IAES International Journal of Robotics and Automation (IJRA) Vol. 14, No. 1, March 2025, pp. 19~30 ISSN: 2722-2586, DOI: 10.11591/ijra.v14i1.pp19-30  19 Journal homepage: http://ijra.iaescore.com Optimizing robot anomaly detection through stochastic differential approximation and Brownian motion Branesh M. Pillai 1 , Arush Mishra 2 , Rijo Jacob Thomas 3 , Jackrit Suthakorn 1 1 Center for Biomedical and Robotics Technology (BART LAB), Faculty of Engineering, Mahidol University, Nakhon Pathom, Thailand 2 Bangkok International Preparatory and Secondary School, Vadhana, Bangkok, Thailand 3 Department of Mechanical Engineering, TKM College of Engineering, Kollam, Kerala, India Article Info ABSTRACT Article history: Received Oct 25, 2024 Revised Jan 21, 2025 Accepted Jan 26, 2025 This paper presents an adaptive approximation method for detecting anomalous patterns in extensive data streams gathered by mobile robots operating in rough terrain. Detecting anomalies in such dynamic environments poses a significant challenge, as it requires continuous monitoring and adjustment of robot movement, which can be resource intensive. To address this, a cost-effective solution is proposed that incorporates a threshold mechanism to track transitions between different regions of the data stream. The approach utilizes stochastic differential approximation (SDA) and optimistic optimization of Brownian motion to determine optimal parameter values and thresholds, ensuring efficient anomaly detection. This method focuses on minimizing the movement cost of the robots while maintaining accuracy in anomaly identification. By applying this technique, robots can dynamically adjust their movements in response to changes in the data stream, reducing operational expenses. Moreover, the temporal performance of the data stream is prioritized, a key factor often overlooked by conventional search engines. This paper demonstrates how the approach enhances the precision of anomaly detection in resource-constrained environments, making it particularly beneficial for real-time applications in rugged terrains. Keywords: Brownian motion Data stream Differential approximation Mobile robot Optimistic optimization This is an open access article under the CC BY-SA license. Corresponding Author: Jackrit Suthakorn, Center for Biomedical and Robotics Technology (BART LAB), Department of Biomedical Engineering, Faculty of Engineering, Mahidol University 999, Phuttamonthon Sai 4, Salaya, Nakorn Pathom, 73170, Thailand Email: jackrit.sut@mahidol.ac.th 1. INTRODUCTION The primary signal and sensor processing issue is anomaly identification during the data stream [1]. This research's primary focus is identifying anomalies within data streams, particularly emphasizing the element of time. The objective is to enhance the efficiency of representing a specific subset of temporal data streams through a sequential design of experiments, facilitating accurate and rapid anomaly detection [2], [3]. A significant challenge in time-based anomaly identification, especially in the context of mobile robots used in rough terrain rescue missions, is the associated cost of transitioning the data stream from one geographical region to another [4]. This cost primarily arises from the movement of robots. Various approximation algorithms have been developed to address this issue, with the Brownian motion algorithm being a prominent choice due to its experience in managing time and cost-effective model construction [5]. However, the standard Brownian motion algorithm faces challenges, including handling vast datasets, memory limitations, and the inability to adapt to a behavior-based system with infinite variance [6], [7]. To address the challenges