Concerns Report: 'A projection-based algorithm for optimal formation and optimal matching of multi-robot system' (DOI: 10.1007/s11071-020-06189-y)

Academic fraud report · Geng Detector

Summary

Verdict: Suspect — likely typographical or copy-paste error rather than intentional fraud. Key issues: (1) Internal contradiction between the text and figure caption in Example 3 — the body states the restricted region is [0,20]^2, while Figure 7's caption claims [0,60]^{2m}; this discrepancy makes the reported simulation irreproducible as published. (2) Reference-list formatting errors (mismatched parentheses in Refs [27] and [29], and a missing space in Ref [29]) indicate careless proofreading. (3) A 2020-dated reference ([9]) was cited by a paper accepted in June 2020, which is possible via early-access but is noted for completeness. No figures are original photographic images, so pixel-level image forensics could not be performed; no raw numerical tables are provided, so statistical distribution tests were not applicable. Confidence is moderate: the contradictions are clearly documented in the source PDF, but their cause (typo vs. altered parameters) cannot be determined without author clarification or code. Recommended actions are contacting the authors for an erratum and attempting independent reproduction.

Verdict

🟡 Suspect — the inconsistencies are most plausibly explained as serious typographical or copy-paste errors rather than deliberate fabrication. The findings do not constitute proof of academic fraud, but they materially undermine the reproducibility of Example 3 and reflect poor editorial/proofreading quality.

Key findings

Internal contradiction in Example 3 (Section 5, p. 448): the body text defines the restricted region as [0,20]^2 (with Ω = [0,20]^{nm}), while Figure 7's caption states Ω=[0,60]^{2m}. The same example cannot be defined by both 20 and 60 simultaneously.
Reproducibility impact: without knowing the true parameter value, the Figure 7 trajectory cannot be re-derived from the algorithm description.
Reference-list errors: Ref [27] is missing a closing parenthesis (...144–152 (2017); Ref [29] has an extra closing parenthesis and a missing space (Syst27(2), 322–333 (2016))). These signal careless copy-editing.
Timeline observation: the paper was accepted 14 June 2020 and cites Ref [9] (Ebel et al.) as a 2020 publication; plausible via early access but noted as a short-cycle dependency.
Non-applicable checks: no photographic figures are present (all figures appear to be programmatically generated scatter/trajectory plots), so image-manipulation forensics were not possible; no numeric data tables were provided, so Benford-style and last-digit tests were not performed.

Evidence highlights

Body, p. 448: "We set the restrict region for every robot is [0,20]^2, i.e., Ω=[0,20]^{nm}. Fig.7 depicts the obtained formation..."
Figure 7 caption, p. 448: "Optimal formation with restricted region Ω=[0,60]^{2m} in Example 3..."
Reference [27]: unbalanced parentheses (missing )).
Reference [29]: double closing parenthesis and Syst27 formatting glitch.
Dates: Received/accepted context places Ref [9] within the same calendar year as acceptance.
DOI: 10.1007/s11071-020-06189-y (Nonlinear Dynamics, published online 13 March 2021).

Notes

Severity of the region mismatch: 🟠 (reproducibility-affecting).
Severity of the reference-list errors: 🟡 (attitude/proofreading signal only).
The detection limit of this report is the PDF text layer only; pixel-level analysis of simulation plots is not meaningful without underlying data.
Recommended follow-up: contact corresponding author Qingshan Liu to confirm the true region for Example 3, request an Erratum, and attempt independent reproduction using parameters 20 and 60 respectively.