  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.
