American Institute of Aeronautics and Astronautics 1

THREE-DIMENSIONAL MULTI-OBJECTIVE UAV PATH PLANNER USING TERRAIN INFORMATION

Levi Swartzentruber i, Jung Leng Fooii, and Eliot H. Wineriii

Virtual Reality Applications Center, Iowa State University, Ames, IA 50010, USA

Military operations are turning to more complex and advanced automation technology for minimum risk and maximum efficiency. A critical piece to this strategy is unmanned aerial vehicles (UAVs). UAVs require the intelligence to safely maneuver along a path to an intended target, avoiding obstacles such as other aircrafts or enemy threats. Often automated path planning algorithms are employed to specify targets for a UAV to fly to. To date, path-planning algorithms have been limited to providing only a single solution (alternate) path without further inputs from the UAV controller. This paper presents a unique platform for decision making in a three-dimensional path planner where multiple solution paths are generated in the form of meta-paths. The path planner uses Particle Swarm Optimization (PSO) to generate multiple solution paths based on predefined criteria. The problem formulation was designed to minimize risk due to enemy threats, to minimize fuel consumption incurred by deviating from the original path, and takes into account reconnaissance targets. Using PSO, alternate paths are generated using B-spline curves, optimized based on preferences set for the three objectives. The resulting paths can be optimized with a preference towards maximum safety, minimum fuel consumption, or target reconnaissance. By incorporating terrain data into the path planner, the algorithm ensures that the generated alternate paths are feasible and at a safe height above ground. Viewing the paths in an immersive environment allows the decision making process to be completed in an efficient and organized manner. The problem formulation and solution implementation is described along with the results from several simulated scenarios.

I. Introductionilitary combat of the future will become highly dependent on the use of unmanned aerial vehicles (UAVs). In recent years, there has been rapid development in UAV technology

such as swarm communication, command and control, and developing usable interfaces 1. The complexity in UAV technology is rapidly growing, and according to the Department of Defense (DOD) Roadmap 2, by the year 2012 it is estimated that F-16 size UAVs will be able to perform a complete range of combat and combat support missions. Thus, the ground control station – the human operator’s portal to the UAV – must evolve as UAVs grow in autonomy. The ground control station must facilitate the transformation of the human from pilot, to operator, to supervisor, as the level of interaction with UAVs moves to ever-higher levels. As humans interface with UAVs at more abstract levels, a UAV will be trusted to do more 3. To develop and maintain that trust, a human must be able to understand a UAV’s situation quickly. Future ground control stations will need to provide an operator with situational awareness and quality information at a glance. i Research Assistant, Department of Mechanical Engineering & Human Computer Interaction, Virtual Reality Applications Center, 2274 Howe Hall, Iowa State University, Ames, IA 50010, USA, Student Member. ii Post-Doctoral Research Associate, Department of Mechanical Engineering & Human Computer Interaction, Virtual Reality Applications Center, 2274 Howe Hall, Iowa State University, Ames, IA 50010, USA, Member. iii Assistant Professor, Department of Mechanical Engineering & Human Computer Interaction, Virtual Reality Applications Center, 2274 Howe Hall, Iowa State University, Ames, IA 50010, USA, Member.

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50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference <br>17th4 - 7 May 2009, Palm Springs, California

AIAA 2009-2222

Copyright © 2009 by Levi Swartzentruber. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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To address the many research issues involved in the command and control that the DOD roadmap requires, a “Virtual Battlespace” at Iowa State University was created. In this paper, research into the issue of three-dimensional (3D) path planning for UAVs using terrain data as part of the Virtual Battlespace project is presented. The method described allows a human operator to focus on selecting an appropriate path from a set of alternate paths produced by the path planner, easing the decision making process. Using a Particle Swarm Optimization (PSO) algorithm, the task of generating alternate paths is formulated into an optimization problem consisting of three main components: 1) to avoid obstacles such as threats (e.g., surface to air missile sites, tanks, and aircraft), 2) maintaining a fuel-efficient path to maximize mission range, and 3) minimal deviation from the original way-points for reconnaissance purposes.

In the following sections of this paper, the background of the Virtual Battlespace project is presented. This is followed by a detailed description of the development and implementation of the 3D path planner using a Particle Swarm Optimization algorithm. The process of generating the alternate paths using terrain information is also discussed. The resulting paths generated from the planner from multiple simulated scenarios are then presented, with conclusions and future work discussed at the end.

II. Background

A. Virtual Battlespace Development of the Virtual Battlespace originated in 2000 when a research team at Iowa

State University’s Virtual Reality Applications Center (VRAC) began collaboration with the Air Force Research Lab’s Human Effectiveness Directorate and the Iowa National Guard’s 133rd Air Control Squadron. Virtual Battlespace integrates information about tracks, targets, sensors and threats into an interactive virtual reality environment that fuses the available information about the battlespace into a coherent picture that can be viewed from multiple perspectives and scales 4,5. Visualizing engagements in this way is useful in a wide variety of contexts including historical mission review, mission planning, prebriefing, post-briefing, and live observation of mission training scenarios. This system comprises of set of tools developed to enhance the user experience using voice recognition, immersive visualization, and intuitive interaction using a wireless gamepad controller. The Virtual Battlespace in a VR environment is shown in Fig. 1.

Figure 1. Virtual Battlespace in the C6 six-wall projection system at Iowa State University’s Virtual Reality Applications Center.

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B. Path Planning for UAVs There has been extensive research in the area of path planning especially in the artificial

intelligence, optimization, and video game communities. An example would be the A* algorithm 6, one of the more popular path planning algorithms in the video game/artificial intelligence. The strength of the A* algorithm lies in the ability to heuristically judge or value the best path from point to point. However, with the dynamic nature of a battlefield scenario, criteria the method relies on is constantly changing. An improvement to the A* algorithm is the D* 7 and the D* Lite algorithm 8, and has been successfully implemented in robot path planning situations in unknown terrain 9.

Recently, many realized the limitations of two-dimensional UAV path planning and began implementing three-dimensional path planners, taking advantage of the additional two degrees of freedom when generating alternate paths10,11. However, the additional information from one extra dimension can create new computational and visualization challenges. An additional degree of freedom results in more alternate path choices, which need to be explored. And to accommodate the multiple criteria and dynamic requirements when re-planning a path, various multi-objective path planners have been developed.

In instances when optimization has been applied during the path planning process, the results have been positive with improved computation time and more flexible control of the alternate path criteria 12,13. Marti and Qu 14 implemented a path planner based on stochastic uncertainties of the robot’s environment and then solving the solution numerically with artificial neural network. The results showed that the solution paths were obtained in close to real time based on the information relayed back by the robot. Another example would be the work done by Li et al 15 with their work on obstacle avoidance for soccer robots using Particle Swarm Optimization (PSO) to find an optimal alternate path based on the robot’s current position, shape, and size.

C. Terrain Data The use of terrain data has grown as the quality of the data available has improved. Many

applications now take advantage of this information with earth sciences leading the way. For example, the National Geophysical Data Center is currently building detailed elevation models for specific US costal regions to better model and predict tsunamis 16. Others are investigating how terrain data can be used to determine soil moisture levels and the data point resolution required to get good results 17. The field of landscape architecture is making use of digital terrain data and the increasing power of computer game engines to virtually render and manipulate real worksites 18. In the design world, others are creating techniques to piece together bits of real terrain data to create realistic virtual landscapes 19. In the area of robotics and path planning, terrain data has become an important component of computing feasible or alternative paths for unmanned vehicles 20.

Terrain data is presented in a variety of formats. The National Oceanic and Atmospheric Administration of the United States produces the most widely available formats. The USGS Digital Elevation Model (DEM) data sets simply store a regular rectangular grid of height values.The point separation can range between 10 meters and 90 meters or more depending on the data set. This data was only generated for the United States and can be downloaded from the Internet.A second available format is the Digital Terrain Elevation Data (DTED). This information was originally collected for military use but since then some of it has been made public. There are several levels of accuracy with level 0 having data points separated by 1000 meters down to level 2 with data points separated by 30 meters 21. For worldwide data, there are several possibilities

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including the Global Land One-km Base Elevation Project 22. Generally, high-resolution terrain data is much harder to find for areas outside of the United States.

Originally elevation data was stored in ASCII text files. While it is human readable, it uses a great deal of memory and takes the computer longer to process. Now a wide variety of formats exist for storing terrain elevation data ranging from binary formats to proprietary formats, depending on who created the data.

This has given rise to many different programs that read in the various terrain data formats and then display it for the user or allow the user to manipulate it. Some software is available free online such as GRASS or the ArcGIS viewer. Other software, like MetaVR, or the Unreal Engine are quite expensive but offer much higher graphics capabilities. Then there are libraries like GDAL that are designed to take a wide variety of terrain files and allow other applications to load them even if there are differences in formatting.

D. Particle Swarm Optimization (PSO) Because of the variable cost nature of the types of path planning that will be done with UAVs,

a multi-objective path planner was developed. For the optimization of the generated alternate paths, the Particle Swarm Optimization algorithm is used 23, since an evolutionary optimization algorithm would be very well fitted to handle a multi-modal optimization problem such as this. In this case, the PSO algorithm was also selected because of its simplicity in implementation with fewer parameters to be defined by the user, as opposed to algorithms such as the Genetic Algorithm, while still being able to handle non-linear problems of high dimensionality. Statistical analysis has showed that while both PSO and GA attained high quality solutions on a wide variety of multi-modal unconstrained problems, PSO was more computationally efficient 24, thus making PSO very suitable for this path planning application where the alternate paths need to be generated as quickly as possible. To maintain a human input in the decision making process, several paths are generated by the developed method. The generated alternate paths are represented by B-Spline curves to minimize computation, since a simple curve can easily be defined by as little as three control points.

In PSO, an initial randomly generated population swarm (a collection of particles) propagates towards an optimal point in the design space, and reaches the global optimum over a series of iterations. Each particle in the swarm explores the design space based on the information provided by previous best particles. PSO then uses this information to generate a velocity vector indicating a search direction towards a promising design point, and updates the locations of the particles.

III. Methodology After reviewing the various current methods and research being done for path planning of UAVs, it is evident that heuristic optimization methods have been successfully implemented as a means to solve path-planning problems. However, there are still issues that must be addressed, namely: 1) developing a path planning process that yields multiple alternate paths quickly and effectively, and 2) allowing a UAV controller (pilot) to visualize the alternate paths and interact with the environment in the decision making process. These are the issues that the presented path planner will address in this paper.

Determining the starting and ending points of the current path initializes the path planning process. The waypoints from the original path are then mapped as reconnaissance targets. The start and end points and any waypoints in between form the initial design points of the problem. From this initial design point, a search space is defined to scan and locate other UAVs within

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range and identify possible threats. The size of the search space is left open to the user’s judgment, setting it too large will incur a longer computation time, while having a search space that is too small might cause some UAVs to be unaccounted for. Fig. 2 shows the process flowchart of the path planning using PSO.

Once position data of the UAVs within range are obtained, enemy entities are singled out and a 3D threat zone is generated for each of them. A threat zone is defined as a sphere (a hemisphere for ground vehicles) of radius RT (user defined) surrounding the obstacle that the path needs to avoid. Threat zones are also generated for non-enemy (friendly) entities to avoid collision, but with a smaller radius. In addition, reconnaissance zones are also defined as hemispheres of radius RR. By default, the values for RT are set to be 20,000 feet and RR at 2,000 feet, but can be changed to suit the UAV controller’s preferences.

A. Cost Formulation Formulation of the optimization cost function begins with the description of a B-spline curve

to represent the path of the UAV. Consider the B-spline curve p0(ui), where ui is a sequence of line segments forming the curve, that requires re-planning when it violates a threat zone ZT (inred), shown in Fig. 4. A resulting alternate curve path p(ui) is generated that avoids the threat zone while still attempting to be within the reconnaissance zones (in green) and is illustrated by the red curve in Fig. 4.

The cost function components also depend on the number of parametric samples (line segments that form the curve) N that define the resolution of the curve. Here, N is user defined

Figure 4. Two-dimensional illustration of a simple threat zone avoidance problem.

p0(u)

p(u)ZR

ZT

Figure 2. Flowchart of the path planning process using Particle Swarm Optimization.

Identify waypoints of original path and set as reconnaissance targets

Identify enemies or obstacles and generate threat zones.

Run Particle Swarm Optimization (PSO) to obtain optimal path(s).

Identify start and end points for path planning.

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and the value of N brings a trade-off effect between accuracy of the curve and computational efficiency. The cost function components are summations of the curve characteristics sampled at the regular parametric intervals,

(1)

The initial solution to begin the optimization process is the original path that breaches the threat zone thus violating the constraint, illustrated in Fig. 4 by the blue dashed line. A new path can be computed by running the PSO such that the interior control points (between the end-points) satisfy the constraints. To achieve this, the cost function needs to accommodate the preferences of safety, reconnaissance missions, as well as fuel efficiency of the alternate paths. The total cost function is represented by the following components:

(2)

where, CT is the cost due to proximity of enemy entities and violation of the threat zones, CLreflects the cost incurred from excessive arc length and deviation from the original path, and CRis the cost incurred by deviating from the reconnaissance locations. The last term, T, is a cost component for flying too close to the terrain or completely underneath the terrain.

The constants K1, K2, and K3, in Eq. (2), are component weights that determine the relative emphasis of the various cost components with respect to the overall cost function. Each weight is normalized between zero and one. If a weight is zero then that particular cost function is unimportant for a particular run. All weights sum up to 1.0 in total. These weighted cost components are then added together to form the total cost function of a particular path. Table 1 shows an example of generating a set of three different alternate paths, each with its own preference. The T term is has no weighting factor because it needs to be present for any weighting arrangement to ensure feasible paths are generated.

Table 1. Example of component weights used to generate a set of alternate paths. Threat Weight, K1 Fuel Weight, K2 Recon Weight, K3

Threat Avoidance 0.50 0.25 0.25 Fuel Efficiency 0.25 0.50 0.25 Reconnaissance 0.25 0.25 0.50

All of the cost components are calculated in such a way as to generate values that, with a few exceptions, will fall between 10 and 100. The decision to scale the calculations in this manner was made for two reasons. First, it preserves the desired behavior of the weightings on the cost components. For example, if the threat cost consistently generates values two orders of magnitude larger than the fuel cost, the threat component could drive the solutions even though it might be weighted only a tenth as much as fuel. Second, this allows for a better understanding of the effects of the terrain cost on the overall cost of the path. How this information is used to formulate the terrain cost function will be discussed in the next section. From experimentation with the cost functions, the calculations presented below proved to be the least complicated to implement.

The threat component CT requires a function to determine the distance from a point p(ui)along the curve p(u) to a UAV inside the threat zone ZT and is denoted here as d(p, ZT). The function will return a positive value if there is a violation of the threat zone, and negative one

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otherwise. This violation is then scaled by the radius of the threat zone, RT, and the number of threats, ST. It is possible for a path to generate a threat cost of zero, so a value of 10 was added to maintain the proper order of magnitude in the calculations. With this, the threat cost is then defined as:

(3)

(4)

A significant violation of the threat zone will result in a significant increase in the threat component of the cost function. Since this simple zone violation constraint allows many possible solution curves, including ones with unacceptably large length, the second component will simultaneously minimize the curve arc length, thus providing a solution with the best fit possible along the obstacles.

The curve length component of the cost function is computed using a chordal approximation of the total curve length, L. The length is computed relative to the shortest possible path, L0,obtained from a line connecting the endpoints. The scale factor of 10 makes the lowest possible cost 10 with values ranging up toward 50 or 60 for very long paths. Curve length is used as an estimator of fuel consumption. A smaller value means a shorter path that will require less fuel to complete. The curve length component is expressed as follows:

(5)

A third and final component is for reconnaissance, CR. The quality of the data gathered by the UAV on a reconnaissance point depends on the field of view occupied by that object in the UAV’s sensor. The field of view is determined by the distance from the airplane to the target and the angle between the UAV and the target location, as shown in Fig. 5. As the angle becomes larger, the view becomes more oblique and the target occupies a smaller portion of the sensor’s field of view. Similarly, as distance from the target to the UAV increases, the target will become smaller to the sensor. The smaller the distance and angle, the better view the UAV will get of the target.

The cost function determines the distance from a point p(ui) along the curve p(u) to a particular target location LR and is denoted here as d(p, LR). The target zone radius ZR scales this distance. A larger the distance between the closest curve point and the waypoint generates a larger the cost. The angle , in radians is also calculated. A value of zero means the UAV is passing directly over the target. As this angle increases, the cost increases.

The reconnaissance cost function is a local function. Only the best reconnaissance value is chosen for each target because the path needs to pass over the designated areas once to satisfy this requirement. Again, through testing, it was determined by testing that a scale factor of 10

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was needed to achieve the desired order of magnitude for the cost function. The reconnaissance cost is defined as:

Figure 5. Key parameters for reconnaissance cost and their effects

(6)

(7)

(8)

B. Incorporating Terrain Data The terrain used to create and test the Virtual Battlespace environment extends from 114

degrees west longitude and 35 degrees north latitude to 118 degrees west and 38 degrees north. This area encompasses Nellis Air Force Base. The data is DTED level zero elevation data, which means there is a measurement every kilometer. The information is stored in units of meters. Locations are measured and reported with respect to world coordinate system, which has its origin at the center of the loaded terrain in the east-west and north-south directions. Vertically the origin is located at sea level.

The open source terrain engine called Demeter is used to render the elevation data. Demeter is built on top of the Geospatial Data Abstraction Library (GDAL), allowing Demeter to read in the DTED files. The Demeter library contains functions that allow the user to query for the overall dimensions of the terrain, the maximum and minimum values and the height at a specific location for the loaded terrain. Because the position at which the height is requested will

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most likely not align directly with a data point, Demeter uses the surrounding points to interpolate the height value to return. This makes it possible to obtain terrain height information at any surface location within the Virtual Battlespace.

During the optimization process, the PSO algorithm uses the terrain height information to check if the generated paths are safe and to avoid collision with the ground. A safe path is defined as one that maintains a 500-meter minimum height above the terrain. But, the path is still feasible if it does not collide with the terrain.

Every segment endpoint of a generated path is checked. For a specific path point’s latitude and longitude, the corresponding terrain height value, HT, is obtained. This value is subtracted from the height of that path point HP to obtain the separation distance h. If that value is negative, it lies below the terrain boundary and is infeasible. The value of 1000 will instantly make this path a factor of ten times more expensive than a feasible path. If the distance is between 0 meters and 500 meters, the point is below the safe height limit. In this case the cost increases linearly according to the violation from 0 at 500 meters to 10 at ground height. Above 500 meters, there is no penalty.

The paths are not reset if they violate the terrain boundary. The goal is to let the paths explore the design space and come up with solutions that come close to the terrain if those are the best options. It is likely in the exploration process that some paths will move into infeasible territory but the extra cost should then push them back into feasible territory. The cost functions for terrain is defined as:

(9)

(10)

C. Meta-path generation The PSO algorithm is run three times with the weightings described earlier. To better utilize

the information generated by the PSO algorithm, five of the top paths from each of the three PSO runs are made available to the UAV operator.

In order to avoid an overload of visual information to the user, the total of 15 alternate paths are presented as meta-paths. Three meta-paths are created for visualization; one for each group of five paths. As an intermediate step in the decision-making process, the three meta-paths need to present the operator with enough information to make a decision on which set of paths to investigate further. The specific data for individual paths is not needed until the final step. They are designed to preserve the trends of the underlying data in a simplified fashion so the user can quickly evaluate the alternatives. For a detailed description of meta-paths, please refer to previous work published in25.

For each of these selected paths, a relative fitness value is computed. With the path planner returning multiple paths, sub-optimal paths are also presented to the operator. The user needs a measure of how far the solutions are from optimal to make an intelligent selection. Relative fitness is a ratio of the fitness of a given path to the fitness of the best path found through the evolutionary algorithm. This is chosen over presenting the raw fitness values because the ratio

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presents the operator with a standard baseline for what is good when fitness values can vary significantly between test cases.

D. Path Selection The second aspect of path planning is the decision making process performed by the operator.

The operator must select a meta-path, an individual path, and then confirm that selection for the alternate path to replace the current path. It is possible to navigate freely between the individual path mode and meta-path mode so the operator can investigate all 15 possibilities if that is necessary to find a suitable solution. The operator also reserves the ability to quit at any time and use the original path tasked to the UAV.

IV. Implementation of PSO Path Planner into Virtual Battlespace The purpose of an immersive command and control station is to permit the operator to focus

on the overall mission status. As the number of aircraft under an operator’s control increases, it becomes impossible to constantly monitor and manage every aircraft. To facilitate this, an alert subsystem was developed as part of the Virtual Battlespace to alert the operator of any issues. The alert subsystem plays a vital role in reassuring the operator that when UAVs run into situations that require user input, the operator will be made aware of them.

The path planning process begins when a threat is detected by the alert subsystem of Virtual Battlespace, which prompts the controller for a decision on the next action. The controller can either ignore the alert or choose to inspect it. The process ends here and does not execute the path planner if the controller decides to ignore the alert.

The alert subsystem, seen in the right image of Fig. 6, notifies the operator of the presence of an alert and when the operator chooses to examine an alert posted by a threatened UAV, the operator will see a variety of automatically generated path options. These path options will appear at a distance corresponding to a default value of 30 seconds ahead of the UAV’s current position and reengage with the path when in a safe region. The operator can adjust the lead-time. These points on the old path are used as the start and end points of the path planner. All relevant threats, reconnaissance targets, and the start and end points are passed to the path planner to calculate new candidate paths.

Figure 6. Illustration of a path in the Virtual Battlespace environment (left) and a threat alert display (right).

Several distinct scenarios were used to test the developed path planner. Each scenario ran 5 times with no terrain checking and then with the terrain checking. The multiple runs were to gather an average calculation time and For the purpose of this paper the parameter settings used were those in Table 1. However, an operator can adjust these weights if additional paths for

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review are desired. The first alternate path has preference towards reconnaissance locations. This is significant when the importance of a UAV’s current mission or future mission may demand that the UAV stay as close as possible to its original waypoints. The second path is weighted towards threat avoidance, and the last path makes a preference for fuel efficiency (minimal fuel expense for an alternate path). The operator also has the option to vary these parameters to fit the mission objective.

The generated paths are represented in different colors with unique labels for easy identification and inspection, and are represented as follows:

Table 2. Color and label representations of generated alternate paths.Color Label

Reconnaissance Blue AThreat Avoidance Green XFuel Efficiency White Y

A. Simulated Test Scenario #1 The first scenario test is a simple case where there is one enemy fighter plane that is flying

close to the UAV’s original path as can be seen on the left in Fig. 7. The threat is represented as a red sphere as seen on the right in Fig. 7. After running the PSO path planner, the resulting meta-paths were generated and displayed as shown in Fig. 7.

Figure 7. Original path for scenario 1 with an enemy fighter, left, and spherical representation, right.

Fig. 8 shows the paths that were generated from one run of the PSO path planner algorithm that did not take into account terrain information. Five paths are generated for each objective. From top to bottom, the paths are weighted toward reconnaissance, threat avoidance and fuel efficiency. The terrain violations are circled in red in the figure. The paths are attempting to fly underneath the incoming aerial threat. Since terrain information is not considered, the paths violate the terrain boundary to achieve a lower fitness value. In this situation, this behavior is expected, as it would be a shorter route, and therefore a less costly route, to go under the enemy aerial threat than to try and go around or over it. On this particular run, all 15 of the paths violate the terrain boundary.

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Figure 8. Alternate paths generated without terrain information. Areas circled show sections of the paths that violate the terrain boundary.

Fig. 9 shows the same situation with terrain information added to the PSO optimization through the terrain cost component. The same tendency is seen in the paths to want to go under the aerial threat as was seen in the case with no terrain information. Now, the additional terrain cost keeps the paths from violating the terrain boundary. In this case, none of the paths violate the terrain.

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Figure 9. Alternate paths generated with terrain information.

Figure 10 presents a possible resulting path from each case. On the left is a path selected from those generated by a path planner that did not use terrain information. It is clearly infeasible as it is hidden below the terrain. The path on the right was generated with terrain information and follows the same general trend but does not violate the terrain boundary and so remains feasible.

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Figure 10. Updated paths; left without terrain and right with terrain.

B. Simulated Test Scenario #2 The second scenario added an extra element of complexity. There is an aerial threat as before

with an added surface-to-air missile site positioned along the UAV’s path. This is a multiple threat zone problem. Fig. 11 shows this scenario with the UAV approaching the threat location.

Figure 12. Original path with an aerial and ground threat.

As before, paths were generated both with and without accounting for the terrain. Each time, 15 paths were returned in three groups of five for threat avoidance, reconnaissance and fuel efficiency. In Fig. 13, the paths generated without terrain data are presented. Here one of the 15 paths would actually be feasible. All other paths violate the terrain at some point. The terrain violations are noted by red circles in Fig. 13. Among the paths found with terrain information, there were no ground issues, as seen in Fig. 14. The results in this case are very similar to those obtained with test scenario 1.

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Figure 13. Paths generated without using terrain information. Areas circled show sections of the paths that violate the terrain boundary.

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Figure 14. Paths generated with terrain information.

C. Performance Evaluation The figures from the two test cases above demonstrate how adding terrain information to

the cost function is effective in preventing infeasible paths. They also demonstrate that the terrain cost component does not fundamentally alter the type of path that is optimal. In both cases, the optimal paths tend to follow similar trajectories. The terrain information simply moves the cost function minimum from infeasible space below the terrain to feasible space above the terrain.

Using terrain information has a cost associated with it. It takes longer to generate the alternate paths when terrain information is included because for every iteration, path, and path point the algorithm must get the terrain height and compute that component of the cost. Figure 15 helps

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quantify this tradeoff. This same test scenario was run five times. For each run, the time to complete the calculations and the number of infeasible paths were recorded. This was repeated for six different scenarios. Test scenario 1 and 2 in this paper were two of the six scenarios that were used.

Figure 15. Calculation time and infeasible path count averages over 5 tests for 6 scenarios

Figure 15 clearly shows two trends. First, it is clear that adding terrain information to the optimization increases the time significantly. On average, the time increase is between 1 and 3 seconds, which in some of the cases doubles the planning time. This takes away time the operator previously had for selecting a path. But, more path selection time is not beneficial if there are no feasible paths to select. The time variation is largely due to the heuristic nature of the algorithm. If the PSO algorithm finds a good path quickly, it will not need as much time to optimize than if it does not find a good path and has to search longer.

The second trend is the drop in infeasible paths. On average, without terrain information, over half the paths were not feasible. With terrain information, occasionally one of the 15 paths will be infeasible. This happens because the algorithm attempts to return 5 unique paths from one PSO optimization. If it did not find 5 feasible paths that are unique, it could return an infeasible path to the operator. This is not a problem as the operator can simply ignore that path in favor of better ones.

V. ConclusionA three-dimensional path planner was developed to intelligently generate a set of alternate

paths to be selected by an operator of a UAV. Based on the top generated paths for each preference, a meta-path is generated. Meta-paths allow for effective visualization of multiple paths for decision making purposes. Using terrain information embedded in the Virtual Battlespace, the paths generated are feasible and safe from terrain interference. From the test cases using different simulated scenarios, the three-dimensional PSO path planner successfully generated alternate paths satisfying its respective objective as set in the component weight parameters. The three objectives to either maintain as much of the original path as possible for reconnaissance purposes, to ensure maximum safety, or to maintain maximum fuel efficiency

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were successfully satisfied. Most importantly, these paths were generated in real time to allow for efficient decision making by the UAV controller. The option of selecting a particular path from a set of solutions ensures that the human factor is still part of the decision making process. With multiple views to evaluate the generated alternated paths allows the operator to make informed decisions based on the current mission objective.

VI. Future Work Work continues to progress on this path planner. Currently a user study is being done to

evaluate its effectiveness. The study is designed to help answer two different questions. The first question is whether the operator is better able to understand the alternate paths in 2D or in 3D. Second is how effective the algorithm is at aiding a novice operator in the choice of an optimal alternative path.

A second area of work is to better inform the user of the tradeoffs between the alternate paths. Each path has a cost for fuel efficiency, reconnaissance, and threat avoidance. When a path is selected, these values will be displayed in graphical form. As the operator highlights different paths, the values will update accordingly to reflect performance in each area.

AcknowledgmentsThis research was supported by the Air Force Office of Special Research Labs.

References

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