Distance-Based Control of $\mathcal {K}_{n}$ Formations in General Space With Almost Global Convergence
Myoung‐Chul Park, Zhiyong Sun, Brian D. O. Anderson, Hyo‐Sung Ahn · IEEE Transactions on Automatic Control · 2017
In this paper, we propose a distance-based formation control strategy for a group of mobile agents to achieve almost global convergence to a target formation shape provided that the formation is represented by a complete graph, and each agent is governed by a single-integrator model. The fundamental idea of achieving almost global convergence is to use a virtual formation of which the dimension is augmented with some virtual coordinates. We define a cost function associated with the virtual formation and apply the gradient-descent algorithm to the cost function so that the function has a global minimum at the target formation shape. We show that all agents finally achieve the target formation shape for almost all initial conditions under the proposed control law.