Ionela Prodan, Florin Stoican, Sorin Olaru, Cristina Stoica, Silviu-Iulian Niculescu

This chapter proposes a distributed approach for the resolution of a multi-agent problem under collision and obstacle avoidance conditions. Using hyperplane arrangements and mixed integer programming, we provide an efficient description of the feasible region verifying the avoidance constraints. We exploit geometric properties of hyperplane arrangements and adapt this description to the distributed scheme in order to provide an efficient Model Predictive Control (MPC) solution. Furthermore, we prove constraint validation for a hierarchical ordering of the agents.