Improved Heuristic and Evolutionary Methods for Tactical Missile Mission Planning

Transcription

1 Improved Heuristic and Evolutionary Methods for Tactical Missile Mission Planning Çağatay Tanıl Engineering Development Directorate, Tactical Systems Roketsan Missile Industries Inc., Ankara, Turkey Abstract In this paper, improved heuristic and evolutionary methods are presented for pre-launch trajectory optimization of a tactical missile. Computation time and trajectory length are minimized as objectives whereas maneuverability of the missile, total amount of fuel, obstacles, no-fly zones, islands, shorelines are considered to be constraints. There are two main methods developed for this purpose. One method is based on heuristic search by adaptive-based A * algorithm. In this method, sub-optimal path is obtained by constructing a network in which node distance (leg length) and node intensity can be changed adaptively with respect to mission environment in the search time. This enhancement in conventional A * method leads to closer optimal trajectories in less computation load especially in complex mission scenarios such as shorelines having narrow pass, too many unintended targets or friends etc. The other proposed path planning method is improved genetic algorithm. This algorithm has a variable-length chromosome and a realvalued encoding as well as an intelligent population creation method that produces feasible individuals only. By means of starting with a feasible population, it is observed that convergence time is far less than using random creation of initial population. Furthermore, for rapid analysis and comparison of the two proposed methods in different environments, a generic graphical user interface (MPT-The Mission Planning Tool) is developed. TABLE OF CONTENTS 1. INTRODUCTION CONSTRAINT DEFINITIONS AND ENVIRONMENT MODEL ADAPTIVE A* ALGORITHM FOR PATH PLANNING IMPROVED GENETIC ALGORITHM FOR PATH PLANNING SIMULATION RESULTS AND DISCUSSIONS CONCLUSION AND FUTURE WORK... 7 REFERENCES 7 BIOGRAPHY INTRODUCTION Trajectory planning is crucial for a variety of applications including intelligent transportation systems, aerospace, robotics, and military guidance and navigation systems [1]. This work was motivated by autonomous offline route planning for tactical missiles, but is applicable to any two-dimensional path planning problem involving obstacles. The primary concern of route planning is to determine a trajectory that avoids obstacles in the environment. Another not less important issue is to compute realizable and, if possible, optimal path, delivering the missile to the target [2]. A desirable trajectory can be considered a route that does not exceed the physical limitations of the missile and should meet several requirements (objectives/constraints) on the resultant path in order to maximize the probability of success of the mission. In particular, the optimal/sub-optimal trajectory is expected not to exceed the physical limitations of the missile and should not violate the mission scenario parameters. Physical capability of missile points maximum route distance due to limited fuel amount and maximum turn angle due to maneuverability of missile. In addition to physical constraints, there are also constraints from mission scenario including flight avoidance and safety zones, shoreline buffer zones, minimum approach distance and angle to the target, etc. For the purpose of evaluating trajectory plan autonomously while considering above requirements, there are several path planning algorithms. These algorithms can be classified into classic (deterministic) and heuristic according to their way of creating search space [3]. Classic methods aim to find an exact optimum solution if one exists. On the other hand, heuristic algorithms aim to search for a good quality near-optimal solution in a short time by generating the search space in an intelligent way. Classic methods have two main drawbacks: too much computational cost and possibility of trapping in local minima especially in solving high dimensional and highly nonlinear problems like missile mission planning. On the other hand, heuristic algorithms are more suitable for global optimization problems although it may fail to find a good solution for complex problems [3]. In recent years, many methods for missile path planning have been proposed and most of them are based on heuristics, such as Genetic Algorithm, Ant Colony Optimization, Neural Network, A * Algorithm, Simulated Annealing, Particle Swarm Optimization [4]. The main problem with most of the trajectory optimization techniques is their heavy numerical computation cost which makes them not applicable in real time (online) implementations. Therefore, it is usually solved offline based on the known information before takeoff [5]. Even though mission plan is evaluated in pre-launch phase, it still has to be quick enough for time-critical missions especially in dynamic combat zones. The main aim of this research is to minimize computation time without deteriorating the sub-optimality. For this purpose, there are two improved path planning algorithm proposed in this paper: adaptive A * Algorithm and improved /12/$ IEEE

2 Genetic Algorithm (GA). Their pros and cons are also discussed in detail. Path planning algorithms usually look for the global optimal path in all passable regions among the obstacles. If the search space does not cover whole passable regions, the algorithm may not end up with the global optimal trajectory [6]. In this paper, a new technique and one of the proposed method is based on adaptive A * algorithm that settles network in the search time to cover almost all passable regions. By means of searching a larger span in a heuristic way, the possibility of missing the optimum solution and time of convergence are reduced. Conventional A * algorithm is one of the most popular search algorithm and is used quite extensively in route planning and graph searching applications. A * is a heuristic search method which enhances the search effectiveness by using the heuristic cost together with the actual cost in order to lead searching based on decision-making while guaranteeing the superiority of the path at the same time [7]. On the other hand, in complex problems (i.e., complex shaped shorelines/islands, too much threat/no-fly/safety zones etc.) requiring more intense search, the computation load increases exponentially in A * approach and uses an unbounded amount of memory to converge a solution [1]. This paper comes up with a new technique to overcome the computation cost: improve the conventional A * algorithm by making search parameters adaptive which can be varied during search with respect to complexity of current region of the combat zone. In addition, in order to avoid searching unnecessary parts of whole combat zone, the search space (network) is generated in the search time intelligently. The search space tree is started to be constructed from the launch platform and propagates toward to the target considering terrain, combat scenario, maneuverability limits and fuel consumption of the missile. The proposed adaptive A * algorithm is expressed in detail in the third section. In recent years, A * algorithm and genetic algorithm (GA) have become very popular for solving complex optimization problems in global scope. GA is heuristic evolutionary optimization method inspired in Darwin s theory of evolution and survival of the fittest. It reaches an optimal or suboptimal solution by using inheritance, mutation, crossover and selection mechanisms to form next enhanced generations and result in an optimal solution at the end [8]. In path planning problems especially in robotics applications, vertex heuristics is mostly used in creating chromosomes in the GAs since the shortest path must be pass through the vertices of the obstacles between start and target point. This assumption shortens the convergence time of the algorithm as it searches only the vertices instead of searching the entire continuous environment [9]. However, this works well with the environment having obstacles having infinite number of vertices. In tactical missile mission planning, the operation zone have circular threat zones without any vertex and complex geographical shorelines which can only be represented by numerous number of vertices. Therefore, vertex planner seems not to be an efficient method for GAs. In this paper, a new technique is introduced that can create feasible individual paths for initial population within a very short time without deteriorating the diversity of the population. By means of starting with a feasible population, the GA does not need to spend time to obtain feasible individuals. For the encoding of the paths in GAs, some of the motion planner algorithms use a binary string with fixed length which is difficult to construct in an obstacle environment and, as a result, speed of evolution in GA slows down [10]. Instead of limiting encoding with fixed length chromosomes, variablelength and real-valued encoding technique are used in this research in order to increase the flexibility of the evolutionary algorithm, as will be discussed in detail in the fourth section. 2. CONSTRAINT DEFINITIONS AND ENVIRONMENT MODEL In this section, constraints on specific tactical missile problem and the routines followed in determining search space are explained. In order to determine the boundary of the problem, the components of the scenario as well as physical limitations of the missile should be investigated. Assuming that the guided missile can fly only over the sea, waypoints must be used during single firing for deceptive maneuvers or for bypassing threat zones, non-targets, landmasses and no-fly zones. Figure 1 Digital Avoidance Zone Map In Figure 1, the blue shaded area represents the zone within which waypoints can be assigned. The whole trajectory that is a combination of the waypoints should not intersect the boundary of this zone. In the operation zone, the main factors that shape the digital avoidance zone map are listed below: Safety zones: Launch platform safety is of utmost importance in any mission plan. Also, when the missile is at sea-skim cruise flight, there is blind impact risk or inadvertent acquisition of launch platform, friend platforms or non-targets. In order to avoid this, circular buffer zones should be put around them. Shorelines and landmasses: Because of the position errors due to mid-course guidance errors and environmental factors such as winds, the shorelines should be enlarged toward to sea in order to prevent blind impact or acquisition of the lands. Minimum approach distance from target: To enhance the probability of the target acquisition, last way point

3 should be at least minimum seeker turn-on distance from target. No-fly zones: In order to prevent detection by enemy radars, the flight path of the missile should be kept at a minimum distance from non-targets and land radar threats. Maximum maneuver angle through successive waypoints: The angle between consecutive legs composed of three waypoints should not exceed the maximum maneuverability limits of the missile. Minimum distance between two successive waypoints: It represents the minimum straight distance to perform two consecutive turns. Maximum range of missile: It puts a limit on the number of waypoints that can be produced by auto router. Also, it determines how large the area of interest (AOI) in the operation zone must be. The radius of safety/no-fly zones are a function of their speed and type. For instance, smaller targets are more maneuverable, therefore their area of uncertainty (AOU) would be bigger (larger safety radius) than larger targets. The auto router will not route flight path segments within land avoidance boundaries (shoreline buffer lines). The avoidance zone around shorelines and islands is based on the missile's midcourse guidance error and weather (wind etc.) compensation correction value. The amount of land standoff avoidance increases as the range to the target increases since the position errors of the missile increases in time. Avoidance zones shown in Figure 1 are digital maps composed of grids, the resolution of which should be determined according to the maximum range of the missile or to the required accuracy of the search algorithm. Every grid has its own value 1 or 0 which shows whether it is in avoidance zone (0) or in safe flyable zone (1). In our approach, the search algorithms both in A * and GA starts searching in a backward direction from target to launch platform in the digital avoidance map. The reason for this is because approach distance and angle to the target is very important since it directly determines the success of the target acquisition after seeker turn-on and therefore must be the first thing to be calculated. 3. ADAPTIVE A * ALGORITHM FOR PATH PLANNING A * uses a best-first search and finds the least-cost path from a given initial node to one goal node [1]. It uses a distance-pluscost heuristic function ( f ) to determine the order in which the search visits nodes in the search tree. The distance-plus-cost heuristic is a sum of two functions: f ( n) = g( n) + h( n) (1) g( n) = wr. r( s, c) + wm. m( c, p) (2) the actual cost function ( g ), which is the cost from the starting node to the current node and an admissible "heuristic estimate" of the distance to the goal ( h ) from current node. Figure 2 The Fan-tail Parameters of the Search The heuristic term h(n) of the cost function f(n) must be an admissible heuristic; that is, it must not overestimate the distance to the goal. Thus, for an application like tactical missile routing, h(n) might represent the straight line distance to the target, since that is physically the smallest possible distance between any two points. In the Equation (2), r(s,c) denotes the total range from starting point (s) to the current node (c) and m(c,p) represents total maneuver needed to go from parent node (p) to the current node. Also, w r and w m are the weightings of the range and maneuver minimization respectively. They directly affect the resultant path and should be decided according to which one is more important: minimizing the route length? or having a smoothest path? An Adaptive Approach for the Search Parameters There are mainly three parameters in constructing the network by A * search method. As seen in the Figure 1, one is the fantail angle of search (2α), another one is the sector angle or angular resolution of the sectors (β) and last parameter is the leg length (L) between current node and parent node. Fan-tail angle of the search is determined by the maximum turning angle and it can be taken as 2 times the maximum turning angle. A missile can turn right or left not more than the maximum turning angle. Setting fan-tail angle larger, the search would grow in a bigger zone which means more computation load. Also, it is obvious that the smaller the value of sector angle, the greater the probability of finding an optimal solution. However, the memory and the time required to converge also increases exponentially which is an undesirable situation. Similarly, leg length is also dependent in minimum leg length; that is, the route should be straight for a predetermined minimum distance before initiating a turn after previous turn. As mentioned in above paragraph, each search parameter has great effect in both resultant path and the convergence time of the algorithm. Although conventional methods use default values for these parameters without considering mission scenario, there are some common practices in the literature such as [1] and [11] that apply some intelligent methods to

4 determine the search parameters according to the tactical situation and scenario. They evaluate different pre-calculated values for different mission scenarios and use these values during whole search which provides less computation compared to using unique default values for every scenario. However, it is still too slow to obtain a sub-optimal solution for some complex scenarios in which the operation zone differs from some part to another. This paper presents a method that can adjust the values of the search parameters adaptively during search time according to the complexity of the regions in the operation zone. For example, in the parts of the operation zone that have few and simple geographical map or obstacles, the search resolution can be reduced (rough search) to gain time; however, in the complex parts of the operation zone that have difficult and less passable regions among avoidance zones, the resolution is increased (intense search) in order not to miss the desirable path candidates. Figure 3 Adaptive Change in the Search Parameters during A* Search in a Complex Operation Zone (by MPT). In Figure 3, a mission planning for a complex scenario is illustrated. In the early stages of the search (upper half of the operation zone), the search resolution is set low since the obstacle environment is not that complex; however, through the middle of the operation zone, the avoidance zones seems more congested and have narrow passages. Therefore, the search resolution must be improved to overcome it. The blue dotted lines represent the resultant path calculated with default search parameters which is rather worse than red path in terms of total trajectory length. The only way to obtain better paths while keeping search parameters constant during the search is to improve the resolution of the search. However, more intense search means more computation load. As seen in Figure 4, decreasing the values of leg length and sector angle higher resolution leads to obtain shorter paths and causes the computation time to increase exponentially. Instead of using high resolution with constant search parameters, the proposed method provides almost the same quality path with a vast amount of computation time reduction (more than 3 times). Figure 4 The Effect of Changing the Search Resolution in the Resultant Path Length and the Computation Time. The Steps of the Algorithm The routine of the proposed adaptive A * Search Algorithm is summarized below: 1) Find all possible non-intersecting approach legs from target, the length of which is equal to minimum approach distance. Calculate the cost of each approach leg and put the one with minimum cost into a close list and put the rest of approach legs into an open list. 2) Set the resolution parameters to the minimum values for the parameters of the fan-tail (L=L max & β=β max ). 3) Create a fan-tail of twice the maximum maneuver angle (α) by using the search parameters (L & β) from the end of the leg in the open list which has minimum cost. Put the minimum cost leg in the open list into the closed list. 4) Check the obstacle avoidance of the legs produced in the step 3. If any of the legs are intersecting with the avoidance zone, go to step 5. Otherwise, proceed to step 6. 5) Increase the resolution at a factor of n (L=L/n & β=β/n) unless either L<L min or β<β min. Otherwise, eliminate the intersecting legs and put the rest of the legs into the open list. Then, go to step 3. 6) Put the produced legs into the open list. 7) Make the minimum-cost leg in the closed list, the parent of the newly produced legs in the open list in order to track the parent legs of a leg in the open list. Go to the step 3. 8) Repeat procedures above until there is no obstacle between launch platform (a) and the current leg in the open list or until the open list is empty (b). 9) If the case is (a), it means there is a solution. Find out the resultant path by tracking the parents of the current leg in the open list. 10) If the case is (b), it means there is no solution. Finally, in order to shorten the length of the path found by adaptive A * method, path straightening mechanism was employed. Once applied to the resultant path, the straightening

5 mechanism tries to remove redundant waypoints in a deterministic manner. 4. IMPROVED GENETIC ALGORITHM FOR PATH PLANNING The application of GA to the tactical missile path planning problem should be employed with a suitable encoding method for chromosome representation of the path, an obstacle avoidance algorithm, and an appropriate constraint definition providing mechanisms to minimize trajectory length and smooth paths [4]. In this section, the proposed sub-algorithms used in GA are to be presented. Encoding Method A chromosome (path) is represented as a sequence of way points. Also, in order to make the algorithm more flexible in the search space, variable-length and real-valued encoding method are employed for the problem. That is, the number of nodes (waypoints) might vary from one path to another but should not exceed the maximum allowable waypoints determined by considering the maneuverability of the missile. Fitness Evaluation Method Fitness function is composed of total path length and total maneuver terms with an appropriate weighting factors as expressed in A * algorithm section. As all the path candidates are feasible in the proposed GA, there is no penalty term. Population Creation Method While common procedure in GA is to select the initial population randomly to provide wide diversity of solutions, there are some disadvantages to it. Since there might be many obstacles in the operation zone, the randomly chosen paths in the initial population might have intersections with the obstacles which means that they are infeasible. Starting GA with an infeasible population means the algorithm has to spend some time to first obtain feasible candidates by using crossover and mutation randomly. Most of the time, its execution may take a long time which decreases the performance in the convergence of the overall GA. There are various study in the literature that GA is performed by starting with random infeasible population. One of an example is mobile robot path planning studied in [9]. In this study, environment 2 can be referenced since it is very similar to mission environment in Figure 5. The results shows that the first feasible path in the environment 2 is obtained in the 23 rd generation with an execution time of 2.59 s. which is very slow and impractical for time-critical mission planning systems. On the other hand, this paper proposes a new technique for generating feasible initial paths within a reasonable short time in the creation of the initial population instead of waiting to obtain it by mutation and creating operators randomly. By starting with a feasible population already, the convergence of the GA is enhanced. However, the risk of starting with a feasible population is the possibility of losing the diversity in the population. To deal with this, the proposed technique uses random factors in producing feasible path candidates to keep the search space varied and large. An algorithm based on simple tree search is employed to create initial paths. The main steps of the algorithm are briefly: 1) Set current node to the starting point. 2) Create a fan-tail of twice the angle of the maximum maneuver angle (α) from the current node with a resolution parameters (L & β). Set the leg number (nl) to unity. 3) Check obstacle avoidance of each of the fan-tail legs produced currently. Eliminate the ones which intersects the avoidance zones. 4) Generate a random integer r such that 1 r nw + 1 where nw is the number of maximum allowable waypoints. 5) Check if the random assigned factor is equal or less than the leg number. If r nl, go to step 4; otherwise, go to step 5. 6) Select one of the legs in the fan-tail randomly. Then, go to step 2. It means path segments should grow randomly until r > nl. By doing this, the diversity within feasible initial paths is provided and stuck in local minima situations are prevented. 7) Calculate the straight line distance from the end of the legs to the target point. Select the leg which has a minimum distance to the target instead of random selection. Then go to step 2. Parameter r determines when the random selection is stopped and deliberative selection is started to be applied. Random selection helps to increase diversity in paths whereas deliberative selection guides the path segments toward to the target. For example, if r is large, the obtained initial path might be long and tortuous including zigzags which is required for maintaining the diversity of initial population. On the other hand, once shrinking the value r, the shorter and the smoother paths are obtained. It is also useful for improving the convergence rate of GA. 8) Repeat the procedures between 2 and 5 until there is no obstacle between current node and the target node in order to obtain a feasible path candidate. Figure 5 Diversity of the Initial Population Produced by the Proposed Population Creation Method (by MPT).

6 As seen in Figure 5, 20 feasible paths are produced in a very short time (0.37 s.) by the proposed creation method. Also, the initial network covers almost all of the passable regions in the obstacle environment in Figure 5 which shows that diversity in paths is satisfied. Similarly, the total convergence time (1.03 s.) of the improved GA is quite fast and converges to an optimal solution in the 32 nd generation. Crossover Operator (C) The operator combines two selected paths to generate an offspring. Single-point crossover method is used. One random node is selected on each parent path, and the parts of parent paths are combined by a straight line between selected crossover nodes. If the bond line is intersected any of the obstacles, the repair mechanism are employed to make it feasible. (a) Crossover Operator Obstacle Parent # 1 Parent # 2 Crossover Path (b) Mutation Operator Parent Path Mutant Path (c) Repair Operator Infeasible Path Repaired Path Figure 5 GA Operators (Crossover-Mutation-Repair). Mutation Operator (M) The operator makes a change in a path by shifting a selected mutation node to another position in the operation zone randomly as seen in Figure 6. It repeats itself until a feasible mutant child is obtained. The individual is refused and substituted, by simply employing another mutation operation until a feasible individual is obtained or by selecting a different individual to mutate. Repair Operator (R) Repair operator is used only for supporting the crossover and mutation operators. It prevents obtaining an unfeasible solution after crossover or mutation operations by repairing them. In this study, there is no stretching mechanism used for smoothing the paths candidates during GA since it may reduce the diversity of the search and trap in local minima. 5. SIMULATION RESULTS AND DISCUSSIONS In this section, the experimental results are obtained by employing both the improved GA and the adaptive A * algorithms in three operation scenarios having different difficulty levels. The same environments are used in order to make comparisons with the performance of adaptive A * algorithm and improved GA proposed. Note that all of the scenarios in this research are simulated in MATLAB 2009a running under Windows XP on a 2.67 GHz Intel Core 2 Duo T7700. Also, the geographical maps used in the scenarios are gridded by 100 x 100 m. resolution and a generic graphical user interface called MPT (Mission Planning Tool) has been prepared by MATLAB Guide toolbox. Table 1. Comparison of Execution Time and Final Path Lengths Obtained by the Adaptive A * Algorithm and the Improved Genetic Algorithm. The results are the medians obtained over 20 runs. Operation Zone Trajectory Planning Method Adaptive A * Improved GA Adaptive A * Improved GA Adaptive A * Improved GA Search Parameters 7 L 25 km 10º β 30º M=0.2, C=0.5, R=0.1 PopSize=20 7 L 25 km 10º β 30º M=0.2, C=0.5, R=0.1 PopSize=20 7 L 25 km (a) 10º β 30º 7 L 15 km (b) 10º β 20º M=0.2, C=0.5, R=0.1 PopSize=20 Execution Time to Find the Final Path [ms] Resultant Path Length [km] The three environments are shown in Figure 7. The difficulty levels of the operation zones increases from 1 st to 3 rd. The relative complexities of the test zones are reflected by the total number of obstacles including lands, non-targets and friends. In Table I, the execution times of the two algorithms and the resultant trajectories length are presented. According to this, although the run time of GA has an increasing trend from the simple to complex environment, there is no big distinguishable change in the execution time of the A * method. It shows that proposed A * algorithm is able to adapt to the different environment using adaptive search parameters. Execution time is not substantially affected one environment to another. Also, the total run-time is very short making it very practical to use even in online mission planning problems. Although improved GA falls behind the adaptive A * in total convergence time (more than 10 times slower), it obtains more accurate and optimal solutions (15% shorter path in the second case). However, since our main concern in this study is an offline mission planning, the execution time of the proposed GA is considered to still be in admissible limits ( 1 s.) even for such complex operation scenarios. In the first and second scenarios, the paths found by the algorithms look very similar except GA tighten the paths found by A * a little bit to make it shorter. On the other hand, in the third case, two algorithms, A * with default resolution interval (a) and GA, obtain quite separate paths whose the difference in total path length is very small (3%). The reason that A * is not able to explore the passable regions that GA discover, might be due to the interval of adaptive search parameters used in (a). By increasing either angular resolution angle (β) or decreasing search leg length (L), it is always possible to obtained better path. For this purpose, the interval of β and L are shrunk by

7 pulling down the upper limits. As a result of using higher resolution (b) in A *, better route which is similar to the path found by GA are obtained as seen in the operation zone 3 in Figure 5. Note that, although A * with higher resolution is achieved to converge to the route found in GA in the 3 rd scenario, it is still 2 km longer than the path obtained by GA. This implies that resolution is still not sufficient. On the other hand, increasing resolution excessively in A * method may lead to grow the computation time exponentially. Operation Zone 1 Operation Zone 2 Operation Zone 3 Algorithm. In the simulation results, it is observed that the convergence time was significantly reduced by adding adaptive approach to the conventional A * methods and by adding an intelligent population creation technique to the traditional GAs without deteriorating the accuracy of the solution. Both of our preferred techniques have some pros and cons with respect to each other. After the comparison of these two algorithms; it is shown that, although adaptive-based A * algorithm is superior to the improved genetic algorithm in computation time, it falls behind the genetic algorithm in optimality. Therefore, adaptive A * algorithm seems to be more convenient for the timecritical path planning problems especially in case of an urgent mission plan needed in dynamic environments. On the contrary, improved GA can be applied effectively for the high-precision and mission-critical path planning problems in the pre-launch phase. Although the current study is focused on single mission planning only, A * and GA can be extended to coordinate multiple agents to perform the path planning task collaboratively. Algorithms can be run in parallel offline, and communicate each other to optimize the cooperation of the missiles as well as each missiles mission. Researches in multipath planning is continuing and the results of the application of the proposed methods will be reported in a subsequent paper. ACKNOWLEDGMENT This study was sponsored and carried out at Tactical Systems Engineering Development Directorate, Roketsan Missile Industries Inc. My Group Director, Dr. Sartuk Karasoy, and Group Manager, Mr. Bülent Semerci, are greatly acknowledged for their encouragement and insight during the preparation of the study. In addition, I would also like to thank my colleagues Mr. Gökhan Tüşün and Mr. Görkem Seçer for their technical assistance and critical suggestions. REFERENCES Figure 5 The Paths Generated by the Proposed Adaptive A* and Improved Genetic Algorithm for each of the Simulated Operation Zones. 6. CONCLUSION AND FUTURE WORK The main problem in the path planning algorithms is their high computation time and their need in unbounded amount of memory to converge a sub-optimal solution. In order to enhance the speed of the algorithms, two different path planning techniques have been proposed for the mission planning of tactical missiles based on A * Search and Genetic [1] R. J. Szczerba, P. Galkowski, I. S. Glickstein, N. Ternullo, Robust Algorithm for Real-Time Route Planning, IEEE Transactions on Aerospace and Electronic Systems, vol. 36, no. 3, pp , July [2] V. Kroumov, J. Yu, H. Negishi, Optimal Path Planner for Mobile Robot in 2D Environment, The Journal on Systemics Cybernetics and Informatics, vol. 2, pp , [3] A. Elshamli, H. A. Abdullah, S. Areibi, Genetic Algorithm for Dynamic Path Planning, Proc. of the IEEE CCECE-CCGEI, Niagara Falls, May [4] E. Masehian, D. Sedighizadeh, Classic and Heuristic Approaches in Robot Motion Planning A Chronological Review, World Acedemy of Science, Engineering and Technology 29, pp , [5] Y. Qu, Q. Pan, J. Yan, Flight Path Planning of UAV Based on Heuristically Search and Genetic Algorithms, Proc. of the IEEE IECON, pp , [6] D. Xin, C. Hua-Hua, G. Wei-kang, Neural Network and Genetic Algorithm Based Global Path Planning in a Static Environment, Journal of Zhejiang University Science, 6A(6): pp , [7] L., X., C. Manyi, X., W. Zhike, Path Planning for UAV Based on Improved Heuristic A * Algorithm, Proc. of the IEEE ICEMI, pp , [8] D. Portugal, C. H. Antunes, R. Rocha, A Study of Genetic Algorithms for Approximating the Longest Path in Generic Graphs, Proc. of the IEEE SMC, pp , 2010.

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