A Novel Line of Sight Constraint for Mixed-Integer Programming Models with Applications to Multi-Agent Motion Planning

Mixed-Integer Programming (MIP) is an established method used to develop Multi-Agent System (MAS) motion planning algorithms under particular requirements, such as Line of Sight (LOS) connectivity. However, maintaining the tractability of the ensuing models is a known issue. In this paper, we propose a novel sufficient condition for LOS between agents of a MAS and discuss its implementation in a (MIP) model as constraints. The functionality of the proposal is demonstrated through simulations in a connectivity-constrained motion planning and decision-making problem. A comparison between the novel method and an earlier approach shows that the new proposal requires fewer optimization variables and constraints to be implemented. Finally, we employ Monte Carlo simulations to demonstrate that this reduction in the complexity of the models consistently decreases the time required to solve them.