Three dimensional circuit layouts
SIAM Journal on Computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Introduction to Algorithms
Computing shortest paths for any number of hops
IEEE/ACM Transactions on Networking (TON)
Fast Horizon Computation at All Points of a Terrain With Visibility and Shading Applications
IEEE Transactions on Visualization and Computer Graphics
Planning Algorithms
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Local strategies for maintaining a chain of relay stations between an explorer and a base station
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Approximating the Visible Region of a Point on a Terrain
Geoinformatica
Unmanned ground vehicle radio relay deployment system for non-line-of-sight operations
RA '07 Proceedings of the 13th IASTED International Conference on Robotics and Applications
A UAV search and rescue scenario with human body detection and geolocalization
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
Relay Positioning for Unmanned Aerial Vehicle Surveillance*
International Journal of Robotics Research
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We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base station located in another point. One or more unmanned aerial or ground vehicles (UAVs or UGVs) can be used for this purpose as communications relays. The decision variables are the number of unmanned vehicles (UVs) and the UV positions. The objective function is assumed to access the placement quality. We suggest one instance of such a function which is more suitable for accessing UAV placement. The constraints are determined by, firstly, a free line of sight requirement for every consecutive pair in the chain and, secondly, a limited communication range. Because of these requirements, our constrained optimization problem is a difficult multi-extremal problem for any fixed number of UVs. Moreover, the feasible set of real variables is typically disjoint. We present an approach that allows us to efficiently find a practically acceptable approximation to a global minimum in the problem of optimal placement of communications relay nodes. It is based on a spatial discretization with a subsequent reduction to a shortest path problem. The case of a restricted number of available UVs is also considered here. We introduce two label correcting algorithms which are able to take advantage of using some peculiarities of the resulting restricted shortest path problem. The algorithms produce a Pareto solution to the two-objective problem of minimizing the path cost and the number of hops. We justify their correctness. The presented results of numerical 3D experiments show that our algorithms are superior to the conventional Bellman-Ford algorithm tailored to solving this problem.