversal timing plots in the revised manuscript that directly compare the JAX simulation outputs against the corresponding hardware measurements to validate the modeling assumptions. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical RL results independent of self-referential derivations

full rationale

The paper proposes an RL-based policy modulation framework for bidirectional-thrust quadrotor inversions, trained separately for nominal-to-inverted and inverted-to-nominal transitions. All performance claims (32% RMSE reduction, 57% settling-time reduction in JAX sim; hardware RMSE <0.35 m) are obtained from direct simulation rollouts and physical experiments rather than any first-principles derivation, fitted-parameter prediction, or self-citation chain. No equations or uniqueness theorems are invoked that reduce to the method's own inputs; the work is self-contained against external simulation and hardware benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the effectiveness of RL in learning the inversion maneuvers and the assumption that simulation-to-real transfer is feasible, with no new physical entities postulated.

free parameters (2)
  • Policy network parameters
    Learned via RL but specific values not provided in abstract
  • Reward function weights
    Typical in RL, chosen to balance position error and other terms
axioms (2)
  • domain assumption The bidirectional thrust quadrotor dynamics are accurately modeled in simulation
    Essential for training policies that transfer to hardware
  • domain assumption Separate policies for each transition direction are sufficient without a unified policy
    Stated approach in the abstract

pith-pipeline@v0.9.1-grok · 5756 in / 1368 out tokens · 60537 ms · 2026-06-30T13:53:13.849037+00:00 · methodology

discussion (0)

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Reference graph

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