Cooperative Distance-Based Leader-Following Formation Control Using SDRE for Multi-Agents with Energy Constraints

Abstract

We present an optimal cooperative control method for a distance-based, leader-following formation control of multi-agent systems with energy constraints. In order to develop distributed control algorithms, we introduce a local rigidity matrix. We combine the rigidity theory and State-Dependent Riccati Equation (SDRE) method to develop a formation control scheme. The proposed method asymptotically minimizes a weighted cost function that includes formation cost and energy consumption for a given mission. The leader agent is aware of the desired trajectory and the followers measure relative distances of their neighbors only. We choose the weighting factors of the cost function to be dependent on the energy level of the agents. The proposed method guarantees the local asymptotic stability of the system. Moreover, we offer a solution for the global asymptotic stability of the closed-loop system. Simulation results illustrate the effectiveness of the proposed method in two- and three-dimensional spaces.