The First IFToMM Asian Conference on Mechanism and Machine Science October 21 - 25, 2010, Taipei, Taiwan

TORQUE SENSITIVE MANIPULATOR WITH

HIGH-RIGIDITY TORQUE ENCODER

Hiroshi Kaminaga1, Tomohiro Kawakami2, Ko Ayusawa3, and Yoshihiko Nakamura4

1,2,3,4The University of Tokyo

To realize advanced performance in robots, torque sensitivity is crucial. However, torque sensitivity and mobility performance were contradicting conditions. To overcome such problem, we developed highly rigid and high fidelity torque sensor utilizing linear encoders; we call them torque encoders. In our previous works, we used feedfoward torque controller based on identified motor parameters. To eliminate errors in transient states and have better correspondence with physical values, we need high speed current feedback controller. In this paper, we focused on developing FPGA based highly responsive hardware current controller that realizes reliable impedance control. We also built two-link manipulator consisting of two torque encoder joints, and realized impedance controller with gravity compensation.

Keywords: torque sensor, impedance control, asymmetric processing, vector control

1 Assistant Professor, kaminaga@ynl.t.u-tokyo.ac.jp 2 Student, tomohiro@ynl.t.u-tokyo.ac.jp 3 Student, ayusawa@ynl.t.u-tokyo.ac.jp 4 Professor, nakamura@ynl.t.u-tokyo.ac.jp

1 Introduction

In majority of modern robots, high speed motors are used in conjunction with harmonic drives or planetary gears. This technique has enabled advanced power to weight ratio, however, by sacrificing backdrivability. To add force sensitive behavior to such robots, following issues needs to be solved: torque sensing and actuator backdrivability.

In this paper, we focus on realizing high-fidelity torque measurement. Torque sensing, in general, is performed by deformation measurement; usually either by strain (Refs. [1,2]) or displacement (Ref. [3]) measurement. From its nature, to realize high measure-ment resolution, stiffness of the torque sensor must be decreased to acquire large deformation. This tradeoff becomes relevant in robotics as the trade-off between measurement resolution and mobility performance because low stiffness joint leads to low resonance frequency, which limits the control bandwidth.

In Ref. [4] we introduced “Torque Encoder” that realizes high stiffness and high resolution simultaneously. In torque encoder, we measure deformation of the sensing element with linear encoder, which have following advantages:

1) This measurement principle eliminates the necessity of stress concentration since measurement is done for total deformation. Uniform stress distribution enables very rigid sensing element.

2) Since linear encoders have minimum analog signal processing, usage of linear encoders reduces electromagnetic noise drastically which enables high resolution measurement with high signal-to-noise ratio.

To fully utilize its capability, and realize wide range of variable stiffness with impedance control, high speed closed loop torque control is necessary.

Our objectives in this paper are as follows: development of high power density motor driver and implementation of controller that realize low impedance; development of multi axes manipulator with torque encoder joints. In section 2, we introduce torque measurement principle of torque encoders. In section 3, high speed control method of motor current is explained together with the evaluation test results. In section 4, impedance control using current control is explained together with evaluation test results. In section 5, torque control of multi joint manipulator is explained. Section 6 is the conclusion.

Figure 1: Basic structure of Torque Encoder. Solid gray arrow shows force transmission path and dashed dark gray line shows measurement path. Measurement path is placed so that this path does not contain input or output flange where mechanical connections, thus where stress concentrations occur.

The First IFToMM Asian Conference on Mechanism and Machine Science October 21 - 25, 2010, Taipei, Taiwan

2 Torque Encoder

Torque encoder is a torque measurement instru-mentation method developed by Kawakami et al. in Ref. [4]. Conventional torque sensors suffered from trade-offs between sensor stiffness and mobility performance. The reasons are as follows:

1) To achieve high measurement resolution, large deformation, thus less stiffness was necessary. Low stiffness reduces resonance frequency of the actuation system that limits control bandwidth.

2) If the stiffness was considered in front of measurement resolution, then smooth torque control becomes difficult. Non smooth torque signal induces vibrating behavior.

3) If the measurement resolution was achieved electrically, the effective measurement resolution is still limited by noise floor, or in other word, signal to noise ratio (S/N ratio). In static measurement purpose, it was possible to enhance measurement resolution by statistic signal processing, but with low S/N ratio, measurement introduces large phase delay, which makes it practically impossible to use the signal for dynamic control purpose. Furthermore, in strain gauge based measurements, measurements are done in local deformation. Hence the measurement may include microscopic nonlinearity of materials.

To overcome these issues, noise contamination must be minimized by minimizing mechanical dimension of analog signal processing portion. By mechanically reducing the dimension, noise frequency can be raised, that can easily be removed by filtering. Also, the global deformation should be measured to eliminate local microscopic effect of sensing element. This, in turn, result in higher stiffness because the stress concentration can be minimized.

However, to realize measurement with global deformation, strain gauge based measurement cannot be used and the fundamental change in design philosophy is necessary. In strain gauge torque sensing element, stress had to be concentrated because the local strain must be maximized without enlarging global deformation. In global deformation measurement, uniform stress is desirable.

In Ref. [4] Kawakami et al. proposed torque encoder, that measures global deformation of the sensing element using optical encoder. Linear encoders were used since the deformation is small enough that the deflection between input and output of the sensing element can be approximated linear. This method has following advantages:

1) Linear encoders have high measurement resolution, thus only small deformation is necessary. For torque measurement, measurement value can be mechanically magnified by placing the encoders farther from the rotational axis.

2) Linear encoders have high S/N ratio, so only minimum filtering is necessary. This eliminates the measurement phase delay.

3) Linear encoders transmit the measured value in digital signal. This feature eliminates any noise contamination during signal transmission.

4) Chance of plastic deformation is minimized by elimination of stress concentration. In this type of measurement, stress concentration should be avoided in measurement path. Hence, we placed connection portion of the sensing element outside of the measurement path, and the shape of the sensing element was designed as smooth as possible. The conceptual sketch of the torque encoder is shown in Fig. 1 and the outlook of the torque encoder is shown in Fig. 2. In the design of Ref. [4] uses dedicated torque sensing element, but from the principle, sensing element and the actuator housing can be integrated.

3 High Power Density Motor Controller and High Speed Torque Controller

To fully utilize the wide torque measurement bandwidth achieved by torque encoder, fast torque control is necessary. In the control strategy involving torque control, motor current control is generally performed because the torque is proportional to the supplied current in DC and brushless DC (hereafter BDC) motors.

In this research we use inner rotor BDC motor from power to weight ratio and cooling performance consideration. In BDC motors, magnetic field created by stator must be rotated to produce rotating torque; namely electric rectification. In Ref. [4], rectangular rectification with PWM open loop control was used. Putting aR an armature resistance, av armature voltage,

and TK torque constant, we assumed output torque of the motor mτ to be

a

aTm

R

vK=τ (1)

av is approximated as Eq. (2).

Figure 2: Outlook of Torque Encoder sensor element

The First IFToMM Asian Conference on Mechanism and Machine Science October 21 - 25, 2010, Taipei, Taiwan

100%PWM

Vv Sa = (2)

Here, SV is the source voltage of the power circuitry and %PWM a duty cycle in percent. Rectangular

rectification only uses hall sensors to detect the position of field magnet, and from its nature it theoretically has ripple torque of 13.4 (%) against the peak torque.

In this paper, we developed motor controller to achieve motor control without torque ripple. We also implement current control with feedback to have better physical correspondence of the torque control. We implemented vector control (Ref. [5]) and developed feedback controller on direct current di and quadrature current qi . Direct current is the current with direction of direct axis, which is the direction of magnet field. Quadrature axis is the direction perpendicular to direct axis and rotation axis.

The motor torque is given by

qTm iK=τ (3)

Direct current di does not directly effect the torque and usually controlled to 0=di . di is used to control the strength of magnet field and used in field weakening control (Ref. [6]) which is useful in controlling motor speed above rated no load speed. To eliminate the effect of variation of aR , integration is necessary. In this paper, we implemented PI (proportional - integral) controller for both qi and di .

In Ref. [7], the electric time constant of the motor is few (msec). To have decent control of motor current, we want to achieve the controller sampling about 10 times

faster than the electric time constant. To achieve this speed and reliability of the current controller, current feedback should be performed with hardware. On the other hand, higher control strategy, such as impedance controller and position controller, it is desirable to have flexible architecture. We developed asymmetric multiprocessor architecture for motor controller that uses FPGA for hardware control and CPU for upper layer controller. Basic architecture of the motor controller is shown in Fig. 3 and specification of the controller is shown in Table 1. Outlook of the controller is shown in Fig. 4. This architecture enabled us to implement low level controller as current feedback controller in the hardware layer (FPGA) that is processed fast and reliable. Different type of controller can still be used by changing the firmware for FPGA.

We implemented the vector current controller on FPGA that runs with 8(kHz). This controller runs independent from the upper layer controller

Figure 3: Block diagram of motor driver

Table 1: Specification of motor driver

CPU SH-2A (200MHz) FPGA Cyclone III AD Converter 12bit × 32ch Serial RS-485× 2 (4MBPS) Motor 3 Phase BDC motor

(48[V], 20[A]) × 1 Encoder RS-422 Receiver× 2 GPIO 8bit (3.3V) Size 36(mm) × 50(mm) × 15(mm) Weight 49(g)

Figure 4: Outlook of small high output motor driver

Figure 5: Step response (50Hz) of motor current under PI control

Figure 6: Bode plot of current control with amplitude of 2( ppA − )

The First IFToMM Asian Conference on Mechanism and Machine Science October 21 - 25, 2010, Taipei, Taiwan

implemented on CPU, so even in the case of failure in CPU, actuation can be disabled safely. On CPU, we implemented impedance controller, explained in next section, with sampling frequency of 2(kHz).

To see the effectivity of the current controller, we observed step response. As an experiment, we applied rectangular shape reference current of (A)1± . The result of current tracking control for step input is shown in Fig. 5. Physically the motor current is three phase current, but we converted it to qi and di in FPGA because the command signal is given in the form of qi and di . As a result tracking error is almost negligible and the tracking latency is less than 2(msec) in any cases.

To observe the frequency response, we applied sinusoidal input of (A)1± amplitude as a command to

qi . The frequency of sinusoid was swept from 1(Hz) to 250(Hz). Fig. 6 shows the result in the form of Bode plot. From this figure, we can see that the gain loss at 100(Hz) is less than 1(dB) and resonance frequency exists at 200(Hz). This result is narrow band measurement, however the similar figure was obtained with wide band measurement using rectangular wave instead of sinusoidal wave. This fact shows the validity of the result.

4 Impedance Control

We implemented the impedance controller on top of the current feedback controller explained in previous section. We measure external torque by torque encoder and control motor position according to the given force, so precisely speaking we implemented admittance controller. Our approach toward the impedance control is as follows:

1) Reduction of apparent inertia by torque feedback. We call this “inertia scaling.”

2) Friction compensation by disturbance observer as in Ref. [8]

3) Gravity torque compensation 4) Compliance and damping control

The basic strategy was discussed in Ref. [4]. In the proposed controller, current is the control input to the motor. However, as mentioned previously, we used the estimated current given by Eq. (1), so the controller output did not have physical connection with the torque output. Thus in case of parameter fluctuation of armature resistance aR , which is likely to differ motor to motor and likely to happen due to variation of the motor temperature, output torque may differ from what is desired.

Since we have closed loop control of current in this paper, we expect to have good physical correspondence of output torque regardless of operation condition. To eliminate the effect of individual difference of torque constant TK , we identified the parameter for every motor. We compare the achieved stiffness of the impedance controller with the desired

value to evaluate the controller performance. The torque was applied to the joint mechanism through the force gauge to measure the exerted force. Joint position was measured with motor encoder.

The result of single joint impedance control is shown in Fig. 7. We used inertia scaling of 1:2, friction compensation, and gravity compensation.

Here are the evaluation results. 1) No hysteresis loop is observed. It shows that

the friction is properly compensated. 2) Achieved stiffness for desired stiffness of

(Nm/rad)1020.1 3×=refK was (Nm/rad)1027.1 3×=actK , hence the error was 5.83(%).

For desired stiffness of (Nm/rad)1078.4 3×=refK , measurement value was (Nm/rad)1099.4 3×=actK , thus the error was 4.39(%). The error was less than 6(%) and good physical correspondence was observed.

3) No stiffness fluctuation was observed due to motor heating.

5 Application to Multi-link Manipulator

To realize manipulator with torque encoder and to realize gravity compensation and Cartesian impedance control, we must implement communication between motor controllers. In the Cartesian impedance control, necessary torque is calculated using the states of all joints and commanded to each motor controller. As the first step, in this paper, we implemented gravity compensation of multi-link manipulator.

Figure 7: Result of impedance control with and without inertia scaling. Square: loading direction.

Triangle: unloading direction.

Table 2: Specification of mmeye PPC CPU MPC5200B (400MHz) OS NetBSD 4.0.1

Serial RS-485× 8 (4MBPS) Size 55(mm) × 92(mm) × 33(mm)

Weight 88(g)

The First IFToMM Asian Conference on Mechanism and Machine Science October 21 - 25, 2010, Taipei, Taiwan

Here, we assume the base link 0 is fixed the the inertial frame. Let us put gravity torque acting on each joint i

gτ0 , unit vector pointing to direction of joint axis

ia0 , rotation matrix from the base link to the link i be iR0 , then the gravity compensation torque at each joint

ign is given as follows.

)( 11

000 +++⋅= i

giigi

ig nn Rτa (4)

It means we must know the torque of joint i + 1 and the joint angles from base link to link i in order to compensate the gravity torque of link i.

We used 4(MBPS) RS-485 serial communication to implement the realtime communication between motor driver and upper layer controller. We used mmEyePPC from Brains Corporation as an upper layer controller to collect, calculate and dispatch states of other joints to motor drivers that is necessary for gravity compensation. Table 2 shows the specification of mmeyePPC. Figure 8 shows the synchronization scheme used in the multi-joint realtime control.

We assembled a two-link manipulator consisting of two torque encoder joints to validate the control scheme. Figure 9 shows the experiment scene. As seen from the figure, link can stop at arbitrary position because the gravity is properly compensated.

6 Conclusions

In this paper, we developed the motor controller hardware and controller firmware that realize fast torque response of the actuator, necessary for fully utilizing measurement resolution and stiffness of the torque encoder joints. We also applied the technology to multi-axis manipulator and developed the multi-axis controller framework that enables force sensitive robots. Listed are the conclusions of this paper.

1) We developed BDC motor controller that realize fast torque response. The controller has the asymmetric processor architecture that use FPGA and CPU. Current PI controller with sampling frequency of 8(kHz) was implemented as hardware on FPGA. From the experiment, control bandwidth was over 150(Hz) and latency was below 2(msec). Static tracking error was below measurement resolution

2) We implemented impedance controller on CPU with sampling frequency of 2(kHz). Inertia scaling, disturbance observer, and compliance/damping controller was implemented. From the evaluation result of single joint impedance control, we achieved the stiffness with error below 6(%). This error contains calibration error between current sensor and force gauge that were used to the measure the exerted torque.

3) We developed framework for realtime communication between multiple joints to realize Cartesian control of the robot. We implemented gravity compensation on two link manipulator and experimentally proven the validity of the controller.

Acknowledgments

There were advises from Brains Corporation on development of FPGA firmware.

This work was supported partially by Grant-in-Aid for Scientific Research (No.20-10620) for Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists and partially by “IRT Foundation to Support Man and Aging Society” under Special Coordination Funds for Promoting Science and Technology from MEXT.

References

[1] Hirzinger, G., Albu-Shäffer, A., Hähnle, M., Schaefer, I., and Sporer, N., On a New Generation of Torque Controlled Light-Weight Robots, in Proc. of IEEE Int’l Conf. on Robotics and Automation, pp.3356–3363, 2001.

Figure 8: Synchronization scheme in multi-joint control

Figure 9: Two joint torque encoder manipulator

under gravity compensation

The First IFToMM Asian Conference on Mechanism and Machine Science October 21 - 25, 2010, Taipei, Taiwan

[2] Godler, I., Hashimoto, M., and Horiuchi, M., Performace of gain tuned harmonic drive torque sensor under load and speed conditons, IEEE/ASME Trans. on Mechatronics, vol. 6, no. 2, pp. 155–160, 2001.

[3] Tsetserukou, D., Tadakuma, R., Kajimoto, H., and Tachi, S., Optical Torque Sensors for Local Impedance Control Realization of an Anthropomorphic Robot Arm, Int’l J. of Robotics and Mechatronics, vol. 18, no. 2, pp. 121–130, 2006.

[4] Kawakami, T., Ayusawa, K., Kaminaga, H., and Nakamura, Y., High-fidelity joint drive system by torque feedback control using high precision linear encoder, in Proc. of IEEE Int’l Conf. on Robotics and Automation, 2010, in print.

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[6] Soong, W. L. and Miller, T. J. E., Field-Weakening Performance of Brushless Synchronous AC Motor Drives, in IEE Proc. of Electric Power Applications, vol. 141, pp. 331–340, 1994.

[7] maxon motor ag, maxon motor, http://www. maxonmotor.com.

[8] Tien, L., Albu-schäffer, A., de Luca, A., and Hirzinger, G., Friction Observer and Compensation for Control of Robots with Joint Torque Measurement, in Proc. of IEEE/RSJ Int’l Conf. on Intelligent Robots and Systems, pp. 3789–3795, 2008.