Almost Global Convergence For Distance- and Area-Constrained Hierarchical Formations Without Reflection

This paper discusses formation shape control systems with both distance and signed area constraints, which aim to avoid the flipping or reflection ambiguity in a target formation shape. We prove an almost global convergence result for a triangle formation with general shape, by choosing a particular value of the control gain associated with the formation area term. This result extends the recent paper [1] on formation shape stabilization from equilateral triangles to general triangles, with an almost global convergence from almost all initial conditions. We then consider a hierarchical formation system comprised of multiple triangular shapes, and prove almost global convergence of a shape control algorithm with appropriate gains. Several simulations are provided to validate the theoretical results.