{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T20:59:49Z","timestamp":1776891589630,"version":"3.51.2"},"reference-count":52,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,15]],"date-time":"2026-02-15T00:00:00Z","timestamp":1771113600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shaanxi Province Natural Science Foundation Research Project","award":["2025JC-YBQN-849"],"award-info":[{"award-number":["2025JC-YBQN-849"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Trajectory prediction is critical for safe robot navigation, yet standard deep learning models predominantly rely on the Mean Squared Error (MSE) criterion. While effective under ideal conditions, MSE-based optimization is inherently fragile to non-Gaussian impulsive noise\u2014such as sensor glitches and occlusions\u2014common in real-world deployment. To address this limitation, this paper proposes MEE-LSTM, a robust forecasting framework that integrates Long Short-Term Memory networks with the Minimum Error Entropy (MEE) criterion. By minimizing Renyi\u2019s quadratic entropy of the prediction error, our loss function introduces an intrinsic \u201cgradient clipping\u201d mechanism that effectively suppresses the influence of outliers. Furthermore, to overcome the convergence challenges of fixed-kernel information theoretic learning, we introduce a Silverman-based Adaptive Annealing (SAA) strategy that dynamically regulates the kernel bandwidth. Extensive evaluations on the ETH and UCY datasets demonstrate that MEE-LSTM maintains competitive accuracy on clean benchmarks while exhibiting superior resilience in degraded sensing environments. Notably, we identify a \u201cScissor Plot\u201d phenomenon under stress testing: in the presence of 20% impulsive noise, the proposed model maintains a stable Average Displacement Error (ADE \u201c\u2248\u201d 0.51 m), whereas MSE baselines suffer catastrophic degradation (ADE &gt; 2.1 m), representing a 75.7% improvement in robustness. This work provides a statistically grounded paradigm for reliable causal inference in hostile robotic perception.<\/jats:p>","DOI":"10.3390\/e28020227","type":"journal-article","created":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T11:11:28Z","timestamp":1771240288000},"page":"227","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Robust Trajectory Prediction for Mobile Robots via Minimum Error Entropy Criterion and Adaptive LSTM Networks"],"prefix":"10.3390","volume":"28","author":[{"given":"Da","family":"Xie","sequence":"first","affiliation":[{"name":"Xi\u2019an Key Laboratory of Active Photoelectric Imaging Detection Technology, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zengxun","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Process Materials Technology, Inner Mongolia North Heavy Industries Group Co., Ltd., Baotou 014030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chun","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Liberal Arts, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9454-0670","authenticated-orcid":false,"given":"Chunyang","family":"Wang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Key Laboratory of Active Photoelectric Imaging Detection Technology, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuyang","family":"Wei","sequence":"additional","affiliation":[{"name":"Xi\u2019an Key Laboratory of Active Photoelectric Imaging Detection Technology, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gao, Y., and Huang, C.-M. 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