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行政院國家科學委員會專題研究計畫 成果報告

無力量回授之馬達驅動順應控制器設計 研究成果報告(精簡版)

計 畫 類 別 : 個別型

計 畫 編 號 : NSC 100-2221-E-011-021-

執 行 期 間 : 100 年 08 月 01 日至 101 年 07 月 31 日 執 行 單 位 : 國立臺灣科技大學機械工程系

計 畫 主 持 人 : 黃安橋

報 告 附 件 : 出席國際會議研究心得報告及發表論文

公 開 資 訊 : 本計畫可公開查詢

中 華 民 國 101 年 09 月 28 日

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中 文 摘 要 : 本計畫開發出一具無力量回授的馬達驅動順應控制器,使得 該系統在與外界互動時,能表現出期望的順應運動,而不致 因為相互作用力過大,造成控制失敗。免除力迴授的理由,

除了成本考量之外,最主要的還是因為力感測訊號屬於高階 訊號,其中往往含有大量的雜訊。更嚴重的是,通常力感測 訊號的頻譜寬廣,並且與雜訊頻譜相互重疊,因此不易設計 有效的濾波器,來濾除雜訊,這樣就直接影響到順應控制在 實作時的性能。由於學界至今對此並無有效對策,也因此大 幅限制了順應控制的工業應用。本計畫提出以函數近似法來 估測作用力,並設計適應控制器來處理系統未知參數,並且 以嚴格的數學證明,以確保閉迴路的穩定性,以及內部訊號 的有界性。另外,為證實開發的控制器有實用價值,本計畫 架設一實驗平台,以測試其在無力量迴授時的順應控制性 能。

中文關鍵詞: 力量控制、順應控制、無感測器

英 文 摘 要 : A sensorless compliant motion controller is designed for a motor driven system to give proper force

regulation performance when interacting with environment. The main reason for the sensorless design is due to the high-order natural of the force feedback which inevitably containing a lot of noise.

What is worse is that normally the force signal spectrum covers the noise window, and effective filtering techniques can seldom be found here. This largely discourages the application of the existing compliant motion strategies in industry. The current project proposes to use the function approximation technique to estimate the force signal as effective information for an adaptive control loop in dealing with system uncertainties. Rigorous mathematical analysis for the closed loop stability and the

boundedness of internal signals is performed as well.

In addition, an experimental setup is built for justifying the effectiveness of the proposed design 英文關鍵詞: Force control; Compliant motion control; Sensorless

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行政院國家科學委員會補助專題研究計畫 成果報告

無力量回授之馬達驅動順應控制器設計

計畫類別:個別型計畫

計畫編號:NSC100-2221-E-011-021

執行期間: 100 年 8 月 1 日至 101 年 7 月 31 日 執行機構及系所: 國立台灣科技大學機械系

計畫主持人: 黃安橋

計畫參與人員: 蓋震宇、洪健偉、李怡萱

成果報告類型:精簡報告

中 華 民 國 101 年 9 月 20 日

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行政院國家科學委員會專題研究計畫成果報告

無力量回授之馬達驅動順應控制器設計

Force-Sensor-Free Compliant Motion Controller Design for Motor-Driven Systems

計劃編號:NSC100-2221-E-011-021 執行期限:100 年 8 月 1 日至 101 年 7 月 31 日

主持人: 黃安橋 國立台灣科技大學機械系

計畫參與人員:蓋震宇、洪健偉、李怡萱 國立台灣科技大學機械系

摘要

本計畫開發出一具無力量回授的馬達驅 動順應控制器,使得該系統在與外界互動 時,能表現出期望的順應運動,而不致因為 相互作用力過大,造成控制失敗。免除力迴 授的理由,除了成本考量之外,最主要的還 是因為力感測訊號屬於高階訊號,其中往往 含有大量的雜訊。更嚴重的是,通常力感測 訊號的頻譜寬廣,並且與雜訊頻譜相互重 疊,因此不易設計有效的濾波器,來濾除雜 訊,這樣就直接影響到順應控制在實作時的 性能。由於學界至今對此並無有效對策,也 因此大幅限制了順應控制的工業應用。本計 畫提出以函數近似法來估測作用力,並設計 適應控制器來處理系統未知參數,並且以嚴 格的數學證明,以確保閉迴路的穩定性,以 及內部訊號的有界性。另外,為證實開發的 控制器有實用價值,本計畫架設一實驗平 台,以測試其在無力量迴授時的順應控制性 能。

關鍵詞:力量控制、順應控制、無感測器 Abstract

A sensorless compliant motion controller is designed for a motor driven system to give proper force regulation performance when interacting with environment. The main reason for the sensorless design is due to the high-order natural of the force feedback which inevitably containing a lot of noise. What is worse is that normally the force signal spectrum covers the noise window, and effective filtering techniques can seldom be found here. This largely discourages the application of the existing compliant motion strategies in industry.

The current project proposes to use the function

approximation technique to estimate the force signal as effective information for an adaptive control loop in dealing with system uncertainties.

Rigorous mathematical analysis for the closed loop stability and the boundedness of internal signals is performed as well. In addition, an experimental setup is built for justifying the effectiveness of the proposed design.

Keywords: Force control; Compliant motion control; Sensorless

1. Introduction

Most of the compliant motion control researches are for the control of robot manipulators when the end-effector interacts with the environment. According to the source of the driving forces, the compliant motion control can be classified into two categories: passive and active designs. To implement a passive complaint motion design, some passive impedance elements are installed on the robot manipulator to provide sufficient compliance for robot-environment interaction. The most famous passive compliant device is the RCC (Spong and Vidyasagar 1989) developed by MIT Draper Lab. On the other hand, the active compliant motion design regulates actively the apparent impedance of the robot manipulator so that the robot-environment interaction can be maintained compliantly as desired. Since the causality requires that either the force or trajectory can be regulated in a specific degree of freedom in the configuration space, the control loop design subjects to some limitations. Besides, the contact force is virtually a disturbance to the control activity, sufficient robustness of the control strategies need to be carefully considered. Because the operation range and dynamics of the passive compliant are

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generally narrow, most of the current researches of the robot compliant control focus on the active schemes.

There are two main approaches in the compliant motion control of robot manipulators:

hybrid control and impedance control. The former integrates the force and position information to fit various geometric constrains in the working space so that the compliant motion control can be realized. Some coordinate transformations are utilized to ensure that in the normal direction of the constraint surface the force control loop is active, while in the tangent direction of the constraint surface the position control loop is valid (Raibert and Craig 1980). This way the causality limitation will not be violated.

However, this method requires knowing precise information of the environment geometric;

otherwise the coordinate transformation can not be found. It is well-known that the industrial environment is never precisely understood, realization of this method is a big challenge.

This is why most of the researches focus on the second method, the impedance control. Hogan (1985) proposed to regulate the dynamics between the robot manipulator and the environment via some target impedance which is determined by the designed in terms of desired mass, damping and stiffness. As long as the controller of the robot manipulator is able to give appropriate control activity so that the robot manipulator dynamics behaves like this target impedance, the interaction of the robot and the environment can be achieved. On advantage of the impedance is that there is no switching in the transition from the free space motion to the constrained motion, and hence a stable transition is easy to obtain. Kazerooni (1986) proposed to look at the impedance control problem in the frequency domain.

Anderson and Spong (1988) integrated the hybrid control and impedance control to perform compliant motion control. Goldenberg (1988) used feedback and feedforward compensation to eliminate uncertainties in the environment model. Chien and Huang (2004) proposed to use regressor-free adaptive controller to deal with both system uncertainties and environment uncertainties. Huang and

Chien (2010) suggested adaptive impedance controllers for flexible-joint robot manipulator to interact with the environment compliantly. They also presented adaptive controller for consideration of actuator dynamics so that high-speed operation in the compliant motion control can be realized.

Hogan’s impedance controller requires the knowledge of the interaction force between the end-effector and the environment. The force information is usually contaminated with various measuring noise which can deteriorate the performance of the control loop or even destabilize the closed-loop stability. In addition, the spectrum of the noise might overlap with the signal band, effective filtering techniques are not available. This largely limits the application of the controller in the industrial environment.

In this project, we propose to design an adaptive controller so that the force information can be estimated instead of force sensor feedback.

Some experiments show that the design can give good performance in compliant motion control with force information.

2. Controller Design

Consider a one degree-of-freedom mechanical system interacting with the environment whose equation of motion can be described with

d u K B

M





  (1) where M is the mass, B is the damping coefficient and K is the stiffness. The interaction force d is assumed to be directly in the same channel of the control effort u. Suppose we are going to make the mechanical system behave like the target impedance

) (

) (

)

( d

b

d

k

d

m

d

     (2)

where m, b and k are known constants and

 is

d the desired trajectory. If there is no interaction force, then

d  0

, and the selection of m, b and k needs to be proper so that the actual trajectory will converge to the desired trajectory. On the other hand, if the system is dissipative, then even with the presence of the interaction the mechanical impedance provided by (2) will still ensure boundedness of the tracking error. Hence, the transition from the free space tracking to the contact phase is smooth if (2) is suitably selected.

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Define the tracking error as

e

1



d

and suppose all parameters are available then the impedance controller can be designed as (Hogan 1985)

1 1 1 1 1

Mke m e Mb m

M K B d Md m

u d

(3)

With this controller the dynamics of the system in (1) will become exactly the dynamics of the target impedance in (2). To implement the controller in (3), we need to know everything in the system dynamics (1). However, in practical applications, it is not easy to ensure that we have the knowledge of all parameters inside the system. So, consideration of uncertainties of system parameters is very important no matter in the sense of theoretical development or from the point of view of industrial applications. To cope with parameter uncertainties, there are two main approaches: robust control and adaptive control. The former needs to know the variation bounds for the uncertain parameters so that a conservative controller can be designed to cover the whole range of their variations. The later requires that the uncertain parameters be time invariant so that adaptive laws can be derived from the Lyapunov or passivity methods. However, in our development, we assume that the unknown parameters are time-varying and we do not know their variation bounds. Because they are time-varying, we may not apply the adaptive control strategies. Since we do not have knowledge of their variation bounds, traditional robust control fails. Here, in this project, we propose to use the function approximation technique to represent the external force as

d T d

d d T d

d d

z w

z w ˆ ˆ

where wd is a coefficient vector, zd is a vector of basis functions and

 is the approximation

d error. Then, the controller can be designed to be

u ke M m e b M m

M K B d d M m

u d

1 1 1 1 1

ˆ ˆ

ˆ ˆ ˆ ˆ

ˆˆ

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where

M ˆ w ˆ

TM

z

M ,

B ˆ w ˆ

TB

z

B and

K ˆ w ˆ

TK

z

K are respectively estimates of M, B and K, and

u

is to be determined. This will give the closed-loop dynamics

ˆ ] ) ˆ

~ ~

~ ( ~

[Mˆ1 MBKdm1dM1u



Ax b x

~ )

~

~ (~

[Mˆ1 wTMzM wTBzB wTKzK wTdzd b

Ax   

 ˆ ]

ˆ 1

1d M u m

 (5)

where x[

e

1

e

1]T , 

 



b m k

m

1 1 1 A 0

and b[0 1]T . w~M, w~ ,B w~K and w~d are all errors between actual values and their estimates. With the Lyapunov like function candidate

d d T d K K T K B B T B M M T M

V xTPx w R w w R w w R w w~ R w~ 2

~ 1

~ 2

~ 1

~ 2

~ 1

~ 2 1 2

1

we may calculate the update law and

u

to be

d m M u

M M M M

T d d

d

T K K

K

T B B

B

T M M

M

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ

1 1 1

1 1

1 1

1 1

Px b z R

w

Px b z R

w

Px b z R

w

Px b z R

w

 

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So, we may have boundedness of all internal variables. Together with the Barbalat’s lemma, we may easily have convergence of the output errors if the approximation error can be neglected.

It is noted that in this realization, we do not need to have the force feedback which is obviously better than the traditional impedance control.

However, there is a singularity problem of

, and we need to feedback the acceleration which might be a trouble in real applications. So, we try to modify the controller to

s K K v B v M s B d

u

ˆˆˆˆˆ

d (7) where

s



e

1

e

1 and

v



 

m

e

1 then the closed loop dynamics becomes

K

T K B

T B M T M d T d

ds v s v

K s

M w~ zw~ z w~ z ( )w~ z

This way we may select the Lyapunov like function candidate as

d d T d K K T K B B T B M M T

Ms M

V w Q w w Q w w Q w w~ Q w~

2

~ 1

~ 2

~ 1

~ 2

~ 1

~ 2 1 2

1 2

to give

s s

s v s

s v

d d d

K K K

B B B

M M M

z Q w

z Q w

z Q w

z Q w

1 1 1 1

ˆ ˆ

) ˆ (

ˆ

 

  

 

 

So now, this design does not need to know the acceleration, nor does it have the singularity problem. It ensures the convergence of the output error with the help of Barbalat’s lemma if the

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approximation error can be neglected.

Therefore, the system dynamics converges to the target impedance even though we do not have the information of the contact force or the system dynamics.

3. Experimental Study

An experimental setup is designed in this project as shown in Figure 1. On top of the X-Y table, a Z-axis is installed with a linear motion mechanism. The Z-axis may move down to touch the platform so that contact force can be generated. The X-Y table is used to present trajectory tracking performance. The system is operated under the DOS environment whose sampling period is set to 2ms by using the time interrupt. The LM1875 is employed to drive the DC motors. Several HCTL2020 are used to decode the encoder pulses to feedback the motion information.

It is required that the Z-axis to travel down 10mm in 16sec and then go back by following the same trajectory (dotted line in Figure 2).

However, a hard limit is at 8.5mm (horizontal line in Figure 2) and the Z-axis can not go beyond so there will be contact force generated.

The actual trajectory of the Z-axis is the solid line in Figure 2 which gives good tracking performance in the free space and it keeps touching at the hard limit when it is not allowed to go beyond. It is seen that the transition from the free space motion to the constrained motion is smooth. The estimated contact force is shown in Figure 3. The control effort is presented in Figure 4.

5. Conclusions

This project proposed an adaptive impedance controller which do not need to feedback the contact force or acceleration information and the system is allowed to contain various uncertainties. The Lyapunov-like analysis is used to verify system stability. The experiment results show that the proposed method is feasible in real-time implementation.

References

1. R. J. Anderson and M. W. Spong, “Hybrid Impedance Control of Robotic Manipulators,”

IEEE Trans. on Robotics and Automation, vol.

4, no. 5, pp. 549-556, 1988.

2. P. C. Chen and A. C. Huang, “Adaptive Sliding Control of Active Suspension Systems based on Function Approximation Technique,”Journal of Sound and Vibration, vol. 282, issue 3-5, pp. 1119-1135, April 2005a.

3. P. C. Chen and A. C. Huang, “Adaptive Multiple Surface Sliding Control of Hydraulic Active Suspension Systems Based on Function Approximation Technique,” Journal of Vibration and Control, vol. 11, no. 5, pp.685-706, 2005b.

4. P. C. Chen and A. C. Huang, “Adaptive Sliding Control of Active Suspension Systems with Uncertain Hydraulic Actuator Dynamics, Vehicle System Dynamics, vol. 44, no. 5, pp357-368, May 2006.

5. M. C. Chien and A. C. Huang, “Adaptive Impedance Control of Robot Manipulators based on Function Approximation Technique,” Robotica, vol. 22, issue 04, pp.395-403, August, 2004.

6. M. C. Chien and A. C. Huang, “Adaptive control of flexible-joint electrically-driven robot with time- varying uncertainties,”IEEE Trans. on Industrial Electronics, vol.54, no.2, pp 1032-1038, April 2007.

7. M. C. Chien and A. C. Huang, “An Adaptive Controller Design for Flexible-Joint Electrically-Driven Robots with Consideration of Time-Varying Uncertainties,”Chapter 5 in the book “Frontiers in Adaptive Control,”

I-Tech Education and Publishing, Vienna, Austria, 2009.

8. M. C. Chien and A. C. Huang, “A Regressor-free Adaptive Control for Flexible-joint Robots based on Function Approximation Technique,”Chapter 2 in the book Advances in Robot Manipulators, I-Tech Education and Publishing, Vienna, Austria, 2010a.

9. M. C. Chien and A. C. Huang, “Design ofa FAT-based Adaptive Visual Servoing for Robots with Time Varying Uncertainties,”

International J. of Optomechatronics, vol. 4, Issue 2, pp.93-114, 2010b.

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10. S. S. Ge, C. C. Hang, T. H. Lee and T.

Zang, Stable Adaptive Neural Network Control, Boston: Kluwer Academic, 2001.

11. A. A. Goldenberg, “Implementation f force and impedance control in robot manipulators,” in Proceedings of IEEE International Conf. on Robotics and Automation, vol. 3, pp. 1626-1632, 1988.

12. N. Hogan, “Impedance Control: an approach to manipulation: Part 1: theory, Part 2: implementation, Part 3: an approach to manipulation,” ASME Journal of Dynamic Systems, Measurement, and Control, vol.107, pp. 1-24, 1985.

13. A. C. Huang and Y. C. Chen, “Adaptive Sliding Control for Single-Link Flexible-Joint Robot with Mismatched Uncertainties,”IEEE Trans. Control Systems Tech., vol.12, no.5, pp.770-775, 2004a.

14. A. C. Huang and Y. C. Chen, “Adaptive Multiple Surface Sliding Control for Nonautonomous Systems with Mismatched Uncertainties,”Automatica, vol. 40, issue 11, pp.1939-1945, Nov. 2004b.

15. A. C. Huang and M. C. Chien, Adaptive Control of Robot Manipulators –A Unified Regressor Approach, World Scientific, 2010.

16. A. C. Huang and Y. S. Kuo, “Sliding Control of Nonlinear Systems Containing Time-varying Uncertainties with Unknown Bounds,”InternationalJ. of Control, vol. 74, no. 3, pp. 252-264, 2001.

17. A. C. Huang and K. K. Liao “FAT-based Adaptive Sliding Control for Flexible Arms, Theory and Experiments,”Journal of Sound and Vibration, vol. 298, issue 1-2, pp.

194-205, Nov. 2006.

18. A. C. Huang, S. C. Wu and W. F. Ting,

“An FAT-based Adaptive Controller for Robot Manipulators without Regressor Matrix: Theory and Experiments,”Robotica, vol. 24, pp. 205-210, 2006.

19. L. Huang, S. S. Ge, and T. H. Lee, “Neural Network based Adaptive Impedance Control of Constrained Robots,”in Proc. of the IEEE Int’l Symposium on Intelligent Control, pp.

615-619, 2002.

20. H. Kazerooni, J. J. Bausch and Kramer,

“An Approach to Automated Deburring by Robot Manipulators,”ASME J. of Dynamic

Sys., Meas. and Control, vol.108, no.4, pp.354-359, 1986.

21. R. Kelly, R. Carelli, M. Amestegui and R.

Ortega, An Adaptive Impedance Control of Robot Manipulators,”in Proceedings of IEEE Conference on Robotics and Automation, pp.

572-557, 1989.

22. T. F. Lee and A. C. Huang, “Vibration Suppression in Belt-driven Servo Systems Containing Uncertain Nonlinear Dynamics,” Journal of Sound and Vibration, vol. 330, Issue 1, pp.17-26, 2011.

23. N. H. McClamroch and D. Wang,

“Feedback Stabilization and Tracking of Constrained Robots,” IEEE Trans. on Automatic Control, vol. 33, no. 5, pp. 419-426, 1998.

24. M. H. Raibert and J. J. Craig, “Hybrid Position/Force Control of Manipulators,”

ASME Journal of Dynamics Systems, Measurement and Control, vol. 102, pp.

126-133, 1981.

25. M. W. Spong and M. Vidyasagar, Robot Dynamics and Control, J. Wiley, 1989.

26. J. T. Spooner, M. Maggiore, R. Ordonez and K. M. Passino, Stable Adaptive Control and Estimation for Nonlinear Systems –Neural and Fuzzy Approximator Techniques, NY:

John Wiley & Sons, 2002.

27. Y. C. Tsai and A. C. Huang, “FAT based adaptive control for pneumatic servo system with mismatched uncertainties,”Mechanical Sys. and Signal Proc., vol.22, no.6, pp.1263-1273, 2008a.

28. Y. C. Tsai and A. C. Huang, “Multiple Surface Sliding Controller Design for Pneumatic Servo Systems,”Mechatronics, no.

18, pp. 506-512, Nov. 2008b.

Figure 1 Experimental setup

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0 5 10 15 20 25 30 35 40 0

2 4 6 8 10 12

position(mm)

time(s)

system output design trajectory paper position

Figure 2 Trajectory tracking performance

0 5 10 15 20 25 30 35

-0.5 0 0.5 1 1.5 2 2.5 3 3.5x 10-5

d-hat(N-m)

time(s)

Figure 3 Contact force

0 5 10 15 20 25 30 35

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

controlinput(v)

time(s)

Figure 4 Control effort

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本人原擬於 101 年 7 月 18 至 20 日赴新加坡參加「

The 7th IEEE Conference on Industrial Electronics and Applications

」研討會。然因日前在榮 總檢查發現大腸長有一顆大型蒠肉(2 公分),醫囑立即切 除,不宜拖延,因此排定於 7 月 9 日進行手術。由於鄰近研 討會,所以無法成行。

相關公文如下所示。

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醫囑單

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論文接受函:

Dear Prof. An-Chyau HUANG

Paper ID : P0196

Paper Title : Adaptive Control of Horizontal Magnetic Levitation System Subject to External Disturbances

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Please note that the submission of your final paper should correspond to your Paper ID, ie, P0196.pdf. Please strictly adhere to the format given in the template for ICIEA 2012 while preparing your final paper.

In addition to excellent technical sessions, we will also have stimulating and enriching keynote speeches by renowned researchers. For the most updated information on the conference, please check the conference website athttp://www.ieeeiciea.org/. The Preliminary Program will be available at the website in early May 2012.

I would like to take this opportunity to thank you for choosing ICIEA 2012 to present your research results.

I look forward to seeing you in Singapore!

Yours sincerely,

Xing ZHU

Technical Program Chair for ICIEA 2012

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(15)

國科會補助計畫衍生研發成果推廣資料表

日期:2012/09/28

國科會補助計畫

計畫名稱: 無力量回授之馬達驅動順應控制器設計 計畫主持人: 黃安橋

計畫編號: 100-2221-E-011-021- 學門領域: 機器人學及應用

無研發成果推廣資料

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100 年度專題研究計畫研究成果彙整表

計畫主持人:黃安橋 計畫編號:100-2221-E-011-021- 計畫名稱:無力量回授之馬達驅動順應控制器設計

量化

成果項目 實際已達成

數(被接受 或已發表)

預期總達成 數(含實際已

達成數)

本計畫實 際貢獻百

分比

單位

備 註 質 化 說 明:如 數 個 計 畫 共 同 成 果、成 果 列 為 該 期 刊 之 封 面 故 事 ...

期刊論文 0 0 100%

研究報告/技術報告 0 0 100%

研討會論文 2 0 50%

論文著作 篇

專書 0 0 100%

申請中件數 0 0 100%

專利 已獲得件數 0 0 100% 件

件數 0 0 100% 件

技術移轉

權利金 0 0 100% 千元

碩士生 2 0 30%

博士生 1 0 50%

博士後研究員 0 0 100%

國內

參與計畫人力

(本國籍)

專任助理 0 0 100%

人次

期刊論文 0 0 100%

研究報告/技術報告 0 0 100%

研討會論文 1 0 50%

論文著作 篇

專書 0 0 100% 章/本

申請中件數 0 0 100%

專利 已獲得件數 0 0 100% 件

件數 0 0 100% 件

技術移轉

權利金 0 0 100% 千元

碩士生 0 0 100%

博士生 0 0 100%

博士後研究員 0 0 100%

國外

參與計畫人力

(外國籍)

專任助理 0 0 100%

人次

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其他成果

(

無法以量化表達之成

果如辦理學術活動、獲 得獎項、重要國際合 作、研究成果國際影響 力及其他協助產業技 術發展之具體效益事 項等,請以文字敘述填 列。)

The method we developed has already attracted some attentions from industrial people on the drilling automations. Some expectations on the coorperations might be formulated.

成果項目 量化 名稱或內容性質簡述

測驗工具(含質性與量性) 0

課程/模組 0

電腦及網路系統或工具 0

教材 0

舉辦之活動/競賽 0

研討會/工作坊 0

電子報、網站 0

目 計畫成果推廣之參與(閱聽)人數 0

(18)

國科會補助專題研究計畫成果報告自評表

請就研究內容與原計畫相符程度、達成預期目標情況、研究成果之學術或應用價 值(簡要敘述成果所代表之意義、價值、影響或進一步發展之可能性) 、是否適 合在學術期刊發表或申請專利、主要發現或其他有關價值等,作一綜合評估。

1. 請就研究內容與原計畫相符程度、達成預期目標情況作一綜合評估

■達成目標

□未達成目標(請說明,以 100 字為限)

□實驗失敗

□因故實驗中斷

□其他原因 說明:

2. 研究成果在學術期刊發表或申請專利等情形:

論文:□已發表 □未發表之文稿 ■撰寫中 □無 專利:□已獲得 □申請中 ■無

技轉:□已技轉 □洽談中 ■無 其他:(以 100 字為限)

3. 請依學術成就、技術創新、社會影響等方面,評估研究成果之學術或應用價 值(簡要敘述成果所代表之意義、價值、影響或進一步發展之可能性)(以 500 字為限)

Interacting of a mechanical system with the environment has long been challenging in the control related field. It attracts researchers simply because of its wide spectrum of applications in industry. In this project, we have developed a new strategy to ensure stability and performance of compliant motion control of a mechanical system interacting with its environment where force sensors are not really needed in the force feedback loop. The idea is new with justifications not only from mathematical proofs but also from experimental verifications. It is important in both the academic view point as industrial implementation. Some real applications can be developed based on the results obtained here. Some other theoretical extensions can also be proceeded to enhance the scheme. We do believe that the present project has been completed with satisfactory results.

數據

Figure 3 Contact force

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