Global and robust formation-shape stabilization of relative sensing networks

This paper proposes a simple, distributed algorithm that achieves global stabilization of formations for relative sensing networks in arbitrary dimensions with fixed topology. Assuming the network runs an initialization procedure to equally orient all agent reference frames, convergence to the desired formation shape is guaranteed even in partially asynchronous settings. We characterize the algorithm robustness against several sources of errors: link failures, measurement errors, and frame initialization errors. The technical approach merges ideas from graph drawing, algebraic graph theory, multidimensional scaling, and distributed linear iterations.