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This paper presents an angle-based approach for distributed formation shapestabilization of multi-agent systems in the plane. We develop an angle rigiditytheory to study whether a planar framework can be determined by angles betweensegments uniquely up to translations, rotations, scalings and reflections. Theproposed angle rigidity theory is applied to the formation stabilizationproblem, where multiple single-integrator modeled agents cooperatively achievean angle-constrained formation. During the formation process, the globalcoordinate system is unknown for each agent and wireless communications betweenagents are not required. Moreover, by utilizing the advantage of high degreesof freedom, we propose a distributed control law for agents to stabilize atarget formation shape with desired orientation and scale. Simulation examplesare performed for illustrating effectiveness of the proposed controlstrategies.

Angle-based Shape Determination Theory of Planar Graphs with Application to Formation Stabilization