Optimal obstacle avoidance via distributed consensus algorithms with communication delay

A consensus problem of multi-agent system subject to the communication delay with fixed and switching topologies as well as optimal obstacle avoidance is investigated. An innovative non-quadratic obstacle avoidance cost function is designed from an inverse optimal control perspective and a novel dynamic potential field whose vectors are rotating around the obstacle is introduced to avoid obstacles. The asymptotic stability condition of dynamical networks based on the Lyapunov-Krasovskii function is obtained via a linear matrix inequality (LMI) formulation. Finally, numerical examples are presented to show the effectiveness of the proposed theoretical results.