Fast on-ship route planning using improved sparse A-star algorithm for ...

Fast on-ship route planning using improved sparse A-star algorithm for UAVs Xin Yanga, Mingyue Dingb, a, Chengping Zhou*, a, Chao Caia, Qi Yua, Shuai Shaoa a

Institute for Pattern Recognition and Artificial Intelligence, State Key Laboratory for Multi-spectral Information Processing Technologies, Huazhong University of Science and Technology, Wuhan 430074, China b College of Life Science and Technology, “Image Processing and Intelligence Control” Key Laboratory of Education Ministry of China, Huazhong University of Science and Technology, Wuhan 430074, China ABSTRACT

This paper presented improved Sparse A-Star Search (SAS) algorithm to pursue a fast route planner for Unmanned Aerial Vehicles (UAVs) on-ship applications. Our approach can quickly produce 3-D trajectories composed by a set of successive navigation points from certain known initial locations to predetermined target locations. The result routes are not only ensuring collision avoidance with the environmental obstacles, but also satisfying specific routes constraints and objectives. The experiment results demonstrated the feasibility of the method, which makes our route planner be more useful in real systems.

Keywords: Sparse A-Star Search (SAS); route planning; Unmanned Aerial Vehicle (UAV); marine; on-ship.

1.

INTRODUCTION

Route planning is to generate an optimal or near-optimal trajectory from an initial location to the desired destination.[1] The planner of Unmanned Air Vehicles (UAVs) should not only find out the way avoiding forbidden and threat areas, but also accomplish searching within limited time by making usage of geographical situation, information of enemy and comprehensively regarding certain kinds of constraints such as UAV navigation precision and physical limitations.[2] This is a non-robust and high-dimension problem which needs a large amount of transmission of information, collection of each UAV’s information of flight state, function constraints, threats and targets by similar formation planners for a large-scale optimization so as it can create a trajectory which meets all constraints of aircrafts and send back to each of them.[3] Regarding above difficulties, planning time is so important that dominates the key to victory in a defeat. This paper improves Sparse A-Star Search (SAS) algorithm to pursue a fast route planner for UAVs on ship applications. Considering UAVs started from different initial locations, 3-D trajectories are designed to be composed of a series of way-points. One of the fundamental task characteristics is to perform the route planning, which can avoid collisions with obstacles, keep distance to local hazards and as well as meet the motions requirements in the planning region. Planning time is limited within minutes for a single route and less than half-hour for a group of routes in one attack in our demand. This paper is organized as follows. Section 2 introduces the improvements of Sparse A* Search algorithm. Section 3 shows experimental results. Conclusions and future work are discussed in Section 4. * [email protected]; +862787544512(o). MIPPR 2009: Medical Imaging, Parallel Processing of Images, and Optimization Techniques, edited by Jianguo Liu, Kunio Doi, Aaron Fenster, S. C. Chan, Proc. of SPIE Vol. 7497, 749705 © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.833330 Proc. of SPIE Vol. 7497 749705-1

2.

IMPROVEMENTS OF SPARSE A* SEARCH ALGORITHM

This paper improved the well-known Sparse A-Star Search (SAS) algorithm in order to develop a fast route planning method for UAVs on ship application. SAS is one of the most often used deterministic method extended from the A-Star Search (A*) algorithm. The improvements to the SAS (Improved-SAS, I-SAS) are represented in the four aspects: 1) pre-processing; 2) routes searching; 3) cost-functions design and 4) re-planning ability. 2.1 Pre-processing Pre-processing is vital to the route planner, because of a large number of preliminary work have to be done. At the beginning, islands in the marine environment are classified into two categories: available fly-zone, unavailable fly-zone. The classification is based on islands altitude and UAVs’ mobility. The heights and acreages of islands have to be considered in this case, because the climb-up, dive-down abilities and detouring areas are the rigid constraint for most of UAVs. The height of an available fly-zone is the tiptop height on the island. Then, manually set the static known forbid-zones and threat-zones in the environment strictly. Here forbid-zone is defined as the area is prohibited go through, while threat-zone is defined as the area is could go through but would reducing the UAV surviving probability. Furthermore, the longer over the threat-zone or closer to the center, the smaller of the probability of survival is. Sequentially fit all the available fly-zones, unavailable fly-zones, forbid-zones and threat-zones with ellipses, which could be rotated for fitting the zones most properly. All these kinds of zones may have intersection and the rest area of planning region without masked by the ellipses is default as free-fly-zone. Finally, clip the planning space with purpose of decreasing the planning region. Some areas are impossible for the candidate routes, such as forbidden areas like rocks, firepower, armadas, or bad weather regions and out of the maximal voyage, etc. Those regions should be eliminated from the planning space. 2.2 Routes Searching The speed up of routes searching needs to pay more attention at this step. The Sparse A* Search (SAS) technique is a novel variation of the standard heuristic searching algorithm A* (pronounced as “A star”) which is used extremely extensively in route planning and graph searching applications. Equation (2-1) is the cost function that is minimized at X

X

each step of the A* propagation.

f ( x ) = g ( x ) + h( x)

(2-1)

In Equation (2-1) , the term g ( x ) is the real cost from the start position to intermediate position x . The term h( x ) is X

X

the estimated cost from the intermediate position x to goal position. At each step in the A* propagation, the lowest f ( x ) value is selected and inserted into a sorted list of possible paths (in Open List). It has been proven that if the actual cost from x to the goal is larger than or equal to the estimate ( h( x ) ) of this cost, then the solution produced by A* is guaranteed to be a minimum cost solution. [4] Details comparison between A* and SAS were presented in [5] and a brief overview of SAS in general was presented here. To overcome the defects of A*, such as the A* algorithm may take a very long time (exponential in nature) and use an unbounded amount of memory to converge to an optimal solution, SAS introduce the following four characteristics:

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1) minimum route leg length; 2) maximum turning angle; 3) route distance constraint; and 4) fixed approach vector to goal position. Though SAS approach accurately and efficiently “prunes” the search space to allow the generation of an acceptable solution that converges in real-time, a true SAS approach will not work due to the time constraint imposed for real-time planning systems especially on the vast expanse of the sea. This paper also based on incorporated various route constraints into the SAS approach to improve the algorithm for applicable to the special on-ship applications. The next several subsections outline how the improvements can be made into the SAS approach. 2.2.1 Dynamic Route leg-length and Dynamic turning-angle Note that, for some applications, the minimum leg length and maximum turning angle can vary during the route. For example, a shorter leg length, a smaller turning angle may be allowed at the end of a mission than at the start to ensure the accuracy in the attacks. Our Improved Spares A* Search (I-SAS) as shown in Fig.1, dynamically determines the minimum leg length and the maximum turning angle according to the flight time and the UAV location. This way allows for the consideration since each fan-tail may be of a unique size and shape during the search process.

Fig.1 Snapshot of I-SAS with dynamic route leg-length and

Fig.2 Sampling-based navigation node expanding with different kinds

dynamic turning-angle

of zones

2.2.2 Sampling-based Navigation Node Expanding Sampling the segment route between two nodes along certain sample-distance within the 2-D environments as shown in Fig.2 , the route planner judges whether the piece of the route goes through forbidden, threat and flyable zone or not. If any of the sampling-points was in a forbidden zone, the node will be abandoned without expanding; if the segment of route went through the threat-zone, an extra cost would be made up for the expanding node and if it went through the available fly-zone, height plan would be necessary for climbing up or round over the island. We reverse sampling along the opposite direction, from the expanding node to the current node on the segment route. There is a trick for the quick judgment to avoid too much computing time. 2.3 Cost Function Design Cost function plays an important role in the step. Therefore, more reasonable cost function is, the better the results are. The original heuristic function listed in Equation (2-1) is modified here. X

X

2.3.1 Design Cost of Flight Route The cost function of flight route is defined as follows: n

C = ∑ ( w1li 2 + w2 hi 2 + w3 fTAi + w4 f FAi + w5 f Angle _ S + w6 f Angle _ T + w7 f Angle _ Oi + w8 f other ) i =1

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(2-2)

where li is the length of the i th segment which penalizes the length of the route to prevent the aircraft from wandering too far away from the line connecting the start and target points, hi is the average altitude above the sea level of the i th route segment which minimizes the aircraft’s altitude and causes the algorithm to seek a lower altitude penetration

route enhancing the terrain masking effect (over the islands), and penalizes penetration routes that come dangerously close to “known” ground threat sites. In our situation, fTA in Equation (2-2) is expressed as follows: [6] X

X

fTA =

N Site

Kj

j =1

Sj

∑ (R

)4

(2-3)

where K j is a scale which reflects the danger of the j th known threat, RSj is the aircraft’s slant range to the threat site, and N Site is the number of distinct threat sites. For the threat sites whose locations are not precisely perceived, we assume that they are uniformly distributed in the penetration area. f FA in Equation (2-2) is heuristic function reducing the times of blind-searching and keeping the distance to hazards as X

X

far as possible. f Angle _ S in Equation (2-2) is the cost of launch direction: X

X

f Angle _ S = K s × fabs( Angle _ S − Angle _ ST )

(2-4)

where K s is a scale factor, Angle _ S is required launch angle, Angle _ ST is the link angle between launching point and target. Similarly, f Angle _ T in Equation (2-2) is the cost of attack direction: X

X

f Angle _ T = K t × fabs ( Angle _ T − Angle _ ST )

(2-5)

where K t is a scale factor too, Angle _ T is required attack angle, Angle _ ST is the link angle between launching point and target. In the progress of expanding and searching, the expending node has its own flying angle, so f Angle _ O in Equation (2-2) X

X

is the flying angle cost of each expanding node: f Angle _ O = K o × fabs ( Angle _ O − Angle _ OT )

(2-6)

where K o is a scale factor, Angle _ O is angle of building track from previous node to the current node which is also the fly-direction of the current node, Angle _ OT is the link angle between current node and target. Finally, f other in Equation (2-2) is the rest of costs like the launch angle with big difference comparing with the attack X

X

angle. All the weighting coefficients wi (i = 1, 2, ⋅⋅⋅,8) control the effects of flying over terrain obstacles, threat and forbidden zones, and flying around them with enactment angle on the cost function. 2.3.2 Searching Process

Our algorithm characterization is composed of the following steps:

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• Step1: Compare current point with target. If they were the same, the algorithm is terminated; otherwise go to Step2. • Step2: Expand nodes from current point. Create a fan-tail of 2 times the maximum turning angle from the current position, because an aircraft can turn right or left not more than the maximum turning angle. The length of the fan-tail is of minimum leg length. • Step3: Calculate the cost of each expanded points within the fan shaped area. • Step4: Sort the expanded points by the cost ranked from smallest to biggest, update the current point to be the minimum cost point, and then go to Step1. Note that, at the very beginning the current point is the start point. We speeded up the whole search circle process from the four basic modules of the program, 1) Comparison, 2) Expanding, 3) Calculating, and 4) Sorting. The comparison would be more effective because of the introduction of the depth information of the expanding nodes. Expanding would be more quickly as it is described in Section 2.2. Compute the cost based on the modified cost-function listed in Equation (2-2) . All the nodes of the I-SAS search space are sorted and stored in a min-heap data structure.

X

X

2.4 Re-planning

Re-planning ability for pop-up threats is vital for the planner especially in the real-system. In order to cope with variation of the planning region, I-SAS algorithm has to be aware of pop-up threats, such as weather diversification and undiscovered fleets. The updated information could be added to the current environment easily as soon as possible and we cannot use the same loop as before to check for the path being completed. As soon as it receiving the latest battle threat information, which could be added manually by commander in the simulation, the route planner adjusts the weighting coefficients as a response. Then the cost would be modified, and then the route would be bending over the new threat ultimately. In this sudden situation, the prior optimal objective should shift from route distance to UAV survival ability. Therefore, increasing in threat-cost and reducing distance-cost in relative would achieve the goal of re-planning for avoiding pop-up threats.

3.

EXPERIMENTAL RESULTS

3.1 Experiment Environment

The I-SAS route planning algorithm was implemented in a Visual C++ 6.0 programming environment, together with Qt 4.2 version, on a Pentium IV PC with 2 Duo CPU E7200 @ 2.53GHz, under Windows XP. No commercial EA tools were used. The experiments were conducted using a real DTED with a resolution of 100m by 100m and different sets of synthetic forbidden and threat data were tested. In all experiments, the same set of parameter values shown below was used. • Real planning region is limited from [1220 E, 1330 E] to [190 N, 300 N], which is 1620km square kilometers with marine environment as shown in Fig.3. • Forbidden zones, threat zones, available fly-zones and unavailable fly-zones are fitted with eclipses as shown in Fig.4 and represented as different shapes and colors in Fig.5. All the zones are stored as vector graph.

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• The maximum voyage is 2.5 times the length of the straight-line distance between the start and goal locations. • If there is not additional explanation, the weighting coefficients wi (i = 1, 2, ⋅⋅⋅,8) in the cost function are all equal to 1.0. • The angle is defined as: coming into the point heading north corresponds to an approach angle of 0 degree; heading east is an approach angle of 90 degree, etc. All simulations are terminated after reaching the target.

Fig.3 Real planning region with marine

Fig.4 Representing different kinds of “zones ” by

Fig.5 Different shapes and

environment

fitting ellipses

colors to distinguish the zones

3.2 Route Planning for a Single UAV

The I-SAS algorithm was implemented and four representative examples of the single route produced are shown in Figs.6, 7, 8, and 9. Real world elevation and feature data were used from the planning region. Each of these routes consists of launching point and target location, in an area populated by forbidden-zones, high-lethality threat zones and flyable-zones. The resultant flyable routes are indicated by the orange trajectories. The launching and target locations are represented by flags at the starts and filled triangles at the endpoints of the routes. The six large ellipses with diagonal lines pattern represent areas of perceived threats and there will be some pop-up threats later. Each of the smaller dots on the trajectories indicates locations in the route where a UAV would have to adjust track. The locations are these kinds of navigation nodes, like turn points, lead points or GPS points. In Fig.6, both the SAS and I-SAS algorithms planned the route with the same conditions. The result is shown in Table 1.

(a) the route implement by SAS

(b) the route implement by I-SAS

Fig.6 SAS vs. I-SAS when the route going through the threat-zone

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Table 1 Result of planning route by SAS vs. I-SAS in the same conditions

SAS I-SAS

Line Distance

Actual Distance

Sum of the Points

Planning Time

km

km

unit

second

664.29

104

10

688.35

186

8

650

In Figure7, the I-SAS algorithm was allowed to plan a 3-D route going over a series of islands under the conditions of UAV motion ability. Note that the route climbed up and down in order to follow the islands terrain, but still remained a certain safety distance to the earth.

(a) vertical view

(b) profile view

Fig.7 A 3-D route going over the island implemented by I-SAS

In Figure 8, the adjustments of the weighting coefficients could obviously affect the routes.

(a) w1 = w2 = 1.0

(b), w1 = 1.6; w2 = 0.4 , others wi = 1.0

Fig.8 Different weighting coefficients impacting on the route

In Fig.9, the UAV requested a route with a pop-up threat to do re-planning. Once detect a new pop-up threat; update the battlefield environment immediately; change the weighting coefficients w1 , w2 to adjust the cost and re-plan the route quickly. Note that pop-up threat means that the original route is facing high visibility probability, since the enemies may have prepared to retort at once. So let the re-planned route keep away with new threat, even having longer distance, is worth of increasing the UAV survival ability. The computation time for each of the demonstration routes was well under a couple of minutes. 3.3 Route Planning for Multiple UAVs

A group of UAVs assaulting at the same time is much more powerful than the single one in one attack. Therefore, we

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researched on the route planning for multiple UAVs based on the former studies. Three different 3-D routes are obtained as a group at the same time as shown in Fig.10. Routes have considered avoiding collisions to each other in the group. The actual computation times and some more details about the performance are considered proprietary information. Unfortunately they are not able to be presented in the paper. More detailed information or parameters can be obtained directly through the corresponding author.

(a) original route, w1 = w2 = 1.0

(b) a pop-up threat appear on the route, w1 = 0.5; w2 = 1.5

Fig.9 A pop-up threat effect the result route: first update information, then

Fig.10 Route planning for multiple UAVs in a

change the weighting coefficients, and then modify the cost

group by I-SAS

4.

CONCLUSION

This paper presented improved Sparse A* to pursue a fast route planning method for UAVs on ship applications. Preliminary experiments demonstrated our method is feasible and faster than the SAS, which makes our planner be more useful in real systems. An important further issue is how to connect the on-land planning and on-ship planning together. The processing in the boundary of the earth and sea, like the continental shelf area, is a big challenge for finding routes for UAVs.

REFERENCES [1] Changwan Min, Jiangpin Yuan. “Summarization of warplane route planning”, Flight Dynamo. 16(4), December, (1998). [2] Shaomei Song, “Research of cooperative route planning algorithm for Unmanned Air Vehicles”, [Master Thesis]. Xian: Northwestern Technical University, (2003). [3] Mehdi Alighanbari, Yoshiaki Kuwata. “Coordination and Control of Multiple UAVs with Timing Constraints and Loitering”, Proc. of the American Control Conference Denver, Colorado June 4-6, (2003). [4] Hart, P., Nilsson, N., and Raphael, B. “A formal basis for the heuristic determination of minimum cost paths”, IEEE Transactions of Systems Science and Cybernetics, 4, 2, 100-107 (1968). [5] Szczerba Robert J, “Robust Algorithm for Real-Time Route Planning”, IEEE Transactions on Aerospace and Electronic Systems. 36(3), 869-878 (2000). [6] Changwen Zheng, Lei Li, Fangjiang Xu, Fuchun Sun. “Evolutionary Route Planner for Unmanned Air Vehicles”, IEEE Transactions on robotics. 21(4), 609-620 (2005).

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