Collision Free Dynamic Stability of Formations Using Projection Based Estimators

Transient instability is a phenomenon where interagent collisions can occur in dynamically stable formations of autonomous agents. Therefore, the necessity to manage and mitigate transient instabilities is essential for successfully deploying formation structures. This paper develops a novel control architecture that augments the baseline formation maintenance controller to mitigate transient instabilities. At its heart, the proposed architecture consists of a projection operator based estimator disguised as a reference model that generates collision-free trajectories for the agents to follow. This paper's main theoretical result shows that the proposed control architecture can simultaneously mitigate transient instabilities and guarantee asymptotic convergence of the formation dynamics. Also, an illustrative example demonstrates the theoretical developments presented in this paper.