A Modular Optimal Formation Control Scheme of Multiagent Systems With Application to Multiple Mobile Robots

In this article, we studied an optimal formation control problem of general integrator chain multiagent systems with strongly convex local cost functions. The control goal is to design appropriate controllers for the agents such that they reach a desired formation shape and the global cost function is minimized. To achieve the goal, a modular control scheme with two modules is proposed. First, in Module I, an optimal formation signal generator is designed, whose outputs asymptotically converge to the minimizer of the global cost function. Second, in Module II, by employing the outputs into the feedback loop as the agents’ reference trajectories, some linear-tracking controllers are designed for the agents to track the references asymptotically. With both modules, the proposed control scheme realizes the optimal formation control goal asymptotically. Moreover, the proposed control scheme is also applied to solving an optimal formation control problem of multiple mobile robots, where the robots’ total “relative” weighted squared moving distance requires minimization. The simulations and experiments validate the effectiveness and practicality of the proposed control scheme.