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 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：预测行人运动仍是机器人导航研究中一项复杂且持续的挑战。为了实现准确预测，我们需要评估多种因素，例如行人交互、环境、人群密度以及社会文化规范。精确预测行人轨迹对于确保人机交互的安全性至关重要，尤其在机器人导航场景中。此外，这项研究在自动驾驶车辆、行人追踪以及人机协作领域也具有潜在应用价值。因此，本文提出了FlowMNO——一种光流集成马尔可夫神经算子，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，其中未来行人坐标仅依赖于当前状态。这种问题建模方式无需存储历史状态信息。我们使用标准基准数据集（如ETH、HOTEL、ZARA1、ZARA2、UCY和RGB-D行人数据集）进行了实验。研究表明，在预测行人轨迹时，FlowMNO相较于部分最先进的深度学习方法（如基于LSTM、GAN和CNN的方法）性能提升约86.46%。因此，我们证明了FlowMNO能够无缝集成到机器人导航系统中，显著增强其在拥挤区域平稳导航的能力。