Distributed Adaptive Formation Control for Second-Order Multi-Agent Systems Without Collisions

This paper presents an adaptive strategy to solve the formation control problem for a set of second-order agents with parametric uncertainty and nonlinearity. The strategy regards a group of agents where the nonlinearities and uncertainties are represented by a linearly parametrized term, which allows us to consider non-identical agents. In order to ensure the collision-free motion of agents, we propose the use of a repulsive vector field component that is applied only when a pair of agents becomes nearer than a predefined minimum bound. Numerical simulations were carried out to show the effectiveness of the proposed scheme. First, a simplified example was used to verify the key features of the control law, followed by a general case to illustrate the performance of the algorithm in a more complex scenario.