In this study, we address the consensus formation problem in multi-agent systems, specifically focusing on wheeled mobile robots (WMRs). The paper proposes a hybrid consensus framework that integrates both pairwise and higher-order interactions among robots, aiming to model real-world scenarios involving dense formations and multi-agent group coordination. The framework accounts for nonholonomic constraints of WMRs and incorporates a non-smooth Lyapunov function for stability analysis. By extending classical consensus models with group-level feedback and proving stability using the upper Dini derivative, the proposed solution ensures robust consensus even in the presence of contrarian agents and dynamic environments. The simulation results demonstrate the effectiveness of the proposed model in achieving synchronization and convergence across a network of WMRs.

Circadian rhythms, which follow a roughly 24-hour cycle, are crucial for regulating sleep-wake cycles, hormone secretion, and other physiological processes. Disruptions in these rhythms are linked to various mental health disorders, including depression, anxiety, and panic disorders. Understanding and synchronizing these rhythms requires analyzing coupled nonlinear systems. The coupled Kim-Forger oscillator dynamics, a non-linear system represented by ordinary differential equations, better describe circadian rhythms dynamics. Synchronizing these oscillators involves adding coupling terms, but determining the precise amount of coupling required can be challenging. Contraction theory offers a framework for ensuring robust synchronization by analyzing the stability and convergence of dynamical systems. This paper explores the application of contraction theory to the Kim-Forger oscillator model, aiming to identify sufficient conditions for synchronization (at coupling point=0.6). Numerical simulations validate the results, highlighting the potential of this approach to normalize disrupted circadian rhythms and alleviate related mental health symptoms.