Crowd Control of Nonlinear Systems

Abstract: We study a multi-agent system in R2 where agents have unicycle dynamics with time varying speed and control inputs corresponding to acceleration and angular velocity. The system has a dynamic communication topology based on proximity. We propose a novel decentralized control algorithm derived from a double integrator model using a pairwise potential function. By using an energy function we show that a leaderless system converges to a set where connected agents have equal direction and velocity and potential contributions to the control action cancel each other out. The concept of formation density is defined and studied by numerical simulation. We find a relation between parameters of the controller and the system that makes the system converge to a formation with low density, corresponding to agents being at appropriate distances from each other, also when agents are not restricted to communicating only with their closest neighbors. The algorithm is tested for a system with leaders and properties of this system are investigated numerically. The results confirm that the proportion of leaders needed to guide a certain proportion of the agent in average is nonlinear and decreasing with respect to the number of agents.