Controlling Formations of Autonomous Agents with Distance Disagreements

We address the robustness issue for controlling, using only local information, the shapes of undirected rigid formations of autonomous agents when the agents disagree with their neighboring peers on the prescribed or measured distances between them. We propose to make use of simple local estimators as part of the distributed controllers. It is proved then that for infinitesimally rigid undirected formations satisfying a specific condition determined by the geometric shape of the desired formation and which agents are chosen to estimate the disagreements, our controller locally stabilizes exponentially the formations when the distance disagreements are small. In addition, the formation under control stops moving in the end and does not exhibit any undesirable motion caused by the distance disagreements. The final actual distances between the neighboring agents can be calculated directly from the steady-state values of the estimators. The simulation results for a six-agent formation validates the performance of the proposed controller.