外文翻译-Enforce工业补偿控制的具有自主能力的机器人手臂
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外文翻译-Enforce工业补偿控制的具有自主能力的机器人手臂
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外文翻译-Enforce工业补偿控制的具有自主能力的机器人手臂,外文翻译-Enforce工业补偿控制的具有自主能力的机器人手臂
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Control Engineering Practice 15 (2007) 627638 Forcefree control with independent compensation for industrial articulated robot arms Satoru Gotoa,?, Tatsumi Usuia, Nobuhiro Kyurab, Masatoshi Nakamuraa aDepartment of Advanced Systems Control Engineering, Saga University, Honjomachi, Saga 840-8502, Japan bDepartment of Electrical and Communication Engineering, School of Humanity-Oriented Science and Engineering, Kinki University, 11-6 Kayanomori, Iizuka 820-8555, Japan Received 22 August 2005; accepted 2 November 2006 Available online 15 December 2006 Abstract Forcefree control of robot manipulators so far has been the passive motion of the arm due to the infl uence of external force under ideal conditions of zero gravity and zero friction, whereas this paper demonstrates forcefree control under assigned friction, gravity and inertia. The effectiveness of the proposed forcefree control with independent compensation is confi rmed by comparing the experimental results with simulation results. Comparisons of the forcefree control with independent compensation to the other force control methods are also presented. r 2006 Elsevier Ltd. All rights reserved. Keywords: Industrial robots; Robotic manipulators; Force control; Passive motion; Control algorithm 1. Introduction Among wide variety of tasks for which robot arms are used in the industry, one particular task is where robot arms are used to pull out die-casted components. This application requires the robot arm be guided by an external force. Industrial robot arms, however, are diffi cult to be moved by an external force because the servo controller of the industrial robot arm controls the motion of the robot arm excited by an input signal responsible for the motion. The torque generated by the external force is a kind of disturbance for the robot control system and it can be compensated by the servo controller. Some of the major previous work on position, velocity, andtorquecontrolofrobotarmsareasfollows: polynomial family of PD-type controller (Reyes Sciavicco Michael,John,Timothy,Tomas, fax: +81952288666. E-mail address: gotoee.saga-u.ac.jp (S. Goto). motion of the end-effector outside a predefi ned part of the free space cannot be realized by the sensorless fl exible control. On the other hand, the authors have proposed the forcefree control (Kushida, Nakamura, Goto, Kyura, 1996). The servo controller adopts P and PI type cascade control; the P controller is used for the position loop control and the PI controller is used for the velocity loop control. The servo controller generates the torque input to the robot arm as ss KtKvKpqd? q ? _ q sd sg? sf,(2) where qdis the input of joint angle, sdis the friction compensation torque and sgis the gravity compensation torque. As expressed in (2), the servo controller includes the friction compensation and the gravity compensation through integral action of PI control. The friction and the gravity are assumed to be ideally compensated by the servo controller as sd D_ q Nmsgn_ q(3) and sg gq.(4) The torque caused by an external force sfis also compensated by the servo controller because the servo controller of an industrial robot arm is designed such that the stiffness of the robot arm is high enough and the robot arm cannot be moved by the external force. The joint dynamics with the servo controller included can be obtained by substituting (2), (3), and (4) into (1) as follows: Hq q hq; _ q KtKvKpqd? q ? _ q(5) which shows the possibility of independently compensating the effects of inertia, friction, and gravity, while being able to assign these effects arbitrarily. The whole dynamics of ARTICLE IN PRESS Position input (3) Gravity torque calculation (2) Friction torque calculation Forcefree control part Servo motor and mechanism - Industrial articulated robot arm ControllerControlled object Servo controller s q Kp s KvK (5) Torque monitor f s (9) f/cf (10) cd d (11) cg g (12) qd (1) External torque calculation cd cg 1/cf (4) External force df (8) f (7) g (6) d g f - Fig. 1. Block diagram of forcefree control with independent compensation. S. Goto et al. / Control Engineering Practice 15 (2007) 627638628 the industrial robot arms controlled by the forcefree control with independent compensation is described by Hq q hq; _ q sf=cf? cdsd? cgsg,(6) where cf, cdand cg are the coeffi cients of the inertia, friction and gravity terms, respectively. They can be tuned to adjust the respective effects, independently. For in- stance, cf 1, cd 0 and cg 0, corresponds to the original forcefree control (Kushida et al., 2003) and cf cd cg 0 corresponds to the perfect compensation of the inertia, friction and gravity. Limit of the forcefree control with independent compensation will be discussed in Section 5.1. Theblockdiagramoftheforcefreecontrolwith independent compensation is shown in Fig. 1. The desired joint angle (qd) for the forcefree control with independent compensation is obtained by substituting (6) into (5) and by solving for qdas qd K?1 p K?1 v K?1 t 1=cfsf? cdsd? cgsg _ q q,(7) where sfis the joint torque corresponding to the external force f on the tip of robot arm and it is obtained by substituting (2) into (5) as sf ?ss? sd? sg? Hq q hq_ q.(8) Here, ssis measured by the torque monitor, which is usually attached to the servo controller, and is used to monitor the torque of the joint motors. Generally, the speed of the guided motion of an industrial robot arm is relatively slow, usually less than 1 5 of the rated speed. Hence, the inertia and nonlinear terms of the robot arm are negligibly small Hq q hq_ q ? 0, and the external torque is approximately given by sf ?ss? sd? sg.(9) Finally, the control law of the forcefree control with independent compensation is obtained by substituting (9), (3) and (4) into (7) as qd K?1 p K?1 v K?1 t ?ss=cf 1=cf? cdD_ q Nmsgn_ q 1=cf? cggq _ q q.10 Then, the dynamics of the robot arm controlled by the forcefree control with independent compensation is given in (6) and the control input is as in (10). When the robot arm is in a singular confi guration, the restriction of the motion of the robot arm such as unmovable directions exists. If the direction of the external force is along an unmovable direction in a sin- gular confi guration, the torque caused by the external force will be zero. Even in this case, problems such as the divergence of the control input (10) will not occur. This is an advantage of using torque to detect an external force. 2.2. Estimation of friction term and gravity term 2.2.1. Friction term Friction term sdconsists of Viscous friction D_ q and Coulomb friction Nmsgn_ q as in (3). The friction effect to the motion of robot arm is estimated by the torque output under constant velocity motion. The friction term is obtained through the following procedure: ?To cancel the gravity effect, the robot arm is vertically positioned. ?Various constant velocity inputs are applied to each link of the robot arm. ?Respective torque outputs corresponding to the applied velocities are measured by using the torque monitor. ?Torque output is plotted against applied velocity. ? Viscous friction coeffi cient D and magnitude of Cou- lomb friction Nmin (3) are estimated by using the least- squares method from the plotted data. The estimation of the friction term from the experiment is discussed in Section 3.2.1. 2.2.2. Gravity term The gravity term is a function of the robot arm confi guration q in (4). Here, the gravity is modeled by gq Cqa b,(11) where Cq is the arm confi guration dependent matrix, e.g., Cq cosq1cosq1 q2 0cosq1 q2 ! for an articulated robot arm with 2 degrees-of-freedom. In (11), constant term b is usually neglected in robot arm dynamics, however, it is introduced to represent the actual behavior of the robot arm. The parameters a and b are estimated by using the least-squares method from the experimental data of the steady-state torque monitor outputs for various confi gurations of the robot arm. For the estimation of parameters a and b in (11), the steady- state torque monitor outputs are used because the torque monitor output contains transient component, which is caused by the integral action of the servo controller. Hence, the gravity compensation torque can be represented by sg I ? eAtgq,(12) where eAt e?t=T10?0 0e?t=T2 . . . . . . . . . 0 0?0e?t=Tn 0 B B B B B 1 C C C C C A and T1;.;Tnare time constants which are estimated from the actual torque monitor outputs. The estimation of ARTICLE IN PRESS S. Goto et al. / Control Engineering Practice 15 (2007) 627638629 the gravity term from the experiment is discussed in Section 3.2.2. The effect of badly estimated parameters in the gravity and friction compensation causes to deteriorate the control performance.Quantitatively,over-compensationofthe gravity and the friction terms causes an unexpected behavior. Hence, accurate estimation of the parameters is required. 2.3. Algorithm of forcefree control with independent compensation The algorithm of the forcefree control with independent compensation is shown in Fig. 2. Initial setting of the forcefree control with independent compensation is ex- pressed in the following fi rst three items: ?Servo parameters Kp, Kvand Ktare obtained from the servo controller. ?Friction term (3) is estimated as explained in Section 2.2.1. ?Gravity term (12) is estimated as explained in Section 2.2.2. The forcefree control with independent compensation is executed according to the following nine items: ?External force (f ) is applied to the robot arm. ?Torque monitor detects the external force (f ). ?The friction torque (sd) is estimated by Eq. (3). ?The gravity torque (sg) is estimated by Eq. (12). ?External torque (sf) is calculated by Eq. (9). ?Torque of inertia compensation (1=cfsf) is calculated. ?The friction compensation torque (cdsd) is calculated. ?The gravity compensation torque (cgsg) is calculated. ?The position input (qd) is generated by Eq. (7). Finally, the reference position input (qd) is given to the servo controller. According to the above algorithm, the forcefree control with independent compensation is realized. The inertia matrix Hq and the coupling nonlinear term hq; _ qintherobotarmdynamicsinEq.(5)are not required in order to realize the forcefree control with independent compensation. The torque input to the robot arm ssis measured by the torque monitor, the friction term, D_ q Nmsgn_ q and the gravity term, gq are estimated in the algorithm as explained in Section 2.2. Servo parameters Kp, Kvand Ktin the servo controller are necessary in the algorithm and these parameters are known from the specifi cations of the servo controller. 3. Verifi cation of forcefree control with independent compensation 3.1. Conditions Robot arm motion by using the forcefree control with independent compensation was confi rmed by simulation study and experiments. The simulation study shows ideal motion of the forcefree control with independent compen- sation. An industrial articulated robot arm (Performer- MK3S, YAHATA Electric Machinery Mfg., Co., Ltd.) was used for the experiment on the forcefree control with independent compensation. The schematic of an experi- mental setup is shown in Fig. 3. Two links of Performer- MK3S was used for the experiment. The link lengths of the robot arm are l1 0:25 (m), l2 0:215 (m), and masses of the links are m1 2:86 (kg), m2 2:19 (kg), respectively. The position loop gain was Kp diagf25;25g (1/s), the velocity loop gain was Kv diagf150;150g (1/s), and the torque constant was Kt diagf0:017426;0:036952g Nm=rad=s2. The technical details of hardware and software char- acteristics are shown in Table 1 and an illustration of the robotic experimental setup is shown in Fig. 4. 3.2. Estimation results of friction term and gravity term 3.2.1. Friction term Fig. 5 shows a sample output of the friction term and the actual data. The dots and the curves in Fig. 5 are the experimental results and the estimated friction terms using (3) under the conditions (a) _ q140, (b) _ q240, (c) _ q1o0 and (d) _ q2o0, respectively, using the least-squares method. ARTICLE IN PRESS External force (f) Measurement of torque input (s) by using torque monitor Calculation of external torque ( f) Calculation of position input (qd) from total torque (4) (5) (8) (12) Calculation of friction torque (d)(6) Calculation of gravity torque (g)(7) Torque of inertia compensation (f/cf) Forcefree control (9) Torque of friction compensation (cddf)(10) Torque of gravity compensation (cgg)(11) Servo parameters (Kp, Kv, K ) Derivation of gravity model ( g) (1) (2) Derivation of friction model ( d) (3) Initial setting Fig. 2. Flowchart of forcefree control with independent compensation. S. Goto et al. / Control Engineering Practice 15 (2007) 627638630 The estimated friction terms are: (a) td 1 0:345_ q1 0:027 _ q140; (b) td 2 0:141_ q2 0:019 _ q240; (c) td 1 0:442_ q1? 0:007 _ q1o0; (d) td 2 0:159_ q2? 0:005 _ q2o0. A close proximity of the results show the accuracy of friction model. 3.2.2. Gravity term The gravity term as in (12) is estimated by the procedure described in 2.2.2 as a 0:114 0:041T, b 0:0012 ARTICLE IN PRESS A/D Conv. D/A Conv. X-axis F Y-axis Force sensor Link1 Link2 A/D Conv. Velocity input Torque monitor Position output Pulse counter Personal computer Articulated robot arm Servo controller Performer MK3S Force signal Fig. 3. Schematic diagram of experimental setup. Table 1 Hardware and software characteristics of the experimental setup (a) Performer MK3S Degree-of-freedom5 Driving property (V/(pulse/s) 4:88 ? 10?6 Detecting property (V/(pulse/s) 1:46 ? 10?5 Encoder resolution (pulse/rev)8192 Transportable mass (kg)2(max speed), 3(low speed) Body mass (kg)32 (b) Specifi cation of each axis of Performer MK3S Axis123 Length of arm (mm)135250215 Power (W)808080 Rated torque (Nm)0.3190.3190.159 Rated rotation frequency (rev/s)404050 Rated voltage (V)100100100 Rated current (A)2.22.20.9 Reduction-gear ratio1/1201/1601/160 Inertia moment of motor axis Nms2 4:0 ? 10?74:0 ? 10?72:7 ? 10?7 (c) Computer and interfaces OSRT-Linux 3.1 (Linux Kernel 2.4.4) Sampling interval4 (ms) AD converter (Interface Co., Ltd. PCI-3153)?5 (V), 12 (bit), 16 (ch) DA converter (Interface Co., Ltd. PCI-3338)?5 (V), 12 (bit), 8 (ch) Pulse counter (Interface Co., Ltd. PCI-6201)24 (bit), 4 (ch) Force sensor (Nitta Co., Ltd IFS-50M31A)Linearity p0.1 (%), Hysteresis p 0.1 (%), Stiffness: p 0.025 (mm) (Force), p 0.035 (mm) (Moment), Resolution 1/16384, 100 (N) (Fx, Fy), 200 (N) (Fz), 5 (Nm) (Mx;My;Mz) S. Goto et al. / Control Engineering Practice 15 (2007) 627638631 0:0317T, T1 0:6 s and T2 0:5 s. Fig. 6 shows a sample output of the gravity term and the experimental data where the position x;y 0:3;0:3 (m). The results show a good comparability between the model output and the experimental data. 3.3. Experimental results Step input of 10 (N) to X-axis direction was applied to the tip of the robot arm. The force sensor was used to measure the value of the external force. The initial end- effector position of the robot arm was at 0:3;0:3 (m). Experimental results of theforcefreecontrol with independent compensation are shown in Fig. 7, where the coeffi cients of compensation are: (i) cf 1;cd 0;cg 0, (ii) cf 0:8;cd 0;cg 0, and (iii) cf 1;cd 1;cg 0. In Fig. 7, the dotted lines show the theoretical responses through simulation and the bold lines show the experi- mental results. Comparing Fig. 7(i) with (ii), the robot arm under the condition of cf 0:8 moved longer than that of cf 1. The results show the effect of inertia compensation. Comparing (i) with (iii), the robot arm under the condition of cd 0 moved longer than that of cd 1. When cd 1, the friction torque acted on the robot arm motion and the robot arm stopped quickly compared with the perfect compensation of the friction cd 0. The results show the effect of friction compensation. As in Fig. 7, the experimental results and theoretical response are almost the same and thereby it shows that the ideal forcefree control with independent compensation can be achieved in practice. The results show that the forcefree control with independent compensation is realized with an actual industrial robot arm. To check the generality of the proposed forcefree control with independent compensation, an experiment was carried out using an articulated robot arm with 3 degrees-of- freedom. The experimental result is shown in Fig. 8. As shown in Fig. 8, the forcefree control with independent compensation is equally applicable to the articulated robot arms with 3 degrees-of-freedom. 4. Applications of forcefree control with independent compensation 4.1. Direct teaching Direct teaching for teaching playback type robot arms is an application of the forcefree control with independent compensation, where the robot arm is manually moved by the human operators hand. Usually, teaching of industrial articulated robot arms is carried out by using operational equipment and smooth teaching can be achieved if direct- teaching is realized. Fig. 9 shows the experimental result of direct-teaching where the compensation coeffi cients are cf 0:5, cd 1 ARTICLE IN PRESS Fig. 4. An illustration of the robotic experimental setup. 024 0 0.1 Torque Nm Time s 024 Time s Link 1 0 0.1 Torque Nm Link 2 Fig. 6. Estimation of gravity term x;y 0:3;0:3 (m). 0.0500.05 0.05 0 0.05 link 1 link 2 Velocity rad/s TorqueNm a d c b Fig. 5. Estimation of friction term. S. Goto et al. / Control Engineering Practice 15 (2007) 627638632 and cg 0. The experimental equipment is the same as described in Section 3.1. As shown in Fig. 9, teaching was successfully done
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