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Multi-Objective UAV Path Planning with Refined Reconnaissance and Threat Formulations
Levi Swartzentruber 1, Jung Leng Foo2, and Eliot H. Winer3
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 aircraft or enemy threats. Often automated path planning algorithms are employed to specify targets for a UAV to investigate. To date, path-planning algorithms have been limited to providing only a single solution (alternate path) without further input from a pilot. This paper improves upon a previously developed multi-objective path planner that uses Particle Swarm Optimization (PSO) to generate multiple solution paths based on predefined criteria. The original path planner consisted of 4 components: fuel efficiency, reconnaissance, threat avoidance, and terrain. In this paper, the focus will be on improvements made to the formulations of the cost functions for reconnaissance and threat avoidance as well as the ability of the pilot to adjust the weights for the mission objectives. The alternate paths can be optimized with a preference towards maximum safety, minimum fuel consumption, or target reconnaissance. The weight adjustment techniques presented enhance the pilot’s ability to find desirable solutions when re-tasking the UAV. Most importantly, the paths were generated in real time to allow efficient decision making by the UAV pilot. These improvements were noted in the simulated test scenarios used to evaluate the path planner.
I. Introduction ilitary 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 i. The complexity in UAV technology is growing rapidly, and according to the Department of Defense Unmanned Systems Roadmap 2007-2032 ii, by the year 2030 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 pilot’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 supervisor, as the level of interaction with UAVs moves is increasingly abstracted. As humans interface with UAVs at higher levels, a UAV will be trusted to do more iii
To address the many research issues involved in command and control that the DOD roadmap requires, a “Virtual Battlespace” at Iowa State University was created. In this paper, research
. 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 a pilot with situational awareness and quality information at a glance.
1 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. 2 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. 3 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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51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR> 18th12 - 15 April 2010, Orlando, Florida
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into the issue of three-dimensional (3D) path planning for UAVs is presented as part of the Virtual Battlespace project. The method described allows a human pilot 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 four main components: 1) avoiding obstacles such as threats (e.g., surface to air missile sites, tanks, and aircraft), 2) maintaining a fuel-efficient path to maximize mission range, 3) minimizing deviation from the original way-points for reconnaissance purposes, and 4) avoiding collisions with the terrain.
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, utilizing a Particle Swarm Optimization algorithm. The resulting paths generated from the planner for multiple simulated scenarios are then presented, with conclusions and future work discussed at the end.
II. Background
A. Path Planning for UAVs Path planning continues to be an extensively researched topic with much of the effort focused
on UAVs, as this is a complex problem. A representative selection of these path planners will be mentioned in this section. Some algorithms simplify the problem by limiting the vehicle to maneuver only in two-dimensional space iv. Recently, many researchers have realized the limitations of this method and have begun to implement three-dimensional path planners v,vi
Offline path planners tend to be the most sophisticated, attempting to use information about the mission objectives, enemy locations, and the environment in the computations. They also include better models of the vehicle’s dynamics to ensure path feasibility
. With the increased flexibility come new challenges in computation and visualization.
vii,viii. Yet, these methods are too slow to deal with in-flight situations where a UAV needs to be re-tasked in real time. Online path planners are designed to deal with this problem. Some update a portion of the original path that is no longer desirable ix while others continuously extend the UAV’s path in short increments x. A variety of objectives and mathematical models are included in these path planners. For example, one is designed only to minimize aircraft radar cross section xi and another considers four objectives: path length, terrain avoidance, minimum and maximum altitude, and minimum radius of curvature for the path xii
The use of terrain data in path planners has grown as more high quality data becomes available. Sinopoli et al. have developed a vision based path planner that uses a coarse terrain representation for global planning and a refined grid for local evaluation to allow the UAV to fly close to the terrain while avoiding obstacles
.
xiii. Another path planner seeks to optimize the competing goals of minimizing path length and maximizing safety, considering terrain and ground obstacles xiv
Very few algorithms have been designed for pilot input in the decision making process. One algorithm incorporating multiple paths was designed for dynamic environments using cluster analysis
.
xv
. Most path planners simply take the best solution from the optimization algorithm and implement it, neglecting the possibility that differences between the model and the real world may make that path undesirable to the pilot.
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B. Particle Swarm Optimization (PSO) Particle Swarm Optimization is used xvi for the optimization of the generated alternate paths.
An evolutionary optimization algorithm is well suited to handle a multi-modal optimization problem such as this. PSO was also selected because of its simplicity in implementation due to fewer user-defined parameters (as opposed to algorithms such as the Genetic Algorithm) and its ability to handle non-linear problems of high dimensionality. Statistical analysis has shown that while both PSO and GA attain high quality solutions on a wide variety of multi-modal unconstrained problems, PSO is more computationally efficient xvii
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.
. To maintain human input in the decision making process, several paths are generated by this algorithm. The generated alternate paths are represented by B-Spline curves to minimize computation, since a simple curve can easily be defined by as few as three control points.
C. Previous Work Development of the Virtual Battlespace began in 2000. It 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 xviii,xix
. This system is comprised of set of tools developed to enhance the user experience: 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
The original path planner consisted of 4 components: fuel efficiency, reconnaissance, threat avoidance, and terrain. Details of this implementation are presented in xx
III. Methodology
. In this paper, the focus will be on improvements made to the formulations of the cost functions for reconnaissance and threat avoidance as well as the pilot’s ability to adjust the weights for the mission objectives.
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
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means to solve path-planning problems. However, there is still need 1) to improve the formulation of the optimization problem to better match the reality of the UAV’s situation, and 2) to allow the pilot to participate in the path planning process. These are the issues that this paper will address. The path planning process begins when a UAV detects an unexpected situation and alerts the pilot. If the pilot chooses to investigate, the section of the current path that must be re-planned is found. Any intermediate waypoints from the original path are mapped as reconnaissance targets ZR with reconnaissance zones of radius RR around them. Enemy entities are singled out and a 3D threat zone ZT is generated for each of them (of radius RT). Threat zones are also generated for friendly entities to avoid collision, but with a smaller radius.
Formulation of the optimization cost function begins with the description of a B-spline curve
to represent the path of the UAV. Consider the blue B-spline curve p0(ui), where ui is a sequence of line segments forming the curve. The B-spline path requires re-planning when it violates a threat zone ZT, shown in Fig. 2. A resulting alternate path p(ui) is generated that avoids the threat zone while still attempting to be within the reconnaissance zones, as illustrated by the red curve in Fig. 2.
The initial solution to begin the optimization process is the original path. A new path is computed by running the PSO algorithm, using the cost function to evaluate the fitness of a given solution. To calculate the cost, a path is broken into a user-defined number of segments p(ui). The component cost is found for each segment and summed to generate the total cost for a path. The total cost function accommodates the preferences of threat avoidance, reconnaissance, and fuel efficiency of the alternate paths:
(1)
Where, CF reflects the cost incurred from excessive arc length, CR is the cost incurred by deviating from the reconnaissance locations, and CS is the cost due to proximity of enemy entities and violation of the threat zones. The last term, T, is a cost component for flying too close to the terrain or completely underneath the terrain.
The constants KF, KR, and KS, in Eq. (1), are component weights that determine the relative emphasis of the various cost components with respect to the overall cost function and sum to 1.0. Table 1 shows an example of generating a set of three different alternate paths, each with its own
p0(u)
p(u) ZR
ZT
Figure 2. Two-dimensional illustration of a simple threat zone avoidance problem
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preference. The terrain component T has no weight factor because it needs to be present to ensure that feasible paths are generated.
Table 1. Example of component weights used to generate a set of alternate paths.
All of the updated cost components are formulated to generate values of the same order of magnitude, with a few exceptions for extreme cases. This was necessary first to ensure the desired behavior of the weights and second to allow the terrain component to work properly. First, without this scaling, it could easily happen that one component would be orders of magnitude larger than another so that even if fuel efficiency was ten times as important to the operator, threat avoidance would still be driving the solution. This is clearly not desirable. Second, knowing the range of cost values for feasible paths, the terrain cost can be formulated so that infeasible paths are more expensive than any feasible path and dangerous paths are relatively expensive but are not immediately prohibited from being selected as good alternatives.
A. Fuel Efficiency Cost Component Because vehicle dynamics are not incorporated into this path planner, the fuel efficiency cost
component CF is dependent only on path length. The value of CF was modeled as the ratio of the length of the alternate path L over the shortest path possible, L0. With this formulation, the cost increases linearly with length:
(2)
B. Reconnaissance Cost Component The second objective is reconnaissance. Two assumptions are made to formulate this cost
function.
Figure 8. Key parameters for reconnaissance cost and their effects on a UAV’s view of a target
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First, it is assumed that the waypoint locations (reconnaissance targets) are the optimal locations from which to view the respective targets. The optimal viewing position is directly above the target (small angle) and as close as possible to the target (small distance). Any deviation from that location in distance or angle will degrade the quality of the data the UAV gathers, as illustrated in Fig. 8.
The second assumption is that the longer a UAV stays over a target the more desirable that path is to the pilot. As long as the UAV is within a user-defined distance of the target it can gather information on that target and the more information it can gather the more successful the reconnaissance mission will be.
From these assumptions there are three necessary components to the reconnaissance cost function: distance, angle, and time-over-target. Each reconnaissance target ZR is handled in turn according to:
(3)
(4)
(5)
(6)
For a specific reconnaissance target, ZR,j, only the cost of the best point along the curve is kept:
(7) In parallel with the distance and angle calculations, the cost for time-over-target is computed.
For each segment p(ui) the distance to the target is calculated. If that distance is less than RR, the length of that segment Li is added to the total length of the path that is considered close to the target Lj. The cost is then the fraction of the diameter of the reconnaissance zone that the UAV does not traverse:
(8)
(9)
To determine the total reconnaissance cost, the values for each of the NR reconnaissance
targets are averaged:
(10)
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C. Threat Avoidance Cost Component Avoiding threat zones (and thus preventing the loss of the UAV) is the third objective of the
path planner. Each threat location ZS has a spherical (hemispherical for ground vehicles) threat dome around it of radius RS.
As with reconnaissance, the threat avoidance cost is calculated for each threat in turn. A distinction is made between the calculations for stationary ground targets and moving threats (usually aerial threats). For stationary threats, the location ZS and the threat zone radius RS are constant. For moving targets, the last known position ZS,0 and velocity VS,0 of the threat are used in the calculations. The time ti it takes the UAV to reach path segment p(ui) is known and so the threat can be advanced using dead reckoning as follows:
(11) The dead reckoning formulation assumes the threat’s velocity does not change. To account for
the decreasing certainty of where the threat might be as time progresses, the radius of the threat zone for a moving threat RS,i is increased as the UAV progresses along the path:
(12)
For each path segment p(ui) the 3D distance to the threat is found. Outside the threat dome,
the UAV is considered safe. Inside the dome, the cost increases non-linearly as the UAV approaches the threat location:
(13)
(14)
A second threat avoidance cost component is included that depends on the length of time the
UAV is exposed to the threat:
(15)
(16) For a given threat, the costs for proximity to exposure time are summed. The total threat
avoidance cost CS is then found as:
(17)
(18)
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D. Terrain Collision Avoidance Component The goal of this component was to prevent infeasible paths from being returned to the pilot.
During the optimization process, the terrain height information is used to check if the alternate paths are feasible and safe. A feasible path does not violate the terrain boundary while a safe path is one that stays a user-specified distance above the terrain. This cost can be modified by adjusting the user-defined parameters that set the cost and the minimum safe height for the UAV in the following equations:
(19)
(20)
E. Weight Adjustment Two methods were explored to allow the pilot to interact with the weights and change the
paths that are displayed (in real time). The first method allows the pilot to adjust the component weights and re-run the PSO algorithm. In this framework, when a path planning alert comes up, the pilot is given the ability to set the weights for the algorithm and then optimize (using those weights). To allow this type of interaction, the PSO algorithm was modified slightly to operate more quickly: a single PSO optimization is performed (instead of three) and the swarm size is decreased.
The second interaction method for decision-making involves a post-analysis of the paths generated by the PSO algorithm. PSO operates as in the other cases, optimizing once each for fuel efficiency, reconnaissance, and threat avoidance. The weights used in optimization are not adjusted by the pilot. Following optimization, all unique paths (with their un-weighted component costs) are stored. A set of three adjustable bars (one for each objective) is presented to the pilot for weight adjustment. The top paths, according to those weights are displayed to the pilot. The pilot can continue to tweak the weights until a desired set of paths is presented. It is important to note that the optimization algorithm runs only once in this case, so as the pilot adjusts the weights the paths displayed are no longer optimal.
IV. Results Several distinct scenarios were used to test the developed path planner. Each scenario was run
five times, with the weights given in Table 1. The first set of paths are weighted for fuel efficiency (white paths), the second set for reconnaissance (blue paths), and the third set for threat avoidance (green paths). Table 2 gives a description of the four test scenarios that were used.
Table 2. Description of scenarios used in testing
Scenario Description
1 One ground threat (simplest possible case) 2 One aerial threat 3 One ground and one aerial threat 4 Two ground and one aerial threat with distinct threat zones
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A. Simulated Test Scenario #4 As a representative case, the fourth scenario is presented. It is a complicated situation
involving two stationary ground threats and an aerial threat flying across its path, as shown in Fig. 4.
Figure 4. Test scenario four with one aerial threat and two distinct ground threats
Each of the path sets (one for fuel efficiency, reconnaissance, and threat avoidance) generated
by the path planner using the final formulation of the cost function will be presented and discussed. First, the fuel efficiency paths are shown in Fig. 5.
Figure 5. Top-down and side views of the fuel efficiency paths with the best path highlighted
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The red arrow in the top-down view indicates the direction of movement of the aerial threat. The thick line is drawn over the optimal path for clarity. As expected, all of these paths take a relatively direct route between the start and end points of the re-planned path segment to minimize path length. It is important to note that the aerial threat is moving up and slightly left in the top-down view of Fig. 5. Thus, it is already well beyond the UAV path before the UAV travels through that area. The UAV weaves between the other two threats to minimize its threat exposure. While the path is good for reconnaissance and fuel efficiency, it does poorly in threat avoidance, traveling quite close to the SAM sites.
The reconnaissance paths are presented in Fig. 6. These paths are significantly longer and deviate more from the original path than the fuel efficiency ones in an attempt to avoid the threat zones. This is due to the decreased emphasis on the length of the path. When the reconnaissance cost is more heavily weighted the UAV will incur larger threat zone violations to pass close to the bends in the yellow fence (the reconnaissance targets) to maximize data gathering potential.
Figure 6. Top-down and side views of the five reconnaissance paths with the best path highlighted
The threat avoidance paths shown in Fig. 7 are the most widely varied since both fuel
consumption and reconnaissance are significantly less important than avoiding the threat locations. All of the alternate paths go to the right of the original path (from the perspective of the UAV). This is expected behavior because the enemy fighter will be flying to the left of the original path if its course does not change. Figure 8 shows the paths that are generated when the movement of the aerial threat is not taken into account. All of these threat avoidance paths go left of the original path, which is a problem because that will bring the UAV into close proximity with the enemy fighter.
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Figure 7. Top-down and side views of the five threat avoidance paths with the best path highlighted
Figure 8. Top-down view of the five threat avoidance paths generated without considering aerial threat movement
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B. Performance Evaluation The figures from the test case above demonstrate how the updated cost function
formulation produces desirable alternate paths. For the algorithm to be a useful tool, the paths must also be generated quickly. Calculation time is the most important measure in evaluating the ability of this path planner to re-task the UAV in real time. The total time the pilot has to re-task the UAV (set to 30 seconds) includes the time required by PSO to generate the alternate paths. The less time the algorithm takes calculating solutions, the longer the pilot has to evaluate the alternatives and implement one of them.
All the tests were run on a computer with a dual core Intel Xeon 3.2GHz processor. As mentioned earlier, each scenario was run five times and the calculation times were averaged to account for the evolutionary nature of the PSO algorithm, which solves the problem differently each time it is run. Fig. 9 presents a graph of the calculation times (in seconds) for the cost functions for each scenario. The last bar on the right is the average of the other four bars. The final formulation takes on average 3.1 seconds to generate the alternate path choices for a given scenario, though the longest time for any individual run was 8 seconds. This still leaves the operator with time to select from the alternate paths and implement the solution.
Figure 9. Graph of calculation times for the cost functions for each test scenario
V. Conclusion A three-dimensional path planner was developed to intelligently generate a set of alternate
paths to be selected by the pilot of a UAV. Several modifications were made to improve the performance of the PSO path planning algorithm developed for the Virtual Battlespace. The improved version of the PSO algorithm incorporates more accurate models for the reconnaissance and threat avoidance objectives and scales all the component costs to improve the correlation between the weights and the generated alternate paths. The improvements were noted in the sample scenarios. Most importantly, the paths were generated in real time to allow for efficient decision making by the UAV pilot. 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. The weight adjustment techniques presented enhance the pilot’s ability to find desirable solutions when re-tasking the UAV.
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VI. Future Work Work continues to progress on this path planner. Currently work is being done to incorporate
digital pheromones into the Particle Swarm Optimization algorithm used to generate the alternate paths. A second area of work is to add dynamics to the model of the UAV to ensure the vehicle is able to traverse the alternate path. A third area of work is to add line-of-sight calculations to the reconnaissance cost. Obstructions of the UAV’s view of the target created by mountains or man-made obstacles are not accounted for in the present model.
VII. Acknowledgments This research was supported by the Air Force Office of Special Research Labs.
VIII. References
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vii Sanders, G. and Ray, T., “Optimal offline path planning of a fixed wing unmanned aerial vehicle (UAV) using an evolutionary algorithm,” IEEE Congress on Evolutionary Computation, pp. 4410-4416, September 2007.
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xv Hocaoglu, C., and Sanderson, A.C., “Planning Multiple Paths with Evolutionary Speciation,” IEEE Transaction on Evolutionary Computation, pp. 169-191, June 2001.
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xvii Hassan, R., Cohanim, B., de Weck, O., and Venter, G., “A Comparison of Particle Swarm Optimization and
the Genetic Algorithm,” in the Proceedings of 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 18-21 April 2005, Austin Texas, AIAA 2005-1897.
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