Samuel Picton Drake

Multiple UAVs path planning algorithms: a comparative study

Unmanned aerial vehicles (UAVs) are used in team for detecting targets and keeping them in its sensor range. There are various algorithms available for searching and monitoring targets. The complexity of the search algorithm increases if the number of nodes is increased. This paper focuses on multi UAVs path planning and Path Finding algorithms. Number of Path Finding and Search algorithms was applied to various environments, and their performance compared. The number of searches and also the computation time increases as the number of nodes increases. The various algorithms studied are Dijkstra’s algorithm, Bellman Ford’s algorithm, Floyd-Warshall’s algorithm and the AStar algorithm. These search algorithms were compared. The results show that the AStar algorithm performed better than the other search algorithms. These path finding algorithms were compared so that a path for communication can be established and monitored.

Uniqueness of the Newman–Janis Algorithm in Generating the Kerr–Newman Metric

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be “derived” by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einsteins field equations now known as the Kerr–Newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman–Janis algorithm works, many physicist considering it to be an ad hoc procedure or “fluke” and not worthy of further investigation. Contrary to this belief this paper shows why the Newman–Janis algorithm is successful in obtaining the Kerr–Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman–Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein–Maxwell equations is the Kerr–Newman metric.After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be “derived” by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein’s field equations now known as the Kerr-newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman-Janis algorithm works, many physicist considering it to be an ad hoc procedure or “fluke” and not worthy of further investigation. Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric. PACS numbers: 02.30.Dk, 04.20.Cv, 04.20.Jb, 95.30.Sf

Autonomous Control of Multiple UAVs for the Passive Location of Radars

This paper describes an algorithm that has been used for the autonomous control of multiple UAVs tasked with the high level objective of locating a radar subject to a number of real world constraints. The distributed, fully autonomous, cooperative control of the multiple UAV system was executed using sensor input from a heterogenous network of miniaturised Electronic Surveillance (ES) payloads. An ES sensor onboard one UAV detected a radar target and cross-cued ES receivers onboard two other UAVs. Based on the information shared between these UAVs the target radar was approximately located by each UAV Once the UAVs had coarsely located the target they autonomously, dynamically, and continuously adapted their flight trajectories to progressively improve the accuracy with which they were able to co-operatively locate the radar target. The UAVs were able to accurately locate the radar while simultaneously avoiding no-fly zones, one another and remaining within communication range.

Some applications of tensor algebra to estimation theory

Tensor algebra and tensor calculus are widely used in the the fields of mathematics and physics but their usefulness in estimation theory has not been widely appreciated. In this paper we give a short introduction to tensor algebra and provide a few examples of how to use it. None of the results presented in this paper are original but they are novel in showing how tensor algebra can be used to derive results that take much longer and are more cumbersome using a traditional linear algebra approach.

Design Challenges for an Autonomous Cooperative of UAVs

The Defence Science & Technology Organisation (DSTO), which is part of the Australian Department of Defence, is developing a research capability that uses small, inexpensive, autonomous uninhabited air vehicles (UAVs) to detect, identify, target, track, and electronically engage ground-based targets such as radars. The UAVs, which act autonomously and cooperatively, use a geographically distributed and heterogenous mix of relatively unsophisticated electronic warfare (EW) sensors and other miniaturised payloads networked together to deliver a distributed situational awareness picture that can be shared across the command echelons. If the many design challenges are overcome, the cooperation and networking of these platforms and payloads could provide results superior to those of the significantly more expensive, platform-centric systems, but with the added advantage of robustness. This paper outlines the challenges relating to autonomy, supervision, and control that the developers face and reports on the development of DSTOs multi-UAV cooperative to date.

UAV Team Formation for Emitter Geolocation

In this paper we study a scenario in which uninhabited aerial vehicles (UAVs) are tasked with locating a group of active emitters. The time difference of arrival (TDOA) technique is used by the UAVs to geolocate the active emitters. As TDOA requires at least three UAVs to perform geolocation, an algorithm to team three or more UAVs and task this team to geolocate an emitter is required. We discuss two approaches for teaming the UAVs, which we have developed and tested via simulation. The first approach is a simple heuristic that assigns the closest three UAVs to the highest priority emitter. This approach was simple and efficient to run, but improvements in performance could be made. Because TDOA works best when the UAVs are angularly separated evenly around the emitter, the next teaming algorithm developed takes into account the geometry between all UAVs and emitters. It assigns a cost for each UAV team and emitter combination based on the current angular separation of the UAVs around an emitter, and by how much each UAV team can perfect its geometry in a given time period. Two search techniques are explored, which search the solution space for efficient solutions. Results from simulation tests of the two approaches indicate that the second algorithm on average geolocates the emitters in the simulation faster than the heuristic approach, and provides an efficient solution to this UAV teaming and allocation problem.

Collinearity problems in passive target localization using direction finding sensors

In passive target localization using direction finding (DF), there are particular sensor-target placements that cause large biases in the estimates or the failure of estimates to converge to a unique solution. Identification of such problematic configurations is crucial for implementing estimation and tracking algorithms effectively. In this paper we propose four methods for characterizing near-collinearity problems in a sensor-target configuration which enable one to quickly and easily identify cases in which DF-based localization will fail to obtain a solution or give unreliable results.

Optimal path planning and sensor placement for mobile target detection

For a flying military vehicle, avoiding detection can be a key objective. To achieve this, flying the least-probability-of-detection path from A to B through a field of detectors is a fundamental strategy. While most of the previous optimization models aim to minimize the cumulative radar exposure, this paper derives a model that can directly minimize the probability of being detected. Furthermore, a variational dynamic programming method is applied to this model which allows one to find a precise locally optimal path with low computational complexity, even when Doppler effects increase the dimension of this problem. In addition, a homotopy method with exceptionally low computational complexity is derived to adjust the optimal path when the detection rate function changes due to the removal of detectors, the addition of detectors or other changes of detectors. Finally, the paper also shows how to apply a convex optimization method to find optimal positions of detectors when vehicles can do path planning.

Centralized path planning for unmanned aerial vehicles with a heterogeneous mix of sensors

This paper is concerned with real-time optimal UAV path planning in a multi-emitter geolocation environment. All UAVs are assumed to be controlled by a central processing unit. A UAV waypoint-update/steering algorithm is developed based on maximizing the determinant of Fisher information matrix for localization of stationary emitters. Soft and hard geometric constraints for threat/collision avoidance are also implemented. An effective joint path optimization and dynamic sensor allocation algorithm is proposed to handle communication bandwidth constraints. The performance of the developed steering algorithm is illustrated with extensive simulation examples.

Causal association of Electromagnetic Signals using the Cayley Menger Determinant

In complex electromagnetic environments it can often be difficult to determine whether signals received by an antenna array emanated from the same source. The failure to appropriately assign signal reception events to the correct emission event makes accurate localization of the signal source impossible. In this paper we show that as the received signal events must lie on the light-cone of the emission event the Cayley–Menger determinate calculated from using the light-cone geodesic distances between received signals must be zero. This result enables us to construct an algorithm for sorting received signals into groups corresponding to the same far-field emission.