The Motion Path Study of Measuring Robot Based on Variable Universe Fuzzy Control

Transcription

1 MATEC Web of Conferences 95, 8 (27) DOI:.5/ matecconf/27958 ICMME 26 The Motion Path Study of Measuring Robot Based on Variable Universe Fuzzy Control Ma Guoqing, Yu Zhenglin, Cao Guohua, Zhang Ruoyan and Zheng Yanbin School of Mechatronical Engineering, Changchun University of Science and Technology, Changchun 322 Abstract. For the roblem of measuring robot requires a higher ositioning, firstly learning about the error overview of the system, analysised the influence of attitude, seed and other factors on systematic errors. Then collected and analyzed the systematic error curve in the track to comlete the lanning rocess. The last adding fuzzy control in both cases, by comaring with the original system, can found that the method based on fuzzy control system can significantly reduce the error during the motion. Introduction Robots are comlex mechatronic system and easily influenced by external and self structure []. Modern control technology for solving robot self adatation, selflearning ability rovides a owerful hel. At resent, the common robot control technology includes adative control, robust control, otimal control, neural network control and sliding mode control. Chang-Min o take a heavy industrial robot as the research object, PI control and fuzzy PD control are studied resectively. The result roves that the fuzzy PD control is more effective [2]. Yu mingliang designed the fuzzy PD control and searate integral control for the mobile robot, simulation results show that the tracking error of the robot becomes very small [3]. The fuzzy control was alied to a three freedom arallel robot by Jingjun Zhang [4]. To rove the control recision of the robot is imroved by using fuzzy control, ADAMS and MATLAB joint simulation were used; Gao yanfeng roved that the redictive fuzzy control is more advantage than traditional fuzzy controller by arc seam tracking exeriments [5]. 2 Establish a model of measuring robot Robot kinematics study the relationshi between the the each joint variable and the end osition, in order to describe movement or rotation relationshi between the joint and the end. Denavit and Hartenberg ut forward DH arameter method. This section establishing the robot joint coordinates (as shown in Fig. ) based on DH arameter method. Its corresonding DH arameters as shown in Table. is Joint angle, which reresents angle between the the xi and x i axis about the zi d is link offset, which reresents the distance from the origin of frame i to the x i axis along the zi is link twist, which reresents the angle from z i axis to the z i axis about the xi a is link length, which reresents the distance from the the zi axis and the z i axis along the xi axis, for intersecting axis is arallel to z i z ; i Z X Y X3 Y3 Z3 X2 Z2 a2 Y Y2 Z X Figure.. Measuring robot DH model. d4 Y5 X5 X4 Y4 Table. DH arameters. Axis ( ) a (m) ( ) d (mm) PID arameters otimization based on variable universe fuzzy theory For a low stiffness series system such as a measurement robot, with a PID arameters cannot meet the control recision of the system obviously. Controller can adjust PID arameters according to the system overshoot and Z5 Z4 Y6 X6 Z6 The Authors, ublished by EDP Sciences. This is an oen access article distributed under the terms of the Creative Commons Attribution License 4. (htt://creativecommons.org/licenses/by/4./).

2 MATEC Web of Conferences 95, 8 (27) DOI:.5/ matecconf/27958 ICMME 26 time, steady-state error, and so on, in order to achieve the urose of otimal control. The detailed rocess is as follows: the object of fuzzy control is roortional gain, integral gain i and differential gain d.for the velocity vff and acceleration feed-forward coefficient aff.after initial osition on the robot manually setting will no longer changed. 3. The design of fuzzy controller 3.. Language and language variable value Fuzzy language is used to describe an object by fuzzy control, fuzzy control objects has 5. Set the language of error variable is E, linguistic variable error rate of change of E c, the roortional gain correction amount of linguistic variables is, integral gain correction amount of linguistic variables is i, differential gain correction amount of linguistic variables is d. They are the domain 3, 2,,,, 2,3 the corresonding language is {NB NM NS ZO PS PM PB}, exressed great negative, negative, small medium large zero, forward small medium, large forward great Language membershi function values Membershi function of fuzzy control is mainly used for object describe the extent of the value, the language is related to the actual situation of this system and the objects understanding and judgment of oerator. Membershi function in comliance with objective reality as the standard,the membershi function have many form, commonly used trigonometric functions, Gaussian function and so on, using the trigonometric functions in this roject as shown in Fig. 2, the membershi function of the secific value show in Table 2: NB NM NS ZO PS PM PB 3..3 Language and language variable value Fuzzy rules is comosed of a series of fuzzy conditional statement each statement on behalf of a relationshi, such as when the error and error change rate is great The outut of the negative is great, This statement can be reresented as IF E = PB and E c = PB THEN=NB. Fuzzy rules to a large extent affected the effect of fuzzy control. Here according to the exerience of the engineering ractice, set u shown in Table 3. i and d Table 3. Fuzzy rule table of, fuzzy rule Ec E NB NM NS ZO PS PM PB NB PB PB PM PM PS ZO ZO NM PB PB PM PS PS ZO NS NS PM PM PM PS ZO NS NS ZO PM PM PS ZO NS NM NM PS PS PS ZO NS NS NM NM PM PS ZO NS NM NM NM NB PB ZO ZO NM NM NM NB NB 3..4 Defuzzification The result is a collection of fuzzy reasoning the rocess of transforming the fuzzy set to the outut is called fuzzy solution, fuzzy methods include weighted average method and the maximum membershi degree method.maximum membershi degree method, just as its name imlies is to maximum membershi degree in fuzzy set value corresonding linguistic variables as outut.set the outut fields to A, then the outut value of the maximum membershi degree method is U { e ( e ) ( e) e, e A} () In the actual situation of Chinese style e may have more than one, then you can take the average or maximum minimum value, this article USES the method of minimum maximum, the descrition is as follows U Min{ e ( e ) ( e) e, e A} (2) Variable universe factor Figure. 2. Triangular membershi function Table 2. Membershi function value inut E E NB.65.3 NM NS ZO PS PM PB.3.65 x In fuzzy control, as the error decreases, error corresonding language variable values can also reduce accordingly. This will affect the recision of the fuzzy control, but the introduction of the theory of domain factor can contribute to real-time exansion theory domain.imrove the fine degree of control. In the literature [6] uts forward a new theory of variable domain factor,not only few arameters and is also small amount of calculation, front design, with reference to the literatur [7] to be considered at the same time, designed variable domain factors as follows: () x 3 x ( ) (3) 2

3 MATEC Web of Conferences 95, 8 (27) DOI:.5/ matecconf/27958 ICMME 26 in the tye: - scaling factor arameters, this article take.5 - the smallest ositive number, this article take. Literature ointed out that the theory of variable domain factor in theory domain U [3 3] need to meet the dual character, avoid zero, monotonicity, coordination and normality. For tye (3) the variable domain factor to fully meet the above requirements. 4 The fuzzy otimization exeriments of measuring robot ath 4. The design of fuzzy controller In Table 4 for the exeriment of four osture of the robot, under the initial osture has comleted the system manual adjustment of PID arameters, take shaft, the ste resonse as shown in Fig. 3 (a). Now by robot ste resonse under different attitude to observe attitude of the influence of system error,this article selects three kinds of tyical gesture,concrete numerical value shown in table 6.Tests found only shaft has obvious change under the three attitude dynamic erformance. Fig. 3(b)/3(c)/3(d) in addition to osition 3, the remaining shaft dynamic erformance under two kinds of gestures are getting worse, ste resonse show obvious fluctuation.contrast three kinds of attitude discovery, all dynamic erformance with oor osture (a) ste resonse of initial osture (b) ste resonse of ose (c) ste resonse of ose x (d) ste resonse of ose3 Figure. 3. The ste resonse of axis in different osture Table 4. Pose data of robot(uint ( )). ose A A2 A3 A4 A5 A6 ose ose ose The change of system error in the motion From the revious section, the big arm forward shaft dynamic erformance is oorer, so when lanning robot trajectory. Ensure the rotraction of the big arm as far as ossible. This aer shows a way to teach the lanning of a straight line (two oints determine a straight line) and a circular arc (three oints to determine a circular arc). Concrete numerical value shown in table 5 and table 6.The seed of the robot is 9 mm/s and 7 mm/s in the finish line and arc trajectory. Table 5. Trajectory data of line(uint ( )) Axis Point A A2 A3 A4 A5 A6 origin Start end Table 6. Trajectory data of circle(uint ( )) Axis Point A A2 A3 A4 A5 A6 origin Aoint Boint Coint Fig. 4 and Fig. 5 is sindle motor error variation of shaft in the motion of robot, can see from the diagram, whether a straight line trajectory or circular trajectory, and can match with velocity changes.in the rocess of robot movement, the following error is the dominance in error sources,and the error is relatively large. Linear and circular arc in the rocess of movement error range resectively is [285.83, ] and [226.42, 36.73], unit is ulse. Now as an examle, analysis the change of the error in a straight line motion, for the convenience of descrition. Set shaft motor corresonding to the origin, the osition of the starting oint and end oint of A, B, C resectively. As shown in Fig. 5, when the motor received instructions from A to B, motor acceleration 3

4 MATEC Web of Conferences 95, 8 (27) DOI:.5/ matecconf/27958 ICMME 26 instantaneous added to a larger values, making seed u in a short time. The resulting is follow error also rising sharly, when the seed reaches a certain value when the basic remain unchanged.at this oint, the following error is similar to the horizontal line, will soon arrived at oint B,seed quickly droed to zero seed error caused by suddenly disaeared. is the above rocess in Fig. 7, 2 is shaft sindle motor curves in the rocess of the robot in a straight line (from B to C), the motor is reverse. The seed is negative. There for when the error is negative, due to the robot slower (9 mm/s). At this time of the error value relative to the revious inhibits PTP (A to B) are smaller. The formation of 3 and are similar, just the distance of the robot walk further seed is relatively large, so the error value also rose slightly Figure 4. Error variation of axis during linear motion Figure 5. Error variation of axis during arc motion Through the above analysis that can draw the following conclusion, the following error in the rocess of movement is the main error; he greater the velocity and acceleration, the greater the error also; the lus or minus of error deend on the direction of seed Exeriment and analysis To make u for the defects, this article into the fuzzy adative control. Through the otimization of PID arameters to further reduce the error. Consider safety factors, in ractical alications the PID arameters, set the uer and lower limits effect of the fuzzy control is shown in Fig. 6 and Fig. 7, you can see that the feedforward, fuzzy control effect is more obvious. In linear motion, for examle, when the error suddenly rises, fuzzy control quickly down the overshoot () in Fig. 6, Once to set the uer and lower limit of PID arameters, PID arameters will not change, the error of line aroximation (2 in Fig. 6). After movement has stoed, the seed of error caused by raidly disaearing.at this time of the error is mainly comosed of noise, friction factors, such as its value in the range of 3 cts change. Due to the change range is relatively small.aroximation error line is a horizontal line (3) in Fig. 7. Here it should be ointed out that, the robot in the movement rocess and motion stos, the main factors causing error are not the same. So use movement at the end of the otimization of the PID arameters to adjust the system error of resting, the effect is not very ideal.this toic research the reositioning recision of the robot in between.6mm, the PID value of manual setting in the system when the seed suddenly means that the error of the effect is satisfying, so when the velocity is zero, PID value is given the system initialization Figure 6. Linear motion error Figure 7. Circular motion error Mentioned earlier, the PID value is set the uer and lower, many times exeriments show that the PID adjustable range is wide, error dro, the more obvious. But if the PID adjustment range is too wide, PID values has far deviated from initial value when seed is zero, if once the seed is zero at this time, PID suddenly give initial value, when system occur large overshoot and oscillation, it will be stabilized at about 2cts even after the shock elimination of error value. This is deadly, because it will greatly influence the ositioning recision of the system reeated, so the PID uer and lower s setting needs to be aroriate.after many exeriments, can found,when the quantitative factor was set to., the scaling factor is set to,change PID arameters in between, and the tracking accuracy and reeat ositioning accuracy 2 3 4

5 MATEC Web of Conferences 95, 8 (27) DOI:.5/ matecconf/27958 ICMME 26 are in good level (see Table 9 and Table ).As shown in figure,because suddenly initialise cause slight overshoot, the suer tone value for 9 cts, but it can be seen that overshoot is almost just a moment, then the system back to the ideal level (3 cts).visible is reasonable setting in front of the uer and lower limits. Table 9 and Table is the otimization effect comared with the before. Table 7. Set of quantization and scaling factor factor E E c i d vale arameters Table 8. PID arameter range of motor initial range [22,36] [3,45] [34,48] Table 9. Effect comarison before and after otimization Line d scheme max error(cts) rimeval fuzzy control rocess origin->start Start->end end->start Seed of Table. Effect comarison before and after otimization (circle) scheme max error(cts) rimeval fuzzy control rocess forward direction negative direction Seed of Summary Analysised the influence of attitude, seed and other factors on systematic errors, laned the two trajectories (lines and circles), collected and analyzed the systematic i error curve in the track to comlete the lanning rocess. added fuzzy control in both cases, by comaring with the original system, can found that the method based on fuzzy control system can significantly reduce the error during the motion ath. This rovide a basis for conduct robot motion ath lanning and otimization based on fuzzy adative control in the future References. Matveev A S, Hoy M, atuitiya J, et al Nonlinear sliding mode control of an unmanned agricultural tractor in the resence of sliding and control saturation. Robotics and Autonomous Systems, 6(9): , (23). 2. Chang-Min o, Seung-yu Park, Tae-SungYoon, et al. Comarative Study of Fuzzy PD Control and PI Control for Heavy Duty Robot. International Conference on Industrial Technology, (29). 3. Yuming Liang, Lihong Xu, Ruihua Wei, et al. Adative Fuzzy Control for Trajectory Tracking of Mobile Robot. International Conference onintelligent Robots and Systems, Taiei, Taiwan: , (2). 4. Jingjun Zhang, Chaoyang Lian, Ruizhen Gao, et al. 3-Degree-of-freedom Parallel Robot Control Based Fuzzy Theory. International Conference on Intelligent Human-Machine Systems and Cybernetics: , (2). 5. Gao yanfeng, Zhang hua, Mao zhiwei, et al.predictive Fuzzy Control for a Mobile Welding RobotSeam Tracking. World Congress on Intelligent Control and Automation: , (28). 6. Cheng Shao, Dong Xiwen, Wang Xiaofang, etc. Variable Universe Fuzzy Controller Selection Factor telescoic. Information and Control, 39(5): , (2). 7. Li Hongxing variable universe adative fuzzy controller. Science in China: Series E., 29(): 32-42, (999). 5