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REVIEW 4 major objections 4 minor 3 cited by

Trajectory Tracking Using Frenet Coordinates with Deep Deterministic Policy Gradient

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A DDPG controller that expresses its state in Frenet coordinates tracks a predefined path with lower lateral error than Cartesian-state DDPG and PPO.

desk verdict The DDPG training objective is never defined, so the central trajectory-tracking claim is unsupported — a desk reject despite a sensible starting idea. read the letter →

arxiv 2411.13885 v1 pith:KN5W3V7Y submitted 2024-11-21 cs.RO

Tongzhou Jiang , Lipeng Liu , Junyue Jiang , Tianyao Zheng , Yuhui Jin , Kunpeng Xu This is my paper · ORCID
classification cs.RO
keywords DDPGFrenetcoordinatestrajectorytrackingpathautonomousdrivingreinforcementlearninglateralerrorrobotnavigation
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 proposes a trajectory-tracking controller for autonomous driving in which the reinforcement-learning state is expressed in Frenet coordinates: distance traveled along the reference path, lateral deviation from it, and their velocities and accelerations. The claim is that this path-relative representation lets a DDPG agent separate along-road from cross-road motion, so the learned policy follows a predefined path with smaller and smoother lateral error. The authors support the claim with simulation training curves and tracking comparisons in which Frenet-based DDPG keeps the lowest loss and the smallest lateral deviation against Cartesian-state DDPG and PPO. If correct, the result is an algorithm-level improvement: no new network architecture or reward design is needed, only a change of coordinates for the state the policy sees.

What carries the argument

The load-bearing object is the Serret-Frenet coordinate map in Eq. (1), which rewrites the vehicle's Cartesian state relative to the reference path in terms of longitudinal coordinate $s$, lateral offset $l$, and their derivatives, including the reference-path curvature $k_r$ and its derivative $k_r'$. The DDPG agent receives this re-expressed state, chooses continuous steering and acceleration actions, and is trained against the loss $L = l + \dot{l} + \ddot{l}$, which concentrates the gradient on lateral behavior. The paper's argument is that this path-relative frame makes the policy's gradient point more directly at reducing cross-track error, so the same Actor-Critic machinery with experience replay and target networks converges to tighter and smoother tracking than it does with Cartesian states.

What would settle it

Re-run the comparison on a curved reference path using an independently verified Serret-Frenet transformation that includes the curvature terms of Eq. (1), and report the full distribution of lateral error over many episodes and seeds. If Frenet-state DDPG does not show a clear reduction in lateral error relative to Cartesian-state DDPG, or if dropping the curvature terms changes the result, the central claim is falsified.

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Extended reading notes

Core claim

The central discovery claimed is that replacing the Cartesian state representation of a DDPG trajectory-tracking agent with a Serret-Frenet representation materially improves tracking performance. Concretely, the paper converts the vehicle's position, heading, velocity, and acceleration into the Frenet coordinates $(s, \dot{s}, \ddot{s}, l, \dot{l}, \ddot{l}, l', l'')$, where $s$ is arc length along the reference path and $l$ is the lateral offset, and uses this state as the input to the DDPG actor and critic. The training objective is the loss $L = l + \dot{l} + \ddot{l}$, which penalizes lateral deviation, lateral velocity, and lateral acceleration. In the reported simulation experiments, the Frenet-state DDPG agent tracks the reference path more closely, keeps the lowest loss during training, and produces a smoother and smaller lateral-error curve than Cartesian-state DDPG and PPO.

Load-bearing premise

The comparison depends on Eq. (1) being a correctly implemented Frenet transformation, including the reference-path curvature $k_r$ and its derivative $k_r'$; the text at one point says road curvature need not be considered even though Eq. (1) explicitly contains curvature terms, so a sloppy implementation would not actually be using a true Frenet frame.

Editorial extensions

If this is right

  • Frenet-coordinate state encoding can be dropped into existing DDPG path-tracking pipelines without changing the network architecture or reward design.
  • The reported smoother lateral-error curve implies the learned policy is stable enough to follow a reference path without oscillation, a prerequisite for passenger comfort and safety.
  • Because the controller uses the vehicle's speed and position in the path-relative frame, steering can adapt to the current velocity rather than treating the path as a fixed geometric curve.
  • The method extends DDPG trajectory tracking to what the paper calls complex environments, supporting path planning and control for autonomous vehicles and mobile robots.

Reading between the lines

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

  • Editorial inference: the performance gain most likely comes from making the state invariant to the path's absolute position and heading, so a policy trained in Frenet coordinates should generalize to unseen roads without retraining; the paper does not test this.
  • Editorial inference: the same coordinate change should also help other continuous-action reinforcement-learning algorithms such as PPO or soft actor-critic; the paper only tests PPO in Cartesian form, not PPO with Frenet states.
  • Editorial inference: the loss $L = l + \dot{l} + \ddot{l}$ adds quantities with different units and no weighting, so part of the reported gain may be implicit reward shaping; testing squared or weighted variants would show whether the benefit is robust.
  • Editorial inference: a direct extension is to benchmark Frenet-state DDPG against a model-predictive controller on the same paths, which would reveal how close the learned policy comes to a controller-based floor on lateral error.
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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 / 4 minor

Summary. The paper proposes combining a Serret-Frenet coordinate transformation with the deep deterministic policy gradient (DDPG) algorithm for vehicle trajectory tracking. It claims that a DDPG controller operating on Frenet-state observations tracks predefined paths with high accuracy and stability, significantly reducing lateral error relative to Cartesian-state DDPG and PPO in Gazebo simulations. The paper presents the Frenet transformation in Eq. (1), standard DDPG update equations in Eqs. (2)-(5), and a 'loss function' in Eq. (6), followed by a qualitative experimental section with training-loss and tracking-error figures.

Significance. If the central claim were fully supported, a Frenet-state DDPG controller that reliably reduces lateral error compared with Cartesian-state DDPG and PPO in a realistic simulator would be a useful empirical contribution to autonomous driving research. The choice of baselines and the use of a local frame for lateral control are well motivated. However, as submitted, the paper does not define the learning objective actually optimized by DDPG, provides no quantitative performance values, and gives no experimental protocol that would allow reproduction. The contribution is therefore prospective rather than established; no code, data, or machine-checked results are supplied that would mitigate the missing details.

major comments (4)
  1. [II-C, Eq. (6)] The central learning objective is undefined. Equation (6), L = l + l_dot + l_ddot, is introduced as 'the loss function,' but no connection is made to the DDPG objective in Eqs. (2)-(5): the critic in Eq. (3) minimizes a Bellman residual, and the actor in Eq. (4) maximizes the critic's Q-value. No reward function r_i is defined anywhere in the paper. If Eq. (6) is intended to be the reward, that must be stated and substituted into Eq. (2), but the paper never says this. As written, the reported 'DDPG+Frenet' procedure could be a supervised minimizer of lateral-error terms rather than a policy-gradient method, which makes the comparison and the central claim uninterpretable.
  2. [III-B, Fig. 4] The central quantitative claim is not supported by any reported numbers. Figure 4(b) is described qualitatively as showing the smallest and smoothest lateral error, but the manuscript reports no lateral-error values, no standard deviations, no number of trials or seeds, and no statistical tests. Figure 3 plots 'average losses' that are never defined in relation to the DDPG updates of Eqs. (2)-(5). Without such quantitative results, the claimed 'significantly reducing lateral errors' cannot be assessed.
  3. [II-A, Eq. (1)] The paper's motivation and implementation appear contradictory. The text says the Frenet coordinate system avoids considering road curvature, yet Eq. (1) explicitly includes the reference-path curvature k_r and its derivative k_r'. The authors must state whether curvature terms enter the implemented state; if they do not, the transformation is not a proper Frenet frame, and if they do, the accompanying motivating sentence is incorrect.
  4. [II-C and III] The evaluation metric overlaps with the training objective in a way that is not acknowledged. Since Eq. (6) minimizes lateral position, velocity, and acceleration, and Fig. 4(b) evaluates lateral error, part of the reported success is by construction. The comparison against Cartesian-state DDPG and PPO provides some independent grounding, but only if the same reward or loss specification is given for all baselines; no such specification appears.
minor comments (4)
  1. [III] The experimental protocol is incomplete: road shape, vehicle model, sampling frequency, action bounds, neural-network architectures, learning rates, discount factor, soft-update coefficient, replay buffer size, exploration-noise schedule, and number of training episodes are all missing. The statement that the 'SGD optimizer' was used is insufficient for reproduction of DDPG.
  2. [II-A, Eq. (1)] Equation (1) is typeset in garbled form with unpaired parentheses and split expressions, and the notation is inconsistent (for example, dot derivatives versus derivatives with respect to s). A clean, self-contained derivation of the Frenet transformation is needed.
  3. [III, Figs. 3 and 4] The figures are not self-explanatory: Fig. 3 does not define what 'loss value' means, and Fig. 4(b) has no axis labels or units on the lateral-error plot.
  4. [References] Several references, such as [19], [20], [25], [29], and [31], are unrelated to trajectory tracking or Frenet coordinates and are never discussed in the body; the bibliography should be aligned with the content of the paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's central claim is an empirical comparison, and the relative-advantage claim does not reduce to the training loss by construction.

full rationale

This paper makes an empirical comparison claim rather than deriving a prediction from first principles; there is no derivation chain that reduces to its inputs. The only apparent overlap is that Eq. (6) defines a 'loss' L = l + l_dot + l_ddot in terms of lateral error and its derivatives, while Fig. 4(b) evaluates lateral error. That is training on the task metric, not a self-definitional prediction: the paper's substantive claim is the relative improvement of the Frenet-state DDPG over Cartesian-state DDPG and PPO, and that comparison does not collapse into the definition of the loss. The paper's larger problem is rigor, not circularity: no reward signal is defined, Eq. (6) is never connected to the DDPG critic/actor objectives in Eqs. (2)-(5), the Frenet transform in Eq. (1) is stated without derivation and contradicts the prose about ignoring curvature, and no numerical lateral-error statistics or seeds are reported. These are correctness and reproducibility defects; they do not make the claimed result equivalent to its inputs by construction. No load-bearing self-citations or imported uniqueness claims appear.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical entities. It relies on a standard coordinate transformation, an unspecified loss-to-reward connection, and simulation fidelity. The implicit loss weights are hand-chosen free parameters, and all DDPG hyperparameters are undisclosed.

free parameters (2)
  • Loss coefficients for lateral terms (l, \dot l, \ddot l) in Eq. (6) = 1 (implicit)
    The loss is written as an unweighted sum; no tuning or ablation is reported. The relative weights control the trade-off between lateral error, lateral velocity, and lateral acceleration, and the central tracking result depends on them.
  • DDPG hyperparameters (learning rate, discount factor gamma, soft update tau, exploration noise, replay buffer size) = not reported
    No values are given in the paper; these standard DDPG settings materially affect convergence and final performance. Their absence makes the comparison impossible to reproduce.
assumptions (3)
  • domain assumption The Frenet/Serret-Frenet transformation in Eq. (1) is correct and implementable for the test trajectory, and reference-path curvature k_r and its derivative k_r' are available.
    The method's state representation depends on this transformation. The prose says road curvature can be ignored, yet Eq. (1) uses k_r and k_r', so the implementation must resolve this contradiction.
  • ad hoc to paper The reward used by DDPG in the Gazebo environment is either the loss in Eq. (6) or is otherwise defined.
    DDPG optimizes expected reward, but the paper never defines a reward function. Section II-C describes a loss function, not an RL reward, so the training objective is unspecified.
  • domain assumption The Gazebo simulator provides an adequate vehicle model and reference path for evaluating trajectory tracking.
    All results depend on simulation fidelity; no sensor or dynamics model details are given.

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Cite this review

Pith. "Pith review of Trajectory Tracking Using Frenet Coordinates with Deep Deterministic Policy Gradient." pith.science (2026). https://pith.science/paper/KN5W3V7Y

@misc{pith2026241113885,
  author       = {Pith},
  title        = {Pith review of: Trajectory Tracking Using Frenet Coordinates with Deep Deterministic Policy Gradient},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KN5W3V7Y}},
  note         = {Machine review of arXiv:2411.13885}
}
read the original abstract

This paper studies the application of the DDPG algorithm in trajectory-tracking tasks and proposes a trajectorytracking control method combined with Frenet coordinate system. By converting the vehicle's position and velocity information from the Cartesian coordinate system to Frenet coordinate system, this method can more accurately describe the vehicle's deviation and travel distance relative to the center line of the road. The DDPG algorithm adopts the Actor-Critic framework, uses deep neural networks for strategy and value evaluation, and combines the experience replay mechanism and target network to improve the algorithm's stability and data utilization efficiency. Experimental results show that the DDPG algorithm based on Frenet coordinate system performs well in trajectory-tracking tasks in complex environments, achieves high-precision and stable path tracking, and demonstrates its application potential in autonomous driving and intelligent transportation systems. Keywords- DDPG; path tracking; robot navigation

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Reviewed August 12, 2026 · model on record in the stance chip above.