# Robust Trajectory Prediction for Mobile Robots via Minimum Error Entropy Criterion and Adaptive LSTM Networks

## TL;DR

This paper introduces a robust trajectory prediction method for robots that handles sensor noise better than traditional approaches.

## Contribution

The novel MEE-LSTM framework combines adaptive LSTM networks with the Minimum Error Entropy criterion to improve robustness against impulsive noise.

## Key findings

- MEE-LSTM outperforms MSE-based models in noisy environments with a 75.7% improvement in robustness.
- The model maintains an ADE of ≈0.51 m under 20% impulsive noise, while MSE baselines degrade to over 2.1 m.
- The proposed SAA strategy dynamically regulates kernel bandwidth for better convergence in information theoretic learning.

## Abstract

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—such as sensor glitches and occlusions—common 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’s quadratic entropy of the prediction error, our loss function introduces an intrinsic “gradient clipping” 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 “Scissor Plot” phenomenon under stress testing: in the presence of 20% impulsive noise, the proposed model maintains a stable Average Displacement Error (ADE “≈” 0.51 m), whereas MSE baselines suffer catastrophic degradation (ADE > 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.