A gain matrix approach for robust distributed 3D formation control with second order swarm systems

This article addresses the problem of shape formation and control in robust distributed second order swarm systems in 3D space. The control strategy described is based on a gain matrix approach and can be executed using only relative position measurements in each agent’s local coordinate frame, which does not rely on inter-agent communication. First, a 3D formation shaping control method for second order swarm systems is proposed, and global stability is proved by constructing the candidate Lyapunov function. The gain matrix can be calculated by convex optimization, and the disturbance and input saturation is eliminated by the robustness of the proposed control law. Additionally, a heuristic algorithm for collision avoidance is introduced during the formation shaping process. After shaping the desired formation, the formation control law with required distances is proposed for maintaining a fixed formation shape in swarm systems. The control laws are then extended to 3D second order systems with leader–follower networks. Finally, the correctness of theoretical results is verified using simulations.