Trajectory control of electro-hydraulic excavator using fuzzy self tuning algorithm with neural network

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1 Jornal of Mechanical Science and Technology 3 (009) 49~60 Jornal of Mechanical Science and Technology DOI 0.007/s Trajectory control of electro-hydralic excavator sing fzzy self tning algorithm with neral network Le Dc Hanh, Kyong Kwan AHN,*, Ngyen Bao Kha and Woo Ken Jo Gradate School of Mechanical and Atomotive Engineering, University of Ulsan, Korea School of Mechanical and Atomotive Engineering, University of Ulsan, Korea (Manscrit Received Setember 3, 007; Revised Jne 0, 008; Acceted Agst 4, 008) Abstract This aer resents the trajectory control of a DOF mini electro-hydralic excavator by sing fzzy self tning with neral network algorithm. First, the mathematical model is derived for the DOF mini electro-hydralic excavator. The fzzy PID and fzzy self tning with neral network are designed for circle trajectory following. Its two links are driven by an electric motor controlled m system. The exerimental reslts demonstrated that the roosed controllers have better control erformance than the conventional controller. Keywords: Intelligent control; Trajectory following control; Fzzy self tning control; Fzzy PID control Introdction Nowadays, excavators lay an imortant indstrial role, esecially in constrction, forestry and mining. These machines are sed for a variety of tasks: lifting, carrying, digging and grond leveling. Most of them are now oerated by hmans, which leads to low efficiency, low oeration seed and inability to oerate in area that hmans cannot access. The atomatic control of excavation tasks is an imortant ste that will make feasible the ftre atomation of constrction work even in a hostile environment. Atomation romises to imrove rodctivity by enabling machines to drive at a higher average seed, imrove safety by searating the hman from the machine and minimizing the risk of accident, and redce oerational costs by minimizing the labor and maintenance needed for each machine. Also, it can be sed in lnar and lanetary constrction sites or in sitations where the direct hysical resence of hman oerators is This aer was recommended for blication in revised form by Associate Editor Kyongs Yi * Corresonding athor , Fax.: address: kkahn@lsan.ac.kr KSME & Sringer 009 hazardos. Varios athors have stdied isses related to the atomatic robotic excavator oeration in recent years [, ] to redce hman interaction with the vehicle. The main long-term goal of this work is to move a tracked vehicle from a starting oint to a target oint in an nstrctred otdoor environment. The kinematics and dynamics of an excavator in both Newton- Eler and Eler-Lagrange formlation were derived in [, ]. However, the oeration of the conventional excavator is controlled by a hydralic system (valve controlled system), ths a great deal of energy is wasted to heat de to throttle losses at the control valves. These models are very difficlt to aly for mobile machines becase of comlicated comonents. Moreover, in recent years, hydralic technology has been develoing raidly to enhance their erformance arameters sch as accrate seed control, high ower weight ratios, hysical size, controllability, reliability, cost and so on. To overcome these weak oints and to satisfy new reqirements, a new concet of hydralic actator, which is called a hybrid actator, has been roosed. In this aer we resent the difference techniqe for control hydralic system by

2 50 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~60 Table. MMP Secification. Rated Ott 50W Rated Voltage DCV 3 Rated Flow 0.9LPM 4 Rated Pressre 6.4MPa 5 Cylinder rod diameter 0mm 6 Cylinder stroke 300mm Fig.. The oeration rinciles of the MMP system. Fig.. The strctre of mini motion ackage (MMP). sing the mini motion ackage (MMP). The strctre and the secification of the MMP are shown in the following Fig. and Table, resectively. From Fig., it can be seen that the MMP consists of one DC servo motor, one variable bidirectional rotational m, one hydralic tank, and one cylinder. The osition of the cylinder can be controlled by the DC servo motor which will adjst and sly the ressre and flow rate to the hydralic m. Becase the hydralic m here is a bidirectional rotational m it is very convenient to change the direction of the actator by changing the direction of the DC motor. The MMP system has not only energy saving and low noise featres bt also a cometitive rice with other drives de to the se of a DC motor as the ower sly. In addition, it can be installed easily by flexible sction ie and sed withot any lbrication. The oeration rinciles of the MMP Fig. 3. Photograh of exerimental aarats. system are shown in Fig.. For measring the axis osition, each controlled axe of the excavator is attached one rotary encoder. It is connected directly to the comter by PCI-QUAD04 card. This MMP and rotary encoder are eqied for boom, arm, and bcket of the mini electro hydralic excavator as shown in Fig. 3. Conventional control theories have roven to be very effective for systems that can be modeled relatively recisely by mathematical eqations. However, they have been fond to be inefficient in handling systems that are either too comlex or too vage to be described by accrate mathematical models. The control of a robotic excavator is difficlt from the standoint of the following roblems: arameter variations in mechanical strctres, varios

3 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~60 5 nonlinearities in hydralic actators, and distrbances de to the contact with the grond. In mechanical strctres, the inertial and gravitational forces vary largely with joint motions. To overcome these difficlties, this aer resents the fzzy self tning control with neral network (FN) algorithm, which does not reqire a recise system model in the control design for the trajectory control of the mini excavator. Exeriments have been imlemented to test the erformance of the roosed control algorithm.. Mathematical model Since the immediate concern is control of ath following motion, which does not excavate the soil, the end-effector and the swing angle are held constant. It follows that the movements of the excavator mechanism dring digging occr in a vertical lane, and the object now is concentrated to control the osition of the boom and arm. For the control task, the forward kinematics and inverse kinematics of excavator are derived. Both forward and inverse kinematics eqations are derived from the fndamental theory for a robotic manilator. These eqations have been develoed to describe the exerimental excavator as a robotic manilator with degree of freedom.. Forward kinematics eqation Kinematics is described as motion of the system. In kinematics, direction and osition lay an imortant role. Robot kinematics is necessary for calclating the osition of the robot. In other words, robot excavator kinematics observes all of the arm motions of the robot withot force and moment [3]. The DOF mini excavator is shown in the following diagram: Forward kinematics will give the coordinates of link as a fnction of the joint angles and arm lengths. The lengths of two links excavator are l, l and the rotation angle are θ, θ resectively Fig. 4. Diagram of DOF mini electro-hydralic excavator. The homogeneos matrix H = R ( θ ) T ( l ) R ( θ ) T ( l ) () z x z x where the rotation matrix arond z axis and translation matrix of link and link are, resectively, as follows: cos( θ) sin( θ) 0 R z ( θ ) = sin( θ) cos( θ) cos( θ) sin( θ) 0 R z ( θ ) = sin( θ) cos( θ) l l Tx ( l) = 0, Tx ( l) = Then the x, y coordinate of the end-effector of link is x l cos( θ)+ l cos( θ + θ) y l sin( θ)+ l sin( θ θ) = +. Inverse kinematics () (3) (4) (5) The inverse kinematics eqation will give a set of joint angles that will achieve a desired Cartesian osition. From Fig. 4 the joint angles θ and θ are derived as follows: c l l cos( θ ) = l l Then c l l sin( θ ) = l l sin( θ ) tan( θ ) = = Therefore θ = c l l l l cos( θ ) c l l l l c l l l l c l l l l tan (6) (7) (8) (9)

4 5 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~60 The angle θ is calclated as follows: θ = β ψ (0) sin sin A Asin l θ θ = c c () y lsinθ θ = Asin Asin x + y x + y () 3. Conventional PID controller The PID controller has been widely sed becase of its simle strctre. It assres accetable erformance for the majority of indstrial rojects. It is a kind of linear controller which forms a control variable by linearly combining the roortional, integral, and derivative of the error e (t). The exression of the conventional PID controller is as follows: t dt + i 0 K = T () t K e() t + e() t K The Lalace transform of (3) is: U T d de() t dt () s K E() s + E() s K T E() s (3) K = + d (4) T s i And the reslting PID transfer fnction is: () s U () = K + + Td s (5) E s Ti s 4. Fzzy PID and fzzy self tning controller It is generally known that the conventional PID controller does not work very well for nonlinear systems, higher order and time-delayed linear systems, and articlarly comlex and vage systems that have no recise mathematical models. To overcome these difficlties, varios tyes of modified conventional PID controllers have been develoed sch as fzzy PID, fzzy self tning controllers and so on. 4. Fzzy controller Fzzy logic consists of three arts: fzzification, fzzy inference and defzzification. The fzzification is an interface that rodces a fzzy sbset from measrement. The fzzy inference is an interface that rodces a new fzzy sbset from the reslt of the fzzification. The defzzification is an interface that rodces a cris ott from the reslts of the fzzy inference. In this aer the fzzy logic controller has two ints, the osition error () e, change of the error ( e ) and one ott ( ). The int ( µ ( e), µ ()) e and ott ( µ ( )) fzzy membershi fnctions were selected symmetrically as shown in Fig. 5. Triangle membershi fnctions were sed in this work. The osition error, change rate of osition error and the ott signal were artitioned in to seven fzzy sets: negative large (NL), negative medim (NM), negative small (NS), zero (ZR), ositive small (PS), ositive medim (PM), ositive large (PL). The imortant art of the fzzy logic controller is to design a rle table. In this work, the rle table consists of the rles that connect the error and the change in error with the control int. It contains lingistic µ ( e), µ ( e ) A tyical real-time imlementation at samling seqence k can be exressed as follows: NL NM NS ZR PS PM PL ( k) = ( k ) + K e( k) K T + e T i ( k) + K T +... d e ( k) e( k ) T (6) Where (k), e (k) are control int to the DC servo motor and error between reference and ott signal, resectively e, e Fig. 5. The membershi fnction of osition error and the change rate of error. µ ( ) NL NM NS ZR PS PM PL Fig. 6. The membershi fnctions of ott signal.

5 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~60 53 Table. Rle table of fzzy controller. e e NL NM NS ZR PS PM PL PL ZR PS PM PL PL PL PL α + + PI PM NS ZR PS PM PL PL PL β PS NM NS ZR PS PM PL PL ZR NL NM NS ZR PS PM PL Fig. 8. PI controller. NS NL NL NM NS ZR PS PM NM NL NL NL NM NS ZR PS NL NL NL NL NL NM NS ZR Fig. 9. Fzzy PID controller. Fig. 0. Overall strctre of control system by sing the fzzy PID controller. Fig. 7. Srface of fzzy rle. rles of the form: If e is e k and e is e k then is where e k, e k, k are the fzzy sbsets of e, e, k, resectively. According to seven fzzy sbsets of e and e, we have 49 rles, and therefore the rle base is reresented in a 7x7 matrix in Table. 4. Fzzy PID controller For comlex nonlinear systems like the excavator, it is not easy to design a good fzzy controller so the fzzy PID control algorithm is alied becase its heristic natre is associated with simlicity and effectiveness. Its nonlinear roerty of control gains can imrove and achieve better system erformance than a conventional PID controller. The fzzy PID controller consists of two main blocks: fzzy controller block and PI block. The fzzy controller block has two ints, signal error e and error change e, and one control signal ott as introdced in chater 4.. The PI block, which consists of a conventional integral block and roortional k block, is introdced in Fig. 8. The roosed fzzy PID controller is shown in Fig. 9, and Fig. 0 shows the overall strctre of the control system by sing the fzzy PID controller of the mini excavator. From Fig. 9, the control signal = α dt + β PID PID is = ( βa + αat) + ( βkp + αkd) e + αkp edt+ βkde (7) where K, K, α, β, A, P and D are scaling factors for e and e, integral gain, roortional gain, i+ i i+ i fzzy set of error, P = and D =, ei+ ei e i+ e i resectively. Hence the fzzy controller becomes a PID controller with varying arameter [4], where its eqivalent roortional control, integral control and derivative control comonents are βkp+ αkd, α KP and β KD, resectively.

6 54 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~ Fzzy self tning with neral network (FN) controller Clearly, the advantage of the roosed fzzy PID algorithm is in simlifying the control rle base significantly and ths greatly increasing the inference efficiency. On the other hand, the disadvantage of this aroach is that the controller arameters are coled with each other and have to be reglated in combination. This roblem can be resolved by introdcing arameter learning and otimization algorithms, sch as neral-network-based algorithms. Nowadays, the fzzy self tning controller has been widely sed for indstrial rocesses becase of its heristic natre associated with simlicity and effectiveness for both linear and nonlinear systems. The on-line arameter adjstment of the fzzy self tning controller has racticability in real-time rocess control. The fzzy self tning controller roosed in this aer has three blocks: fzzy block, neral network block and the conventional PD tning block Fzzy block In order to comare the erformance reslt between fzzy PID and fzzy self tning with neral network which are alied to the mini excavator, the fzzy block has the same membershi fnctions and the same control rle table as introdced in section 4.. The ott of this block is divided into three arts, then each art is fed into the neral block. A diagram of this rocess is resented in Fig.. The control ott signal is tned online by the date rocess of the weight coefficient weight of the neral network w, w, w 3. = ( w + w + w ) (8) nn 3 Where F is the ott signal from the fzzy and nn is the signal ott from the neral network block. F 4.3. Neral block Artificial neral network (ANN) is a class of nonlinear regression and discrimination models. It offers great advantages in learning, adatation, falt tolerance, arallelism, and generalization. Becase of the comlexity of the excavator system, the ott of the fzzy controller is fed back to the int of the neral network, which is resented in Fig.. With its ability to learn, this hybrid techniqe can be sed to imrove the erformance of the control system. The roosed neral block is designed with a single node neral strctre and consists of one int layer and ott layer where the int layer receives the signal ott from fzzy block. The ott layer contains a set of adjstable arameter w i, only one neral node with int fnction. m f = wi F with m = 3 (9) i i= where F i is the int signal of this node The activation fnction of the neral ott is given by eqation: a = nn m i= f F i (0) The learning algorithm of the neral block is based on the minimization of the cost fnction which is defined as E = ε () where ε is calclated as the following eqation: ε = control nn = PD () This means that the energy of the control effort is F w F w nn w 3 F Fig.. Strctre of roosed fzzy self tning with neral network algorithm. Fig.. Neral ott node.

7 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~60 55 minimized. The date rocess of the synatic weights or adjstable arameters w is comted as follows F i wi( t + ) = wi( t) + η PD m i i= F i (3) where η is the learning rate [5]. This eqation is imlemented on each ste of the learning algorithm for the arameters which corresond to the otts of the fzzy controller Tning block It has been known that the fzzy algorithm has some limitation in being directly alied to robot control roblems. First, the fzzy sbsets are defined on the discrete niverse of discorse and the fzzy inference is erformed over sch fzzy sets; the control int is also determined by a qantized vale. Therefore, the effect is insensitive to noise, so smooth motion cannot be exected. Second, the rocedre of the fzzy inference which calclates the overall relationshi matrix reqires mch comtational time in roortion to the nmber of rles. Finally, a dedicated electronic device for high seed fzzy reasoning is needed. To avoid these restrictions the fzzy with neral is modified by an additional conventional feedback controller (CFC) PD tning block. This CFC was roosed by Gomi and Kawato to aly for a nonlinear feedback controller (Hiroaki GOMI., 990). This PD tning block is added in arallel with the neral block, as shown in the block diagram of fzzy self tning controller in Fig. 3. Therefore, the control int to the excavator is algorithm. The calclated control int is sent to the PWM block and is converted to an on/off digital signal by sing DIO (PCI-7). This signal then controls the electric DC motor. 5. Exerimental reslts In the exeriment, the mini excavator was controlled by sing three algorithms: conventional PID, fzzy PID and fzzy self tning with neral network control. The samling time was set at T=0.00s in all exeriments. The length and mass of the boom and arm are l=0.6m, m=.836kg, l=0.95m, m=.348kg, resectively. The feedback signal is read to the comter by the rotary encoder. The system hardware consists of an IBM comatible ersonal comter (Pentim GHz), which is sed to get the feedback signal throgh the encoder board (Advantech, PCI-QUAD 04) and give the control int signal throgh the I/O board (Advantech, PCI-7). The DC motor is controlled by the PWM algorithm. The system hardware is resented in Fig. 5 and Fig. 6. Fig. 4. Overall strctre of control system by sing FN. control = nn + PD (4) From the block diagram in Fig. 3, the overall strctre of the control system by sing FN can be constrcted in the following figre. In Fig. 4, the reference trajectory is generated by PC and the control int is calclated by sing the fzzy self tning Fig. 3. Block diagram of fzzy self tning controller. Fig. 5. Schematic diagram of the exerimental eqiment.

8 56 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~60 Table 3. Reference Trajectory for Case. Time (s) st joint angle (boom) nd joint angle (arm) (a) Boom Fig. 6. Exerimental aarats. (b) Arm Fig. 8. FPID control reslts of two links of the excavator. (a) Boom (a) Boom (b) Arm Fig. 7. PID control reslts of two links of the excavator. Based on the reference trajectory, the angle of each link is calclated and converted to the nmber of lses for generating a control signal PWM ott. For doing the exeriments, two cases of trajectory were investigated as follows: Case: (b) Arm Fig. 9. FN control reslts of two links of the excavator. The setting trajectory of the boom and arm of mini excavator is resented in Table 3. The trajectory is given to check the ste resonse of the roosed control algorithm. The mltile ste resonses of the conventional

9 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~60 57 PID, fzzy PID and fzzy self tning controllers with neral network are shown in Figs. 7, 8 and 9, resectively. It was verified from these figres that fzzy self tning with neral network (FN) and fzzy PID algorithm has a better control erformance than the conventional PID algorithm with faster resonse and smaller error. Case : In this case, the trajectory of the boom and arm of the mini excavator is selected as a circle with a diameter of 70 [mm]. From Fig. 0, it is nderstood that the maximm error of the angle between the ref erence trajectory and measred angle of joint and joint is.6 [ ] and 3 [ ], resectively, by sing the PID algorithm. The error is still large and the amlitde of error is also large. It is abot. [ ] for joint and 5 [ ] for joint and it will be redced by sing the fzzy PID and the FN control algorithm. From Fig., it can be realized that with the fzzy PID algorithm, the accracy is better than the conventional PID algorithm with the maximm error of the Fig. 0. PID control reslts and the error of angle between reference and real signal of the boom and arm of the excavator. Fig.. Fzzy PID control reslts and the error of angle between reference and real signal of the boom and arm of the excavator.

10 58 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~60 Fig. 3. Circle ath following the mini electro hydralic excavator by sing PID controller. Fig. 4. Circle ath following the mini electro hydralic excavator by sing Fzzy PID controller. Fig.. Fzzy self tning control reslts and the error of angle between reference and real signal of boom and arm of the mini electro hydralic excavator. angle between the reference trajectory and measred angle of joint and joint of jst 0.7 [ ] and [ ], resectively. Comared with the PID algorithm, the error is redced 50% for joint and abot 30% for joint. Bt the amlitde of the error is still qite large: abot.4 [ ] for joint and abot 4 [ ] for joint. From Fig., with ability of learning and sing the otimization algorithm, the error is now the smallest comared with PID and fzzy PID algorithm Fig. 5. Circle ath following the mini electro hydralic excavator by sing FN controller. with the maximm error of the angle between the reference trajectory and measred angle of joint and joint of jst 0.6 [ ] and 0.6 [ ], resectively. The error is redced 65% for joint and abot 80% for joint comared with PID algorithm and the amlitde of error is small. It is abot. [ ] for joint and abot. [ ] for joint. It can be seen from Figs. 3, 4, 5 that the fabricated electro hydralic excavator follows the desired trajectory with good agreement in the case of the intelligent fzzy PID and FN controller.

11 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~ Conclsion De to the disadvantages of the traditional PID controller in the mini excavator system, two controllers based on fzzy logic, inclding the fzzy PID controller and fzzy self tning with neral network, were develoed to control the electro hydralic mini excavator. The exerimental reslts show that the fzzy PID controller and FN obviosly have better control erformance than the conventional PID. The fzzy self tning with neral network is more flexible becase the control ott signal is tned online by the date rocess of the neral network. The tracking erformance was imroved by alying the fzzy self tning controller with neral network becase of its better adatability to distrbances and nonlinear systems. Acknowledgment This research was financially sorted by the Ministry of Commerce, Indstry and Energy (MC- OIE) and Korea Indstrial Technology Fondation (KOTEF) throgh the Hman Resorce Training Project for Regional Innovation. References [] M. bodr, M. Zontl, A. Ersak, A. J. Koivo, H. O. Yrtseven, E. Kokaoglan, G. Pasamehmetogl., Jne 999, Dynamic cognitive force control for an atomatic land excavator robot, IEEE Transactions on Robotics and Atomation Vol. 5, [] J. Medanic, M. Yan, B. Medanic, December 997, Robst Mltivariable Nonlinear control of a two links excavator: art, Proceedings of the 36 th Conference on Decision and Control, [3] Mstafa Nil, Ugr Yzgec, Mrat Sonmez Bekir Cakir, May 9-3, 006, Fzzy Neral Network Based intelligent Controller for 3-DOF Robot Manilators, Proceedings of 5 th International Symosim on Intelligent Manfactring Systems, , Sakarya University, Deartment of Indstrial Engineering. [4] Tsng-Tai Hang, Hng-Yan Chng and Jin-Jye Lin, 999, A Fzzy PID Controller Being Like Parameter Varying PID, 999 IEEE International Fzzy Systems Conference Proceedings, [5] Mikhail Petrove, 997, Fzzy Logic Controller With Neral Defzzifier, INCON 97, Le Dc Hanh received the B. S. degree in the deartment of Mechanical Engineering from Hochiminh City University of Technology in 006, the M.Sc. degree in Mechanical and Atomotive Engineering from University of Ulsan in 008. His research interests are electro-hydralic excavator, remote control, intelligent control. Kyong Kwan Ahn received the B. S. degree in the deartment of Mechanical Engineering from Seol National University in 990, the M. Sc. degree in Mechanical Engineering from Korea Advanced Institte of Science and Technology (KAIST) in 99 and the Ph.D. degree with the title A stdy on the atomation of ot-door tasks sing link electro-hydralic manilator from Tokyo Institte of Technology in 999, resectively. He is crrently a Professor in the school of Mechanical and Atomotive Engineering, University of Ulsan, Ulsan, Korea. His research interests are hybrid excavator, flid ower control, design and control of smart atator sing smart material, rehabilization robot and active daming control. He is a member of IEEE, ASME, SICE, RSJ, JSME, KSME, KSPE, KSAE, KFPS, and JFPS.

12 60 L. D. Hanh et al. / Jornal of Mechanical Science and Technology 3 (009) 49~60 Bao Kha Ngyen received the B. S. and M. S. degree from Hochiminh City University of Technology in 00 and 003, resectively, all in Atomatic Control Engineering and the Ph.D. degree from University of Ulsan in 006. His research interests focs on intelligent control, modern control theory and their alications, design and control of smart actator systems. WooKen Jo received the B.S. degree in the deartment of Mechanical and Atomotive Engineering from University of Ulsan in 007. And he matriclated M.S. at University of Ulsan. Crrently, he s sydying on it. His research interests focs on flid control, welfare vehicle, mobile robot