Stabilizing Formation Systems with Nonholonomic Agents

This letter investigates the effects of adapting decentralized gradient-based control laws to nonholonomic agents in networked formation systems. Using the unicycle agent model and a standard cascade control structure, it is shown that the stability margins of the cascaded systems deteriorate as the numbers of agents increase. This trend indicates problems with both convergence and scalability. It is then shown that the asymptotic behaviors of the nominal gradient-based control laws can be recovered by introducing a bump function that allows forward motion only when the agents are oriented in appropriate directions. The proposed solution ensures almost global convergence and can be applied to formation systems of all sizes. Finally, comprehensive simulation results show that the usage of a bump function also reduces the total energy consumption required to reach a target formation.