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Development of a three-axis gripper force sensor and the intelligent gripper using it
Sensors and Actuators A 137 (2007) 213–222
Development of a three-axis gripper force sensor and the intelligent gripper using it Gab-Soon Kim ∗ Department of Control and Instrumentation Engineering, Gyeongsang National University, 900 Gajaw-Dong, Jinju, Geongnam 660-701, Republic of Korea Received 31 August 2006; received in revised form 28 February 2007; accepted 2 March 2007 Available online 12 March 2007
Abstract This paper describes the development of a three-axis gripper force sensor that measure forces Fx , Fy and Fz simultaneously, and the intelligent gripper using two three-axis gripper force sensors for grasping an unknown object stably. In order to grasp an unknown object using an intelligent gripper safely, it should measure the forces in the grasping direction and in the gravity direction, and perform the force control with the measured forces. Thus, the intelligent gripper should be composed of two three-axis gripper force sensors that measure forces Fx , Fy and Fz at the same time. In this paper, two three-axis gripper force sensors for measuring forces Fx , Fy and Fz simultaneously were newly modeled using five parallel plate-beams, designed, and fabricated. The characteristic tests of the manufactured sensors were carried out, and their interference errors of the developed sensors were less than 3%. Also, the intelligent gripper was manufactured using two three-axis gripper force sensors, and their characteristic tests were carried out. It was conformed that the developed gripper could grasp an unknown object stably. © 2007 Elsevier B.V. All rights reserved. Keywords: Three-axis gripper force sensor; Intelligent gripper; Parallel plate-beam; Rated strain; Interference error
1. Introduction Robot’s gripper has been researched to grasp an unknown object safely. Some grippers [1–4] were manufactured using two one-direction force sensors to measure the force in grasping direction. Above grippers cannot grasp an unknown object safely, because it cannot measure the weight of them. In order to grip an unknown object stably, first, robot’s gripper should measure the force (weight of object) in gravity direction, second, determine the force of grasping direction, then control the gripper using its force in grasping direction. Therefore, the robot’s gripper should be manufactured with two three-axis gripper force sensors that measure three forces Fx , Fy and Fz simultaneously. In order to measure three forces accurately using two three-axis gripper force sensors in the intelligent gripper, the interference errors of them should be smaller [5,6]. The inter-
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0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2007.03.002
ference error means the values (errors) of the forces measured from other directional sensors except for the directional sensor of the applied force under any direction applied force. For example, it is the values of forces from Fy and Fz sensors under the applied x-direction force Fx . The accuracy of three-axis gripper force sensor usually shows as the interference error of it, because the interference error is much larger than the non-linearity error, the repeatability error, etc., of it [5,6]. In this paper, two three-axis gripper force sensors were developed to measure three forces (Fx , Fy and Fz ) simultaneously, and the intelligent gripper was manufactured using two sensors to grasp an unknown object safely. The sensors were newly modeled by the body with five parallel plate-beams (PPB), and the theoretical equations were derived and the finite element method (FEM) was analyzed with ANSYS software to get the strains of at the attachment positions of strain-gages. Then, the sensors were manufactured with strain-gages, and the characteristic tests of them were carried out. Finally, the intelligent gripper was designed and fabricated using two three-axis gripper force sensors, and their characteristic tests were carried out to grasp an unknown object safely.
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Fig. 2. Model of a three-axis gripper force sensor.
PPB4 is width b1 , thickness t1 and length l1 , and that of PPB5 is width b2 , thickness t2 and length l2 . 2.3. Theoretical analysis Fig. 1. The grasping shape using the gripper with two three-axis gripper force sensors.
2. Three-axis gripper force sensor 2.1. Grasping method of intelligent gripper Fig. 1 shows the grasping shape using the gripper with two three-axis gripper force sensors. In order to grasp an unknown object in an intelligent gripper safely, it should measure the weight of an object, and determine the force of grasping direction according to the gotten weight, finally, grasp the object according to the force of grasping direction. If the x, y, z-direction forces of three-axis gripper force sensors 1 and 2 are Fx1 , Fy1 and Fz1 , and Fx2 , Fy2 and Fz2 , respectively, the equation for calculating the weight of an object can be written as F = mg = (Fx1 − Fx2 )2 + (Fy1 − Fy2 )2 + (Fz1 − Fz2 )2 (1) where m is mass of an object and g is acceleration of gravity.
2.3.1. Under applied force Fx or Fy Fig. 3 shows the free body diagram of plate-beams for a threeaxis gripper force sensor under the forces Fx (or Fy ). PPB1 and PPB2 are symmetrical with respect to x-axis line, and the platebeams 1 and 2 are symmetrical with respect to z-axis line. Thus, the derived equations for analyzing the strains of the plate-beam 1 may be applied to the plate-beams 2, 3 and 4. And they can be applied to the PPB3 and PPB4 under the force Fy , because PPB1 and PPB2, PPB3 and PPB4 have the same structure. When the force Fx is applied to the block between PPB1 and PPB2, the x-direction force FFxx at point z = 0 in the plate-beam 1 can be expressed as [5,6] FFxx =
Fx 4
(2)
The moment equilibrium condition at point 0 ( Mo = 0) can be written as 2MFxy − FFxx l1 = 0
(3)
where MFxy is the y-direction moment due to force Fx .
2.2. Modeling of three-axis gripper force sensor The sensing elements of a three-axis gripper force sensor which measure x, y, z-direction forces Fx , Fy and Fz are newly modeled as shown in Fig. 2. They are composed of five parallel plate-beams, and the PPB gets two plate-beams. The PPB1 and PPB2 are located in horizontal direction, the PPB3 and PPB4 are located in vertical direction, and the PPB5 is located in front–back direction. The B1 and B2 are the blocks to fix the sensor, and B3 is the block to apply the forces to the sensor. If the B1 and B2 of the sensor are fixed on other fixture and forces apply to B3, the forces transfer to each sensor of three-axis force/moment sensor. The PPB1 and PPB2, the PPB3 and PPB4, and PPB5 perceive the forces Fx , Fy and Fz . The size of PPB1, PPB2, PPB3 and
Fig. 3. Free body diagram of plate-beams for a three-axis gripper force sensor under the force Fx (or Fy ).
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The moment equilibrium condition at the point O ( Mo = 0) can be written as d1 Fz − 2d2 FFzx + 2MFzy = 0
(10)
By substituting Eqs. (8) and (9) into (10), the rotational angle of the block φ and the vertical displacement ν can be derived as (2d1 + l2 )Fz + (2/3)l2 ) + (4A2 Ed22 / l2 )
φ= ν= Fig. 4. Free body diagram of plate-beams for a three-axis gripper force sensor under the force Fz .
By substituting Eq. (2) into (3), the moment MFxy is can be derived as Fx l1 MFxy = (4) 8 The moment Mz at arbitrary point z can be derived as Fx l1 z− (5) Mz = 4 2 The equations εFx-U and εFx-L for analyzing the rated strains on the upper and lower surfaces of the plate-beam 1 are derived by substituting Eq. (5) into the bending strain equation ε = Mz /EZ1p , which can be written as l1 Fx z− εFx-U = (6-a) 4EZ1p 2 l1 Fx εFx-L = −z (6-b) 4EZ1p 2 where Z1p is the polar moment of inertia of the plate-beam 1, E the modulus of longitudinal elasticity and l1 is length of platebeam 1. 2.3.2. Under applied force Fz Fig. 4 shows the free body diagram of plate-beams for a threeaxis gripper force sensor under the force Fz . PPB5 is symmetrical with respect to x-axis line, and composed of the plate-beams 9 and 10 in the same size. Thus, the derived equations for analyzing the strains of the plate-beam 9 may be applied to the plate-beam 10. When the force Fz is applied to the end point O2 of the PPB5, the z-direction force FFzz at point x = 0 in the plate-beam 9 is gotten, and the y-direction moment MFzy and x-direction force FFzx due to force Fz can be derived as [5,6] 12EI2 l2 ν + d1 + φ (7) FFzz = 2 l23 A2 Ed2 φ FFzx = l2 12EI2 ν d1 l2 + + φ MFzy = 2 2 3 l22
(8) (9)
(48EI2 / l22 )((3/2)d1
(Fz − (24EI2 / l22 ))(d1 + (l2 /2))φ 24EI2 /l2 2
(11)
(12)
where I2 is the moment of inertia of the area of the plate-beam 9, A2 the area of the plate-beam 9, d1 the distance between the block B3 and the end of the PPB5, d2 the distance between the center line of the block B3, l2 the length of plate-beam 9, and ν is the vertical displacement of the block and the center line of the thickness t2 of the plate-beam 9. The moment Mx at arbitrary point x can be expressed as Mx = FFzz x − MFzy 12EI2 x l2 ν + d1 + = φ 2 l23 d1 l2 12EI2 ν + + φ − 2 2 2 3 l2
(13)
The equations εFz-U and εFz-L for analyzing the rated strains on the upper and lower surfaces of the plate-beam 9 are derived by substituting the equations the bending strain equation ε = Mx /EZ2p and the tension and compression strain equation ε = F/A2 E into Eqs. (11)–(13), which can be written as 6t2 x l2 ν + d1 + εFz-U = 3 φ 2 l2 d1 l2 d2 φ 6t2 ν + + φ + − 2 (14-a) 2 3 l2 l2 2
εFz-L
6t2 x l2 ν + d1 + =− 3 φ 2 l2 6t2 ν d1 l2 d2 φ + 2 + + φ − 2 3 l2 l2 2
(14-b)
where Z2p is the polar moment of inertia of the plate-beam 9. 2.4. Design of three-axis gripper force sensor 2.4.1. Design of the sensing element using theoretical analysis The design variables of the sensing element of three-axis gripper force sensor are the rated capacities and the rated strains of each sensor, and the width, the length and the thickness of the plate-beams, and so on. The variables for designing the three-
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axis gripper force sensor are determined as follows: (1) The rated capacities of Fx , Fy and Fz sensors are 20 N, respectively, taking into consideration of the grasping force of the intelligent gripper. (2) The rated strains of each sensor are about 1000 m/m (about 0.5 mV/V) taking into consideration of the same rated outputs and sensitivities in each sensor [5,6]. (3) The attachment locations of strain-gages for all sensors are 1.5 mm from the end of the plate-beams in the length direction, and the center of the plate-beams in the width direction taking into consideration of the size 17.6 mm2 (3.2 mm × 5.5 mm) of the used straingages. The sizes of the sensing elements were calculated by substituting the determined variables into Eqs. (6-a), (6-b), (14-a) and (14-b). The sizes of the sensing elements in the rated capacities of forces Fx = Fy = Fz = 20 N are as follows: the widths b1 and b2 are 12 mm, the lengths l1 and l2 are 10 mm, the thickness (heights) t1 and t2 are 0.7 and 0.84 mm, and the distances d1 and d2 are 5 and 9.58 mm, respectively. The material of the sensing elements of the three-axis gripper force sensor is Al 2024-T351. 2.4.2. Design of the sensing element using FEM The sensing elements (PBB1–5 (beam 1–10)) of each sensor are analyzed by using the FEM to confirm the strains calculated from the derived Eqs. (6-a), (6-b), (14-a) and (14-b) when the forces Fx , Fy and Fz applied to each sensor, respectively. The strains on the surfaces of the plate-beams are analyzed in three dimensions. The material constants of the plate-beams require that the modulus of the longitudinal elasticity is 70 GPa and the Poisson’s ratio is 0.3. The meshes of the plate-beams have the size of 0.5 mm in the length, three divisions into equal parts in the thickness and six divisions into equal parts in the width. Fig. 5 shows the finite element meshes of sensing elements for FEM analysis. Figs. 6–8 show the deformed shapes when the forces Fx , Fy and Fz applied to each sensor. The PPB1 and PPB2, the
Fig. 5. The finite element meshes of sensing elements for FEM analysis.
Fig. 6. The deformed shape under force Fx .
Fig. 7. The deformed shape under force Fy .
PPB3 and PPB4, the PPB5 were deformed under the force Fx , Fy and Fz , respectively. The rated strains at the attachment locations of strain-gages have gotten. The used software to analyze is ANSYS.
Fig. 8. The deformed shape under force Fz .
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Fig. 9. Locations of strain-gages of three-axis gripper force sensor. Fig. 10. Full bridge circuit.
2.5. Strain analysis and sensor manufacture Fig. 9 shows the attachment locations of the strain-gages for the three-axis gripper force sensor. The attachment locations of strain-gages for each sensor are as follows: Fx sensor is S1, S2, S3 and S4, Fy sensor is S5, S6, S7 and S8, and Fz sensor is S9, S10, S11 and S12. The full bridge circuit for each sensor is constructed using the selected strain-gages for them. Thus, the sensing elements of each sensor are designed using the derived equations ((6-a), (6-b), (14-a) and (14-b)) at the full bridge circuit, they have the rated strains of about 1000 m/m and the interference errors of 0 m/m. The rated strain and the interference strain are calculated using Eq. (15) [5,6]. ε = εT1 − εC1 + εT2 − εC2
(15)
where ε is the rated strain or the interference error, εT1 the strain from the tension strain-gage T1 , εT2 the strain from the tension strain-gage T2 , εC1 the strain from the compression strain-gage C1 and εC2 is the strain from the compression strain-gage C2 . Table 1 shows the results of the rated strains and the interference strains from the theory and FEM analysis. The rated strains from the theory analysis are determined that Fx and Fy sensors are all 1020 m/m and Fz sensor is 1014 m/m. It is that the cutting unit of thickness of 0.1 mm is determined taking into consideration of the cutting capability. The rated strains from the FEM analysis are gotten that Fx , Fy and Fz sensors are 938, 936 and 941 m/m. The strain from theoretical analy-
sis is compared to that from the FEM analysis, and its range of error is less than 8.24%. Because the amount of the error usually appears in FEM analysis, the derived equations can be used to design the modeled three-axis gripper force sensor. Thus, the three-axis gripper force sensor was manufactured by attaching the strain-gages (N2A-13-T001N-350) to the selected attachment locations as shown in Fig. 9 using a bond (M-bond 200) made by Micro-Measurement Company, and constructing the full bridge circuit using the strain-gages for each sensor as shown in Fig. 10. Fig. 11 shows the fabricated three-axis gripper force sensor. 2.6. Results of characteristic test and considerations Fig. 12 shows the experimental set up for the characteristic test of the three-axis gripper force sensor. It is composed of an arm, weights, a body, a measuring device (DMP40). The manufactured three-axis gripper force sensor should be carried out the characteristic test by using the experimental set up to evaluate its rated strains and interference errors. Each sensor was tested three times by using the experimental set up, and
Table 1 Rated strain in theory and FEM analysis Sensor
Analysis
Rated strain (m/m)
Error (%)
Fx sensor
Theory FEM
1020 938
8.03
Fy sensor
Theory FEM
1020 936
8.24
Fz sensor
Theory FEM
1014 941
7.20 Fig. 11. Fabricated three-axis gripper force sensor.
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Fig. 12. Experimental set up for three-axis gripper force sensor: (a) applied Fx force, (b) applied Fy force and (c) applied Fz force.
the output values from each sensor were averaged. In order to compare the rated strains in theory and those in the characteristic test, the unit of the rated strains in theory (m/m) should be changed into the unit of the rated outputs in characteristic test (mV/V). The equation for it is as follows [5,6]: Eo 1 = Kε Ei 4
(16)
where Ei is the input voltage (V) of the full bridge circuit, Eo the output voltage (V) of the full bridge circuit, K the factor of strain-gage (the used factor of strain-gage is 2.03) and ε is the rated strain-gage of each sensor (m/m). The rated strains (m/m) in the theoretical analysis are changed into the rated outputs (mV/V) using Eq. (16). Tables 2 and 3 show the rated outputs of the three-axis gripper force sensors 1 and 2 from the theoretical analysis and the characteristic test. The maximum error of the rated strain from theoretical analysis compared with that from the characteristic test was less than 13.89%. The error may be generated due to the cutting error of the sensing element, the error of the characteristic test, the attachment error of the strain gage, and so
Table 2 Rated strains of three-axis force sensor 1 in theory and characteristic test Sensor
Analysis
Rated strain (mV/V)
Error (%)
Fx sensor
Theory Test
0.518 0.449
13.32
Fy sensor
Theory Test
0.518 0.457
11.78
Fz sensor
Theory Test
0.514 0.493
4.08
Table 4 Interference error of three-axis force sensor 1 in characteristic test Force (N)
Fx = 20 Fy = 20 Fz = 20
Sensor Fx sensor (%)
Fy sensor (%)
Fz sensor (%)
– −0.45 0.22
0.28 – −0.28
0.20 −0.20 –
Table 5 Interference error of three-axis force sensor 2 in characteristic test Force (N)
Sensor Fx sensor (%)
Fx = 20 Fy = 20 Fz = 20
– −0.90 0.90
Fy sensor (%) 0.29 – 0.58
Fz sensor (%) 0.20 −0.20 –
on. Tables 4 and 5 show the interference errors of the three-axis gripper force sensors 1 and 2 from the characteristic test. The maximum interference error of the fabricated three-axis gripper force sensor is below 0.9%, and it is similar or less than that of commercial multi-axis force/moment sensor [7,8]. It is thought that the interference error of the three-axis gripper force sensor is expressed as the error of the sensing elements in processing, the error of the attachment of the strain-gages, and the error of measurement from the fluctuation of the sensor at measuring environment. Thus, it is thought the derived Eqs. (6-a), (6-b), (14-a) and (14-b) could be usefully used to design the modeled three-axis gripper force sensor. 3. Intelligent gripper
Table 3 Rated strains of three-axis force sensor 2 in theory and characteristic test
3.1. Intelligent gripper
Sensor
Analysis
Rated strain (mV/V)
Error (%)
Fx sensor
Theory Test
0.518 0.446
13.89
Fy sensor
Theory Test
0.518 0.452
12.74
Fz sensor
Theory Test
0.514 0.503
2.14
In order to grasp an unknown object safely, the robot’s intelligent gripper should get the function on measuring the weight of the object, controlling the force in the grasping direction. Fig. 13 shows photograph of the manufactured gripper with two threeaxis gripper force sensors. It is composed of a controller, three motor drive, two three-axis gripper force sensors, a grasping motor, a up–down rotating motor, a left–right rotating motor, a body, a LM guide, and so on.
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Fig. 13. Photograph of the manufactured gripper with two three-axis gripper force sensors.
The controller measures the forces from the three-axis gripper force sensors 1 and 2, calculates the weight of an unknown object, and operates a grasping motor, a up–down rotating motor and left–right rotating motor. The three-axis gripper force sensors 1 and 2 were fixed to a LM guide, and moved to grasping direction simultaneously due to operating the grasping motor and rotating the screw, and the rubbers are attached to the cases of two three-axis sensors to prevent the sliding between the object and the two three-axis force sensors. They were used to measure the weight of an unknown object, and were developed in this research. Their maximum capacity is 20 N. The grasping motor (RE-max24, 222037) is used to operate the three-axis gripper force sensors 1 and 2 in grasping direction, and its specifications is that the maximum number of rotations is 9800 rpm, the power is 11 W, the voltage is 12 V, the ratio of gear (GP22C, 14398) is 53:1 and the encoder (MR201940). The up–down rotating motor (RE30, 268193) is used to rotate the grasping motor, two threeaxis gripper force sensors, and so on, in the up–down direction, and its range is 360◦ . The specifications of the motor are that the maximum number of rotations is 8200 rpm, the power is 60 W, the voltage is 12 V, the ratio of gear (GP32C, 166940) is 66:1 and the encoder (MR225785). The left–right rotating motor is used to rotate the grasping motor, up–down rotating motor, two threeaxis gripper force sensors, and so on, in the left–right direction, and its range is 360◦ . It is kind of the same as the up–down rotating motor. The operation of the intelligent gripper is as follows: first, the three-axis gripper force sensors 1 and 2 grasp an unknown object by controlling the grasping motor, and the up–down rotating motor rotates the gripper with the object in range of 5◦ . Second, the controller measures the forces from the three-axis gripper sensors 1 and 2, and calculates the weight of the object taking use of Eq. (1), and determines the force of the grasping direction. Third, the gripper grasps the object by controlling the grasping motor with the grasping force. Fourth, the controller rotates the intelligent gripper by controlling the up–down
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Fig. 14. Block diagram of controller of the intelligent gripper.
rotating motor and the left–right rotating motor. The developed intelligent gripper can safely grasps an unknown object having the size of 85 mm and the weight of 20 N, it can rotates the range of 0–360◦ . 3.2. Controller of intelligent gripper Fig. 14 shows block diagram of controller of the intelligent gripper, and Fig. 15 shows photograph of controller of the intelligent gripper. The gripper is composed of a -processor (80C196KC), a grasping motor (motor 1), an up–down rotating motor (motor 2), a left–right rotating motor (motor 3), two three-axis gripper force sensors, six amplifier, and so on. The controller was manufactured using -processor (80C196KC), this operates with frequency of 20 MHz and gets several function on analog/digital converter, PWM, timer/counter and so on. The controller gets the amplified signals of the sensors, and calculates the weight and the grasping force.
Fig. 15. Photograph of controller of the intelligent gripper.
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Fig. 16. Electric circuit of amplifier.
And its PWM ports supply some voltage to the motor drives to operate the up–down rotating motor and the left–right rotating motor, and its timer/counters get the pulses from the encoders attached to each motor. The motor drives were manufactured by using IC (HD74HC14P). The three-axis gripper force sensors 1 and 2 perceive the forces Fx1 , Fy1 , Fz1 , and Fx2 , Fy2 , Fz2 , and they are sent to two amplifier. Fig. 16 shows electric circuit of amplifier, it is composed of six amplifiers (AD627AN), few resisters and capacitors. The resister (R19), which is a variable resister, adjusts the zero balance of the full bridge circuit in each sensor, the resister (R18), which is a variable resister, adjusts the amplification ratio of the amplifiers to amplify the signals from each sensor. The amplifiers 1 and 2 amplify about 1000 times under the rated loads (Fx = Fy = Fz = 20 N), send the voltage 2 V to the controller. Fig. 17 shows block diagram for control system of the intelligent gripper, it is composed of a controller, three motor drives, a grasping motor, six amplifiers and so on. The reference value (grasping force) is 2 N in the case of the weight of the object under 4 N calculated from Eq. (1), that is, the weight is divided by 2 in the case of more than 4 N. The controller calculates the voltage to input the motor drive, the three-axis gripper force sensors 1 and 2 grasp an unknown object by operating the grasping motor, and the amplifiers amplify the force signals from the force sensors and send them to the controller. Fig. 18 shows flow chart for the control of the intelligent gripper. The program orders are as follows: (1) Initialization of the controller. (2) Gripper grasps an unknown object by controlling the grasping motor with the reference value of 2 N.
Fig. 17. Block diagram for control system of the intelligent gripper.
Fig. 18. Flow chart for the control of the intelligent gripper.
(3) Gripper is rotated about 5◦ by operating the up–down rotating motor. (4) Three-axis gripper force sensors perceive the weight of the object. (5) Controller calculates the weight of the object by using Eq. (1). (6) If the weight is under 0.2 N, the controller judges that the gripper does not grasp the object (the object slide down between the two three-axis gripper force sensor) because the weight is above 4 N, and the above process (2)–(5) is repeated again with the reference value of 4 N. Then, if it
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Fig. 19. Block diagram of characteristic test for grasping force of gripper: (a) block diagram and (b) photograph.
is not the weight value, the reference value is increased and increased 2 N until 20 N. (7) If the weight is 0.2–4 N, the grasping force keeps 2 N, and if the weight is above 4 N, the grasping force is determined by dividing the weight to 2. (8) Gripper grasps the object with the determined grasping force (reference) again. (9) Gripper with the object is moved by operating the up–down rotating motor and the left–right rotating motor. 3.3. Characteristic test and considerations In order to grasp an unknown object safely, the grasping characteristic test to determine the grasping force is carried out. Fig. 19 shows block diagram of characteristic test for grasping force of gripper. The method of the test is that the gripper with grasping force from 2 to 20 N (increasing step is 2 N) grasps the block with the contacting surface (800 mm2 (32 mm × 25 mm)), the weights of 5 N are handed up on the block, then, the weights are countered when the block just slide down between two three-axis gripper force sensors. In the results, the weight is more than 2.5 times. Thus, the grasping force was determined as the value of the weight of the object divided by 2. If the contacting surface between two force sensors and the object is different, the determined grasping force is different. The grasping force (Fx ) is 2 N at first time, the grasping force keeps its value in the case of 0.2–4 N calculated due to Eq. (1). The reason of the initial value of 2 N is that the gripper could safely grasp an egg, a plastic bottle for water, and so on. If the weight is above 4–20 N, the grasping force is the weight divided by 2. (For example, if the weight is 11 N, the grasping force is 5.5 N ((11 N)/2 = 5.5 N).) The characteristic test of the gripper for grasping an unknown object was carried out. The PI control is performed, and the output equation of PI controller is written as u(k) = Kp e(k) + Ki
k n=1
e(n)
where u(k) is the output value of k times of PI controller, Kp the proportional gain, Ki the integral gain, e(k) the error, that is, the value which subtract the output value of the three-axis gripper force sensor (1) from reference value and kn=1 e(n) is the sum of errors. The characteristic test to get the proportional gain Kp of the PI controller and the integral gain Ki was carried out. In order to get these values, the unit step response was carried out increasing the proportional gain from 10 to 90 with the unit step of 10, and increasing the integral gain from 0.05 to 0.40 with the unit step of 0.05. As the results, the proportional gain Kp of 30 and the integral gain Ki of 0.15 were gotten. Fig. 20 shows the unit step response test of the controller. By this time the overshoot is below 0.1 N, the steady state error is below 0.1 N, the rising time is below 0.5 s, and the dead time is 0.2 s. It is thought that the proportional gain and the integral gain are not the gotten optimal values and there are noses in the controller. And, to get the dead time of 0.2 s in the controller is because of the rubbers on the cases of two three-axis force sensors. The controller could safely grasp an unknown object with the proportional gain and the integral gain, because the error is small. Fig. 21 shows the photograph of the gripper with objects, (a) egg, (b) plastic paste bottle, (c) plastic water bottle and (d) weight. As shown in Fig. 21, it is conformed that the developed gripper could safely grasp them.
(10) Fig. 20. Unit step response test of the controller.
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simultaneously, and the design and the manufacture of the intelligent gripper using two sensors to grasp an unknown object stably. It could be conformed that the developed three-axis gripper force sensor is excellent in the maximum interference error [7,8], that the developed intelligent gripper using two sensors safely grasps the objects. Thus, it is thought that the developed three-axis gripper force sensor can be used for manufacturing an intelligent gripper, and the developed intelligent gripper can be used to grasp an unknown object safely. Acknowledgement This work was supported by grant no. R01-2006-000-104680 from the Basic Research Program of the Korea Science & Engineering Foundation. References [1] J.A. Domnguez-Lpez, R.I. Damper, R.M. Crowder, C.J. Harris, Adaptive neurofuzzy control of a robotic gripper with on-line machine learning, Robot. Auton. Syst. 48 (September (2–3)) (2004) 93–110. [2] J. Zhang, B. Rssler, Self-valuing learning and generalization with application invisually guided grasping of complex objects, Robot. Auton. Syst. 47 (June (2–3)) (2004) 117–127. [3] J.J. Steil, F. Rthling, R. Haschke, H. Ritter, Situated robot learning for multimodal instruction and imitation of grasping, Robot. Auton. Syst. 47 (June (2–3)) (2004) 129–141. [4] X. Yin, D. Guo, M. Xie, Handimage segmentation using color and RCE neural network, Robot. Auton. Syst. 34 (March (4)) (2001) 235– 250. [5] G.S. Kim, D.I. Kang, S.H. Rhee, Design and fabrication of a threecomponent force/moment sensor using plate-beam, Meas. Sci. Technol. 10 (1999) 295–301. [6] G.S. Kim, Design of 3-component force/moment sensor with force/moment ratio of wide range, Kor. Soc. Precision Eng. 18 (2) (2001) 214–221. [7] Ati Industrial Automation, Multi-Axis Force/Torque Sensor, Ati Industrial Automation, 2005, pp. 4–45. [8] BL Autotec, BL Sensor, Multi-Axis Force/Torque Sensor (BL-FTS-E020), BL Autotec, 2003, pp. 5–50.
Biography
Fig. 21. Photograph of the gripper grasping objects: (a) object (egg), (b) object (plastic paste bottle), (c) object (plastic water bottle) and (d) object (weight).
4. Conclusions This paper describes the development of the three-axis gripper force sensor, which detects forces Fx , Fy and Fz
Gab-Soon Kim got BS degree in precision mechanical engineering from Jeonbook National University, MS and PhD degrees in precision mechanical engineering from Hanyang University, Republic of Korea, in 1986, 1990 and 1999, respectively. He was a senior researcher at Department of Force Laboratory, Korean Research Institute of Standards and Science, Republic of Korea, from February 1990 to February 2000, and a visiting researcher at Department of Intelligent Robot Laboratory, University of Tsukuba, Japan, from July 2003 to June 2004. Since 2000, he has been with Gyeongsang National University, where he is currently associate professor at Department of Control & Instrumentation Engineering. His main research interests are in the areas of multi-axis force/moment sensor of intelligent robot, intelligent service robot and intelligent system.
Development of a three-axis gripper force sensor and the intelligent gripper using it Gab-Soon Kim ∗ Department of Control and Instrumentation Engineering, Gyeongsang National University, 900 Gajaw-Dong, Jinju, Geongnam 660-701, Republic of Korea Received 31 August 2006; received in revised form 28 February 2007; accepted 2 March 2007 Available online 12 March 2007
Abstract This paper describes the development of a three-axis gripper force sensor that measure forces Fx , Fy and Fz simultaneously, and the intelligent gripper using two three-axis gripper force sensors for grasping an unknown object stably. In order to grasp an unknown object using an intelligent gripper safely, it should measure the forces in the grasping direction and in the gravity direction, and perform the force control with the measured forces. Thus, the intelligent gripper should be composed of two three-axis gripper force sensors that measure forces Fx , Fy and Fz at the same time. In this paper, two three-axis gripper force sensors for measuring forces Fx , Fy and Fz simultaneously were newly modeled using five parallel plate-beams, designed, and fabricated. The characteristic tests of the manufactured sensors were carried out, and their interference errors of the developed sensors were less than 3%. Also, the intelligent gripper was manufactured using two three-axis gripper force sensors, and their characteristic tests were carried out. It was conformed that the developed gripper could grasp an unknown object stably. © 2007 Elsevier B.V. All rights reserved. Keywords: Three-axis gripper force sensor; Intelligent gripper; Parallel plate-beam; Rated strain; Interference error
1. Introduction Robot’s gripper has been researched to grasp an unknown object safely. Some grippers [1–4] were manufactured using two one-direction force sensors to measure the force in grasping direction. Above grippers cannot grasp an unknown object safely, because it cannot measure the weight of them. In order to grip an unknown object stably, first, robot’s gripper should measure the force (weight of object) in gravity direction, second, determine the force of grasping direction, then control the gripper using its force in grasping direction. Therefore, the robot’s gripper should be manufactured with two three-axis gripper force sensors that measure three forces Fx , Fy and Fz simultaneously. In order to measure three forces accurately using two three-axis gripper force sensors in the intelligent gripper, the interference errors of them should be smaller [5,6]. The inter-
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0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2007.03.002
ference error means the values (errors) of the forces measured from other directional sensors except for the directional sensor of the applied force under any direction applied force. For example, it is the values of forces from Fy and Fz sensors under the applied x-direction force Fx . The accuracy of three-axis gripper force sensor usually shows as the interference error of it, because the interference error is much larger than the non-linearity error, the repeatability error, etc., of it [5,6]. In this paper, two three-axis gripper force sensors were developed to measure three forces (Fx , Fy and Fz ) simultaneously, and the intelligent gripper was manufactured using two sensors to grasp an unknown object safely. The sensors were newly modeled by the body with five parallel plate-beams (PPB), and the theoretical equations were derived and the finite element method (FEM) was analyzed with ANSYS software to get the strains of at the attachment positions of strain-gages. Then, the sensors were manufactured with strain-gages, and the characteristic tests of them were carried out. Finally, the intelligent gripper was designed and fabricated using two three-axis gripper force sensors, and their characteristic tests were carried out to grasp an unknown object safely.
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Fig. 2. Model of a three-axis gripper force sensor.
PPB4 is width b1 , thickness t1 and length l1 , and that of PPB5 is width b2 , thickness t2 and length l2 . 2.3. Theoretical analysis Fig. 1. The grasping shape using the gripper with two three-axis gripper force sensors.
2. Three-axis gripper force sensor 2.1. Grasping method of intelligent gripper Fig. 1 shows the grasping shape using the gripper with two three-axis gripper force sensors. In order to grasp an unknown object in an intelligent gripper safely, it should measure the weight of an object, and determine the force of grasping direction according to the gotten weight, finally, grasp the object according to the force of grasping direction. If the x, y, z-direction forces of three-axis gripper force sensors 1 and 2 are Fx1 , Fy1 and Fz1 , and Fx2 , Fy2 and Fz2 , respectively, the equation for calculating the weight of an object can be written as F = mg = (Fx1 − Fx2 )2 + (Fy1 − Fy2 )2 + (Fz1 − Fz2 )2 (1) where m is mass of an object and g is acceleration of gravity.
2.3.1. Under applied force Fx or Fy Fig. 3 shows the free body diagram of plate-beams for a threeaxis gripper force sensor under the forces Fx (or Fy ). PPB1 and PPB2 are symmetrical with respect to x-axis line, and the platebeams 1 and 2 are symmetrical with respect to z-axis line. Thus, the derived equations for analyzing the strains of the plate-beam 1 may be applied to the plate-beams 2, 3 and 4. And they can be applied to the PPB3 and PPB4 under the force Fy , because PPB1 and PPB2, PPB3 and PPB4 have the same structure. When the force Fx is applied to the block between PPB1 and PPB2, the x-direction force FFxx at point z = 0 in the plate-beam 1 can be expressed as [5,6] FFxx =
Fx 4
(2)
The moment equilibrium condition at point 0 ( Mo = 0) can be written as 2MFxy − FFxx l1 = 0
(3)
where MFxy is the y-direction moment due to force Fx .
2.2. Modeling of three-axis gripper force sensor The sensing elements of a three-axis gripper force sensor which measure x, y, z-direction forces Fx , Fy and Fz are newly modeled as shown in Fig. 2. They are composed of five parallel plate-beams, and the PPB gets two plate-beams. The PPB1 and PPB2 are located in horizontal direction, the PPB3 and PPB4 are located in vertical direction, and the PPB5 is located in front–back direction. The B1 and B2 are the blocks to fix the sensor, and B3 is the block to apply the forces to the sensor. If the B1 and B2 of the sensor are fixed on other fixture and forces apply to B3, the forces transfer to each sensor of three-axis force/moment sensor. The PPB1 and PPB2, the PPB3 and PPB4, and PPB5 perceive the forces Fx , Fy and Fz . The size of PPB1, PPB2, PPB3 and
Fig. 3. Free body diagram of plate-beams for a three-axis gripper force sensor under the force Fx (or Fy ).
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The moment equilibrium condition at the point O ( Mo = 0) can be written as d1 Fz − 2d2 FFzx + 2MFzy = 0
(10)
By substituting Eqs. (8) and (9) into (10), the rotational angle of the block φ and the vertical displacement ν can be derived as (2d1 + l2 )Fz + (2/3)l2 ) + (4A2 Ed22 / l2 )
φ= ν= Fig. 4. Free body diagram of plate-beams for a three-axis gripper force sensor under the force Fz .
By substituting Eq. (2) into (3), the moment MFxy is can be derived as Fx l1 MFxy = (4) 8 The moment Mz at arbitrary point z can be derived as Fx l1 z− (5) Mz = 4 2 The equations εFx-U and εFx-L for analyzing the rated strains on the upper and lower surfaces of the plate-beam 1 are derived by substituting Eq. (5) into the bending strain equation ε = Mz /EZ1p , which can be written as l1 Fx z− εFx-U = (6-a) 4EZ1p 2 l1 Fx εFx-L = −z (6-b) 4EZ1p 2 where Z1p is the polar moment of inertia of the plate-beam 1, E the modulus of longitudinal elasticity and l1 is length of platebeam 1. 2.3.2. Under applied force Fz Fig. 4 shows the free body diagram of plate-beams for a threeaxis gripper force sensor under the force Fz . PPB5 is symmetrical with respect to x-axis line, and composed of the plate-beams 9 and 10 in the same size. Thus, the derived equations for analyzing the strains of the plate-beam 9 may be applied to the plate-beam 10. When the force Fz is applied to the end point O2 of the PPB5, the z-direction force FFzz at point x = 0 in the plate-beam 9 is gotten, and the y-direction moment MFzy and x-direction force FFzx due to force Fz can be derived as [5,6] 12EI2 l2 ν + d1 + φ (7) FFzz = 2 l23 A2 Ed2 φ FFzx = l2 12EI2 ν d1 l2 + + φ MFzy = 2 2 3 l22
(8) (9)
(48EI2 / l22 )((3/2)d1
(Fz − (24EI2 / l22 ))(d1 + (l2 /2))φ 24EI2 /l2 2
(11)
(12)
where I2 is the moment of inertia of the area of the plate-beam 9, A2 the area of the plate-beam 9, d1 the distance between the block B3 and the end of the PPB5, d2 the distance between the center line of the block B3, l2 the length of plate-beam 9, and ν is the vertical displacement of the block and the center line of the thickness t2 of the plate-beam 9. The moment Mx at arbitrary point x can be expressed as Mx = FFzz x − MFzy 12EI2 x l2 ν + d1 + = φ 2 l23 d1 l2 12EI2 ν + + φ − 2 2 2 3 l2
(13)
The equations εFz-U and εFz-L for analyzing the rated strains on the upper and lower surfaces of the plate-beam 9 are derived by substituting the equations the bending strain equation ε = Mx /EZ2p and the tension and compression strain equation ε = F/A2 E into Eqs. (11)–(13), which can be written as 6t2 x l2 ν + d1 + εFz-U = 3 φ 2 l2 d1 l2 d2 φ 6t2 ν + + φ + − 2 (14-a) 2 3 l2 l2 2
εFz-L
6t2 x l2 ν + d1 + =− 3 φ 2 l2 6t2 ν d1 l2 d2 φ + 2 + + φ − 2 3 l2 l2 2
(14-b)
where Z2p is the polar moment of inertia of the plate-beam 9. 2.4. Design of three-axis gripper force sensor 2.4.1. Design of the sensing element using theoretical analysis The design variables of the sensing element of three-axis gripper force sensor are the rated capacities and the rated strains of each sensor, and the width, the length and the thickness of the plate-beams, and so on. The variables for designing the three-
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axis gripper force sensor are determined as follows: (1) The rated capacities of Fx , Fy and Fz sensors are 20 N, respectively, taking into consideration of the grasping force of the intelligent gripper. (2) The rated strains of each sensor are about 1000 m/m (about 0.5 mV/V) taking into consideration of the same rated outputs and sensitivities in each sensor [5,6]. (3) The attachment locations of strain-gages for all sensors are 1.5 mm from the end of the plate-beams in the length direction, and the center of the plate-beams in the width direction taking into consideration of the size 17.6 mm2 (3.2 mm × 5.5 mm) of the used straingages. The sizes of the sensing elements were calculated by substituting the determined variables into Eqs. (6-a), (6-b), (14-a) and (14-b). The sizes of the sensing elements in the rated capacities of forces Fx = Fy = Fz = 20 N are as follows: the widths b1 and b2 are 12 mm, the lengths l1 and l2 are 10 mm, the thickness (heights) t1 and t2 are 0.7 and 0.84 mm, and the distances d1 and d2 are 5 and 9.58 mm, respectively. The material of the sensing elements of the three-axis gripper force sensor is Al 2024-T351. 2.4.2. Design of the sensing element using FEM The sensing elements (PBB1–5 (beam 1–10)) of each sensor are analyzed by using the FEM to confirm the strains calculated from the derived Eqs. (6-a), (6-b), (14-a) and (14-b) when the forces Fx , Fy and Fz applied to each sensor, respectively. The strains on the surfaces of the plate-beams are analyzed in three dimensions. The material constants of the plate-beams require that the modulus of the longitudinal elasticity is 70 GPa and the Poisson’s ratio is 0.3. The meshes of the plate-beams have the size of 0.5 mm in the length, three divisions into equal parts in the thickness and six divisions into equal parts in the width. Fig. 5 shows the finite element meshes of sensing elements for FEM analysis. Figs. 6–8 show the deformed shapes when the forces Fx , Fy and Fz applied to each sensor. The PPB1 and PPB2, the
Fig. 5. The finite element meshes of sensing elements for FEM analysis.
Fig. 6. The deformed shape under force Fx .
Fig. 7. The deformed shape under force Fy .
PPB3 and PPB4, the PPB5 were deformed under the force Fx , Fy and Fz , respectively. The rated strains at the attachment locations of strain-gages have gotten. The used software to analyze is ANSYS.
Fig. 8. The deformed shape under force Fz .
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Fig. 9. Locations of strain-gages of three-axis gripper force sensor. Fig. 10. Full bridge circuit.
2.5. Strain analysis and sensor manufacture Fig. 9 shows the attachment locations of the strain-gages for the three-axis gripper force sensor. The attachment locations of strain-gages for each sensor are as follows: Fx sensor is S1, S2, S3 and S4, Fy sensor is S5, S6, S7 and S8, and Fz sensor is S9, S10, S11 and S12. The full bridge circuit for each sensor is constructed using the selected strain-gages for them. Thus, the sensing elements of each sensor are designed using the derived equations ((6-a), (6-b), (14-a) and (14-b)) at the full bridge circuit, they have the rated strains of about 1000 m/m and the interference errors of 0 m/m. The rated strain and the interference strain are calculated using Eq. (15) [5,6]. ε = εT1 − εC1 + εT2 − εC2
(15)
where ε is the rated strain or the interference error, εT1 the strain from the tension strain-gage T1 , εT2 the strain from the tension strain-gage T2 , εC1 the strain from the compression strain-gage C1 and εC2 is the strain from the compression strain-gage C2 . Table 1 shows the results of the rated strains and the interference strains from the theory and FEM analysis. The rated strains from the theory analysis are determined that Fx and Fy sensors are all 1020 m/m and Fz sensor is 1014 m/m. It is that the cutting unit of thickness of 0.1 mm is determined taking into consideration of the cutting capability. The rated strains from the FEM analysis are gotten that Fx , Fy and Fz sensors are 938, 936 and 941 m/m. The strain from theoretical analy-
sis is compared to that from the FEM analysis, and its range of error is less than 8.24%. Because the amount of the error usually appears in FEM analysis, the derived equations can be used to design the modeled three-axis gripper force sensor. Thus, the three-axis gripper force sensor was manufactured by attaching the strain-gages (N2A-13-T001N-350) to the selected attachment locations as shown in Fig. 9 using a bond (M-bond 200) made by Micro-Measurement Company, and constructing the full bridge circuit using the strain-gages for each sensor as shown in Fig. 10. Fig. 11 shows the fabricated three-axis gripper force sensor. 2.6. Results of characteristic test and considerations Fig. 12 shows the experimental set up for the characteristic test of the three-axis gripper force sensor. It is composed of an arm, weights, a body, a measuring device (DMP40). The manufactured three-axis gripper force sensor should be carried out the characteristic test by using the experimental set up to evaluate its rated strains and interference errors. Each sensor was tested three times by using the experimental set up, and
Table 1 Rated strain in theory and FEM analysis Sensor
Analysis
Rated strain (m/m)
Error (%)
Fx sensor
Theory FEM
1020 938
8.03
Fy sensor
Theory FEM
1020 936
8.24
Fz sensor
Theory FEM
1014 941
7.20 Fig. 11. Fabricated three-axis gripper force sensor.
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Fig. 12. Experimental set up for three-axis gripper force sensor: (a) applied Fx force, (b) applied Fy force and (c) applied Fz force.
the output values from each sensor were averaged. In order to compare the rated strains in theory and those in the characteristic test, the unit of the rated strains in theory (m/m) should be changed into the unit of the rated outputs in characteristic test (mV/V). The equation for it is as follows [5,6]: Eo 1 = Kε Ei 4
(16)
where Ei is the input voltage (V) of the full bridge circuit, Eo the output voltage (V) of the full bridge circuit, K the factor of strain-gage (the used factor of strain-gage is 2.03) and ε is the rated strain-gage of each sensor (m/m). The rated strains (m/m) in the theoretical analysis are changed into the rated outputs (mV/V) using Eq. (16). Tables 2 and 3 show the rated outputs of the three-axis gripper force sensors 1 and 2 from the theoretical analysis and the characteristic test. The maximum error of the rated strain from theoretical analysis compared with that from the characteristic test was less than 13.89%. The error may be generated due to the cutting error of the sensing element, the error of the characteristic test, the attachment error of the strain gage, and so
Table 2 Rated strains of three-axis force sensor 1 in theory and characteristic test Sensor
Analysis
Rated strain (mV/V)
Error (%)
Fx sensor
Theory Test
0.518 0.449
13.32
Fy sensor
Theory Test
0.518 0.457
11.78
Fz sensor
Theory Test
0.514 0.493
4.08
Table 4 Interference error of three-axis force sensor 1 in characteristic test Force (N)
Fx = 20 Fy = 20 Fz = 20
Sensor Fx sensor (%)
Fy sensor (%)
Fz sensor (%)
– −0.45 0.22
0.28 – −0.28
0.20 −0.20 –
Table 5 Interference error of three-axis force sensor 2 in characteristic test Force (N)
Sensor Fx sensor (%)
Fx = 20 Fy = 20 Fz = 20
– −0.90 0.90
Fy sensor (%) 0.29 – 0.58
Fz sensor (%) 0.20 −0.20 –
on. Tables 4 and 5 show the interference errors of the three-axis gripper force sensors 1 and 2 from the characteristic test. The maximum interference error of the fabricated three-axis gripper force sensor is below 0.9%, and it is similar or less than that of commercial multi-axis force/moment sensor [7,8]. It is thought that the interference error of the three-axis gripper force sensor is expressed as the error of the sensing elements in processing, the error of the attachment of the strain-gages, and the error of measurement from the fluctuation of the sensor at measuring environment. Thus, it is thought the derived Eqs. (6-a), (6-b), (14-a) and (14-b) could be usefully used to design the modeled three-axis gripper force sensor. 3. Intelligent gripper
Table 3 Rated strains of three-axis force sensor 2 in theory and characteristic test
3.1. Intelligent gripper
Sensor
Analysis
Rated strain (mV/V)
Error (%)
Fx sensor
Theory Test
0.518 0.446
13.89
Fy sensor
Theory Test
0.518 0.452
12.74
Fz sensor
Theory Test
0.514 0.503
2.14
In order to grasp an unknown object safely, the robot’s intelligent gripper should get the function on measuring the weight of the object, controlling the force in the grasping direction. Fig. 13 shows photograph of the manufactured gripper with two threeaxis gripper force sensors. It is composed of a controller, three motor drive, two three-axis gripper force sensors, a grasping motor, a up–down rotating motor, a left–right rotating motor, a body, a LM guide, and so on.
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Fig. 13. Photograph of the manufactured gripper with two three-axis gripper force sensors.
The controller measures the forces from the three-axis gripper force sensors 1 and 2, calculates the weight of an unknown object, and operates a grasping motor, a up–down rotating motor and left–right rotating motor. The three-axis gripper force sensors 1 and 2 were fixed to a LM guide, and moved to grasping direction simultaneously due to operating the grasping motor and rotating the screw, and the rubbers are attached to the cases of two three-axis sensors to prevent the sliding between the object and the two three-axis force sensors. They were used to measure the weight of an unknown object, and were developed in this research. Their maximum capacity is 20 N. The grasping motor (RE-max24, 222037) is used to operate the three-axis gripper force sensors 1 and 2 in grasping direction, and its specifications is that the maximum number of rotations is 9800 rpm, the power is 11 W, the voltage is 12 V, the ratio of gear (GP22C, 14398) is 53:1 and the encoder (MR201940). The up–down rotating motor (RE30, 268193) is used to rotate the grasping motor, two threeaxis gripper force sensors, and so on, in the up–down direction, and its range is 360◦ . The specifications of the motor are that the maximum number of rotations is 8200 rpm, the power is 60 W, the voltage is 12 V, the ratio of gear (GP32C, 166940) is 66:1 and the encoder (MR225785). The left–right rotating motor is used to rotate the grasping motor, up–down rotating motor, two threeaxis gripper force sensors, and so on, in the left–right direction, and its range is 360◦ . It is kind of the same as the up–down rotating motor. The operation of the intelligent gripper is as follows: first, the three-axis gripper force sensors 1 and 2 grasp an unknown object by controlling the grasping motor, and the up–down rotating motor rotates the gripper with the object in range of 5◦ . Second, the controller measures the forces from the three-axis gripper sensors 1 and 2, and calculates the weight of the object taking use of Eq. (1), and determines the force of the grasping direction. Third, the gripper grasps the object by controlling the grasping motor with the grasping force. Fourth, the controller rotates the intelligent gripper by controlling the up–down
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Fig. 14. Block diagram of controller of the intelligent gripper.
rotating motor and the left–right rotating motor. The developed intelligent gripper can safely grasps an unknown object having the size of 85 mm and the weight of 20 N, it can rotates the range of 0–360◦ . 3.2. Controller of intelligent gripper Fig. 14 shows block diagram of controller of the intelligent gripper, and Fig. 15 shows photograph of controller of the intelligent gripper. The gripper is composed of a -processor (80C196KC), a grasping motor (motor 1), an up–down rotating motor (motor 2), a left–right rotating motor (motor 3), two three-axis gripper force sensors, six amplifier, and so on. The controller was manufactured using -processor (80C196KC), this operates with frequency of 20 MHz and gets several function on analog/digital converter, PWM, timer/counter and so on. The controller gets the amplified signals of the sensors, and calculates the weight and the grasping force.
Fig. 15. Photograph of controller of the intelligent gripper.
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Fig. 16. Electric circuit of amplifier.
And its PWM ports supply some voltage to the motor drives to operate the up–down rotating motor and the left–right rotating motor, and its timer/counters get the pulses from the encoders attached to each motor. The motor drives were manufactured by using IC (HD74HC14P). The three-axis gripper force sensors 1 and 2 perceive the forces Fx1 , Fy1 , Fz1 , and Fx2 , Fy2 , Fz2 , and they are sent to two amplifier. Fig. 16 shows electric circuit of amplifier, it is composed of six amplifiers (AD627AN), few resisters and capacitors. The resister (R19), which is a variable resister, adjusts the zero balance of the full bridge circuit in each sensor, the resister (R18), which is a variable resister, adjusts the amplification ratio of the amplifiers to amplify the signals from each sensor. The amplifiers 1 and 2 amplify about 1000 times under the rated loads (Fx = Fy = Fz = 20 N), send the voltage 2 V to the controller. Fig. 17 shows block diagram for control system of the intelligent gripper, it is composed of a controller, three motor drives, a grasping motor, six amplifiers and so on. The reference value (grasping force) is 2 N in the case of the weight of the object under 4 N calculated from Eq. (1), that is, the weight is divided by 2 in the case of more than 4 N. The controller calculates the voltage to input the motor drive, the three-axis gripper force sensors 1 and 2 grasp an unknown object by operating the grasping motor, and the amplifiers amplify the force signals from the force sensors and send them to the controller. Fig. 18 shows flow chart for the control of the intelligent gripper. The program orders are as follows: (1) Initialization of the controller. (2) Gripper grasps an unknown object by controlling the grasping motor with the reference value of 2 N.
Fig. 17. Block diagram for control system of the intelligent gripper.
Fig. 18. Flow chart for the control of the intelligent gripper.
(3) Gripper is rotated about 5◦ by operating the up–down rotating motor. (4) Three-axis gripper force sensors perceive the weight of the object. (5) Controller calculates the weight of the object by using Eq. (1). (6) If the weight is under 0.2 N, the controller judges that the gripper does not grasp the object (the object slide down between the two three-axis gripper force sensor) because the weight is above 4 N, and the above process (2)–(5) is repeated again with the reference value of 4 N. Then, if it
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Fig. 19. Block diagram of characteristic test for grasping force of gripper: (a) block diagram and (b) photograph.
is not the weight value, the reference value is increased and increased 2 N until 20 N. (7) If the weight is 0.2–4 N, the grasping force keeps 2 N, and if the weight is above 4 N, the grasping force is determined by dividing the weight to 2. (8) Gripper grasps the object with the determined grasping force (reference) again. (9) Gripper with the object is moved by operating the up–down rotating motor and the left–right rotating motor. 3.3. Characteristic test and considerations In order to grasp an unknown object safely, the grasping characteristic test to determine the grasping force is carried out. Fig. 19 shows block diagram of characteristic test for grasping force of gripper. The method of the test is that the gripper with grasping force from 2 to 20 N (increasing step is 2 N) grasps the block with the contacting surface (800 mm2 (32 mm × 25 mm)), the weights of 5 N are handed up on the block, then, the weights are countered when the block just slide down between two three-axis gripper force sensors. In the results, the weight is more than 2.5 times. Thus, the grasping force was determined as the value of the weight of the object divided by 2. If the contacting surface between two force sensors and the object is different, the determined grasping force is different. The grasping force (Fx ) is 2 N at first time, the grasping force keeps its value in the case of 0.2–4 N calculated due to Eq. (1). The reason of the initial value of 2 N is that the gripper could safely grasp an egg, a plastic bottle for water, and so on. If the weight is above 4–20 N, the grasping force is the weight divided by 2. (For example, if the weight is 11 N, the grasping force is 5.5 N ((11 N)/2 = 5.5 N).) The characteristic test of the gripper for grasping an unknown object was carried out. The PI control is performed, and the output equation of PI controller is written as u(k) = Kp e(k) + Ki
k n=1
e(n)
where u(k) is the output value of k times of PI controller, Kp the proportional gain, Ki the integral gain, e(k) the error, that is, the value which subtract the output value of the three-axis gripper force sensor (1) from reference value and kn=1 e(n) is the sum of errors. The characteristic test to get the proportional gain Kp of the PI controller and the integral gain Ki was carried out. In order to get these values, the unit step response was carried out increasing the proportional gain from 10 to 90 with the unit step of 10, and increasing the integral gain from 0.05 to 0.40 with the unit step of 0.05. As the results, the proportional gain Kp of 30 and the integral gain Ki of 0.15 were gotten. Fig. 20 shows the unit step response test of the controller. By this time the overshoot is below 0.1 N, the steady state error is below 0.1 N, the rising time is below 0.5 s, and the dead time is 0.2 s. It is thought that the proportional gain and the integral gain are not the gotten optimal values and there are noses in the controller. And, to get the dead time of 0.2 s in the controller is because of the rubbers on the cases of two three-axis force sensors. The controller could safely grasp an unknown object with the proportional gain and the integral gain, because the error is small. Fig. 21 shows the photograph of the gripper with objects, (a) egg, (b) plastic paste bottle, (c) plastic water bottle and (d) weight. As shown in Fig. 21, it is conformed that the developed gripper could safely grasp them.
(10) Fig. 20. Unit step response test of the controller.
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simultaneously, and the design and the manufacture of the intelligent gripper using two sensors to grasp an unknown object stably. It could be conformed that the developed three-axis gripper force sensor is excellent in the maximum interference error [7,8], that the developed intelligent gripper using two sensors safely grasps the objects. Thus, it is thought that the developed three-axis gripper force sensor can be used for manufacturing an intelligent gripper, and the developed intelligent gripper can be used to grasp an unknown object safely. Acknowledgement This work was supported by grant no. R01-2006-000-104680 from the Basic Research Program of the Korea Science & Engineering Foundation. References [1] J.A. Domnguez-Lpez, R.I. Damper, R.M. Crowder, C.J. Harris, Adaptive neurofuzzy control of a robotic gripper with on-line machine learning, Robot. Auton. Syst. 48 (September (2–3)) (2004) 93–110. [2] J. Zhang, B. Rssler, Self-valuing learning and generalization with application invisually guided grasping of complex objects, Robot. Auton. Syst. 47 (June (2–3)) (2004) 117–127. [3] J.J. Steil, F. Rthling, R. Haschke, H. Ritter, Situated robot learning for multimodal instruction and imitation of grasping, Robot. Auton. Syst. 47 (June (2–3)) (2004) 129–141. [4] X. Yin, D. Guo, M. Xie, Handimage segmentation using color and RCE neural network, Robot. Auton. Syst. 34 (March (4)) (2001) 235– 250. [5] G.S. Kim, D.I. Kang, S.H. Rhee, Design and fabrication of a threecomponent force/moment sensor using plate-beam, Meas. Sci. Technol. 10 (1999) 295–301. [6] G.S. Kim, Design of 3-component force/moment sensor with force/moment ratio of wide range, Kor. Soc. Precision Eng. 18 (2) (2001) 214–221. [7] Ati Industrial Automation, Multi-Axis Force/Torque Sensor, Ati Industrial Automation, 2005, pp. 4–45. [8] BL Autotec, BL Sensor, Multi-Axis Force/Torque Sensor (BL-FTS-E020), BL Autotec, 2003, pp. 5–50.
Biography
Fig. 21. Photograph of the gripper grasping objects: (a) object (egg), (b) object (plastic paste bottle), (c) object (plastic water bottle) and (d) object (weight).
4. Conclusions This paper describes the development of the three-axis gripper force sensor, which detects forces Fx , Fy and Fz
Gab-Soon Kim got BS degree in precision mechanical engineering from Jeonbook National University, MS and PhD degrees in precision mechanical engineering from Hanyang University, Republic of Korea, in 1986, 1990 and 1999, respectively. He was a senior researcher at Department of Force Laboratory, Korean Research Institute of Standards and Science, Republic of Korea, from February 1990 to February 2000, and a visiting researcher at Department of Intelligent Robot Laboratory, University of Tsukuba, Japan, from July 2003 to June 2004. Since 2000, he has been with Gyeongsang National University, where he is currently associate professor at Department of Control & Instrumentation Engineering. His main research interests are in the areas of multi-axis force/moment sensor of intelligent robot, intelligent service robot and intelligent system.