Formation Control of Multi-agent Nonlinear Systems using the State-Dependent Riccati Equation

This work investigates the formation control of a multi-agent robotic system via the state-dependent Riccati equation (SDRE). The system's agents interact with each other and follow a leader in point-to-point motion control (regulation). The number of agents is unlimited in conventional multi-agent formation control considering a complex dynamic for each agent, though the complexities of the algorithms usually result in small-scale simulations. Here a formalism is proposed that considers fully coupled nonlinear dynamics for robotic systems in multi-agent system formation control with a large number of agents. The interaction of the agents with each other and obstacle avoidance are embedded in the design through the weighting matrix of states in the SDRE. The input constraint also limits the actuators to create a more realistic scenario. Two dynamical systems have been modeled and simulated in this work: wheeled mobile robots (WMR) and multirotor unmanned aerial vehicles (UAVs). The simulation results show success in the implementation of a total of 1,089 agents in the desired square formation shape in the UAV case study, and a figure of 45 agents and 1,050 differential wheeled mobile robots in the circular desired shape, considering obstacle avoidance and also collision avoidance between the agents.