Robustness issues in double-integrator undirected rigid formation systems

In this paper we consider rigid formation control systems modelled by double integrators (including formation stabilization systems and flocking control systems), with a focus on their robustness property in the presence of distance mismatch. By introducing additional state variables we show the augmented double-integrator distance error system is self-contained, and we prove the exponential stability of the distance error systems via linearization analysis. As a consequence of the exponential stability, the distance error still converges in the presence of small and constant distance mismatches, while additional motions of the resulted formation will occur. We further analyze the rigid motions induced by constant mismatches for both double-integrator formation stabilisation systems and flocking control systems.