On the Stabilization of Directed Formation Using Geometric Algebra Approach

Distance-based formation control on minimally rigid graphs often encounters ambiguous shapes, where agents form incorrect shape formations due to multiple equilibrium points in the error dynamics. Recent studies on distance-based controllers, even those that introduce extra control variables, struggle to resolve this fundamental issue fully, typically requiring specific conditions or failing to manage reflections effectively. In this paper, we address both flip and reflection ambiguities in formation control by reexamining core geometric constraints and integrating them with traditional bearing-based formation control methods. We propose a novel controller that guarantees convergence to the correct formation without imposing any additional conditions. Numerical simulations demonstrate the controller’s effectiveness in avoiding formation ambiguities.