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In this paper the authors discuss a path planning problem for an autonomous robot-trailer system, while also including some consideration for the physical dimension of the trailer. The trailer equipped with sensing equipments is used to perform a surveillance mission among a collection of waypoint neighborhoods. The concept of a neighborhood is used to model the physical size of the actual sensors on the trailer. The problem is modeled as a Dubins Traveling Salesman Problem with Neighborhoods (DTSPN), where the neighborhoods are represented by disks. The authors firstly design a new algorithm for the Traveling Salesman Problem with Neighborhoods (TSPN), then extend this algorithm to find the shortest path for the DTSPN. The numerical study shows that the proposed algorithm can perform very well for both disjoint and overlapped disks cases.