Generalized weak rigidity: Theory, and local and global convergence of formations
Provides a theoretical foundation for formation control using mixed distance-angle constraints, enabling more flexible formation shapes, though results are incremental extensions of existing rigidity theory.
The paper extends weak rigidity theory to incorporate both distance and angle constraints for formation control, proving local exponential stability in 2D/3D and almost global exponential stability for 3-agent formations in 2D, validated by simulations.
This paper discusses generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient flow law. The generalized weak rigidity theory is utilized in order that desired formations are characterized by a general set of pure inter-agent distances and angles. As the first result of its applications, the paper provides analysis of locally exponential stability for formation systems with pure distance/angle constraints in the $2$- and $3$-dimensional spaces. Then, as the second result, if there are three agents in the $2$-dimensional space, almost globally exponential stability for formation systems is ensured. Through numerical simulations, the validity of analyses is illustrated.