Landmark selection and path planning for unmanned vehicles with position error corrections

Unmanned vehicles have been widely used for sensing, surveillance, surveying, communication, transportation, and many other purposes. Navigation is always an essential operational function in the course of their movements. In the case of the absence of Global Positioning System (GPS) signals, the positioning need of an unmanned vehicle is generally empowered by its onboard Inertial Navigation System (INS). An inherent deficiency of INS, however, is that position errors inevitably occur and will gradually accumulate over time. A feasible approach to correcting errors is to use the fixed reference points with known coordinates in the cruising environment, which we call landmarks, to calibrate the vehicle's position when it passes by. The vehicle must choose a path along which a sufficient number of landmarks can serve the position calibration requirement. In such a context, this paper introduces a joint landmark selection and path planning problem for unmanned vehicles navigating in two-dimensional (2D) and three-dimensional (3D) environments, in which the vehicles' position drifting errors need to be rectified through communicating with preset landmarks. To characterize and tackle the problem, a set of new types of subpaths are defined and a bi-objective integer programming model using this building block is formulated for simultaneously minimizing the landmark deployment cost and the vehicle cruise distance. An efficient dynamic programming algorithm, which features a multi-criterion labelcorrecting form, is developed for searching for the Pareto-optimal solution set of landmark and path selections. Numerical and computational analyses are conducted in both 2D and 3D scenarios, in which a pair of origin and destination places are typically hundreds of kilometers apart and 4 datasets of different scales including 500, 1,000, 1,500, and 2,000 candidate landmarks are randomly generated. A sensitivity analysis reveals the impact of different position drifting increments caused by external environment interferences, varying correction abilities, and heterogeneous landmark deployment costs on the solution behavior. The influence of the number of candidate landmarks, position error limit, and error increment rate on computing time is also evaluated. All these test results conclude that the algorithm is capable of finding in seconds the entire set of Pareto-optimal landmarks and paths in real-world applications.