Planar Leader-Follower Shape Formation Control Using Hybrid Geometric Constraints

Distance-based formation control on minimally rigid graphs is known to suffer from flip ambiguities, which can lead to incorrect formation patterns. Even advanced distance-based controllers that incorporate additional controlled variables often face challenges, either requiring specific conditions to avoid such ambiguities or failing to guarantee that reflected ambiguities are resolved. In this study, we address both flipped and reflected ambiguities in shape formation control by revisiting the essence of hybrid geometrical constraints and integrating them with traditional distance-based formation control. We propose a new formation controller that ensures convergence to the desired formation framework without requiring additional conditions. Experimental results using the TigerSquare platform are presented to demonstrate the efficacy of the proposed controller, highlighting its ability to avoid formation ambiguities.