Y. T. WANG1 R. H WONG1,2 and J. H. Lo1
1Department of Mechanical Engineering,
National Taiwan University of Science and Technology, 43, Keelung Rd. Sec.4, Taipei, Taiwan 106, R.O.C
2Department of mechanical Engineering, Hwa Hsia Institute of Technology,
111 Gong Jhuan Rd., Chung Ho, Taipei, Taiwan 235, R.O.C
Abstract
This paper proposes a CCD to replace contacted displacement sensors. CCD is used
to capture the photo vision of 2D pneumatic arm and then transform to X-Y coordinates as feedback signal. It focuses to compare the measuring accuracy and control performance of different displacement sensors. Since the displacement measuring process of CCD requires lots of computational time, it implements the self-organizing sliding-mode fuzzy controller to simplify and optimize fuzzy rules and to reduce the computer load. The present paper simultaneously provides both trajectory tracking performances of CCD-based and encoder-based 2D pneumatic arms via a variety of experiments. And then, evaluate the feasibility of CCD-based 2D pneumatic arm control system.
Keywords: 2D pneumatic arm, CCD, self organizing sliding mode fuzzy controller
1 Intoduction
Pneumatic muscle actuators are developed to take the place of conventional pneumatic linear actuators in applications of rotational, non-aligned and complicated mechanisms. In industrial applications, 2D mechanical arms are used widely because of their simplification
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and efficiency [1,2]. In this paper, pneumatic muscle actuators driven by pressure type servo-valves are used to setup a 2D pneumatic arm control system to simulate the motion of an excavator.
Instead of the contacted displacement sensors, this paper implements the non-contacted CCD to capture the planer photo vision of pneumatic arm and transforms into two-dimensional displacement signal [3,4]. Both encoders and CCD are installed in this 2D pneumatic arm control system and their two-dimensional displacement can be simultaneously recorded for comparisons. It thus can study the measuring accuracy of CCD signal and evaluate the control performance based on CCD due to the photo vision two-dimensional displacement transformation.
This 2D pneumatic arm is a non-linear control system. Without the detailed model, fuzzy control algorithms have been found to be effective in dealing with non-linear, complicated and ill-defined systems. The sliding-mode fuzzy controller and the self-learning fuzzy controller have been widely applied for pneumatic control systems [5,6].
To integrate the sliding-mode and self-learning fuzzy controllers, this paper proposes the self-organizing sliding-mode fuzzy controller [7] for the trajectory tracking control of 2D pneumatic arm. The sliding surface function is to reduce the two-dimensional into one-dimensional system variables. The one-dimensional self-learning mechanism provides the optimized fuzzy rules online. So, the present paper can compare the trajectory tracking performances of both CCD-based and encoder-based pneumatic arms via variety trajectory tracking experiments. And, it can evaluate the feasibility of replacing classical contacted sensors by the non-contacted CCD in the 2D pneumatic arm control system.
2 System Descriptions
The 2D pneumatic arm control system is shown in Fig. 1. M1 and M2 are muscle
actuators and their specifications are 20φ ×305mm and 20φ ×204mm respectively. They are driven by pressure type servo valves FESTO MPPES-3-1/8-010. The contraction range of muscle actuator is -3 ~ 20%. The work space of this 2D pneumatic arm is limited due to the limitations of contraction range. The first arm’s length l1 is 440mm and its weight including the encoder is 2.5kg. The second arm’s length l2 is 408mm and the
weight is 0.9kg. The loading is 4kg.
Both CCD and encoders are installed to measure the two-dimensional displacement signal. θ and 1 θ are angular displacements measured by encoders 2 E1 and E2 which
resolutions are 2000pulses/cycle. The CCD camera is SONY LV-75 which is to capture the photo vision of X-Y plane. For a fixed CCD location, its photo vision focuses on 219×164mm and its resolution is 640×480pixels. The scaling rate is 59.94Hz. The video capture board is a photo vision decoder to transfer the photo vision signal into X-Y coordinate and determine the 2D pneumatic arm’s location. The resolution of D/A port is 12bits. The personal computer (PC) is a 80586 microcomputer system. The control program is developed by Turbo C++.
3 Control Schemes
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A 2D pneumatic arm control system shown in Fig. 1 is used to simulate the excavator’s motion. Fig. 2 and Fig. 3 are functional block diagrams of control structures using CCD and encoders respectively. The kinetic transformation is the relationship between angular displacements (θ ,1 θ ) and absolute position (X, Y) of loading. 2 And, the inversed kinetic transformation are:
cos )
This 2D pneumatic arm control system is a non-coupled two-inputs two-outputs system.
θ and 1 θ could be individually driven by 2 M1 and M2 muscle actuators respectively.
And thus, the controller can be designed for each sub-system individually.
In comparison with other control algorithms, the fuzzy control approach has been found to be an effective algorithm to deal with complicated, ill-defined and poor mathematically modeled dynamical process. In general, the fuzzy rule base is two-dimensional which depends on system variables ( e , e& ). To optimize a two-dimensional fuzzy rule table requires a lot of effort.
The configuration of the self-organizing sliding-mode fuzzy controller (SOSMFC) is
shown as Fig. 4. The sliding surface is designed to simplify and reduce two-dimensional fuzzy rules into one-dimensional. It is described as
s=α⋅e+e&
where α is a positive constant. The gains G and s G are used to normalize between u
system variables and the universal of fuzzy sets. The fuzzy sets are finely divided into 13 linguistic fuzzy subsets. Fuzzification is adopted the triangular-type membership function to obtain linguistic variables. The fuzzy inference is based on the Max-Min product composition and is used to operate fuzzy control rules. The height method is used to defuzzify the fuzzy sets to attain the control signal. In the self-organizing learning
mechanism, the linguistic approach rule base can be modified as
( )
nTrelationship between input signal of servo-valve and angular displacement output. T is the sampling time.
4 Measuring Error of CCD
In general, the encoder is more accurate and has fast response than CCD. Both (X,Y) signals obtained by encoders and CCD are simultaneously recorded to justify the CCD’s measuring accuracy, and their difference is defined as the measuring error. Table 1 is the static projecting error and measuring error at the working space of experiments in Section
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5. The projecting error is the portion of measuring error in X or Y coordinates. It indicates that the projecting errors of X and Y coordinates are slightly different. But, the measuring errors are very consistent and the average measuring error is 1.08mm.
Fig. 5 is the dynamic measuring error of point-point control experiment in Section 5.
While the object’s velocity is under 10mm/s, the dynamic measuring error is near to the static measuring error. However, the dynamic measuring error becomes more significant at high objective’s velocity. The measuring error is up to 10mm at 45mm/s. It means the CCD measurement system be reliable at low speed applications.
5 Experimental Results
In the present paper, this 2D pneumatic arm control system is applied for variety trajectory tracking applications including step, ramp and parabolic commands. The sampling frequency of CCD-based system is valid within 28Hz. due to the limitations of photo vision capture process and computational loading. Although the encoder-based system could provide the high sampling frequency, the sampling time of following experiments of both CCD-based and encoder-based systems is fixed at 0.35 sec. in order to ignore the sampling effects. Parameters of SOSMFC are properly chosen as Gs =0.3, Gu =3.8,
=4
α , γ =0.1 and M =1.
To evaluate the control accuracy, the absolute position error is defined as
2 and, the average position error is
N
The following experiments are included to compare the control performances of CCD-based and encoder-based systems.
Case 1 is a point-to-point control experiment and its commands are Xd =150 tu( ) and Yd =70 tu( ). Fig. 6 is the time response of Case 1. Due to the characteristics of CCD
measuring process, the time delay of CCD-based system is slightly greater than encoder-based system. Except the slight oscillations in the steady state of CCD-based system, their overall behaviors in time responses are very similar. To compare their steady state performance, the steady state error of CCD-based system is 1.06mm and the encoder-based system is 0.92mm, which are summarized in Table 2.
Case 2 is a trajectory tracking control case of a ramp input. Its commands are )
tracking performance of both CCD-based and encoder-based systems. Their performance are similar. Fig. 8 is the error analysis of Case 2. The maximum errors of CCD-based and encoder-based systems are 14.6 and 12.1mm respectively. Except the slight oscillations of CCD-based system, their overall performances have no significant difference. Their
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average errors and steady state errors are summarized in Table 2. The average error of CCD-based system is 3.23mm, and encoder-based system is 2.75mm. Thus, CCD applied for measuring two-dimensional displacement in the 2D pneumatic arm control system is acceptable.
Case 3 is a quadratic trajectory tracking control case. Its commands are )
tracking performance. The influence of system delay is tremendously decreased in both systems owing to the characteristics of parabolic function. Except the slight oscillations in the CCD-based system, the tracking performances of both CCD and encoder-based systems match well with the command. Fig 10 is their error analysis. In comparison with Case 2, the maximum errors have been tremendously reduced in the transient process, and the average errors are 2.51 and 2.35mm respectively. Again, the performance of CCD-based system is similar to encoder-based system. It is reasonable to replace encoders by CCD in the trajectory tracking control of 2D pneumatic arm control system.
6 Conclusions
In this paper, it uses non-contacted CCD to replace classical contacted sensors in the 2D
same self-organizing sliding-mode fuzzy controller and sampling frequency to evaluate their trajectory tracking control performances. Comparisons of their performances lead to following conclusions.
1. The photo vision capture process requires a lot of computational time. Thus, CCD-based system is valid for low sampling frequency applications only.
2. The two-dimensional displacement measurement via the photo vision of CCD is accurate in the steady state and quasi-static process.
3. The self-organizing sliding-mode fuzzy controller can simplify the fuzzy rules’ optimizing process and can fit for both CCD-based and encoder-based 2D pneumatic arm control systems.
4. Experimental results indicate that the trajectory tracking performance of CCD-based and encoder-based 2D pneumatic arm control systems match well with each other.
Therefore, CCD is an option to replace encoders in the trajectory tracking applications of 2D pneumatic arm control system.
Acknowledgement
This work was supported by Festo Co. and National Science Council of ROC under grant NSC96-2221-E011-103.
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References
1. Kawashima, K., Sasaki, T., Ohkubo, A., N., Miyata T. and Kagawa, T. Application of Robots Arm Using Fiber Knitted Type Pneumatic Artificial Rubber Muscles, IEEE, Robotics and Automation, V.5, N.5, pp.4397-4942, 2004.
2. Sasaki, T., Miyata, T. and Kawashima, K., Development of Remote Control System of Construction Machinery Using Pneumatic Robot Arm, International Conference on Intelligent Robots and Systems, Sendai, pp.748-753, 2004.
3. Hutchinson, S., Hager, G.D. and Corke, P.I., A Tutorial on Visual Servo Control, IEEE, Robotics and Automation, V.12, N.5, pp.651-670, 1996.
4. Chang, W.C. and Morse, A.S., Exponentially Stable Positioning of a Rigid Robot Using Stereo Vision, Proceeding of IEEE International Conference on Robotics and Automation, V.1, pp.605-610, 1999.
5. Lilly, J.H. and Yang, L., Sliding Mode Tracking for Pneumatic Muscle Actuators in Opposing Pair Configuration, IEEE Trans. on Cont. Sys. Tech. V.13, N.4, pp.550-558, 2005.
6. Chang, M.K., Yen, P.I. and Yuan, T.H., Angle Control of a One-Dimensioin Pneumatic Muscle Arm Using Self-Organizing Fuzzy Control, IEEE, International Conference on Sys. Man. and Cyb., V.5, pp.3834-3838, 2006.
7. Allamehzadeh, H., “Sliding Mode Fuzzy Control with Optimal Rule Table”, IEEE
International Conference on Fuzzy Systems, Canada, pp.2048-2055, 2006.
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l1
l2
Fig. 1 Schematic diagram of a 2D pneumatic arm control system.
(
Xd Yd)
P , θ1d,θ2d e1,e2 u1,u2 P
(
X,Y)
+ −
Fig. 2 Functional block diagram of CCD-based control structure.
d d, 2 1 θ
θ e1,e2
2 1,u
u P
(
X,Y)
+ −
(
Xd Yd)
P ,
e e s=α⋅ +&
( )nT T s M
T ) 1 ( + ⋅
⋅ α γ
dt d
e&
e
Fig. 4 Configuration of self-organizing sliding mode fuzzy controller.
Fig. 5 Measuring error of various objective’s velocity.
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Fig. 6 Time response of Case 1. (──：CCD ,……：Encoder )
Fig. 7 The trajectory tracking performance of Case 2.
(──：CCD ,……：Encoder, - - - -：Command )
Fig. 8 Error analysis of Case 2. (──：CCD ,……：Encoder )
Fig. 9 The trajectory tracking performance of Case 3.
(──：CCD ,……：Encoder, - - - -：Command )
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Fig. 10 Error analysis of Case 3. (──：CCD ,……：Encoder )
Table 1. Static measuring errors (unit: mm).
Location Projecting Error
X Y X Y Measuring Error
0 ~ 30 0 ~ 14 0.72 0.91 1.16
30 ~ 60 14 ~ 28 0.84 0.64 1.05
60 ~ 90 28 ~ 42 0.95 0.11 0.95
90 ~ 120 42 ~ 56 1.1 0.43 1.18
120 ~ 150 56 ~ 70 1.08 0.62 1.24
average 0.94 0.54 1.08
Table 2 Average errors and steady state errors of Cases1~3 (unit: mm) .
e e ss
CCD Encoder CCD Encoder Case1 21.65 20.69 1.06 0.92 Case2 3.23 2.75 1.23 1.13 Case3 2.51 2.35 1.15 1.07
計畫成果自評：
1、完成撓性氣壓缸、旋轉氣壓缸等不同組件設計組立之 2D 氣壓手臂，分析這兩種氣壓手 臂的特性，以及不同軌跡追蹤控制實驗的結果與精度，提供 2D 氣壓手臂設計者或使用 者相關技術資料。
2、開發 2D 氣壓手臂的控制器，利用滑動模糊、自組織模糊、自組織滑動模糊等不同控制 理論，撰寫控制之控制程式，應用在 2D 氣壓手臂的軌跡追蹤控制實驗，敘述不同控制 器的優缺點與控制精度。
3、完成非接觸式 CCD 影像視覺在 2D 氣壓手臂的位移量測，並與傳統接觸式感測器的位 移量測結果進行比對，確認 CCD 影像視覺的靜態與動態量測精度。利用 CCD 影像視 覺或傳統感測器提供 2D 位移回授訊號，進行 2D 氣壓手臂的軌跡追蹤控制，比較兩者 之差異，並進一步證實 CCD 影像視覺取代傳統感測器在 2D 氣壓手臂應用的可行性。
4、本計劃的研究成果，有二篇已發表或被接受發表於國際期刊。
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