Theory and Experiments on Robotic Maneuvers

Copyright © IFAC Low Cost Automation 1989 Milan. italy. 1989

THEORY AND EXPERIMENTS ON ROBOTIC MANEUVERS H. Kazerooni Department of Mechanical Engineering, University of Minnesota Minneapolis, MN 55455, U .S.A.

Abstract. In this research, a statically-balanced direct-drive manipulator is designed and constructed to achieve improved dynamic behavior for compliance control (Kazerooni, 1986, 1989c, Kazerooni, Waibel and Kim, 1988). The manipulator mechanism, incorporating a four-bar linkage, is designed so that its functional parts are balanced in all positions without the addition of counterweights. The motors are never loaded by gravity. As a result, smaller motors with less torque can be used to achieve higher speed, accuracy, and repeatability in fine manipulation tasks. The robot is powered by high torque AC synchronous motors . The mechanism is comprised of graphite-epoxy and AA7075T6 aluminum materials. The manipulator is controlled by a parallel processor computer. Keywords. robot , trajectory control, compliance control, parallel proce ssor, balanc e, four-bar linkage , graphit-epoxy, actuators, sensors, precision.

INTRODUCTION

The Minnesota direct drive robot is statically balanced with a four-bar linkage mechanism which compensates for some disadvantages found in the serial-type and parallelogram-type robots. Some common advantages and disadvantages of the direct drive arm, in comparison to non-direct drive arms, are: l. Speed. Maximum speed depends on the transmission ratio which depends on the links' inertia . It is shown that a non-direct drive arm can be faster than a direct drive arm (Kazerooni, 1989a). 2. Static Payload. For a given set of motors, direct drive arms have a lower static payload due to reducer transmission systems . 3. Ov e rheating. Elimination of the transmission means the motors "feel" the inertial and gra vitational forces with no size reduction. Thus, overheating can occur even in the static case. 4. Structural Stiffness. Higher structural stiffness allows for wide bandwidth control. Transmissions in non-direct drive robots cause about 80% of the mechanical compliance (Rivin, 1985). 5. Backlash and Friction. No transmission means no mechanical ba ckla sh or friction. Backlash causes faster wear of gear teeth which causes even greater backlash. Overcoming friction consumes about 25'k of the torque in non-direct drive arms. 6. Performance and Control. The elimination of backla s h in direct drive robots permits more straightforward , not n ecessarily easier, control and performance analvsis. 7. Accuracy. -Accuracy is uncertain : no transmission means no cogging, no backlash, nor its limit cycle; however, motor vibrations are directly transferred to the robot endpoint. To improve dynamic behavior, Asada and Kanade (1983a , 1983b), Kanada and Schmitz (1985) designed serial-type direct drive arms with actuators directl y coupl ed to links without any transmission; this improved performance but required large motors. Asada and Youcef-Toumi (1984, 1986) designed a parallelogram mechanism to eliminate serial-type robot problems. To eliminate gravitational effects at three major joints,

Takase et al. (1984) designed an arm with a counterweight which increased arm inertia . Kuwahara et al. (1985) reduced gravitational effects with a four-bar link for the forearm and a special spring for the upper arm, but this did not perfectly balance the system either. Curren and Mayer (1985) offered a statically balanced robot with five degrees of freedom. In this design, a statically-balanced, directdrive arm eliminates gravitational forces without any counterweights; thus, smaller actuators and amplifiers are chosen (Kazerooni, 1989a, 1989b). Using 50% of the actuator maximum power, an acceleration of 5g at the endpoint is achieved without overheating the motors.

Figure 1: University of Minnesota Direct Drive Robot

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H. Kazerooni

ROBOT CONFIGURATION

This arm is a balanced mechanism with no counterweights and has these features: 1) Since the gravity term has been eliminated from the dynamic equations of the robot. the static load on each motor is zero. and thus. the motors do not overheat. 2) Smaller motors with less stall torque and smaller amplifiers are required for this class of robots. 3) Higher accuracy is achieved because the links have a steady deflection due to constant zero gravity effects. 4) The horizontal workspace is large for tasks such as assembly and deburring (Kazerooni. 1986). 5) Graphite-expoxy composite materials (Thompson and Sung. 1983) are used to construct the robot. The robot weighs 60 Kg and. can be mounted on an autonomous vehicle. The payload without losing precision is 2 kg. The University of Minnesota direct drive arm (schematic in Figure 2) has three degrees of freedom. each an articulated drive joint. Motor 1 powers the system about the vertical axis. motor 2 pitches the four-bar linkage. and motor 3 powers the linkage. Link 2 connects directly to the shaft of motor 2. The coordinate frame. XiYiZ i• is for link i (i=1.2 •...• 5). The center of X1Y 1Z 1 Clink 1) is at point o in figure 3. The center of the inertial global coordinate frame. Xo YoZo. (not shown in figures) is also at point O. Joint angle e 1 is the rotation of link 1; X 1Y 1Z 1 coincides with XoYoZo when e 1 is zero. Joint angle e 2 (shown in Figure 2) is the pitch angle of the four-bar linkage . Joint angle e 3 is between link 2 and link 3.

.

.

~X;-_: ~

_ _ _ _ l. _ _ _ _- '

Figure 3: Motor 2 rotates the plane of the four-bar linkage about Z2 axis. m i, LI = mass and length of each link Xi = the distance to the center of mass from the origin of each coordinate frame m t3 = mass of motor 3

Conditions (1) and (2) result in: (3)

If (3) and (4) are satisfied. the linkage's center of gravity passes through 0 for all possible arm configurations. Even if the linkage plane is tilted by motor 2. the gravity force still passes through 0 for all e2 . ROBOT LINKS

Figure 2: Motor 2 rotates the plane of the four-bar linkage. When the plane of fourbar linkage is hOrizontal, e 2 is zero. Figure 3 shows the linkage with assigned coordinate frames. The conditions under which the gravity vector passes through the origin. O. for all e1and e3. are given by:

(1 ) + msl - m2x2 - m3[L 2 - gl - m~[x~ - gl 0 (2) - [m3x 3 - m~Ls - msxs l cose 3

9 (mt 3

where:

=

To develop wide bandwidth (high speed) closed-loop control. the links are made of graphiteepoxy composite and AA 7075T6 materials . Each link is accurately machined from aluminum alloy and then wrapped with graphite-epoxy composite shrink film . The composite's high structural stiffness and low density cause high structural natural frequencies in the robot structural dynamics . Higher natural frequencies allows the designer to deve lop a wider bandwidth for the closed-loop system. An epoxy adhesive creates a strong bond between the composite and aluminum parts. Link 5 is made of stainless steel. Super precision angular contact light bearings minimize joint clearance and reduce bearing mass. Table 1 shows the values of robot parameters obtained from the engineering drawings. IX!> IYI and Izj are the mass moments of inertia relative to X. Y and Z axis at the center of mass of a link I. The uncertainty in these parameters is about 10%. The material properties are shown in table 2.

315

THEORY ,"""iD L\PERI\IE:--JTS O:--J ROBOT IC \IA:--JEUVERS

Length (cm )

1 2 60 . 33 3 53 .3 4 4 6 0. 33 5 15 . 2 4 g 22 . 23

X,

Me s s

( cm)

«9)

11.17- 13.8 86 15 . 7 0 3 . 2 C6 3 0. 16 2 .924 7.62 C.758

!r.ert l~ ( kg- cm 2 1

! XI

! yi

0.4 21C.C 3 97 OC 2 07 C.CO I6

Table 1:

Itl

3.7 80 50. 4 796 1.3 2 53 0 .0694

1.7 52 3 .7 8050.4 796 0.0 0.C694

Robot Parameters

Graphite Epoxy AA7075T6

stainl ess

Density 155g/ cm 3 2 .82g/ c m 3 7.77g/c m 3 Tensile Stress 2 00 Ks , 83 KSI 19 5Ks ' Modulus 18.7 1OC 106 pSI 10 . 4 - 10 6 pSI 28 . 5 ..:1 0 6 P SI Thermal exp a n s i o n l.ll · ' 0 6 cm/oC 7.17 - 10 6 cm/oC 3 .3 3 - 10 6 cm/ o C melting point 3 649 ' C 629'C 1510 ' C

Table 2:

stator (winding)

Figure 4: Assembly Drawing of Motor 2

The Properties of the Materials Used in Construction of the Robot. ACTUATION

Since AC torque motors tend not to cog at low speeds, this robot is powered by low-speed , hightorque , brushless AC synchronous motors, each with a ring-shaped stator and a ring-shaped permanent magnet rotor with a large number of poles (Schept, 1984, Welburn, 1984). The rotor is made of rare earth magn e tic material (Neodymium ) bonded to a low carbon steel yoke with structural adhesive . The motor stator with winding is fixed to the housing to dissipate heat. Figures 4 and 5 show the a ssembly drawing and components of motor 2. The robot actuators are neodymium (NdFeB) magnet brushless AC synchronous motors. The motors have high torque-to-weight ratios due to the high ma gnetic field strength (maximum energy products: 35 MGOe) of the neodymium magnets. The position and velocity sensors are pancak e-type resolvers . Th e peak torques for motors 1, 2, and 3 are 118, 78 , and 58 Nm , respectively. The charaCteristics of the motors are given in table 3. Each motor was mechanically stall ed, and , via a piezoel ectric force sensor , the stall torque was measured at each input comand. This experiment lead s to m easurem ent of 2.2485, 2.6958 and 6.169 NmJAmpere for K, (torque constant), for motors 1, 2 and 3.

*

In calculating these values , we assume motor 3 is a part of link 2. For example , 13.886 kg in the above table includes mass of link 2 ( 4.626 kg ) and mass of motor 3 (9 .26 kg). The "height" of the robot , from the base to the origin of the X1Y1Zl, is 62.992 cm ( 24 .8 inch ).

-

--.....

Figure 5: Components of Motor 2 mowrl mowr2 mowr3 outer di a meter (s ta w r ), inch inn er diameter (rotor), inch weight, stator, lbf weight, rotor , lbf rotor inertia , lb ft sec' poles motor inductor , mH motor re sistor ~t (torqu e consta nt), X mlAmpere maximum continuou s torque, ~m peak wrque, Km

Table 3:

14 ' 9' 24 . 6 5 .5 2 6-10 - 3

3' 8 .4 2 .4

32 10. 43 0 . 728 6 .0 53 41 11 7

16 27 . 325 2 . 181 3 .0 3 1 16 . 2 78

5' 2' 4 .4 2.0 1. 5 ·Q O-3 1.:31(10- 3 7'

12 26 . 37 3 . 579 1. 927 7 .5 50

Motor Parameters HARDWARE

Figure 6 shows the flow of power and information signals. An IB;\1/AT mlrrocomputer which has a 4-node NCUBE parallel processor with a PC/AT bus interface is the main robot controller. Each node is an independent 32-bit processor with local memory and communication links to the other system nodes . A high speed (250 KHz) ADIDA converter reads the velocity signals and sends analog command signals to the servo controller, The convertor has 12 bit resolution, A parallel VO board (DID converter) between the servo controller and the computer reads the RID (resolver-to,digital) converter.

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H. Kazerooni

REFERENCES An, C. H., Atkeson, C. G., Hollerbach, J. M., (1986),

Position velocity (Analog)

(Y connection)

Figure 6

(.1. connection)

.------------.~--~

The Robot Controller Components

l) Servo Controller. The servo controller unit has an interpolator, RID converter, and a computer interface; it produces three-phase, Pulse-Width-Modulated (PWM), sinusoidal currents for the power amplifier. The unit operates in either a closed-loop velocity or current (torque) control mode. (The latter is used here.) A PWM power amplifier powers the motors with up to 47 amperes from a 325-volt supply. The switching frequency is 4 kHz. The servo controller has the allowable continuous current of 21 ampere and peak torque of 40 ampere. Il) Power Supply. The main DC bus power is derived from full-wave rectifying of the threephase 235VAC incoming power and yields a DC bus voltage of 325 VDC. The continuous power Olltuut is 18 kW. Ill) Isolation Transformer. A Y to !1 isolation transformer with capacity of 20 kW is used to filter the input power. The output voltage drop from line to line is 235 VAC. IV) Force Sensors. A piezoelectric force sensor, which weighs 32 g, measures the forces at the robot end point. The force sensor bandwidth is about 8 kHz with 400 g weight. The force sensor allows for maximum measurement of ! 500 lbf in three directions with a threshold of 0.0001 lbf. Three charge amplifiers, each with 180 kHz bandwidth, are used to convert the force sensor charge signal to voltage. CONCLUSION

The new mechanism for a balanced arm was developed to eliminate the effect of gravity forces. The statically-balanced, direct drive manipulator, with 5g acceleration capability, was built. High torque, low speed, brushless, AC synchronous motors were directly coupled to links to eliminate the transmission systems. The architecture of this manipulator completely eliminates gravity forces in the system dynamic behavior. Removal of gravity terms in the manipulator's dynamics alleviates overheating, enables the selection of smaller actuators, and eliminates the need for a gravity compensator. The mechanism was comprised of graphite-epoxy and AA 7075T6 aluminum materials. High structural stiffness and low mass due to the graphite-epoxy composite materials result in higher natural frequencies and, thus, a wider control system bandwidth.

"Experimental Determination of the Effect of Feedforward Control on Trajectory Tracking Errors," IEEE International Conference on Robotics and Automation, San Francisco, CA, Vo!. 1, pp. 55-60. Asada, H., Kanade, T., (1983a), "Design of Direct Drive Mechanical Arms," ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vo!. 105, No. 3, pp. 312-316. Asada, H., Kanade, T., and Takeyama, 1., (1983b), " Control of a Direct Drive Arm," Journal of Dynamic Systems, Measurements, and Control, Vo!. 105, pp. 136-141. Asada, H., Youcef-Toumi, K., (1984), " Analysis and Design of a Direct Drive Arm with a Five-Bar-Link Parallel Drive Mechanism," ASME Journal of Dynamic Systems, Measurement, and Control, Vo!. 106, No. 3, pp. 225-230. Curren, R. and Mayer, G., (1985), "The Architecture of the Adeptone Direct Drive Robot," American Control Conference, pp. 716-721. Kanade, T. and Schmitz, D., (1985), " Development of CMU Direct Drive Arm II," American Control Conference, pp. 703-709. Kazerooni, H., Bausch, J. J., Kramer, B. K., (1986), "An Approach to Automated Deburring by Robot Manipulators," ASME Journal of Dynamic Systems, Measurements, and Control, Vo!. 108, No. 4. Kazerooni, H., (1986), "Fundamentals of Robust Compliant Motion for Manipulators", IEEE Journal of Robotics and Automation, Vo!. 2, No. 2. Kazerooni, H., Waibel, B. J ., and Kim, S., (1988), "Theory and Experiments on the Stability of Robot Compliance Control," ASME Winter Annual Meeting. Kazerooni, H., (1989a) "Static ally Balanced Direct Drive Manipulator," Robotica, Vo!. 7, 1989, pp 143-149. H. Kazerooni, (1989b), "Design and Analysis of the Static ally Balanced Direct Drive Manipulator," IEEE Control System Magazine, Vo!. 9, No. 2. Kazerooni, H., (1989c), "On the Robot Compliant Motion Control," ASME Journal of Dynamic Systems, Measurements, and Control, Vo!.l11 , No. 3. Kuwahara, H., One, Y., Nikaido, M., and Matsumoto, T., (1~85), "A Precision Direct Drive Robot Arm," Proceedings of American Control Conference, Vo!. 2, pp. 722-7'27, Boston, MA. Rivin, E. 1., (1985) "Effective Rigidity of Robot Structures: Analysis and Enhancement," American Control Conference, Vo!. I, pp. 381-382, Boston, MA. Schept, B., (1984), "A New High-Torque Brushless Motor," Sixth International MOTOR-CON'84 , Atlantic City, NJ, pp. 50-54. Takase, K., Hasegawa, T. , Suehiro, T., (1984), "Design and Control of a Direct Drive Manipulator," Proceedings of the International Symposium on Design and Synthesis, Tokyo, Japan, pp. 333-338. Thompson, B. S., Sung, C. K., (1983 ), "The Design of Robots and Intelligent Manipulators Using Modern Composite Materials, " 8th Applied Mechanisms C01lference, Oklahoma State University, pp. 3-10. Welburn, R., (1984), "Ultra High Torque Motor System for Direct Drive Robotics," Sixth International MOTOR-CON'84, Atlantic City, NJ, pp. 17-24. Youcef-Toumi, K. and Asada, H., (1986), "The Design of Open Loop Manipulator Arms with Decoupled and Configuration Invariant Inertia Tensors," Proc. of the IEEE International Conference on Robotics and Automation, Vo!. 3, pp. 2018-2026.