Predicting pedestrian movements remains a complex and persistent challenge in robot navigation research. We must evaluate several factors to achieve accurate predictions, such as pedestrian interactions, the environment, crowd density, and social and cultural norms. Accurate prediction of pedestrian paths is vital for ensuring safe human-robot interaction, especially in robot navigation. Furthermore, this research has potential applications in autonomous vehicles, pedestrian tracking, and human-robot collaboration. Therefore, in this paper, we introduce \textbf{FlowMNO}, an Optical Flow-Integrated Markov Neural Operator designed to capture pedestrian behavior across diverse scenarios. Our paper models trajectory prediction as a Markovian process, where future pedestrian coordinates depend solely on the current state. This problem formulation eliminates the need to store previous states. We conducted experiments using standard benchmark datasets like ETH, HOTEL, ZARA1, ZARA2, UCY, and RGB-D pedestrian datasets. Our study demonstrates that FlowMNO outperforms some of the state-of-the-art deep learning methods like LSTM, GAN, and CNN-based approaches, by approximately 86.46\% when predicting pedestrian trajectories. Thus, we show that FlowMNO can seamlessly integrate into robot navigation systems, enhancing their ability to navigate crowded areas smoothly.

翻译：行人运动预测仍是机器人导航研究中一个复杂且持久的挑战。为实现准确预测，需评估多重因素，包括行人交互、环境、人群密度以及社会文化规范。行人路径的精确预测对于保障人机交互安全至关重要，尤其在机器人导航领域。此外，该研究在自动驾驶车辆、行人跟踪及人机协作等方面具有潜在应用价值。因此，本文提出FlowMNO——一种融合光流的马尔可夫神经算子，旨在捕捉不同场景下的行人行为。本文将轨迹预测建模为马尔可夫过程，即未来行人坐标仅取决于当前状态。该问题形式化消除了对历史状态存储的需求。我们采用ETH、HOTEL、ZARA1、ZARA2、UCY及RGB-D行人数据集等标准基准数据集进行实验。研究表明，在行人轨迹预测任务中，FlowMNO相较于LSTM、GAN及基于CNN等方法等部分最先进的深度学习方法，性能提升约86.46%。由此证明，FlowMNO可无缝集成至机器人导航系统，显著增强其在密集区域平稳导航的能力。