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arxiv: 2605.01731 · v1 · submitted 2026-05-03 · 💻 cs.RO · cs.SY· eess.SY

Lateral String Stability for Vehicle Platoons: Formulation, Definition, and Analysis

Sixu Li , Swaroop Darbha , Yang Zhou This is my paper

Pith reviewed 2026-05-10 16:13 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords lateral string stabilityvehicle platoonspath-tracking errorsV2V communicationonboard sensingautonomous vehiclesstring stability
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The pith

Onboard sensing alone cannot attenuate path-tracking errors in vehicle platoons, but V2V communication enables true attenuation.

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

This paper develops a framework for lateral string stability that examines how path-tracking errors propagate along a string of vehicles following the same path. It uses an arc-length viewpoint to compare errors consistently from one vehicle to the next. The analysis shows that feedback-feedforward control based only on onboard sensing cannot guarantee error attenuation, which creates a safety limit for close formations. In contrast, a learn-from-predecessor strategy that uses vehicle-to-vehicle communication achieves attenuation of both the full tracking error vector and the lateral cross-track error. The work matters because map-free autonomous navigation and tight platooning increase risks from sensor occlusions and error buildup.

Core claim

The paper defines L2 lateral string stability with respect to path-relative tracking errors viewed in arc-length coordinates. It proves that onboard-sensing-only strategies cannot attenuate these errors and identifies the structural requirement of nonzero feedback on specific measurements for stability. A V2V-based strategy satisfies the stability definition and produces attenuation.

What carries the argument

The arc-length (Eulerian) viewpoint that converts path-tracking errors into a consistent spatial coordinate for propagation analysis across vehicles.

If this is right

  • Controllers using only onboard sensing impose a fundamental safety limit on how tightly vehicles can platoon without risking path deviations.
  • V2V communication removes this limit by enabling attenuation of path-tracking errors along the string.
  • Nonzero feedback gains on lateral error measurements are required to guarantee lateral string stability.
  • The same stability properties hold for both the full tracking error vector and the scalar lateral error.

Where Pith is reading between the lines

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

  • Platoons without communication may need larger lateral safety margins than those with V2V links.
  • The arc-length formulation could extend to other multi-agent path-following problems where agents share a common reference curve.
  • Real-world validation would require testing under wind gusts or road banking to check whether the no-attenuation result persists.

Load-bearing premise

All vehicles follow exactly the same planned path so that path-relative tracking errors can be compared directly in arc-length coordinates.

What would settle it

A controlled test on a curved path where the first vehicle introduces a lateral perturbation and later vehicles measure whether their cross-track errors grow or shrink when using only onboard sensing.

Figures

Figures reproduced from arXiv: 2605.01731 by Sixu Li, Swaroop Darbha, Yang Zhou.

Figure 1
Figure 1. Figure 1: Illustration of a sensor-occlusion scenario in a vehicle platoon A practical solution to this issue is to let the lead vehicle plan a local path for the entire platoon (Hassanain et al., 2020; Liu et al., 2020b), with following vehicles tracking sensor-recorded predecessor paths or receiving shared data via vehicle-to-vehicle (V2V) communication. However, under such schemes, the motion of one vehicle direc… view at source ↗
Figure 2
Figure 2. Figure 2: Lateral error representations 3. A definition of 2 lateral string stability. 4. A general necessary and sufficient condition for 2 lateral string stability. 5. A comprehensive analysis of different combinations of tracking schemes, control strategies, and error measures, including impossibility results and insights derived for controller design. The remainder of this paper is organized as follows. Sectio… view at source ↗
Figure 3
Figure 3. Figure 3: We consider a finite platoon of 𝑚 vehicles, each tasked with tracking the same path by controlling its steering angle. The availability of path information may vary across vehicles [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Heading and position error representation Under standard assumptions (Liu et al., 2020a)—including constant longitudinal speed, small heading errors, negligible 𝑅̇ , large turning radius relative to 𝑒𝑙𝑎𝑡, and omission of higher-order terms—the error dynamics derived are (Rajamani, 2011; Liu et al., 2020a): 𝐌𝐞̈(𝑡) + 𝐂𝐞̇(𝑡) + 𝐋𝐞(𝑡) = 𝐁𝑢(𝑡) − 𝐅𝜅(𝑡), (2) where 𝐞 ∶= [ 𝑒𝑙𝑎𝑡 𝜃̃ ] , 𝑢 ∶= 𝛿𝑓 , 𝐌 ∶= [ 𝑚 0 0 𝐼𝑧 ] , 𝐂… view at source ↗
Figure 5
Figure 5. Figure 5: illustrates a schematic of this projection. Under the commonly adopted small heading error assumption in the literature (Rajamani, 2011; Liu et al., 2020a), Eq. (3) reduces to: 𝑑𝑙 𝑑𝑡 ≈ 𝑣𝑥 . (4) [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Information flow under onboard sensing mode The lead vehicle uses the desired path as its reference path, while each following vehicle uses the path traveled by its immediate predecessor (recorded using onboard sensors) as its reference. We call this tracking scheme predecessor￾tracking (PT). Fig.7 illustrates the computation of reference lateral errors under PT. Heading errors are omitted for clarity. The… view at source ↗
Figure 7
Figure 7. Figure 7: Reference error computation under predecessor tracking 2025), is utilized for this mode. This strategy traces back to foundational work of Fenton et al., 1976 and was subsequently advanced by Guldner et al. 1999 in the area of robust lateral control. The FF strategy is chosen in this mode because each vehicle has access only to the reference path information. The general form of the 𝑖 th vehicle’s FF contr… view at source ↗
Figure 8
Figure 8. Figure 8: Information flow under V2V mode V2V communication is utilized to transmit the desired path to all vehicles in the platoon, and every vehicle uses the desired path directly as its reference path. We call this tracking scheme desired-path tracking (DT). Here, for every 𝑖, we have 𝐞 𝑟𝑒𝑓 𝑖 (𝑙𝑑 ) = 𝐞 𝑑𝑒𝑠 𝑖 (𝑙𝑑 ), ( 𝐞 𝑟𝑒𝑓 𝑖 (𝑙𝑑 ) )′ = ( 𝐞 𝑑𝑒𝑠 𝑖 (𝑙𝑑 ) )′ , and ( 𝜃 𝑟𝑒𝑓 𝑖 (𝑙𝑑 ) )′ = ( 𝜃 𝑑𝑒𝑠(𝑙𝑑 ) )′ [PITH_FULL_IMA… view at source ↗
Figure 9
Figure 9. Figure 9: Reference error computation under desired-path tracking With V2V communication available, we can share additional valuable information beyond the desired path itself, enabling more advanced control strategy designs for better performance. In the V2V mode, we propose a novel learn￾from-predecessor (LFP) strategy to improve tracking error attenuation. This strategy is formulated directly in the spatial domai… view at source ↗
Figure 10
Figure 10. Figure 10: Illustration of spatially induced time gap 2.7. Problem formulation summary In the previous parts of this section, we introduced two control strategies of interest: the FF strategy using only onboard sensors and the LFP strategy utilizing V2V. For each strategy, the governing equations for analysis and V2V communication requirements were discussed. These are summarized in [PITH_FULL_IMAGE:figures/full_fi… view at source ↗
Figure 11
Figure 11. Figure 11: The "virtual" closed-loop system Since 𝐊𝐟𝐛 is designed to stabilize the error vector’s evolution, we have all the roots of det ( 𝐌̂ (𝑠) + 𝐁𝐊𝐟𝐛(𝑠) ) in the left-half plane and 𝐺(𝑠) being stable for any practical controller. It has been shown from Eq. (48) that 𝐺(𝑠) is proper with a relative degree of 2. Hence, 𝑠𝐺(𝑠) has a relative degree of 1. By Lemma 7, ∫ ∞ 0 ln |𝑆(𝑗𝜔)| 𝑑𝜔 = − 𝜋 2 lim 𝑠→∞ 𝑠𝐺(𝑠) = 0. (49)… view at source ↗
Figure 12
Figure 12. Figure 12: Test track and desired path Using the setup described in the preceding paragraph, we validate the proposed theoretical findings. Specifically, in Subsection 5.1, we design the LFP strategy under V2V mode, following the procedure in Remark 4, and validate that it is 2 lateral string stable with respect to the output 𝐲𝑖 = 𝑒 𝑑𝑒𝑠 𝑙𝑎𝑡,𝑖. In Subsection 5.2, we set the derivative learning gain 𝐊𝐋𝐃 of the LFP st… view at source ↗
Figure 13
Figure 13. Figure 13: Simulation results for the LFP strategy under V2V mode We conduct a simulation experiment using the setup described at the beginning of Section 5 [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Quantitative results for the LFP strategy under V2V mode 5.2. Learn-from-predecessor strategy under V2V mode with 𝐊𝐋𝐃 = 0 In this subsection, we examine the importance of the derivative learning gain 𝐊𝐋𝐃 for 2 lateral string stability, as established in Proposition 8. Starting from the LFP strategy gains in Subsection 5.1, we set 𝐊𝐋𝐃 = 0 while keeping all other gains identical to those in [PITH_FULL_IMA… view at source ↗
Figure 15
Figure 15. Figure 15: Simulation results for the LFP strategy under V2V mode with 𝐊𝐋𝐃 = 0 Using the same simulation setup described at the beginning of Section 5, [PITH_FULL_IMAGE:figures/full_fig_p019_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: , which plots the 2 norms of 𝑒 𝑑𝑒𝑠 𝑙𝑎𝑡 and 𝐞 𝑑𝑒𝑠 in panels (a) and (b), respectively. The 2 norms are obtained by approximating the continuous-time integrals with discrete-time summations over the simulation horizon. As shown, the lateral error norm begins to grow beyond the 5th vehicle, and the error vector norm beyond the 4th, confirming the lack of 2 lateral string stability for both output definiti… view at source ↗
Figure 17
Figure 17. Figure 17: Simulation results for the FF strategy under onboard sensing mode (a) 2 norm of 𝑒 𝑑𝑒𝑠 𝑙𝑎𝑡 (b) 2 norm of 𝐞 𝑑𝑒𝑠 [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Quantitative results for the FF strategy under onboard sensing mode A. Proof of Proposition 5 From Eq. (34), it is evident that the output 𝑒 𝑑𝑒𝑠 𝑙𝑎𝑡,2 depends on both inputs 𝑒 𝑑𝑒𝑠 𝑙𝑎𝑡,1 and 𝜃̃𝑑𝑒𝑠 1 , making Theorem 1 inapplicable. However, we can prove that the platoon is not 2 lateral string stable by finding a counterexample. Consider the case where the desired path is a circular arc, so that ( 𝜃 𝑑𝑒𝑠(𝑙… view at source ↗
read the original abstract

Platooning of connected and automated vehicles provides significant benefits in terms of energy efficiency, traffic throughput, and, most critically, safety. These safety benefits depend on string stability, which dictates how disturbances propagate along a vehicle string. Although longitudinal string stability has been extensively examined, lateral string stability, which governs the propagation of path-tracking errors that can lead to unsafe deviations from the desired path, remains underexplored. Its importance is growing as autonomous vehicles increasingly depend on onboard sensing and map-free navigation, where sensor occlusions and tight formations amplify safety risks. This paper presents a framework for lateral string stability that focuses directly on safety-critical, path-relative tracking errors and enables consistent comparison across vehicles that follow the same planned path. The key element of the framework is an arc-length (Eulerian) viewpoint, a departure from traditional analyses, that clarifies how tracking errors at a given point on the path propagate from one vehicle to the next. Building on this foundation, we propose the definition of L2 lateral string stability along with two control strategies: a feedback-feedforward strategy that relies solely on onboard sensing, and a novel learn-from-predecessor strategy that makes use of vehicle-to-vehicle communication. Both strategies are analyzed for lateral string stability with respect to two error measures: tracking error vector and lateral (cross-track) error. Our results show that onboard sensing alone cannot guarantee attenuation of path-tracking errors, imposing a fundamental safety limitation, while V2V communication enables true error attenuation. The analysis further identifies structural controller requirements, showing that nonzero feedback on specific measurements is essential for guaranteeing stability.

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 introduces an arc-length (Eulerian) framework for lateral string stability in vehicle platoons, defines L2 lateral string stability with respect to path-tracking errors, and analyzes two controllers: an onboard-only feedback-feedforward law and a V2V learn-from-predecessor strategy. It concludes that onboard sensing cannot guarantee attenuation of path-tracking errors (a fundamental safety limitation) while V2V enables attenuation, and identifies structural requirements such as nonzero feedback on specific measurements.

Significance. If the results hold, the work fills a gap in lateral (as opposed to longitudinal) string stability analysis for platoons, which is safety-critical under sensor occlusions and tight formations. The Eulerian viewpoint enables consistent cross-vehicle error comparison and the distinction between onboard and V2V strategies could inform communication requirements in connected automated vehicles.

major comments (2)
  1. [Abstract and onboard control analysis] Abstract and the section analyzing the feedback-feedforward strategy: the claim that 'onboard sensing alone cannot guarantee attenuation of path-tracking errors, imposing a fundamental safety limitation' is demonstrated only for the specific feedback-feedforward controller examined. No general impossibility result (e.g., via observability, information theory, or minimax argument) is provided showing that every possible onboard-only controller must fail L2 lateral string stability; the headline limitation therefore rests on a single instance rather than the full class.
  2. [Framework and assumptions] The framework section: the analysis assumes all vehicles follow the exact same planned path and that path-relative tracking errors are consistently comparable in arc-length coordinates. This assumption is load-bearing for the propagation analysis but is not accompanied by a robustness argument against disturbances or deviations from the common path.
minor comments (1)
  1. [Definition of L2 lateral string stability] The two error measures (tracking error vector and lateral cross-track error) should be defined with explicit equations and notation at the start of the stability definition section to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and constructive review. The comments highlight important points on the scope of our claims and the assumptions in the framework. We address each major comment below and will incorporate revisions to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Abstract and onboard control analysis] Abstract and the section analyzing the feedback-feedforward strategy: the claim that 'onboard sensing alone cannot guarantee attenuation of path-tracking errors, imposing a fundamental safety limitation' is demonstrated only for the specific feedback-feedforward controller examined. No general impossibility result (e.g., via observability, information theory, or minimax argument) is provided showing that every possible onboard-only controller must fail L2 lateral string stability; the headline limitation therefore rests on a single instance rather than the full class.

    Authors: We agree that the analysis is performed for the specific onboard feedback-feedforward controller, which relies solely on local path-tracking errors without predecessor information. This controller is representative of standard onboard-only approaches in the literature. The structural requirements identified in the paper (nonzero feedback gains on particular error components) indicate why attenuation fails in this information structure. To address the concern, we will revise the abstract, introduction, and conclusion to qualify the claim as applying to the analyzed class of onboard controllers without V2V, and add a discussion paragraph explaining the information-theoretic limitation (lack of access to the predecessor's error state prevents error attenuation). We will also attempt to include a brief general argument based on the error propagation equations if it can be done concisely; otherwise, the statement will be appropriately scoped. revision: yes

  2. Referee: [Framework and assumptions] The framework section: the analysis assumes all vehicles follow the exact same planned path and that path-relative tracking errors are consistently comparable in arc-length coordinates. This assumption is load-bearing for the propagation analysis but is not accompanied by a robustness argument against disturbances or deviations from the common path.

    Authors: The common-path assumption is essential to the Eulerian (arc-length) formulation, as it allows direct comparison of path-relative errors across vehicles at corresponding points along the path. This is analogous to the common velocity profile assumption in longitudinal string stability. We will add a dedicated robustness subsection (or appendix) that includes a sensitivity analysis to small path deviations and disturbances, along with numerical simulations demonstrating how the L2 stability margins degrade under bounded perturbations. This will clarify the practical applicability while preserving the core framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper introduces a novel arc-length Eulerian framework and L2 lateral string stability definition, then analyzes two explicit control laws (feedback-feedforward onboard and learn-from-predecessor V2V) against the new criteria for two error measures. The claim that onboard sensing cannot guarantee attenuation follows directly from showing the specific onboard law fails the L2 criterion while the V2V law satisfies it. No equations reduce by construction to fitted parameters, no self-citations are invoked as load-bearing uniqueness theorems, and no ansatz or renaming of prior results is used to derive the central limitation. The analysis stands on its own definitions and controller-specific calculations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; framework rests on standard vehicle platooning assumptions but no explicit free parameters or invented entities are detailed.

axioms (1)
  • domain assumption All vehicles follow the identical planned path allowing consistent path-relative error comparison
    Required for the arc-length viewpoint and cross-vehicle error propagation analysis as stated in the abstract.

pith-pipeline@v0.9.0 · 5596 in / 1242 out tokens · 31330 ms · 2026-05-10T16:13:31.136171+00:00 · methodology

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