Smooth collision avoidance for the formation control of first order multi-agent systems

This work addresses collision avoidance in the formation control of a group of mobile robots with first-order dynamics perturbed by lateral and longitudinal slipping parameters. A Generalized Proportional–Integral Observer (GPIO) is designed to estimate these perturbations. Then, an Active Disturbance Rejection Control (ADRC) is proposed to solve the well-known formation control avoiding collisions among the agents. The control strategy only depends on the agents’ position measurements. On the other hand, Continuous Repulsive Vector Fields (C-RVFs) are developed to avoid collisions among the agents. For this purpose, a parameter depending on the inter-robot distance is developed to scale the RVFs properly. By proposing C-RVFs, the chattering is eliminated when using Discontinuous RVFs (D-RVFs). Numerical simulations and real-time experiments illustrate the agents’ performance when they are at risk of collision. •Solve the problem of collision avoidance and formation in a multi-agent system.•The control design only depends on the agents’ position measurements.•By proposing a smooth function, the RVFs are continuous functions.•It is proven that a surface is repulsive when the agents are at risk of collision.