Optimal Distance-Based Formation Producing Control of Multi-Agent Systems with Energy Constraints and Collision Avoidance

This paper considers the problem of an optimal distance-based formation producing control for multi-agent systems. We use the rigid graph theory in combination with the state-dependent Riccati equation (SDRE) method to develop a multi-agent formation producing scheme. We define a normalized rigidity matrix and use it for the rigorous stability analysis. A quadratic-like cost functional is defined that takes into account the cost of the formation as well as the energy cost. The proposed control law asymptotically minimizes the cost functional while it assures local asymptotic stability of the closed-loop system. Furthermore, we propose a solution for the global asymptotic stability and collision avoidance. In order to verify and validate theoretical results, we present several simulation results in both 2-D and 3-D spaces.