Application of Digging Control based on the Center-of-Mass Velocity of the Attachment of a Hydraulic Excavator IROS2019国际学术会议论文集 0719

Application of Digging Control based on the Center of Mass Velocity of the Attachment of a Hydraulic Excavator Masatoshi Kozui1 Toru Yamamoto1 Kazushige Koiwai2 Koji Yamashita2 and Yoichiro Yamazaki2 Abstract Superior operation skills for hydraulic excavators are learned over time Therefore it is diffi cult to improve the skills of non expert operators quickly and their work needs to be supported This paper presents a control system which realizes smooth digging similar to that performed by expert op erators based on the Center of Mass velocity of the attachment as an index In addition corresponding to the system switching caused by the digging reaction force a controller gain tuning method that uses the Fictitious Exogenous Signal is proposed The proposed method is applied to a hydraulic excavator and its effect is verifi ed I INTRODUCTION At present labor scarcity due to an aging population combined with the diminishing number of children is an important problem in the industrial fi eld of Japan In par ticular there is a marked labor scarcity in the construction industry and there is a concern that the productivity of the construction industry and public engineering works which support the development of industries will deteriorate In order to solve this problem the government in Japan has launched a policy called i Construction 1 By actively utilizing Information and Communication Technology ICT technology labor saving is achieved by automating work etc and maximum productivity is achieved with little labor power 2 However there are still few fi elds where these technologies can be applied and there are many fi elds where the work relies on the judgment of the workers and need to be performed by the workers themselves The operation of hy draulic excavators which are widely used in large number of construction sites is quite complicated Therefore excellent operation techniques are required to obtain high productivity However the number of workers who are experts in such techniques is decreasing due to aging Therefore hydraulic excavators that can achieve with high productivity even with young and non expert operators who have low operation skill need to be developed urgently In a previous research on improving the productivity of hydraulic excavators a method for controlling the movement of the work attachment so that it follows the reference trajectory was proposed 3 However the motion is decided by the operator according to the situation at the actual site and hence it is diffi cult to uniquely determine the reference Moreover even if the motion trajectory followed 1Kozui and Yamamoto are with the Graduate School of Engineering HiroshimaUniversity 1 4 1Kagamiyama Higashi Hiroshima Hiroshima739 8527 Japankozuim hiroshima u ac jp yama hiroshima u ac jp 2Koiwai Yamashita and Yamazaki are with KOBELCO Construction Machinery Co Ltd 2 2 1 Itsukaichikou Saeki ku Hiroshima Japan the reference it cannot be said that the productivity is high in the case of slow motion Therefore in works using hydraulic excavators the dynamics need to be considered in order to improve the productivity by using this control method In another research a control that support based on the predicted and generated motion trajectory dynamically was proposed 4 However original data is required to generate the trajectory in advance and it is considered that an ef fect cannot be obtained easily in the case of performing operations that are different from the assumption On the other hand a smooth motion during digging operations is obtained when it is operated appropriately by an expert This feature is given by combining the Center of Mass CoM of the attachment of a hydraulic excavator 5 It is considered that an expert like motion can be realized by controlling the motion of the attachment according to the CoM velocity without clearly setting any motion trajectory Furthermore the CoM is widely studied in position control of multi arm such as welding robot posture stability control 6 7 However as far as the author knows no example has been reported where a control system based on the CoM including human operations has been constructed This paper proposes a control system based on the combined CoM velocity of the attachment for digging works using a hydraulic excavator The CoM velocity during the digging work is made constant and a smooth digging opera tion similar to that achieved by an expert is realized by opera tion assist Certain system changes are caused by the velocity reduction due to the increase in digging reaction force This system fl uctuation is regarded as a pseudo impulse disturbance in the input In steady state digging velocity even if the system characteristics after system fl uctuation are not known the controller gains are tuned by using this pseudo disturbance as a Fictitious Exogenous Signal A control system that corresponds to the system switching that is a control system with good disturbance responsiveness is constructed The effect of the control system in suppressing the fl uctuation of the CoM velocity during digging work is verifi ed by numerical simulation and a hydraulic excavator II CONTROL OBJECTIVE A Attachment CoM model The CoM model of the attachment is shown in Fig 1 Generally the attachments of a hydraulic excavator include three links boom arm and bucket Although it is diffi cult to extract the characteristics of motion from each movement it is known that the difference in skill appears in the combined 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE2314 Fig 1 Attachment CoM model CoM velocity 5 The coordinates and velocity of the CoM are obtained by using the following equations Xg t Yg t 3 i 1mixi t 3 i 1mi 3 i 1miyi t 3 i 1mi 1 Vg t dXg t dt 2 dYg t dt 2 2 Here miis the mass of each attachment xi t and yi t are the center of mass coordinates of each attachment and i 1 2 and 3 indicate the boom arm and bucket These pa rameters are known from the specifi cations of the hydraulic excavator and the CoM coordinates at each time can be measured or calculated from the angle of the attachment or the length of the hydraulic cylinder which can be measured The target operation is digging As shown in Fig 2 the attachment of the excavator is operated with the two levers on the right and left Generally hydraulic excavators are mostly used for digging works and digging works form a major portion of the work at public engineering work sites In other words digging is an important work that affects productivity The digging operation usually maintains the arm pulling operation at a maximum and it is adjusted by other operations At this time the digging reaction force is increased and the attachment velocity is decreased by digging the soil as shown in Fig 3 In the case of experts boom up of a sub motion is performed to release the reaction force and it is possible to suppress the decrease in the attachment velocity On the other hand it is not easy for non experts to perform this operation properly and the working velocity is considerably lowered Although it is intended to suppress the velocity reduction by performing an operation other than arm pulling it results in an oscillation motion because it is not a smooth operation As a result the work becomes ineffi cient Therefore in this paper a method is proposed to control the boom up operation so that the CoM velocity during digging work will be constant This method aims to perform smooth digging work similar to that performed by experts The block diagram for this method is shown in Fig 4 Fig 2 Operating system of hydraulic excavator Fig 3 Digging motion based on the CoM velocity B Feedback system of CoM velocity The block diagram of the control system based on the CoM velocity of the attachment is shown in Fig 4 The sys tem is the attachment and these movements are represented by the CoM velocity Here r k and y k are the reference and the CoM velocity respectively uarm k uboom k and uc k are the amounts of arm pulling operation boom up operation by the operator and boom up operation calculated by the controller and u k is the input to the system In the system includes human operation the arm pulling operation uarm k given as the input to the system directly and the boom up operation uboom k is controlled so that the CoM velocity y k is maintained at a constant value Specifi cally even if an excessive boom up operation uboom k is input when the CoM velocity by arm pulling is lower than the ref erence r k due to the digging reaction force the amount of operation is adjusted to u k so that it follows the reference velocity As a result it becomes a motion that reduces the digging reaction force by performing the appropriate boom up operation and it becomes similar to the digging motion of an expert III DESIGN OF CONTROL SYSTEM A Design of controller The motion of the hydraulic excavator is quite fast and hence the control system should have good responsiveness Therefore the following discrete PID controller is utilized uc k Kp e k Kie k Kd 2e k 3 Here uc k e k y k and r k indicate the control input control error system output and reference respectively corresponding to Fig 4 Also k indicates the number of steps Kp Ki and Kdare the proportional gain integral 2315 Fig 4 Block diagram of CoM velocity control Fig 5 System fl uctuation during digging gain and differential gain respectively is a differencing operator defi ned by 1 z 1 The control error e k is calculated by the following equation e k r k y k 4 B Controller tuning by Fictitious Exogenous Signal The hydraulic excavator is a nonlinear system due to the characteristics of the internal hydraulic equipment Even though the operation inputs are the same the fl ow rates of the actuators are changed according to the load and the working velocity is changed as shown in Fig 5 Therefore the digging work can be roughly divided into two sections the fi rst half section with the light load and the second half section with the heavy load The time when the CoM velocity cannot be satisfi ed the reference due to increase in load is defi ned as the switching of the system Furthermore the fl uctuation of the output at that time is regarded as the pseudo impulse like disturbance input to the system The pseudo impulse like disturbance is generated from the operating data as a Fictitious Exogenous Signal 8 The operating data is the input output data u0 k y0 k of the experiment using the initial controller gains Here it is necessary to design the reference model Gmd z 1 in order to obtain the controller gains for the desired dynamics First the reference model Gm z 1 is designed by using the Fictitious Reference Iterative Tuning FRIT method 9 Gm z 1 is calculated Fig 6 Block diagram by the following equations 10 Gm z 1 z 1P 1 P z 1 5 P z 1 1 p1z 1 p2z 2 6 Then p1and p2are designed by the following equations p1 2exp 2 cos 4 1 2 7 p2 exp 8 Ts 9 0 25 1 0 51 10 Tsis the sampling time is related to the rising charac teristic of the control and is a parameter related to the attenuation characteristics it can be arbitrarily set by the designer It is desirable that is set between 0 2 When 0 the Binominal model is shown and when 1 the Butterworth model is shown Next the Fictitious Exogenous signal d k is calculated by using the following equation based on the block diagram of Fig 6 d k u0 k uc k 11 The block diagram in Fig 7 shows a control system with disturbance input C z 1 is the PID controller and G z 1 is the system The closed loop transfer characteristic from reference r k to output y k is given by the following equation Gry z 1 G z 1 C z 1 1 G z 1 C z 1 12 The reference model Gm z 1 is expressed by the form of equation 12 In addition the closed loop transfer charac teristic from the disturbance d k to the control error e k is given by the following equation Gde z 1 G z 1 1 G z 1 C z 1 13 The transfer function from a Fictitious Exogenous signal d k to the control error e k is also expressed by the form of equation 13 Therefore the reference model Gmd z 1 can be expressed by the following equation using Gm z 1 Gmd z 1 Gm z 1 C z 1 1 14 2316 Fig 7 Block diagram of closed loop with disturbance input In the stable state the reference model can be designed using equation 14 and a controller having the desired dynamic characteristics can be obtained When d k is input to the reference model Gmd z 1 the reference model output e k is calculated by the following equation e k Gmd z 1 d k 15 Gm z 1 Kp Ki 2Kd d k The controller gains are obtained by performing tuning in such a way that e k approaches e0 k calculated from the operational data It is possible to obtain a controller having desired control performance Therefore the criterion is defi ned by the following equations J 1 N N k 1 e0 k e k 2 16 e0 k r k y0 k 17 Here N represents the total number of steps of data e0 k is calculated by using equation 17 When the criterion J becomes smaller better controller gains are obtained C Optimized calculation In order to obtain the desired control performance it is necessary to set appropriate controller gains based on the criterion J which was described in the previous section However there is an upper limit on the operation input amount of the hydraulic excavator and controller gains that cannot be realized in the actual machine cannot be set There fore the Genetic Algorithm as optimization calculation is used to specify the range of solutions 11 12 First individuals having controller gains as the genes are initially generated Then suboptimal controller gains are obtained through initial evaluation elite selection crossover tournament selection and mutation fl ow In this paper the number of individuals was set as 200 the number of calculation generations was 200 and the calculations were performed using the MATLAB IV NUMERICAL SIMULATION The effect of the proposed controller tuning method is verifi ed by numerical simulation In a system that is switched at the time of digging the responsiveness of the system is deteriorated in the second half section with the heavy load and the velocity is also lowered Therefore the time constant is set larger and the system gain is set smaller compared with the fi rst half 300400500600700800900 step 0 2 4 6 Output y k Reference r k 300400500600700800900 step 0 2 4 Fig 8 Simulation result by the conventional method TABLE I PIDGAIN OF THE CONVENTIONAL METHOD PID gain0 600 0123 0 section with a light load As mentioned above these two systems were set to the following fi rst order system with dead time in the simulation The dead time is determined by the equipment characteristics therefore it is assumed to be the same G1 s 5 1 0 5se 0 1s 18 G2 s 3 1 0 8se 0 1s 19 G1 shows the system before fl uctuation and G2shows the system after fl uctuation When these systems are discretized at discrete time 0 01 sec following equations are obtained respectively Here the Gaussian white noise with zero means and variance 0 01 is given by k y k 0 9802y k 1 0 09901u k 11 k 20 y k 0 9876y k 1 0 03727u k 11 k 21 In the simulation it is assumed that the switching timing of these systems is known and in this study it is switched at the 500th step Next the initial controller gains are determined using the Chien Hrones and Reswick method CHR 13 based on the system parameter given by equation 18 The result of the simulation using these controller gains is utilized as the initial data u0 k y0 k and tuning is performed by the proposed method The simulation results are shown in Figs 8 and 9 Fig 8 and TABLE I show the simulation result of the conventional method CHR It can be confi rmed that the output fl uctuation at the time of system switching is large The output fl uctuates up to 15 relative to the reference and it takes about 110 steps until it returns to within 5 This indicates that the controller gain corresponding to system G1 2317 300400500600700800900 step 0 2 4 6 Output y k Reference r k 300400500600700800900 step 0 2 4 Fig 9 Simulation result by the proposed method TABLE II PIDGAIN OF THE PROPOSED METHOD PID gain2 60 0175 0 is not suffi cient for system G2to obtain good response The simulation result of the proposed tuning method is shown in Fig 9 and TABLE II When the system was changed the system input rose quickly and it can be con fi rmed that the output fl uctuation was suppressed The output fl uctuation is reduced up to 10 relative to the reference and it takes about 25 steps until it returns to within 5 It is found that the control performance of the proposed method is better than that of the conventional method CHR From these results it was confi rmed that the proposed method had an effect on the suppression of output fl uctuation at the time of system switching V EXPERIMENT The proposed method is applied to the digging work based on the CoM velocity of a hydraulic excavator The attachment motion of the hydraulic excavator in Fig 3 is as follows On the horizontal earth surface obtain maximum reach and ground the bucket tip to the earth surface as the initial position Performing digging until the arm is near the vertical The operation pattern for suppressing the unevenness of operation for each experiment is as follows Arm pull maximum operation Boom up maximum operation The hydraulic excavator uses a hydraulic system for opera tion and the operation amount is determined by the hydraulic pressure A hydraulic excavator was modifi ed to install an electrically controllable valve so that it was possible to change the operation amount The boom up operation was controlled by this valve using the proposed method Although the PID controller was used in the simulation the PI controller is applied in the experiment This is because 00 511 522 533 54 Time sec 0 50 100 150 200 CoM velocity non expert expert 00 511 522 533 54 Time sec 0 50 100 Boom up lever input non expert expert Fig 10 Experimental resul