Symmetry Stability Index: Real-Time Formation Monitoring for Robotic Platoons Based on Turn-Induced Lateral Dispersion

Robotic platoons must maintain geometric formation integrity while navigating complex environments, yet existing performance metrics primarily evaluate tracking accuracy or inter-vehicle spacing without directly quantifying the evolution of formation symmetry. This paper presents a real-time symmetry monitoring framework based on the proposed Turn-Induced Lateral Dispersion (TILD) metric and the Symmetry Stability Index (SSI), a normalized indicator that continuously evaluates geometric symmetry degradation during platoon operation. The methodology estimates the lateral geometric error of each follower, accumulates it through the TILD metric, and transforms the resulting dispersion into the bounded SSI. Using predefined thresholds, the framework classifies platoon operation into NORMAL, DEGRADED, and CRITICAL states, enabling continuous online supervision without modifying the underlying controller. The framework was implemented in a ROS 2 and Gazebo environment and validated with a robotic platoon navigating representative BARN benchmark worlds of increasing geometric complexity. The results reveal a consistent inverse relationship between accumulated lateral dispersion and symmetry stability, allowing progressive formation degradation to be quantitatively characterized across operating conditions. The framework thus offers a lightweight, interpretable, and continuously operating symmetry assessment that complements conventional platoon metrics, establishing a foundation for future symmetry-aware supervisory, diagnostic, and cooperative recovery control strategies.