Application of a Distributed Containment Algorithm: Trajectory Tracking for Mobile Robots.

In this work, a distributed containment algorithm is proposed for the control of a formation of unicycle-type robots and mobile manipulators. This algorithm considers an interaction network among the agents in the formation, which is associated with a weighted directed graph. The structure of the formation considers the cases when virtual or real leaders delimit it. Further, the leaders form a convex hull that bounds the formation, and the positions of the followers inside this convex hull are determined by the Laplacian matrix of the network graph. The robot models are separated into a kinematic and a dynamic component. For the kinematic component, a containment algorithm is designed, while for the dynamic component, a controller based on the compensation of the mechanical parameters is proposed. The designed controllers are verified through computer simulations considering distinct number of agents and formation shapes. Additionally, some perturbations and mechanical parameters variations were applied to verify the robustness of the control laws.