A 3D Mixed-Integer Linear Optimization Problem for Bridge Inspection by a UAV Swarm with LOS Connectivity Constraints

In this paper, a motion planning mission is considered for a swarm of Unmanned Aerial Vehicles. In particular, a Mixed-Integer Linear Programming optimization problem is formulated to maximize the number of visited targets and minimize the total control effort, while avoiding obstacles and inter-agent collisions. A Line-Of-Sight constraint is enforced in the optimization procedure to ensure visibility-based inter-agent connectivity for the whole mission duration. Different from similar approaches in the literature, the present work extends the treatment to a 3D configuration and exploits a different graph topology constraint based on a multi-commodity flow model. This graph formulation allows more versatility in the feasible topologies. A bridge inspection mission is selected to frame the algorithm in a real-world scenario. The results show that the proposed algorithm consistently generates feasible multi-agent trajectories with steady connectivity, whereas the baseline approach may fail due to the stronger limitations in the graph formulation.