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In this paper, we propose a distance-based formation control strategy thatcan enable four mobile agents, which are modelled by a group ofsingle-integrators, to achieve the desired formation shape specified by usingsix consistent inter-agent distances in a 2-dimensional space. The control lawis closely related to a gradient-based control law formed from a potentialfunction reflecting the error between the actual inter-agent distances and thedesired inter-agent distances. There are already control strategies achievingthe same objective in a distance-based control manner in the literature, butthe results do not yet include a global as opposed to local stability analysis.We propose a control strategy modified from the existing gradient-based controllaw so that we can achieve almost global convergence to the desired formationshape, and the control law uses known properties for an associated formationshape control problem involving a four-agent tetrahedron formation in3-dimensional space. Simulation results verifying our analysis are alsopresented.

Distance-based Control of K4 Formation with Almost Global Convergence