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REVIEW 4 major objections 7 minor 40 references

Adaptive Learning-based Model Predictive Control Strategy for Drift Vehicles

T0 review · 4 major / 7 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A learning-based MPC supervisor can keep a drifting vehicle on a curved path even when the friction model is wrong.

desk verdict Useful hierarchical drift-control paper with a genuinely novel combination and sensible ablations, but the headline RMSE comparisons are partly in-sample and the drifting-RMSE metric is self-referential. read the letter →

arxiv 2502.04696 v1 pith:NZVNCSNL submitted 2025-02-07 cs.RO

Bei Zhou , Cheng Hu , Jun Zeng , Zhouheng Li , Johannes Betz , Lei Xie , Hongye Su This is my paper · ORCID
classification cs.RO
keywords learning-basedcontrolautonomousdriftingpathtrackingBayesianoptimizationmodelpredictivedriftequilibriumpointsclothoid
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 claims that autonomous drift control can be made both path-accurate and model-robust by giving a lower-level MPC controller a drifting objective and letting an upper-level Bayesian optimizer tune a small set of path-tracking parameters. The optimizer learns three numbers: the drift-equilibrium steering angle and two weights in an adaptive path-tracking law that adjusts the desired drift radius and the equilibrium steering angle from a look-ahead error. Because the upper layer optimizes the parameters directly against closed-loop tracking cost, it can compensate for a misidentified road-friction coefficient without refining the vehicle model. In Matlab-Carsim simulations on a clothoid-based reference path, the resulting ALMPC controller reports lower RMSE for lateral tracking, course error, and most drift states than three MPC baselines, in both the precise-parameter and the 10% friction-error cases. The central payoff would be a drift controller whose tracking performance survives model mismatch, at the cost of an offline Bayesian-optimization session over the reference path.

What carries the argument

The load-bearing object is the triple $\theta = [\delta_{eq}, w_r, w_e]$ learned by Bayesian optimization: $\delta_{eq}$ is the drift-equilibrium steering angle that shifts all other equilibrium states computed from the linearized single-track model, and $w_r, w_e$ are the two gains of the adaptive path-tracking law $R_{eq} = w_r R_r + w_e e_{la}$. A feedback term $\hat{\delta}_{eq} = \delta_{eq} + k e_{la}$ further adjusts the equilibrium steering angle from the look-ahead error. The upper-level BO treats closed-loop tracking performance over the entire clothoid path, measured by $J(\theta)$ in Eq. 18, as an expensive black-box function, models it with a Gaussian process (Matérn 5/2 kernel), and selects new parameter sets by expected improvement. These learned parameters are then frozen and passed to the lower-level MPC, whose quadratic program keeps the vehicle states near the resulting drift equilibrium while respecting input and input-rate limits. The mechanism does the work of replacing both the usual predictive path-tracking loop and the requirement of an accurately identified vehicle model.

What would settle it

Run the learned parameter set (e.g., $\delta_{eq}=-0.471$ rad, $w_r=1.903$, $w_e=1.032$ for the misidentified-friction case) on a different reference path, such as an 8-shaped course or a clothoid with reversed curvature, without re-running BO, and compare lateral-error RMSE against the MPC-PPT baseline; if ALMPC does not maintain a comparable margin there, the generalization claim is not supported.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that the conflicting goals of keeping a drift vehicle near its unstable drift equilibrium and following a general curved path can be separated in a hierarchy: a lower-level MPC tracks the current drift equilibrium point, while an upper-level BO supervisor selects the equilibrium steering angle $\delta_{eq}$ and the weights $(w_r, w_e)$ of an adaptive path-tracking (APT) law. The APT law sets the desired drift radius as $R_{eq} = w_r R_r + w_e e_{la}$, where $R_r$ is the curvature radius of the reference path and $e_{la}$ is a look-ahead lateral error, and shifts the equilibrium steering angle by $\hat{\delta}_{eq} = \delta_{eq} + k e_{la}$. BO minimizes a closed-loop tracking cost $J(\theta)$ built from lateral error, course error, a soft barrier on large deviations, and the increment of lateral error, using a Gaussian-process surrogate with a Matérn-5/2 kernel and expected-improvement acquisition. The paper reports that with both APT and DEP learning (ALMPC), the vehicle follows the clothoid path with lower tracking RMSE and steadier drift states than the baselines MPC-PPT, MPC-APT, and MPC-DEP, and that the advantage grows when the road friction in Carsim is set 10% lower than the value used to derive the model.

Load-bearing premise

The load-bearing premise is that the Bayesian optimizer's cost function, evaluated over the full 18.4-second clothoid path, is identical to the path and metric used in the reported RMSE tables, so the headline gains are in-sample fits; if the learned settings are transferred to a new path, the reported margins may shrink or disappear.

Editorial extensions

If this is right

  • If the central claim is right, drift-vehicle path tracking can be implemented with a one-time BO tuning session instead of continuously solving a prediction-based path-tracking optimization at every control step.
  • The same performance-driven identification should compensate for modeling errors in other sensitive parameters, such as tire stiffness or mass distribution, not only road friction, as long as they shift the DEP.
  • The reported ALMPC gains imply that tuning the controller reference (the DEP) and the tracking law jointly is more effective than tuning either one alone, which is the comparison the paper makes with MPC-APT and MPC-DEP.
  • Because the learned parameters are re-usable across the path used for tuning, the approach is compatible with low-computational hardware at runtime; the paper reports an online execution time of 9.32 s for the BO-based controller.

Reading between the lines

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

  • The reported RMSE comparisons are computed on the same clothoid path used to evaluate the BO objective, so the headline improvements are in-sample fits; a direct test would be re-running the learned parameters on a different path (for example, the 8-shaped maneuver) and reporting numerical tracking errors there.
  • One could plausibly extend the scheme to online or periodic re-tuning by sliding the BO objective window along the path, which would make the controller adaptive to time-varying friction instead of only to a single misidentified value.
  • The BO search space only includes $\delta_{eq}, w_r, w_e$; learning additional equilibrium states, such as $\beta_{eq}$ or $V_{eq}$, could either improve performance or destabilize the lower-level MPC, and the paper's choice to keep them model-derived is a safety-motivated restriction that future work could test.
  • The comparison with DRL suggests that sample-efficient BO may be the more practical route for expensive closed-loop drift tuning, but that comparison is single-scenario and would need repeated runs to confirm.
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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

4 major / 7 minor

Summary. The paper proposes an Adaptive Learning-based Model Predictive Control (ALMPC) strategy for autonomous drift vehicles. The architecture consists of an upper-level Bayesian optimization (BO) supervisor that learns three parameters—the drift equilibrium steering angle δ_eq, and the weights w_r, w_e of an adaptive path tracking (APT) law—and a lower-level MPC that tracks the resulting drift equilibrium states. The APT law adjusts the desired drift radius and steering angle based on look-ahead error. The method is tested in Matlab-Carsim simulations on a clothoid-based reference path under both precise and misidentified road friction parameters, with ablations MPC-PPT, MPC-APT, and MPC-DEP, plus an 8-shaped maneuver and comparisons with DRL, genetic algorithms, and particle swarm optimization. The central claim is that ALMPC achieves lower tracking and drifting RMSE than the baselines, and remains stable under parameter misidentification.

Significance. The problem of controlling a vehicle in sustained drift while tracking a general path is timely and practically relevant for autonomous racing and extreme-condition driving. The proposed hierarchical decomposition—separating path tracking (upper-level learning) from drift stabilization (lower-level MPC)—is a sensible design idea, and the use of BO to directly tune control-relevant parameters rather than refine a model aligns with the performance-driven identification philosophy. The paper is generally well organized, and the simulation platform (Matlab-Carsim) is appropriate for a first evaluation. The ablations that isolate APT learning and DEP learning are a useful contribution. However, the current evidence is weakened by two load-bearing issues: the headline tracking metrics are computed on the same path used to fit the BO objective, and the drifting RMSE is evaluated against controller-specific, online-generated references. If the authors address these with out-of-sample evaluations and a controller-independent drift metric, the work could become a solid contribution to learning-based control for autonomous drifting.

major comments (4)
  1. [§4.2, Tables 4–5, Eq. (18)] The BO objective J(θ) in Eq. (18) is evaluated over the entire clothoid path (N_k = 184 samples, T = 18.4 s) using exactly the same tracking metrics |e_k| and |Δψ_k| that are later reported as RMSE-Tracking in Tables 4 and 5. Consequently, the reported tracking improvements of ALMPC over the baselines are in-sample fits to the test path, not out-of-sample predictions. The only out-of-sample evidence, the 8-shaped maneuver in §4.3.2, is presented qualitatively with no quantitative error metrics, making it insufficient to support the generalization claim. I request a held-out path evaluation (e.g., a different clothoid or a curved track) with the BO-fixed parameters, along with reporting of tracking RMSE on that held-out path for all controllers.
  2. [Tables 4–5, §4.2.1, Eqs. (16)–(17)] The RMSE-Drifting columns in Tables 4 and 5 measure the deviation of actual states from 'the planned drift states at each given time step,' and the text explicitly acknowledges that 'each simulation features a unique planned series of drift states along the path.' For ALMPC, the planned drift states are generated online by the APT law: the desired radius R_eq depends on the look-ahead error through Eq. (16), and the steering equilibrium δ̂_eq is modified by the feedback term k·e_la in Eq. (17). Thus the reference for the drifting RMSE changes with the tracking error, and a controller that lets its reference chase the actual trajectory can trivially reduce this RMSE. This makes the drifting-performance half of the headline claim self-referential. Please report drifting error against a fixed, controller-independent reference (e.g., a nominal DEP trajectory computed from the system model) or use absolute drift-quality indicators such as sustained large sideslip angles and consistent yaw rate, which do not depend on the controller's own reference.
  3. [§4.3.3, Fig. 14, Table 6] The comparison with deep reinforcement learning (DRL) is not quantitatively substantive. The text claims a '10% less RMSE for the steering angle' but does not report tracking RMSE, drift-state RMSE, or any measures of variability. The training-time comparison (0h37min for BO-ALMPC vs 12h17min for DRL-ALMPC) is potentially confounded by different network architectures, hyperparameters, and hardware, and no details are given to assess the fairness of the comparison. This subsection should either be removed or expanded with a proper experimental setup (same vehicle model, same path, multiple seeds, and a table of performance metrics).
  4. [§4.2, all simulation results] All reported results come from single simulation runs. BO is stochastic (random initial samples, GP posterior sampling), and the RMSE differences in Tables 4 and 5 are small in some states (e.g., Δψ RMSE of 0.015 vs 0.018 rad in Table 4, and F_xr RMSE of 492.4 vs 489.1 N). Without repeated trials or confidence intervals, it is not possible to assess whether the observed improvements are statistically significant. Please report mean ± standard deviation over several independent BO runs (or at least over several initializations) for each controller and each case.
minor comments (7)
  1. [Table 2] The entry 'δ0 −0.52 rad/s' appears to be a typo: δ0 is a steering angle, not a steering rate. It should be '−0.52 rad'.
  2. [Eqs. (18)–(20)] The parameters e_max and λ appear in the BO objective (Eq. (18)) and the barrier function (Eq. (19)) but are not listed in Table 2 or defined in the text. Their numerical values should be reported.
  3. [§4.3.2] The 'traditional MPC' used as a baseline in the 8-shaped maneuver is not defined. Please specify its cost function, prediction horizon, and parameter values, or refer explicitly to one of the earlier baselines (MPC-PPT, MPC-APT, or MPC-DEP).
  4. [§4.2.1 and Figs. 7–8] The text states that the 'best parameters are acquired in the 171 iterations' and Fig. 9 shows the performance cost. Please clarify whether the RMSE values in Tables 4 and 5 for ALMPC are obtained by re-simulating the final closed loop with the learned parameters from the best iteration, or are taken directly from that iteration's evaluation. This distinction is important for reproducibility.
  5. [§4.3.3, Fig. 14] The DRL curve in Fig. 14 appears to be a single trajectory. Adding a shaded region over multiple seeds (or at least reporting the mean and variance of the lateral error over episodes) would make the comparison more convincing.
  6. [Throughout] There are several typographical and wording issues: 'maximize lateral deviations' should be 'maximum lateral deviations'; 'undetermined disturbances' is likely 'unmodeled disturbances'; 'promise effective learning' should be 'ensure effective learning'. A careful language pass is recommended.
  7. [§4.2, Fig. 6] Figure 6(b) is captioned only 'Drift Vehicle'; it would be clearer to describe what is being shown (e.g., the steering angle orientation relative to the path) in the caption or in the text.

Circularity Check

2 steps flagged · score 6.0 of 10

The headline tracking and drifting improvements are partially in-sample fits: BO minimizes the same e/Δψ errors later reported as tracking RMSE, and the drifting RMSE is scored against each controller's self-generated drift reference.

  1. fitted input called prediction [Section 3.3, Eq. (18); Section 4.1; Tables 4 and 5]
    "J(θ)= log[ 1/N_k Σ_{k=1}^{N_k}(|e_k|+λ|Δψ_k|)+ B(e_k)+ I(e_k)] ... the objective of BO is evaluated over the whole path in every iteration for T=18.4s and the sampling time is set as ΔT=0.1s, namely N_k=184"

    The BO supervisor selects θ* by minimizing a cost whose dominant terms are the mean lateral error |e_k| and course error |Δψ_k| accumulated over the entire clothoid path. The paper then reports RMSE of e and Δψ on that same path as the headline tracking result (Tables 4 and 5). ALMPC's tracking RMSE is therefore the value of the optimized objective, not an independent out-of-sample prediction; the baselines were not tuned on this objective, so the comparison is in-sample and partly forced by construction. The remaining content is that the learned parameters actually realize low cost through the nonlinear dynamics, which is non-trivial but weaker than the claimed predictive superiority.

  2. self definitional [Section 4.2.1, Tables 4/5; Eqs. (16)-(17)]
    "The RMSEs of V, β, r, δ, and F_xr illustrate the discrepancy between the vehicle’s actual states and the planned drift states at each given time step, which effectively evaluates the drifting performance. ... Since each simulation features a unique planned series of drift states along the path..."

    The drifting RMSE is defined against each controller's own planned drift states, so there is no common reference for the V, β, r, δ, F_xr columns. For ALMPC, the planned states are generated online from the current tracking error through R_eq = w_r R_r + w_e e_la and δ̂_eq = δ_eq + k e_la, i.e., Eqs. (16)-(17). Thus a controller can trivially reduce its RMSE-Drifting by making its reference follow the actual trajectory; the metric measures consistency with a self-generated reference, not the quality of the drift equilibrium. Claiming better drifting RMSE than MPC-PPT/APT/DEP on this basis is self-referential and does not by itself establish superior drifting performance.

full rationale

The core derivation chain is not tautological: the MPC layer solves a genuine optimal control problem, BO is a legitimate optimizer, and the learned parameters still must produce stable drift through the nonlinear vehicle model. However, two evaluation choices make the headline comparisons partly self-referential. First, Eq. (18) defines the BO cost as a function of |e_k| and |Δψ_k| over the full clothoid path (N_k=184, T=18.4s), and Tables 4/5 report RMSE of exactly e and Δψ on that same path; ALMPC's tracking numbers are therefore in-sample optimized values, not out-of-sample predictions, while the baselines are not optimized on this objective. Second, the drifting RMSE columns are computed against each controller's own planned drift states; for ALMPC those planned states are generated online from its own tracking error via Eqs. (16)-(17), so a lower RMSE-Drifting can be obtained by letting the reference chase the actual trajectory rather than by achieving a better common drift equilibrium. The misidentified-friction case and the 8-shaped maneuver provide some independent grounding, but the former is still the BO optimization path and the latter is qualitative. On balance the central quantitative claims are partially forced by the fit, giving a score of 6.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The central results depend on three BO-learned parameters (delta_eq, w_r, w_e), several hand-chosen or unreported tuning constants, and a set of standard vehicle dynamics and BO modeling assumptions. No new physical entities are introduced. The learned parameters are fitted to the same path used for evaluation, which is the main circularity burden.

free parameters (8)
  • delta_eq = -0.482 rad (case 1), -0.471 rad (case 2)
    Initial steering angle equilibrium point, the only DEP component identified by BO, bounded in [-0.7, 0.4] rad (Sec. 3.2 and 4.1).
  • w_r = 1.026 (case 1), 1.903 (case 2)
    APT drift-radius weight in R_eq = w_r R_r + w_e e_la (Eq. 16), learned by BO in [0, 2].
  • w_e = 0.945 (case 1), 1.032 (case 2)
    APT look-ahead error weight in Eq. 16, learned by BO in [-5, 5].
  • k = 0.25
    Steering feedback gain in hat_delta_eq = delta_eq + k e_la (Eq. 17), chosen heuristically from reference [39] and listed in Table 2.
  • x_la = 12 m
    Look-ahead distance in e_la (Eq. 15), chosen heuristically from reference [39] and listed in Table 2.
  • lambda = not reported
    Trade-off weight in the BO cost J(theta) in Eq. 18; the value is not given in the simulation setup or Table 2.
  • e_max = not reported
    Maximum lateral error in the soft barrier B(e_k) in Eq. 19; the value is not specified in the paper.
  • GP hyperparameters = not reported
    Matérn 5/2 kernel amplitude sigma_eta^2, length scale l, and observation noise sigma_w^2 (Eqs. 13, 14, 21) are not specified.
assumptions (7)
  • domain assumption Single-track vehicle model with states V, beta, r around the center of gravity (Eqs. 1-3) adequately represents drift dynamics.
    Standard modeling choice in drift control literature; ignores roll dynamics, load transfer, and tire lag.
  • domain assumption Simplified Pacejka tire model (Eq. 4) plus friction circle rear tire force (Eq. 7) captures coupled tire forces during drift.
    The DEP calculation and MPC linearization depend on this tire force approximation (Sec. 2.1.1).
  • domain assumption Setting all state derivatives to zero yields usable drift equilibrium points, and sustained drift near these unstable equilibria is controllable.
    Sec. 2.1.2 relies on the existence of DEP from prior phase portrait analysis [4-6, 33].
  • domain assumption Linearization of the vehicle model around the DEP (Eqs. 8-9) retains sufficient accuracy over a 2-second prediction horizon.
    The lower-level MPC uses this linearized model for short-term prediction (Sec. 2.1.3).
  • ad hoc to paper The reference path can be locally approximated as a series of circular arcs with radius R_r = 1/kappa.
    This assumption underlies the APT drift radius calculation in Sec. 3.1.1, Eq. 16.
  • standard math The BO surrogate model assumptions (zero mean GP, Matérn kernel, EI acquisition) are appropriate for the path tracking cost.
    Standard BO machinery from references [36-38], applied without validation that the cost is smooth enough for the chosen kernel.
  • domain assumption Carsim simulation with mu_m = 0.9 while the model uses mu = 1 represents a realistic misidentified-friction scenario.
    Sec. 4.2.2 defines the mismatch as a 10 percent decrease in road friction, but no sensitivity analysis over larger mismatches is given.

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Cite this review

Pith. "Pith review of Adaptive Learning-based Model Predictive Control Strategy for Drift Vehicles." pith.science (2026). https://pith.science/paper/NZVNCSNL

@misc{pith2026250204696,
  author       = {Pith},
  title        = {Pith review of: Adaptive Learning-based Model Predictive Control Strategy for Drift Vehicles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NZVNCSNL}},
  note         = {Machine review of arXiv:2502.04696}
}
read the original abstract

Drift vehicle control offers valuable insights to support safe autonomous driving in extreme conditions, which hinges on tracking a particular path while maintaining the vehicle states near the drift equilibrium points (DEP). However, conventional tracking methods are not adaptable for drift vehicles due to their opposite steering angle and yaw rate. In this paper, we propose an adaptive path tracking (APT) control method to dynamically adjust drift states to follow the reference path, improving the commonly utilized predictive path tracking methods with released computation burden. Furthermore, existing control strategies necessitate a precise system model to calculate the DEP, which can be more intractable due to the highly nonlinear drift dynamics and sensitive vehicle parameters. To tackle this problem, an adaptive learning-based model predictive control (ALMPC) strategy is proposed based on the APT method, where an upper-level Bayesian optimization is employed to learn the DEP and APT control law to instruct a lower-level MPC drift controller. This hierarchical system architecture can also resolve the inherent control conflict between path tracking and drifting by separating these objectives into different layers. The ALMPC strategy is verified on the Matlab-Carsim platform, and simulation results demonstrate its effectiveness in controlling the drift vehicle to follow a clothoid-based reference path even with the misidentified road friction parameter.

Figures

Figures reproduced from arXiv: 2502.04696 by the authors.

Figure 1
Figure 1. The principle of DEP identification. goal like computing the minimal-time racing line [27] or striking a harmonious balance among competing objectives [28, 29, 30]. BO can find great potential to bypass the sequential prediction process of PPT control methods by learning an adaptive path tracking (APT) control approach with minimized lateral error. Besides, BO can also com￾pensate for modeling errors and unknown dis… view at source ↗
Figure 2
Figure 2. Single-track vehicle model for drifting. represents the tire sideslip angles for the front and rear tires, which are formulated as: 𝛼𝑓 = tan−1( 𝑉 sin 𝛽 + 𝑎𝑟 𝑉 cos 𝛽 ) − 𝛿 (5) 𝛼𝑟 = tan−1( 𝑉 sin 𝛽 − 𝑏𝑟 𝑉 cos 𝛽 ) (6) However, the longitudinal and lateral tire forces of a drift vehicle can not be represented independently by the Pacejka tire model due to their coupled relationship. For a rear-wheel-drive drift vehicle, … view at source ↗
Figure 3
Figure 3. Prediction-based path tracking (PPT) control. However, these approaches are highly dependent on ac￾curately predicting the vehicle’s position and require sub￾stantial computational resources, which can potentially im￾pact real-time performance. To address this problem, an APT path tracking strategy is proposed in this paper with more details in the following section. 2.3. Bayesian Optimization Bayesian optimization … view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Hierarchical system architecture of the ALMPC strategy. Bayesian optimization consists of two essential ingredi￾ents: the probabilistic surrogate model and the acquisition function. The probabilistic surrogate model provides poste￾rior distribution and predictions over…
Figure 5
Figure 5. Figure 5: The proposed adaptive path tracking (APT) control. 𝜑 and the reference angle 𝜑𝑟 , all in the global coordinate system as depicted in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Clothoid-based path tracking in Matlab-Carsim platform. the arc length of the curve, (𝑥0 , 𝑦0 ) represents the starting point of the vehicle, 𝜃0 represents the initial angle, and (𝑥, 𝑦) represents the current position of the vehicle. Fig. 6a illustrates the clothoid-ba…
Figure 7
Figure 7. Figure 7: Simulations results of the path tracking performance in case 1: the proposed ALMPC significantly reduces tracking error compared to the baseline MPC-PPT owing to the incor￾poration of both APT and DEP learning. While simulations of MPC-APT and MPC-DEP incorporating par…
Figure 9
Figure 9. Figure 9: The path tracking performance cost during BO process in case 1: the lower path tracking performance cost points to the better path tracking performance and the tracking performance is gradually enhanced during the learning process and the optimal set of parameters corr…
Figure 10
Figure 10. Figure 10: Simulations results of the path tracking performance in case 2: the misidentified road friction coefficient triggers the vehicle to undulate around the reference path in simulations except the ALMPC, which can still maintain remarkable path tracking ability. Bei Zhou,…
Figure 12
Figure 12. Figure 12: The path tracking performance cost during BO process in case 2: the BO learning process can significantly improve the path tracking performance and the optimal set of parameters is acquired in iteration 153. 4.3. Discussion The verification of the proposed ALMPC strat…
Figure 11
Figure 11. Figure 11: Simulations results of drift vehicle states in case 2: the drifting performance of the proposed ALMPC proves to be less affected by the misidentified road friction coefficient than other simulations. friction coefficient. The performance cost 𝐽(𝜃) of ALMPC during the …
Figure 15
Figure 15. Figure 15: Comparison among three optimization approaches: BO can achieve superior optimization results with fewer evaluations. DEP derived from system model, which can promote safe drifting behaviors especially in the early stages of training, to serve as a comparison with our …
Figure 14
Figure 14. Figure 14: Path tracking comparison between BO and DRL: DRL exhibits more oscillations compared to BO, with a maximum lateral error of -1.31 m, while BO only 0.51 m [PITH_FULL_IMAGE:figures/full_fig_p012_14.png]

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.