Distributed Optimal Formation Control of Second-Order Multiagent Systems With Obstacle Avoidance

This letter formulates a class of generic optimal formation control problems for second-order multiagent systems, where agents are steered to achieve the optimal formation determined by a convex optimization problem with generic formation constraints and admissible range constraints. These constraints determine the geometric pattern and limit the range of the optimal formation, respectively. A generic optimal algorithm based on the primal-dual dynamics is proposed for various formation requirements. Based on Lyapunov stability and optimization theories, the states of the second-order multiagent system are shown to converge to the optimal solutions. Moreover, an obstacle avoidance mechanism based on the control barrier function is introduced to make our algorithm more practical. Finally, numerical simulations illustrate the effectiveness of the proposed algorithm.