Optimal UGV-UAV Cooperative Partitioning and Inspection of Shortest Paths

We study cooperative shortest path planning for an unmanned ground vehicle (UGV) assisted by an unmanned aerial vehicle (UAV) in environments with unknown road blockages that are only discovered when a robot reaches the damaged point. This formulation generalizes the original Canadian Traveller Problem (CTP), which assumes a single ground vehicle and that the traversability status of all incident edges is revealed upon arrival at a vertex. We first analyze the case where the start and the goal are connected by $k$ disjoint paths, and prove that the worst-case competitive ratio $\rho$ for a single UGV is $2k-1$. With UAV assistance, and under the simplifying assumption of negligible initial transit and deadheading UAV costs, the ratio improves to $\rho = 2\frac{v_G}{v_A + v_G}k - 1$, where $v_G$ and $v_A$ denote the UGV and UAV speed, respectively. To address general graphs and non-negligible UAV initial transit and deadheading costs, we present an optimal path partitioning strategy that assigns path prefix inspection to the UGV and path suffix inspection to the UAV, and prove the optimality of the UAV inspection strategy on general graphs. We evaluate our algorithm by performing experiments on road networks from the world's 50 most populous cities, with randomized blockages, and show that the proposed method reduces UGV travel times by up to 30%.