Unmanned Aerial Vehicles (UAVs) are used for several military and civil applications such as reconnaissance, surveillance etc. The UAVs, due to their design and size limitations, have inherent kinematic constraints, communication constraints etc. This thesis considers the path planning problems for UAVs while satisfying a class of constraints. We consider a multiple depot UAV routing problem, where the vehicles have motion constraints due to bound on their yaw-rate. For a given set of targets, it is required that each target should be on the path of at least one of the vehicles. This problem is hard to solve and currently there are no algorithm that could find an optimal solution. We aim to find tight lower bounds for this problem via Lagrangian relaxation. The complicating constraints of the problem are relaxed, and the cost function is penalized whenever those constraints are violated. This reduces the original problem to a known problem - a standard multiple traveling salesmen problem (MTSP). Simulation results are presented to show that this method significantly improved the existing lower bounds. The second problem we consider is the routing of UAVs in GPS denied environments and with limited communication range. Two different architectures for navigation assisted by an array of Unattended Ground Sensors (UGSs) are considered. In the first case, when an UAV localizes itself by communicating with an UGS, the second UAV can orbit around the first UAV. Contact with UGS allows them to act as beacons for relative navigation eliminating the need for GPS. A randomized algorithm with approximation ratio of 9/2 and a transformation technique are developed to solve this problem. In the second architecture, when two UAVs are located at two different UGSs, the third UAV localizes by triangulation using range measurements from the first two UAVs. This three UAV case is solved using a graph transformation technique to pose it as an one-in-a-set TSP. The solutions produced by these algorithms were used to simulate the UAV routing on AMASE, a simulation tool for routing UAVs developed by the Air Force Research Laboratories.
Unmanned Aerial Vehicles (UAVs) are used for several military and civil applications such as reconnaissance, surveillance etc. The UAVs, due to their design and size limitations, have inherent kinematic constraints, communication constraints etc. This thesis considers the path planning problems for UAVs while satisfying a class of constraints.
We consider a multiple depot UAV routing problem, where the vehicles have motion constraints due to bound on their yaw-rate. For a given set of targets, it is required that each target should be on the path of at least one of the vehicles. This problem is hard to solve and currently there are no algorithm that could find an optimal solution. We aim to find tight lower bounds for this problem via Lagrangian relaxation. The complicating constraints of the problem are relaxed, and the cost function is penalized whenever those constraints are violated. This reduces the original problem to a known problem - a standard multiple traveling salesmen problem (MTSP). Simulation results are presented to show that this method significantly improved the existing lower bounds.
The second problem we consider is the routing of UAVs in GPS denied environments and with limited communication range. Two different architectures for navigation assisted by an array of Unattended Ground Sensors (UGSs) are considered. In the first case, when an UAV localizes itself by communicating with an UGS, the second UAV can orbit around the first UAV. Contact with UGS allows them to act as beacons for relative navigation eliminating the need for GPS. A randomized algorithm with approximation ratio of 9/2 and a transformation technique are developed to solve this problem. In the second architecture, when two UAVs are located at two different UGSs, the third UAV localizes by triangulation using range measurements from the first two UAVs. This three UAV case is solved using a graph transformation technique to pose it as an one-in-a-set TSP. The solutions produced by these algorithms were used to simulate the UAV routing on AMASE, a simulation tool for routing UAVs developed by the Air Force Research Laboratories.