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arxiv: 2606.05480 · v1 · pith:2JBA3QY3 · submitted 2026-06-03 · eess.SY · cs.SY

CAPE: Control Algorithm Performance Evaluation under Learned Vehicle Dynamics Models

Malik Ali , Musabbir Ahmed Arrafi , Nicholas M. Stiffler , Krishna Bhavithavya Kidambi This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-06-28 04:40 UTCgrok-4.3pith:2JBA3QY3record.jsonopen to challenge →

classification eess.SY cs.SY
keywords vehicle dynamics modelinglearned dynamicscontrol benchmarkingracing controllersnonlinear model predictive controldisturbance simulationautonomous racingclosed-loop evaluation
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The pith

The CAPE framework shows that an enhanced physics model yields faster lap times and lower tracking errors than two other learned vehicle dynamics models when tested in closed-loop racing controllers under disturbances.

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

The paper presents the CAPE framework as a way to benchmark racing controllers using learned dynamics models in simulation. It introduces an enhanced physics model (EPM) and compares it to Deep Pacejka Model and Deep-learning Dynamics Model across five controller types. Experiments show EPM produces the lowest lap times and tracking errors, with further gains in robustness when noise, delays, and uncertainty are added to the simulation. A reader would care because accurate dynamics models directly affect whether simulated controller performance translates to real vehicles.

Core claim

The CAPE framework evaluates five closed-loop control architectures under three learned vehicle dynamics models and finds that the proposed enhanced physics model (EPM) achieves the best average lap times and lowest longitudinal and lateral tracking errors across all tested controllers. Specifically, Adaptive NMPC with EPM records 5.82 s lap times versus 12.99 s for DPM and 8.80 s for DDM. When evaluated in a disturbance-aware simulator that includes measurement noise, process disturbances, actuator delay, and parametric uncertainty at moderate scaling, EPM reduces longitudinal tracking error by 29.0% and 17.2%, lateral tracking error by 24.6% and 12.3%, and increases average velocity by 39.

What carries the argument

The enhanced physics model (EPM), a learned vehicle dynamics representation that combines physics structure with data-driven terms to improve closed-loop prediction accuracy.

If this is right

  • Controllers using EPM maintain higher average velocities while reducing both longitudinal and lateral errors under identical configurations.
  • The CAPE benchmark allows direct comparison of model quality through closed-loop metrics rather than open-loop prediction error alone.
  • EPM improves robustness when measurement noise, process disturbances, actuator delay, and parametric uncertainty are present at moderate levels.
  • Average results across controllers show consistent gains in velocity magnitude and error reduction relative to the two comparison models.

Where Pith is reading between the lines

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

  • If EPM generalizes beyond the tested track and vehicle, the same benchmarking approach could rank dynamics models for other autonomous tasks such as highway driving or aerial navigation.
  • The framework could be extended by replacing the simulator with logged real-vehicle data to test how well each model predicts actual closed-loop behavior.
  • Designers of racing controllers might prioritize EPM-style models when simulation-to-reality transfer is the main performance bottleneck.

Load-bearing premise

The learned EPM and the disturbance-aware simulation framework accurately represent the vehicle dynamics and uncertainties that matter for closed-loop controller performance.

What would settle it

Running the same five controllers on a physical vehicle and measuring whether EPM still produces lower lap times and tracking errors than DPM and DDM would confirm or refute the performance advantage.

Figures

Figures reproduced from arXiv: 2606.05480 by Krishna Bhavithavya Kidambi, Malik Ali, Musabbir Ahmed Arrafi, Nicholas M. Stiffler.

Figure 1
Figure 1. Figure 1: Proposed closed-loop benchmarking architecture. The controller generates commands that pass through actuator delay before interacting with the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Failure-penalized tracking error comparison between fixed-parameter [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Failure-penalized lap-time comparison between fixed-parameter bicycle [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Temporal evolution of lateral tracking error [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of closed-loop path-following behavior under different controllers. The left, middle, and right rows present trajectories obtained from DPM [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Failure-penalized average longitudinal tracking error [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Each row shows the closed-loop longitudinal velocity [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Temporal evolution of longitudinal and lateral tracking errors of the five controllers over the uncertainty sweep [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Trajectory comparison on ETHZMobil track under fixed internal [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
read the original abstract

We propose the Control Algorithm Performance Evaluation (CAPE) framework, a systematic methodology for benchmarking racing controllers under our proposed learned enhanced physics model (EPM). The proposed framework enables cross-controller comparison by evaluating five closed-loop control architectures. We further compare our proposed EPM with two state-of-the-art learned vehicle dynamics models: Deep Pacejka Model (DPM) and Deep-learning Dynamics Model (DDM). Closed-loop experiments show that across all models and controllers, the proposed EPM achieves best average lap times. Specifically, the Adaptive NMPC with EPM achieves a time of 5.82 s, compared with 12.99 s for DPM and 8.80 s for DDM, while simultaneously producing substantially lower longitudinal and lateral tracking errors under identical controller configurations. We further evaluate all three models and five controllers using a disturbance-aware simulation framework incorporating measurement noise, process disturbances, actuator delay, and parametric uncertainty. Under moderate global disturbance scaling factor ({\eta} = 1), results averaged across the five controllers show that EPM reduces a) longitudinal tracking error by 29.0% and 17.2%; b) lateral tracking error by 24.6% and 12.3%; c) while increasing average velocity magnitude by 39.9% and 3.1% relative to DPM and DDM, respectively. Overall, CAPE establishes a systematic benchmark for evaluating the performance of learned vehicle dynamics models in a closed-loop control framework and demonstrates that our proposed EPM significantly improves controller robustness and performance under realistic uncertainties.

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 the CAPE framework for systematic benchmarking of racing controllers using learned vehicle dynamics models. It introduces an Enhanced Physics Model (EPM) and compares it to the Deep Pacejka Model (DPM) and Deep-learning Dynamics Model (DDM) in closed-loop simulations involving five control architectures. The key results indicate that EPM achieves the best average lap times across models and controllers, with Adaptive NMPC + EPM at 5.82 s versus 12.99 s for DPM and 8.80 s for DDM, and lower tracking errors. Under disturbance-aware simulations with η = 1, EPM shows reductions in longitudinal and lateral errors and increased velocity compared to the baselines.

Significance. If the learned EPM and the disturbance model faithfully represent the vehicle dynamics and uncertainties, this work offers a valuable methodology for evaluating learned dynamics in closed-loop control settings and demonstrates potential advantages of physics-enhanced models for improving robustness in autonomous racing applications. The use of multiple controllers and disturbance scaling provides a more comprehensive evaluation than open-loop model comparisons alone.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Experiments): The reported numerical results (e.g., lap times of 5.82 s, 12.99 s, 8.80 s and percentage error reductions of 29.0%, 17.2%, etc.) are presented without accompanying details on the training dataset size and source, the neural network architectures for DPM, DDM, and EPM, the validation split or cross-validation procedure, or any statistical tests for significance of the differences. This information is necessary to evaluate whether the performance gains are robust or could be due to overfitting or specific hyperparameter choices.
  2. [Disturbance-aware simulation framework (likely §3 or §5)] Disturbance-aware simulation framework (likely §3 or §5): The parameters for measurement noise, process disturbances, actuator delay, and parametric uncertainty are not specified with reference to physical measurements or literature on real vehicle sensor/actuator characteristics. Without this grounding, the claim that the framework incorporates 'realistic uncertainties' and that EPM improves performance under them rests on unverified modeling choices that could bias the comparison.
minor comments (1)
  1. [Notation] The definition of the global disturbance scaling factor η should be clarified with an equation or explicit formula in the methods section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important aspects of experimental rigor and grounding that will strengthen the presentation. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Experiments): The reported numerical results (e.g., lap times of 5.82 s, 12.99 s, 8.80 s and percentage error reductions of 29.0%, 17.2%, etc.) are presented without accompanying details on the training dataset size and source, the neural network architectures for DPM, DDM, and EPM, the validation split or cross-validation procedure, or any statistical tests for significance of the differences. This information is necessary to evaluate whether the performance gains are robust or could be due to overfitting or specific hyperparameter choices.

    Authors: We agree that these details are essential for assessing reproducibility and robustness. The full manuscript contains some of this information in §4, but we acknowledge it is not presented with sufficient clarity or completeness. In the revised version we will expand §4 to explicitly report: (i) the training dataset size and source (number of trajectories collected from the simulator and any real-vehicle data if used), (ii) the precise neural-network architectures (layer counts, neuron sizes, activation functions) for DPM, DDM and EPM, (iii) the validation split and any cross-validation procedure employed, and (iv) statistical tests (e.g., paired t-tests or Wilcoxon tests) on the lap-time and error differences across the five controllers, including p-values and confidence intervals. These additions will directly address concerns about overfitting or hyperparameter sensitivity. revision: yes

  2. Referee: [Disturbance-aware simulation framework (likely §3 or §5)] Disturbance-aware simulation framework (likely §3 or §5): The parameters for measurement noise, process disturbances, actuator delay, and parametric uncertainty are not specified with reference to physical measurements or literature on real vehicle sensor/actuator characteristics. Without this grounding, the claim that the framework incorporates 'realistic uncertainties' and that EPM improves performance under them rests on unverified modeling choices that could bias the comparison.

    Authors: We accept that the disturbance parameters require explicit grounding. The current manuscript states the functional forms but does not cite supporting literature or measurements. In the revision we will add, in the disturbance-aware simulation section, specific numerical values together with references to established sources (e.g., sensor noise characteristics from automotive IMU datasheets, actuator delay measurements reported in autonomous racing literature, and tire-parameter uncertainty ranges from Pacejka-model identification studies). We will also clarify how the global scaling factor η is applied and why the chosen magnitudes are representative of real-world conditions. This will substantiate the claim of realistic uncertainties and allow readers to judge potential bias. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical simulation benchmarks with independent model comparisons

full rationale

The paper reports direct empirical results from closed-loop simulations comparing EPM, DPM, and DDM under identical controllers and a disturbance-aware framework. Lap times, tracking errors, and velocity metrics are generated outputs of the simulation environment rather than quantities that reduce by construction to fitted inputs or self-citations. No derivation chain, uniqueness theorem, or ansatz is invoked that loops back to the paper's own definitions or prior self-citations. The central claims rest on simulation fidelity assumptions, which is a validity concern but not a circularity reduction per the enumerated patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only review provides no equations or training details, so free parameters and axioms cannot be enumerated; EPM is presented as a learned model whose internal construction is unspecified.

invented entities (1)
  • Enhanced Physics Model (EPM) no independent evidence
    purpose: Learned vehicle dynamics model intended to improve closed-loop controller performance
    Introduced in the abstract as outperforming DPM and DDM; no independent evidence supplied.

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discussion (0)

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