This paper addresses the challenge of controlling the formation of multi-agent system based only on the relative distances between agents obtained individually by local sensors mounted on each autonomous agent in the system. Based on the graph rigidity approach, the inter-agent sensing and communication topology is presented as a rigid graph, and the control model is designed for each agent as a distributed control scheme. This study shows the capability of utilizing graph rigidity in designing distance-based formation control for multi-agent system. It also shows the applicability of the approach to achieve formation control for more complex formations in both two and three-dimensional spaces.
To validate the effectiveness and capability of the proposed formation control strategy, three complex formation scenarios are conducted and simulated using MATLAB. These scenarios involve both formation acquisition and maneuvering problems and consider double-integrator multi-agent systems with 5 and 12 agents. The simulation results show the effectiveness of the distance-based formation control based on the graph rigidity, by demonstrating the exponential stability of the controlled system and the convergence of the agents to the desired formation in less than 3 seconds even for a system of 12 agents. The system stability proof is provided using Lyapunov stability theorem. In addition to ensuring system stability, this study shows that the graph rigidity approach implicitly ensures inter-agent collision avoidance.
This study demonstrates the effectiveness of using graph rigidity approach in designing formation control of multi-agent system based only on the relative distances between agents, which ensures system stability

Red light crossing violations (RLCV) pose a significant hazard due to various factors influencing driver behavior and traffic signal operations. This study explores the efficacy of Deep Residual Neural Networks (DRNNs) in traffic signal optimization, specifically examining their influence on RLCV frequency. Data was collected from twenty signalized intersections over fifteen-minute intervals during weekdays, focusing on traffic volume, signal timing, geometric characteristics of approaches, and instances of the RLCV. The model successfully managed the well-known deep learning problem of vanishing gradient by exploiting DRNNs’ complex design, distinguished by their residual learning framework and identity mapping, easing the training of extremely deep networks. This enables the precise prediction and measurement of traffic flow and RLCV under changing circumstances, with R² = 0.9 for the testing data. The proposed methodology, which requires up to 48,000 samples, guarantees that the variance-based sensitivity analysis method’s indices converge, offering solid insights into the system’s behavior. The findings showed that the maximum queue length (QLmax) and the green and cycle times (G and C) substantially influence RLCV frequency, with a noticeable rise when QLmax exceeds ten vehicles and the G/C ratio falls below 0.15. This study underlines the urgency of addressing these factors to reduce RLCV frequency. It also emphasizes the potential of DRNNs in traffic management and recommends that future research concentrate on integrating real-time data for dynamic traffic signal modifications, therefore maximizing DRNNs’ potential in this sector.