Stochastic Models for Autonomous Systems and Robotics

The field of robotics is rapidly evolving with the development of autonomous systems capable of operating in dynamic and uncertain environments. A key challenge is ensuring that these systems can reliably make decisions and execute tasks despite inherent uncertainties. Stochastic modeling provides a crucial mathematical framework to address these uncertainties by incorporating randomness and variability in system behavior and external conditions. This paper explores the role of stochastic models in autonomous systems, particularly in navigation, decision-making, and task execution, and how they integrate with artificial intelligence and machine learning to enhance system robustness and adaptability. A case study on autonomous vehicles (AVs) demonstrates the application of stochastic models, highlighting the use of Markov Decision Processes (MDPs) for path planning, Kalman filters for sensor fusion, and Monte Carlo methods for probabilistic localization. Through detailed mathematical and computational analyses, we show how these stochastic methods help AVs navigate uncertain urban environments, improving decision-making and overall system performance.