Joint Estimation and Planar Affine Formation Control With Displacement Measurements

This article investigates the problem of planar affine formation maneuver control with a matrix-valued formation shape variation parameter. The matrix representation renders full degree of freedom (DOF) motion associated with linear mappings in the context of affine transformation. Unlike the typical leader-follower setup, where all the leaders know the prescribed formation information, only a portion of leaders are informed of the matrix parameter in this article. To achieve affine formation stabilization, two types of distributed estimators are developed for the remaining leaders to infer constant and dynamic matrix parameters, utilizing only local displacement measurements. Then, we establish a joint estimation and cooperative control framework, generating corresponding formation shape changes in consistent with the matrix parameter. The system stability and precise estimation convergence are verified via both rigorous theoretical analyses and simulations with large-scale swarms. Finally, experiments conducted on the Crazyflie robots also validate the effectiveness and practicality of the proposed control approach.