This paper addresses some alternatives to classical trajectory generation for an unmanned aerial vehicle (UAV) which needs to pass through (or near) a priori given way-points. Using differential flatness for trajectory generation and B-splines for the flat output parameterization, the current study concentrates on flat descriptions which respect to UAV dynamics and verify way-point constraints.
This chapter proposes a distributed approach for the resolution of a multiagent 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.