Bounded Assignment Formation Control of Second-Order Dynamic Agents

A constructive design of bounded formation controllers is proposed to force
$N$
mobile agents with second-order dynamics to track
$N$
reference trajectories and to avoid collision between them. Instead of a prior assignation of the reference trajectories to the agents, optimal assignment algorithms are used to assign desired reference trajectories to the agents to obtain optimal criteria such as linear summation and bottleneck functions of the initial traveling distances of the agents. After the reference trajectories are optimally assigned, the bounded formation control design is based on a new bounded control design technique for second-order systems and new pairwise collision avoidance functions. The pairwise collision functions are functions of both relative positions and relative velocities of the agents instead of only relative positions as in the literature. The proposed results are illustrated on a group of underactuated omnidirectional intelligent navigators in a vertical plane.