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					                                                  International Journal of Research and Reviews in Applicable Mathematics & Computer Science,
                                                                                                                             Vol.2, No.2, 2012

A Novel Dynamic Trajectory Planning for Mobile Robot
  in Alien Environment Based on Genetic Algorithm
                                     Taghi Karimi and 2Seyyed Mohammad Reza Farshchi
                   Department of mathematics, Payame Noor University, P. O. Box 19395-4697, Tehran, Iran.
                      Department of Artificial Intelligence, Islamic Azad University, Mashhad Branch.


       In this paper, a novel path planning scheme based on genetic algorithm (GA) is presented for
      navigation and obstacle avoidance of mobile robot especially in alien environment. The real
      coding, fitness function and specific genetic operators are devised in the algorithm. The unique
      coding technique decreases the conventional computational complexity of genetic algorithm. It
      also speeds up the execution of searching by projecting two dimensional data to one dimensional
      data, which reduce the size of search space. The fitness function of genetic algorithm takes full
      consideration of three factors: the collision avoidance path, the shortest distance and smoothness
      of the path. The specific genetic operators are also selected to make the genetic algorithm more
      effective. The simulation experiments are made under the VC++ 6.0 environment. The
      simulation results verify that the genetic algorithm is high effective under various complex
      dynamic alien environments.

      Keywords: Trajectory Planning, Mobile Robot, Genetic Algorithm, Obstacle Avoidance.

      1. Introduction

          Path planning is one of the important tasks in intelligent robotic systems such as autonomous
      mobile robots. There are two types of path planning problems: (1) static path planning, which allows a
      mobile robot to move through stationary obstacles, and (2) dynamic path planning, which allows a
      mobile robot to generate a new path in response to a changing environment [1-3]. There has been
      much effort put forward by researchers to solve the path planning problems for mobile robots in the
      presence of static and dynamic obstacles. One of the popular path planning methods is the artificial
      potential field [4]. However, it can give only one solution route that may not be the shortest path in a
      static environment. Another method is a position estimation method, a path generation between current
      location and target location for mobile robots.
      However, this method accumulates estimation error [5-6]. There have also been many attempts to use
      fuzzy logic controllers for path planning of mobile robots [2]. In [7], while steering a robot, an off-line
      process modeling develops the fuzzy rules of the system. The fuzzy logic controllers should be
      properly designed to produce an efficient controller and the fuzzy rules must adequately model the
      human approach to control the system [2]. Recently, there has been widespread interest in using
      genetic algorithms. Compared to traditional search and optimization methods, such as calculus-based
      and enumerative strategies [3], the genetic algorithm is a powerful search algorithm based on the
      mechanism of natural selection and uses operations of reproduction, crossover, and mutation on a
      population of strings at finding an optimum path in very large workspace. GA is stochastic search
      techniques analogous to natural evolution [7]. Potential solutions of a problem are encoded as
      chromosomes. These chromosomes form a population. Each individual of the population is evaluated
      by a fitness function. A selection mechanism based on the fitness function is applied to the population
      and the individuals strive for survival. The fitter ones have a better chance to be selected and to
      duplicate offspring by means of genetic transformations, such as crossover and mutation [8] [9] [10].
      The process is repeated and the population is evolved generation by generation. After many
      generations, the population converges to solutions of good quality, and the best individual has good
      chance to be the optimal or near-optimal solution. Genetic algorithm has already been applied in path
      planning for mobile robots.

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                                 International Journal of Research and Reviews in Applicable Mathematics & Computer Science,
                                                                                                           Vol. 2, No.2, 2012
         A number of results in the literature show the application of GA to robotic path planning. Among
     the results, Khoogar and Parker [11] considered the path planning problem in a plane using a planar
     robot. Ram et al. applied GA to a mobile robot navigation problem in a 2-D space with stationary
     obstacles. In [12], Toogood et al. developed a path finding method for stationary avoidance obstacles
     by applying GA to a 3-D robot manipulator. Most researches of robotic path planning in the literature
     focus on the static environment with known obstacles, which have become a more mature stage.
     However, researches of robotic path planning in changing circumstances are still hot spots of robotic
     path planning. In this paper, GA will be applied to generate a dynamic path planning for mobile robot
     in the alien environment. The planning can achieve satisfactory results and speed of convergence. This
     shows that genetic algorithm has a strong environmental adaptability. Section II presents a brief
     description of path planning problem. Section III indicates the resolutions based on GA. Section IV
     displays the results of simulations. Section V gives the concluding remarks.


         In a dynamic environment for successful steering of a mobile robot to the destination, two
     important problems should be solved. One is real-time identification of the moving obstacles. The
     other requests that the shortest and safe path is generated dynamically [11] [13].
         We assume the former issue may be resolved by the higher level visual processing system. This
     research in this paper focuses on the latter one. The aim is to put forward a dynamic path planning
     scheme in the alien environment, and requests that path planning satisfy the following conditions [8]
             The path should not occur collision with any obstacles
             The path should be as short as possible
             The path curves as smooth as possible
     Please use automatic hyphenation and check your spelling. Additionally, be sure your sentences are
     complete and that there is continuity within your paragraphs. Check the numbering of your graphics
     and make sure that all appropriate references are included.


     Path Coding
         In the genetic searching algorithm, the coding technique is a very important aspect. The length of
     binary strings from the parameter sets made up of the via-points of a path, as well as the size of the
     search space, determines the computational time for a given fitness function. In order to shorten the
     length of the binary strings, we adopt a unique coding method. This approach transforms the two-
     dimensional data to one-dimensional data as shown in Fig. 1. In Fig. 1(a), the set of node points Gi is
     located at equal distance along the straight line from the initial position to the goal position. If the
     straight line is treated as x axis, then the set of the node points xi is located at equal distances along the
     x axis. Then yi becomes the search space for each via-point of the path and the via-point candidates
     are specified by one-dimensional data [12]. To further reduce the size of data in each search space and
     thereby accelerate the speed of genetic searching algorithm, the dynamic allocation of starting points at
     each via-point is used, which reduces the search space dramatically as shown in Fig. 1(b). In Fig. 1(b),
     the origin of the ith perpendicular search line is the knot point in the x axis. In Fig. 2, the coding
     structure using the reducing dimensions method is shown.

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                                           Figure 1. Conversion of search space.

                                          y1        y2            y3      …         yn
                                                 Figure 2. Coding structure.

     Fitness Function
         Selection of fitness function should take into account the security of the path, the shortest path, and
     the smoothness of the path. However, the security of the path is primary factor. In view of these, the
     fitness function is composed of three sub-functions:
     1) Sub-function of Path Length
     We could describe path length with integral. The sub-function is as follows:
                                                    fit1   ( Pi , Pi 1 )                     (1)
                                                           i 1

     Where ( Pi , Pi 1 ) is the distance between Pi  P( xi , yi ) and Pi 1  P( xi 1, yi 1 ) .

     2) Sub-function of Path Security
     The condition of collision avoidance is stated as follows: if the distance between every via-point of the
     path and the obstacles is expressed as | Pi S j | for any path, then we get:

                                              n m
                                         min   (| Pi S j |) / S d if min(| Pi S j |)  S d
                                 fit 2     i 1 j 1                                            (2)
                                                                    otherwise

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     Where Pi  P( xi , yi ) is the position of every via points of the path, S j  S ( x j , y j ) is the position of
     each obstacle, i  1,2,...,n, j  1,2,...,m, sd  r0  rk and r0 is the radius of mobile robot, rk is the
     radius of the number k obstacle.

     3) Sub-function of Smoothness
     In this section, the smoothness of path planning is depicted. The path will be considered to be smooth,
     when mobile robot moves from the present point Pi  P( xi , yi ) to the next point
      Pi  P( xi 1, yi 1 ) only forward not circuitously. The sub-function is expressed as:
                                     fit 3  m 1
                                                   (y  y ) (y  y ) 
                                               ( xi  xi 1)  ( xi 1  xi ) 
                                                                               
                                              1  i       i 1      i 1    i 

     4) Fitness Function
     The security of the path was the first factor, which decides the feasibility of the mobile robot reaching
     the goal point, and it is the most weight in fitness function. Based on this, we get the rather short path;
     meanwhile also take smoothness into consideration. The fitness function is shown as follow:
                                         fit  1       2 fit 2  3 fit3         (4)
     Where, i (i  1,2,3) respectively stands for the weighted values of length, security, and smoothness
     degree in the fitness function. Adjusting i may adjust the extent of path length, avoiding obstacles
     and smoothness.

     Genetic Operation
        According to the actual circumstances of path planning, four kinds of genetic operators, namely
     crossover, mutation, smooth, and initialization of population, are introduced in this paper.

     1) Initialization of Population Operator
     Initial population, as the beginning of optimization, may be produced by algorithm itself. N refers to
     the scale of population, namely random produce path R j  { j  1,2, N} , the individual can be chosen
     by being in proportion to fitness value. The operation is described as following:

        o To calculate the individual adaptive value.
        o To calculate the probability of choosing copy.
        o To calculate the expected replication number.
        o To round the expected replication number to the nearest integer and then get the actual replication

        2) Crossover Operator
        The crossover operator combines parts of two different chromosomes to create two new ones. There
        are many ways to do the crossover operation, but for the chromosome formed by a node sequence
        in the path, only single-point and multi-point cross have factual significance. And there is no
        difference in essence between them. So, the single-point cross means is adopted in this paper. Two
        individuals are randomly selected, and then choose a crossing point to cross according to a certain
        crossover probability; replace the individual of the father with individual of the offspring after
        cross, a new population would be produced.

        3) Mutation Operator
        Mutation is to randomly choose a node and replace it with a node that is not included in the path.
        Mutation is served as a key role to diversify the solution population. Therefore, it is not necessary
        that a solution is better after it is mutated. Mutation operation is illustrated in Fig. 3. The mutation

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        probability of each element in the population is Pm (generally within 0.001~0.3). In this paper,
        three kinds of way are adopted as the way of mutation. They are increasing a point, decreasing a
        point and removing a point. Mutation and crossover are co-used abstemiously, aiming at avoiding
        over-mature to lose vital genetic information. But mutation often keeps lower probability for fear
        that should destroy the individual fabric of next generation.

        4) Smooth Operator
        The smooth operators choose feasible path of greater corner, and then randomly inserted three new
        path nodes, if these three new nodes constitute a viable segment of the line, retain new nodes, and
        delete the original nodes. Smooth operation is shown in Fig. 4.


         To verify the correctness and effectiveness of the method put forward in this paper, lots of
     simulation experiments have been done under VC++ 6.0 environment. In this simulation environment,
     selection adopts roulette wheel selection to save the optimal individuals, crossover adopts single point
     random crossovers and mutation employs single point random mutation. Within a square area of
     5m×5m, gray circle represents the mobile robot, while static and dynamic obstacles are exemplified
     with other color circles. Crossover probability Pc is 0.62, mutation probability Pm is 0.1, smooth
     probability is set to 0.2, population size generation is 50, N (the number of evolution era) = 2000, the
     simulation results are shown in Figure 5, 6, 7 and 8 respectively. In order to reflect the capability of
     GA in complex dynamic environments, the numbers of static obstacles and dynamic obstacles vary.
     Figures 5-8 demonstrates path planning for mobile robot under a dynamic and alien environment. It is
     shown that GA is capable to deal with path generation and collision avoidance easily. Figure 5 and
     Figure 6 display that the dynamic path generation and collision avoidance for moving obstacles have
     been accomplished under such dynamic environment, where there are four or six static obstacles
     respectively and one moving obstacle. Fig. 7 and Fig. 8 illustrate that the dynamic path generation and
     collision avoidance for moving obstacles have been accomplished under such dynamic environment,
     where there are five static obstacles and two moving obstacles.

     Figure 3. Mutation operation: increasing a point (higher), decreasing a point (medium), and removing
                                                a point (lower).

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                                        Figure 4. The smooth operation.


        This paper presents a dynamic path planning method based on genetic algorithm for mobile robot
     under an alien environment. The real coding, fitness function and specific genetic operators are
     designed to accelerate the convergence of the algorithm and improve the accuracy of operation. The
     genetic algorithm used in this paper can achieve satisfying path planning results under an alien
     dynamic environment. The simulation results show that the genetic algorithm has strong adaptability of
     dynamic and alien environments and verify the proposed method is high effective.

            Figure 5. Path generation while avoiding four static obstacles and one dynamic obstacle.

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                         Figure 6. Path generation while avoiding six static obstacles.

           Figure 7. Path generation while avoiding five static obstacles and two dynamic obstacles.

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            Figure 8. Path generation while avoiding five static obstacles and two dynamic obstacles.

     5. References

     [1] Z. X. Cai, H. G. He, and H. Chen, “Some issues for mobile robots navigation under unknown environments,”
         Proc. IEEE International Conference on Decision and Control, Vol.17, No.4, 385-390, 2002.

     [2] Jian-ping Tu, Simon X. Yang, “Genetic algorithm based path planning for a mobile robot,” Proceedings of
         the IEEE International Conference on Robotics and Automation, 1221-1226, 2003.

     [3] Yang Linquan, Luo Zhongwen, Tang Zhonghua, and LvWeixian, “Path planning algorithm for mobile robot
         obstacle avoidance adopting bezier curve based on genetic algorithm,” Chinese Control and Decision
         Conference, 3286-3289, 2008.

     [4] J. Kim, P. Khosla, “Real-time obstacle avoidance using harmonic potential functions,” IEEE Transactions on
         Robotics and Automation, Vol.8, No.3, 338-349, 1992.

     [5] H. Chung, L. Ojeda, and J. Borenstein, “Accurate mobile robot dead-reckoning with precision-calibrated
         fiber-optics gyroscope,” IEEE Transaction on Robotics and Automation, Vol.17, No.1, 80-84, 2001.

     [6] K. Park, H. Chung, and J. Lee, “Dead reckoning navigation for autonomous mobile robots,” Proceedings of
         Intelligent Autonomous Vehicle, 775-781, 1998.

     [7] J. Xu, K. Kin, “Intelligent mobile robot path planning with fuzzy system approach,” Proceedings of the 2nd
         IEEE International Workshop on Emerging Technologies and Factory Automation, 28-41, 1993.

     [8] Yong Zhang, Lin Zhang, and Xiao-hua Zhang, “Mobile robot path planning base on the hybrid genetic
         algorithm in unknown environment,” Eighth International Conference on Intelligent Systems Design and
         Applications, 661-665, 2008.

     [9] Xuan-zi Hu, Cun-xi Xie, “Niche genetic algorithm for robot path planning,” 3rd international conference on
         natural computation, 61-65, 2007.

     [10] Wu Lijuan, Xu Xinhe, “Design of an obstacle avoidance strategy based on genetic algorithms in robot soccer
          competition,” Robot, Vol.23, No.2, 142-146, 2001.

     [11] Woong-Gie Han, Seung-Min Baek, and Tae-Yong Kuc, “Genetic algorithm based path planning and dynamic
          obstacle avoidance of mobile robots,” IEEE International Conference on System, Man, and Cybernetics,
          Vol.3, 2747-2751, 1997.

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     [12] H.Toogood, H. Hao, and C. Wong, “Robot path planning using genetic algorithms,” International Conference
          on SMC, Vol.1, 489-494, 1995.

     [13] Lin Lei, Houjun Wang, and Qinsong Wu, “Improved genetic algorithms based path planning of mobile robot
          under dynamic unknown environment,” Proceedings of IEEE International Conference on Mechatronics and
          Automation, 1728-1732, 2006.

     Authors Profile

                                 Dr. Taghi Karimi received the B. Sc degree in mathematics from the Payame Noor
                                 University of Mashhad, Iran in 1996 and the Ph. D degree in mathematics from
                                 Azad University of Mashhad in 2006. He has published over 20 peer-reviewed
                                 journal papers and contributed to more than 7 conference papers and
                                 presentations. His research activities include group theory, number theory,
                                 algebraic topology and game theory.

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