Genetic Fuzzy Logic Control Technique for a Mobile Robot Tracking a Moving Target

Transcription

1 .IJCSI.org 67 Genetic Fuzzy Logic Control Technique for a Mobile Robot Tracking a Moving Target Karim Benbouaballah an Zhu Qi-an College of Automation, Harbin Engineering University Harbin, 151, China Abstract Target tracking is a crucial function for an autonomous mobile robot navigating in unknon environments. This paper presents a mobile robot target tracking approach base on artificial intelligence techniques. The propose controller calculates both the mobile robot linear an angular velocities from the istance an angle that separate it to the moving target. The controller as esigne using fuzzy logics theory an then, a genetic algorithm as applie to optimize the scaling factors of the fuzzy logic controller for better accuracy an smoothness of the robot trajectory. Simulation results illustrate that the propose controller leas to goo performances in terms of computational time an tracking errors convergence. Keyors: Mobile robot, Target tracking, Fuzzy logic controller, Genetic algorithm. 1. Introuction An autonomous mobile robot is a programmable an multitasks mechanical evice, capable to navigate freely or execute ifferent functions such as obstacles avoiance, target tracking etc. The last fe ecaes have itnesse ambitious research efforts in the areas of mobile robotics, ue to their ie range of use in ifferent fiels like military an inustrial applications. These research orks aim to improve their operational capabilities of navigation an interaction ith its surrouning ork environments through the ifferent kins of sensors. Target tracking is one of the basic an an interesting function for a mobile robot, an researchers have orke to propose ifferent control approaches to improve target tracking performances. Several control approaches like PID controllers [1], non linear controllers base Lyapunov stability analysis [] an sliing moe control [3] have been evelope to make the mobile robot track easily a moving target. Hoever, these approaches have shoe some problems, ue to the complexity of the mobile robot surrouning environment to be moele or to the simplification assumptions taken for the elaboration of the mathematical moel of the robot an control la. To overcome these rabacks an the nee to exhibit robust performances hile operating in highly uncertain an ynamic environments, artificial intelligence approaches have been attracting consierable research interest in recent years. Different techniques such as reinforcement learning [4], neural netorks [5], fuzzy logics [6] [7] an genetic algorithms [8] have been applie to synthesize control las enabling the mobile robot to follo a moving target freely. Artificial potential fiel approaches [9] [1] have been also evelope to solve the problem of mobile robots target tracking. The intelligent control oes not require knoing exactly the mathematical moel of the mobile robot or its surrouning ork space, since it uses human reasoning an ecision making in spite of uncertainty an imprecise information provie by the ifferent perception sensors such as cameras, ultrasonic an infrare sensors. A fuzzy logic controller is a control strategy hose ecisions are mae by using a fuzzy inference system, hich is a rule-base or knolege-base system containing a collection of fuzzy if-then rules base on human experts. It utilizes heuristic knolege to evelop perception-action for mobile robots to achieve ifferent tasks (target tracking, obstacle avoiance, path tracking). Furthermore, fuzzy logic controllers methoology is very helpful because it eals ith uncertainties in real or. For more robustness an effectiveness of s, many researchers have explore the use of genetic algorithms to tune in orer to optimize its ifferent parameters (termsets, rules, scaling factors) [11] [1]. The basic concepts of GA ere evelope by Hollan [13], an subsequently in several researches ork [14]. Genetic algorithms are a robust optimization technique because they ensure a graual increasing of a goo solution. Thus, GA oes not nee graient or any prior information of the search space hich is usually not available for the esigner. Therefore, GA has loer chance to converge into local minima because they operate over a population of points.

2 .IJCSI.org 68 Hence, the use of genetic algorithms is more suitable for this kin of situations. In this paper, a control approach for target tracking by a mobile robot is presente, base on fuzzy logics an optimize ith a genetic algorithm for more efficiency an effectiveness. The paper is organize as follos. A general escription of the system moel an problem formulation are given in section. The aopte fuzzy logic controller is presente in section 3. Section 4 escribes the genetic algorithm use to tune the. To valiate the propose approach, simulation results are iscusse in section 5. Conclusion an future orks are given in section 6. Roughly speaking, to achieve the target tracking objectives, the main iea is to esign an intelligent controller enabling the robot to move freely such that it maintains a esire istance to the target an steer in orer to point the target s irection.. Moel System an Problem Formulation The objective of this paper is to make an autonomous mobile robot track a moving target. To realize that, e shall assume that: - The target an the robot move on the same plane in the absence of obstacles. - The target moves along an unknon trajectory an its o (, ) position is enote as T xt yt. - The robot has the kinematics of a unicycle. It is escribe by the folloing equations:. x cos. y sin. here ( xy, ) are the robot coorinates in the orl frame XOY, is its orientation ith respect to the same frame, an an are the robot linear an angular velocities. - The robot is subject to non-holonomic constraint:.. ycos xsin () The linear an angular positions of the mobile robot to the target to be tracke are enote as D an, respectively an can be ritten by the folloing equations: 1 yt y (3) tan ( ) xt x D ( xt x) ( yt y) (1) Fig. 1 Schematic moel of a mobile robot tracking a target. 3. Design of the Fuzzy Logic Controller The funamental objective is to synthesize a robust control la able to force the mobile robot to follo a moving target as closely as possible. We efine the istance an angle errors an the change in angle error variables to mathematically formulate the control objective as follos: ed D D e e e ( k) e ( k 1) Desire istance an angle e D,e e, e TSD TSA Evaluate D an α beteen the robot an the target Fig. block iagram Mobile Robot (4)

3 .IJCSI.org 69 It s clear that to achieve the control objective, it suffices to make the tracking errors ten to zero. Thus, to fuzzy logic Takagi-Sugeno controllers of orer zeros have been esigne: istance controller TSD an angle controller TSA. 3.1 Distance controller TSD This controller aims to keep a esire istance D beteen the mobile robot an the target hen it navigates in its ork space. The control input variables are chosen as the istance an angle errors e an e. The linear velocity of the mobile robot is efine as the output of TSD, so e can rite: K. TSD( K. ed, K '. e ) (5) D 3. Angle controller TSA This controller aims to point the mobile robot in the moving target s irection, hich means reuce the angle error to zero. It has to input variables; the angle error e an the change of error. It returns the angular velocity of the mobile robot, so e can rite: K. TSD( K '. e, K ''. e ) (6) e e K ' K Fuzzification e Rule Base Fuzzy Inference Defuzzification K e D e K K' Fuzzification Rule Base Fuzzy Inference Defuzzification Fig. 3 Distance controller architecture K Fig. 4 Angle controller architecture The inputs/output linguistic variables are efine as: e e The inputs/output linguistic variables are efine as: ed :{ N, ZE, PS, PM, PB} e :{ N, ZE, PS, PM, PB} Triangular istributions in [-1, 1] interval ere chosen as membership functions for the scale inputs ed an e an singletons for. Table 1 shos the rules base of TSD. For example, if the errors are big, it means that the robot is so far from the target, so it shoul be much faster to reuce the istance to D. Table 1: TSD Rules Base Linear Distance Error elocity N ZE PS PM PB NB N PS PM PB PB NM N ZE PS PM PB NS N ZE PS PM PB ZE N ZE PS PM PB PS N ZE PS PM PB PM N ZE PS PM PB PB N PS PM PB PB Angle Error Table : TSA Rules Base Angular Angle Error elocity NB NM NS ZE PS PM PB PB ZE NS NB NB NB NB NB PM PS ZE NS NM NM NB NB PS PB PS ZE NS NS NM NM ZE PB PM PS ZE NS NM NB NS PB PM PS PS ZE NS NB NM PB PB PM PM PS ZE NS NB PB PB PB PB PB PS ZE Change In Error Triangular istributions in [-1, 1] interval ere chosen as membership functions for the scale inputs e an an singletons for. The rules base of the controller TSA is epicte in Table. Note that the inputs scaling factors of the to fuzzy logic controllers ( K, K ', K '') ill be optimize ith the genetic algorithm. The outputs scaling factors ( K, K ) are not optimize because they o not affect the controllers performances. This appears to be ue to the scaling on of the linear velocity to not excee the maximal velocity of the mobile robot. e

4 .IJCSI.org The aopte Genetic Algorithm In this part, a genetic algorithm is applie to tune the s inputs scaling factors in orer to guarantee a fast an smooth robot trajectory by reucing computational time an control errors. A fitness function is use as a convergence criterion to satisfy to measure the best values of the s inputs scaling factors. The fitness function J is chosen as: 1 e (( D ) e ( ) J ) t (7) e (1) e (1) D here ed (1) an e (1) are the tracking errors at the initial positions of the robot an the target. Once the genetic representation of the population an the fitness function are efine, the genetic algorithm procees to initialize a population of solutions, hich is usually generate ranomly an then try to improve it through repetitive application of operators of selection, mutation an crossover. Fig. 5 shos the fitness function evolution accoring to the number of generation of the genetic algorithm. The steps involve in the propose genetic algorithm are summarize ith the folloing steps: Step 1: Generate an initial ranom population of iniviuals for a fixe size accoring to the variation range of each scaling factor. Step : Evaluate the fitness of each iniviual in the population. Step 3: Select fittest iniviuals of the population for reprouction. Step 4: Bree ne iniviuals through reprouction, crossover an mutation operators. Step 5: achieve. Repeat step until the convergence criterion is Once the genetic algorithm is complete, it ill return three parameters corresponing to the inputs scaling factors of the to esigne fuzzy logic controllers TSD an TSA; hich are the best population foun uring the execution of GA. Fitness Function Fitness Generation Fig. 5 Fitness Function s Evolution The population s size an generations number are the most significant parameters of GA since they have irect influence on the convergence of the GA to the optimal solution. Table 3 an 4 sho the genetic algorithm results for ifferent size of population an generations number. Table 3: GA s Results ith Population Size S=3 Generations K K ' K '' Table 4: GA s Results ith Generations G=5 Population size K K ' K '' The Simulation Results an Discussions To perceive the effectiveness of the control scheme propose in this paper, e have simulate both the fuzzy logic controller an its optimization ith the genetic algorithm using Matlab 7. ; hen the mobile robot pursue a target moving along a circular path uring the interval time [, 55s], then a straight line path for the interval [55s, 9s]. The target s trajectory can be escribe by the folloing equations: J J

5 .IJCSI.org 611 yt.5xt 1 ( xt.5) ( yt.5) 9 (8) 6 5 The initial positions of the mobile robot an target are given by (-1, 1) an (5.5,.5) respectively. The linear velocity of the target is set to be. m/s. The esire values of the istance an angle from the robot to the target are set to be D.man. The simulation results are epicte in Fig. 6 to Fig. 1. The trajectories of the target an the robot applying the to esigne control las are plotte in Fig. 6. Fig. 7 an Fig. 8 sho the variation of the tracking errors uring the motion of the target an the robot. Fig. 9 an Fig. 1 sho the evolution of the mobile robot s linear an angular velocities. Y ( m ) X ( m ) Fig. 6 Robot an Target Trajectories Target -GA Table 4 presents the time of convergence of the tracking errors for both an -GA controllers GA Table 5: Time of Convergence of the To Controllers Convergence time (s) Distance Error Angle Error GA 1 15 D i s t a n c e E r r o r ( m ) From Fig. 6, it can be observe that the robot track easily the moving target an catches up ith it as ell the tracking errors ten to zero. In term of robot s velocities, the robot moves forar ith high spees an evolve to stabilize then aroun the target s velocities as the tracking errors are converging to maintain the control s objectives (Fig. 7 to Fig. 1). In the other han, in term of comparison beteen the to controllers performances, it s obvious that the -GA controller is much better than the controller. In fact, the trajectory of the mobile robot uner -GA is much smoother an shorter than that uner, hich presents eviations in its trajectory before it matches ith that of the target. The s outputs exhibit fluctuations at various time instants ith high magnitues than those of the -GA. As shon in Table 5, the -GA is much effective than in term of the spee of convergence of the tracking errors. A n g l e E r r o r ( egree ) Fig. 7 Distance Error Evolution -GA Fig. 8 Angle Error Evolution

6 .IJCSI.org 61 L i n e a r e l o c i t y ( m/s ) GA Fig. 9 Robot s Linear elocity Y ( m ) Target Case 1 Case -1 Case 3 Case X ( m ) Fig. 11 Robot an Target Trajectories uner ifferent outputs scaling factors. A n g u l a r e l o c i t y ( egree/s ) 5-5 -GA Fig. 1 Robot s Angular elocity We have also teste the target tracking uner ifferent outputs scaling factors ( K, K ). The target an robot trajectories are epicte in Fig.11. ( K, K ) Table 5: Outputs scaling factors Case 1 Case Case 3 Case 4 (1.3, 3) (, 3.5) (.5, 4) (3, 4.5) The trajectory of the robot uner the ifferent cases are almost the same an catches up the target at the same point ithin the convergence time; hich can be explaine by the saturation block ae in the output of the TSD controller to scale on the linear velocity hen it excees.7 m/s. Thus, the optimization of these factors is not necessary since they on t affect the controllers performances. 6. Conclusions This paper aresses the problem of the tracking of moving target along an unknon trajectory by a mobile robot. The propose approach aims to esign an intelligent controller base on fuzzy logic techniques an improve by a genetic algorithm. The principal role of artificial intelligence techniques is their ability to esign robust controllers ith goo performances in spite of the lack of information about the mobile robot or its surrouning environment moels. To fuzzy logic controllers base on Takagi-Sugeno moel an have been aopte to etermine the mobile robot s velocities to fulfill the control objectives. A genetic algorithm has been also implemente to improve the by optimizing its inputs scaling factors for better efficiency an effectiveness. The provie simulation results sho that the propose approach acts successfully an enable the robot to track the moving target easily ith goo performances in term of convergence time an accuracy. The use of a genetic algorithm to tune the inputs scaling parameters of the makes the robot s trajectory an the controllers outputs much smoother an reuces consierably the convergence time an the tracking errors. Further orks may be irecte to exten the result in an environment containing obstacles an consiering the target velocities in the esign of the control la.

7 .IJCSI.org 613 References [1] P. K. Pahy, T. Sasaki, S. Nakamura an H. Hashimoto, "Moeling an Position Control of Mobile Robot", in International Workshop on Avance Motion Control, 1, pp [] R. Carelli, C. M. Soria, an B. Morales, "ision-base Tracking Control for Mobile Robots", in IEEE International Conference on Avance Robotics, 5, pp [3] J. Qiuling, X. Xiaojun, an L. Guangen, "Formation Path Tracking Controller of Multiple Robot System by High Orer Sliing Moe", in IEEE International Conference on Automation an Logistics, 7, pp [4] R. Calvo an M. Figueireo, "Reinforcement Learning for Hierarchical an Moular Netork in Autonomous Robot Navigation", in International Joint Conference on Neural Netorks, 3, pp [5] X. Ma, W. Liu, Y. Li an R. Song, " LQ Neural Netork Base Target Differentiation Metho for Mobile Robot ", in IEEE International Conference on Avance Robotics, 5, pp [6] T-H. S. Li, S. J. Chang, an W. Tong, Fuzzy Target Tracking Control of Autonomous Mobile Robots by using Infrare Sensors ", IEEE Transactions on Fuzzy Systems, ol. 1, No. 4, 4, pp [7] L. Ming, G. Zailin an y. Shuzi, "Mobile Robot Fuzzy Control Optimization using Genetic Algorithm", Artificial Intelligence in Engineering, ol. 1, No. 4, 1996, pp [8] L. Moreno, J. M. Armingol, S. Garrio, A. De La Escalera an M. A. Salishs, "Genetic Algorithm for Mobile Robot Localization using Ultrasonic Sensors ", Journal of Intelligent an Robotic System, ol. 34(),, pp [9] M. Taher, H. E. Ibrahim, S. Mahmou an E. Mostafa, "Tracking of Moving Target by Improve Potential Fiel Controller in Cluttere Environments ", International Journal of Computer Science Issues, ol. 9(), No. 3,1, pp [1] L. Huang, "elocity Planning for a Mobile Robot to Track a Moving Target - a Potential Fiel Approach", Robotics an Autonomous Systems, ol. 57(1), No. 3,9, pp [11] Q. Liu, Y-G. Lu an C-X. Xie, "Fuzzy Obstacle-avoiing Controller of Autonomous Mobile Robot Optimize by Genetic Algorithm uner Multi-obstacles Environment", in Worl Congress on Intelligent Control an Automation, 6, pp [1] C. Rekik, M. Jallouli, an N. Derbel, "Optimal Trajectory of a Mobile Robot by a Genetic Design Fuzzy Logic Controller", in International Conference on Avances in Computational Tools for Engineering Applications, 9, pp [13] J. H. Hollan, Aaptation in Natural an Artificial Systems, Ann Arbor: University of Michigan Press, [14] D. E. Golberg, Genetic Algorithms in Search, Optimization an Machine Learning, Ne York: Aison-Wesley Professional, He then joine Harbin Engineering University, China as research staff orking toar a Ph.D egree. His research interests inclue ision in robotics, mobile robots navigation an intelligent control techniques. Zhu Qi-an is a professor at College of Automation, Harbin Engineering University, China. He receive his M.Sc egree from Harbin Shipbuiling Engineering Institute in 1987 an his Ph.D egree in 1 from Harbin Engineering University. He has supervise several master an Ph.D stuents. His research interests are mainly focuse in the area of robotics, machine vision, omniirectional vision an engineering control systems. Karim Benbouaballah receive his first university cycle iploma from National Preparatory School for Engineering stuies, Rouiba, Algeria in 5 an state engineering iploma in Systems Control from Military Polytechnic School, Borj El Bahri, Algeria in 8.