On the Role and Compensation of Distance Mismatches in Rigid Formation Control for Second-Order Agents**This work was supported by the the EU INTERREG program under the auspices of the SMARTBOT project and the work of Cao was also supported by the European Research Council (ERC-StG-307207)

This paper presents a robustness analysis of gradient-based formation control law for second-order agents subjected to distance mismatches or constant disturbances. It is shown that, akin to the first-order case, the existence of these mismatches introduces two undesired group behaviors: a distorted final shape and a stationary group motion. We show that such undesired properties can be compensated by combining the gradient-based rigid formation control law and our proposed distributed estimators.