Subframework-based Bearing Rigidity Maintenance Control in Multirobot Networks

This work presents a novel approach for $\mathit{\text{bearing}}\mathit{\text{rigidity}}$ analysis and control in multi-robot networks with sensing constraints and dynamic topology. By decomposing the system’s framework into $\mathit{\text{subframeworks}}$, we express bearing rigidity – a global property – as a set of $\mathit{\text{local}}$ properties, with rigidity eigenvalues serving as natural $\mathit{\text{local}}\mathit{\text{rigidity}}\mathit{\text{measures}}$. We propose a decentralized gradient-based controller to execute mission-specific commands using only bearing measurements. The controller preserves bearing rigidity by keeping the rigidity eigenvalues above a threshold, using only information exchanged within subframeworks. Simulations evaluate the scheme’s effectiveness, underscoring its scalability and practicality.