Modeling and Force Control of Thin Soft McKibben Actuator
Ahmad Athif Mohd Faudzi∗,∗∗∗,†, Noor Hanis Izzuddin Mat Lazim∗∗, and Koichi Suzumori∗∗∗
∗Center for Artificial Intelligence and Robotics (CAIRO), Universiti Teknologi Malaysia Johor Bahru, Johor 81310, Malaysia
†Corresponding author, E-mail: [email protected]
∗∗Universiti Sains Islam Malaysia, Negeri Sembilan, Malaysia
∗∗∗Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology, Tokyo, Japan [Received January 6, 2016; accepted May 6, 2016]
This paper presents the modeling of a thin soft McK- ibben actuator using the system identification (SI) method and its force control. Procedures from the sys- tem identification method are used to create a math- ematical model (transfer function) from the test data.
The autoregressive with exogenous input (ARX) model was chosen as the model structure of the system. Next, a PSO-PID controller was proposed for the force con- trol of the actuator. The simulation data were verified against the test data for the force control using PSO- PID and conventional PID. Results showed that the de- veloped model represents the actual system by giving the same characteristics in the force control analysis in step, multi-step, and sinusoidal input.
Keywords: system identification, thin soft actuator, ARX model, force control, PID-PSO
1. Introduction
Soft actuators have been used in many applications in recent years because they have non-rigid links, high flex- ibility, and a high power-to-weight ratio [1–2]. They are also safe to use with people and more cost effective than other conventional actuators [3]. J. L. McKibben devel- oped the McKibben actuator in the 1950s. Schulte intro- duced the first contraction behaviour using a pneumatic muscle actuator (PMA) in 1961 [4]. Many applications in rehabilitation and medical devices have been developed.
They can be used in colonoscopy and as a finger exoskele- ton [5], an active support splint [6], and a soft robotic glove [7]. New bio-mimickery robots, such as an elephant trunk [8], omnidirectional locomotion robot [9], and ten- don driven system [10] have also been further explored using soft actuators. Most soft actuators use pneumatics as the medium for actuation, although some researchers have used polymer ion gel [11], piezoelectric [12], ion- exchange polymer metal composite (IPMC) [13], and hy- draulics [14] as driving mechanisms. Regardless of their advantages, soft actuators have the limitations of being slow to respond as well as difficult to model and control due to their nonlinear characteristics and unique system
design.
L. A. Zadeh presents multiple identification pro- cesses [15] that can be utilized as alternatives for normal mathematically-based model development of the transfer function. System identification is a method of modeling that uses the black box model concept by using the output and input information of the system to obtain the trans- fer function. It uses statistical methods to build a mathe- matical model of dynamic systems from the measurement data.
The method has been recognized as an important tool in many areas, coupled with the advancement of digital processing and computing. Preparation for identification and data acquisition was discussed in [16]. In [17], mod- eling using system identification and control of a two- joint planar pneumatic artificial muscle (PAM) were pre- sented. The modeling and identification of the robot arm uses ARX model and optimized by Genetic Algorithm (GA). An active force with fuzzy logic control was pro- posed in [18] to control a two-link arm driven by PAM.
Each links contains two PAM, and the desired position is achieved using the proposed algorithm.
This study implements the SI method to obtain a real- time force model for a thin soft actuator developed by K.
Suzumori et al. [19]. Once a mathematical model that can represent the force dynamic behavior of the soft ac- tuator is obtained, a control algorithm is implemented to achieve the control objective and further improve the per- formance of the actuator. In this study, a PID controller is proposed because of its simplicity, reliability, understand- ability, and robustness [20–21]. This is justified consider- ing the high percentage of PID implementation in indus- try [22]. However, the main issue when one attempts to realize the PID controller in any system is finding the op- timal value of the controller parameters (Kp,Ki, andKd).
Thus, this study proposes the particle swarm optimization (PSO) algorithm to find the ideal PID parameters. PSO is a computational technique that iteratively tries to im- prove the parameters value for optimization with regard to a given measure quality. From these new PID parame- ter values, it will give the best force control performance for the system.
Int. J. of Automation Technology Vol.10 No.4, 2016 487
4 mm șC
Fig. 1. Thin soft actuators [19].
Tetron braid
wall of silicon Air chamber
Fig. 2. Cross-section of thin soft actuators.
2. Thin Soft Actuator System
2.1. Structure of the Actuator
K. Suzumori et al. realized mass production of a thin McKibben actuator ranging from 0.6 mm to 10 mm in diameter [19]. In this work, a thin soft actuator with an outer diameter of 4 mm and length of 150 mm was de- veloped, as shown inFig. 1. Its structure was made from silicon material and reinforced with braided Tetron mate- rial, as shown in the cross section inFig. 2. What made the design of this actuator unique was that it did not have another silicone layer as an outer layer, as in [23].
Braided fiber weave structures are usually incorporated into pneumatic muscle actuators. It is important to keep the pressurized actuator from rupturing, which usually results from over-inflation. Actuators with braided lay- ers can generate axial contraction while actuators without them can produce radial expansion, or ballooning [10].
For applications that require higher driving forces, axial contraction is important. The minimum braid angle can vary depending on the weave pattern, fiber material, and diameter of the chamber itself. In [24], it is stated that a braid angle of around 20◦ can achieve maximum di- lation; however, no theoretical groundwork or minimum braid angle limit has been highlighted [23]. As this re- search is focused on force output, the fiber angle used is 0◦<θC<54.8◦, which has proved to have contraction ability [4]. The value ofθCon this actuator is 18.5◦, and it can contract 18% at 0.3 MPa.
2.2. Experiment Setup
The setup for testing this system is shown in Fig. 3.
One end of the actuator is closed while the other end is connected to an air tube controlled by a proportional
Fig. 3. Experiment setup.
servo valve. Applying pneumatic pressure to the cham- ber causes elastic contraction deformations. For the force model and control of this actuator, both ends of the actu- ator are fixed at the initial stage. At one end, the actuator is connected to a force sensor (FUTEK, LSB200). Once actuated, the actuator contracts, giving a force value with- out any displacement changes. The setup is used for the mathematical model development using the system iden- tification method.
The force sensor and proportional valve are connected to a data acquisition (DAQ) card (National Instrument, NI-PCI 6221). A voltage of 0–3 V is used to regulate the pressure input of 0–300 kPa.
3. System Identification
This section will discuss parametric identification using non-recursive estimation for a linear discrete-time system of the thin soft actuator. The plant mathematical model will be approximated using the MATLAB System Identi- fication toolbox from open-loop input-output test data. In the setup of the experiment, the hardware and PC commu- nicate using the DAQ card over MATLAB software. The basis for the model identification procedure starts with the experiment setup, model structure selection, model esti- mation, model validation, and finally testing with the ba- sic controller to prove the operation of the system.
The design of an identification experiment should con- sider which signal and when it should be measured. The purpose of the experiment is to collect several sets of input-output data over the entire range of the system op- erating points under consideration. This is to vary the in- put signal and observe the response of the output signal.
This includes the choice of the measured variables and the character of the input signals.
3.1. Model Structure Selection
In the system identification method, there are a few parametric model structures that can be used to repre-
1/A
e
Fig. 4. General ARX model. Fig. 5. Overall block diagram for system identification.
Fig. 6. Simulink block diagram of PRBS generator.
sent the system. These are the autoregressive with ex- ogenous input (ARX) model, autoregressive moving aver- age with exogenous input (ARMAX) model, output-error (OE) model, and Box-Jenkins (BJ) model [26]. The plant model is derived from the measured input and output sig- nals of a real plant that needs to be identified. After com- parison with other model structures, the ARX parametric model structure was chosen for its good results, which ful- filled the criteria for the SI model. Assuming that noise is zero, the following equation can be derived from Eq. (1) in time domain and Eq. (2) inzdomain:
y(k) +a1y(k−1) +···+anay(k−na)
=b1u(k−d) +b2u(k−d−1) +···
+bnbu(k−d−nb+1) . . . (1)
Y(z−1)
U(z−1)=z−dB(z−1)
A(z−1) . . . (2)
na≥nb . . . (3) where
kis the discrete time step, dis time delay,
nais the number of poles, nbis the number of zeros, u(k)is input,
y(k)is output, e(k)is noise, and z−1is the delay operator.
Y is output,U is input,Ais the denominator polynomial, andBis the nominator polynomial of the transfer function in z domain. It is assumed the number of poles, na, is
always larger than or equal to the number of zeros,nb. A minimum phase model can be obtained using large sampling times; the non-minimum phase model can be obtained using a small sampling time [27]. Fig. 4shows the general ARX model:uis input,yrepresents output,e indicates the error signal, andAandBare parameters to be determined.
After a suitable model was chosen, the structure of the model had to be decided. The ARX structure can have a different number of poles, zeros, and delay. The form of ARX isna-nb-nk, wherenais the order of the polynomial A,nbis the order of the polynomial B+1, andnkis the input-output delay. The ARX model will have a differ- ent structure from the lower degree 2-2-1 structure to the higher degree 4-3-1 structure. Higher-order models may produce unstable output.
3.2. Model Estimation
Good parameter identification requires the usage of in- put signals rich in frequencies. There are several methods of generating signals, such as pseudo-random binary se- quences (PRBS), sinusoidal input, and step input, among others. PRBS is a binary sequence with a random series of step functions generated by shift registers.
In order to generate the input and obtain the output sig- nal for the soft actuator, an overall block diagram was de- signed, as shown inFig. 5. In the diagram, the PRBS gen- erator output is sent to DAQ analog output to change the actuator’s pressure value. The affected contraction force is recorded using the force sensor through DAQ analog in- put. The PRBS generator is shown inFig. 6. Seven series of JK flip-flops were used to generate a 127 random bi- nary sequence. The minimum time interval between two
Fig. 7. Input and output signals for parameter estimation.
successive pulses was 0.16 s, which took 20.32 s to fin- ish. Model estimation is the process of determining the value of a candidate model’s coefficients from the ob- served data.
3.3. Model Validation
After a suitable model estimation and model structure has been selected, the model validation is conducted. The model validation is to check the measured data against the desired data under a validation requirement. The sim- plest validity check can be performed by observing the convergence of training errors and assessing the predic- tion errors for the test data. By using part of the test data that were not used and were reserved for model validation purposes, the acceptance or rejection of a certain obtained model can be done based on Akaike’s final prediction er- ror (FPE) [26].
The input and output signals used for the estimation and validation process are shown inFig. 7. The signals are divided into two parts: the first part for estimation and the second part for validation. Sets of 4200 input and output data with a sampling time of 0.005 s were collected for model estimation and validation. These input and output data were divided into two parts. The first part was used to estimate the model of the system while the other part was for model validation i.e., 0 to 2100 samples and 2101 to 4200 samples, respectively.
In this study, a few ARX models were simulated and compared to the measured model output, as shown in Fig. 8. The third-order model, the ARX331 model struc- ture, gave the highest best-fit value of 86.46%, which rep- resented the nearest model of the true plant. Thus, it was selected to represent the thin soft actuator. The estimated model for the system is given in Eq. (4) below:
G(z) =−0.000558z2+0.0433z+0.09214
(z3−1.459z2+0.2842z+0.1849) . (4)
Fig. 8. Measured and simulated model output.
Fig. 9. Simulink block diagram for PSO.
4. Control Strategy
By using the mathematical model obtained using the system identification approach in Eq. (4), the value of PID parameters was tuned using the particle swarm optimiza- tion (PSO) technique and the conventional method. The PSO algorithm was used to search for the optimalKp,Ki, andKd values that would give the lowest integral square error (ISE) value. The Simulink block diagram shown in Fig. 9was used with the PSO algorithm with 40 particles
Fig. 10. Convergence graph for PID optimization using PSO.
Table 1. Values of PID parameters.
PID variables PID trial-error PID-PSO
Kp 1.49 1.0353
Ki 7.92 2.7916
Kd 0.001 1.0000e-03
Fig. 11. Simulation comparison of PID-PSO and PID try- error for unit step input.
Table 2. Parameters for PID trial-error and PID-PSO.
Parameters PID trial-error PID-PSO
Rise time, s 0.1663 0.1663
Settling time, s 0.8826 0.2323
Overshoot, % 22.4775 0.7886
for 50 iterations.
The PSO algorithm optimizes the PID parameters by moving the particles towards the best solution. It can be observed that the integral absolute error (IAE) value de- creased with the number of iterations, converging at it- eration 29, as shown inFig. 10. The optimized PID pa-
Fig. 12. PID-PSO step response comparison between ex- periment and simulation.
Fig. 13. PID-PSO multistep response comparison between experiment and simulation.
rameters are tabulated in Table 1for both the PSO and conventional trial-error values.
The force control was simulated in MATLAB with op- timized PSO-PID parameters and verified with PID trial and error, as shown inFig. 11. The performance showed that the percentage of overshoot, %OS, improved from 22.5% to 0.78%. Settling time values also improved from 0.88 s to 0.23 s when the PID-PSO parameter values were used. Details of the validation are tabulated inTable 2.
Next, the PID-PSO was deployed into a real-time ex- periment with different types of target signals. The out- put responses from the simulation were compared to those from the experiment to further validate the mathematical model obtained using system identification. The reference targets used were step, multi-step, and sinusoidal signals shown inFigs. 12,13, and14, respectively.
0 1 2 3 4 5 6 7 8 9 10 -5
0 5 10 15 20 25 30
Time (s)
Force (N)
Experiment Simulation
Fig. 14. PID-PSO sinusoidal signal comparison between experiment and simulation.
It can be observed that the PID-PSO controller was able to drive the soft actuator close to the reference target force. Additionally, the simulation and experiment output were similar for the most part, which indicates a good cor- relation between the mathematical model developed using SI and the real hardware system.
5. Conclusion
A developed force model using the SI method was achieved in Simulink MATLAB. The ARX331 model structure was used, and it proved to be stable in the simu- lation tests and experiments. The force model was tested for force control using PID-PSO and trial-error values for Kp, Ki, andKd variables. The response showed the sys- tem achieved good control for step, multi-step, and sinu- soidal input for both simulations and experiments. The rise time for both PID-PSO and PID-trial and error had similar values of 0.1663 s. However, PID-PSO showed significant improvement of 0.79% overshoot compared to PID-trial and error with 22.48% overshoot. In summary, the model was successfully developed, and force control was achieved in the real-time system.
Acknowledgements
The authors would like to thank Universiti Teknologi Malaysia (UTM), the Tokyo Institute of Technology (TITECH), and AUN/SEED-Net under CRC 4B187 Grants for financial and fa- cilities support.
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Affiliation:
Associate Professor, Universiti Teknologi Malaysia
Address:
Johor Bahru, Johor 81310, Malaysia Brief Biographical History:
2004- Tutor UTM 2006- Lecturer UTM 2011- Senior Lecturer in UTM 2015- Associate Professor in UTM
2015- Visiting Research Fellow, Tokyo Institute of Technology Main Works:
•A. A. M. Faudzi, K. Suzumori, and S. Wakimoto, “Development of an Intelligent Chair Tool System Applying New Intelligent Pneumatic Actuators,” Advanced Robotics, Vol.24, pp. 1503-1528, 2010.
•I. N. A. Mohd Nordin, A.A.M. Faudzi, M.R.M. Razif, E. Natarajan, S.
Wakimoto, and K. Suzumori, “Simulations of Two Patterns Fiber Weaves Reinforced in Rubber Actuator,” J. Teknologi (Sciences and Engineering), Vol.69, No.3, pp. 133-138, 2014.
Membership in Academic Societies:
•Institute of Electrical and Electronics Engineers (IEEE)
•Japan Society of Mechanical Engineers (JSME)
•Institution of Engineering and Technology (IET)
•IEEE Robotics and Automation Society (RAS)
Name:
Noor Hanis Izzuddin Mat Lazim
Affiliation:
Fellowship, Universiti Sains Islam Malaysia
Address:
71800, Nilai, Negeri Sembilan, Malaysia Brief Biographical History:
2011- Engineer, Intel Malaysia 2015- Completed Master Degree 2016- Ph.D. Candidate in UTM Main Works:
•N. H. Izuddin, A. A. M. Faudzi, M. R. Johary, K. Osman, “System Identification and Predictive Functional Control for Electro Hydraulic Actuator System,” IEEE Int. Symposium on Robotics and Intelligent Sensors, Langkawi, 2015.
Membership in Academic Societies:
•Board of Engineers Malaysia (BEM)
Affiliation:
Professor, Tokyo Institute of Technology
Address:
2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan Brief Biographical History:
1984-2001 Toshiba R&D Center 1999-2001 Micro Machine Center, Tokyo 2001- Professor at Okayama University 2014- Professor at Tokyo Institute of Technology Main Works:
•T. Higuchi, K. Suzumori, and S. Tadokoro, “Next-Generation Actuators Leading Breakthroughs,” Springer, 2010.
•D. Hirooka, K. Suzumori, and T. Kanda, “Flow Control Valve for Pneumatic Actuators Using Particle Excitation by PZT Vibrator,” Sensors and Actuators A: Physical, Vol.155, pp. 285-289, Nov. 2009.
Membership in Academic Societies:
•American Society of Mechanical Engineers (ASME)
•Japan Society of Mechanical Engineers (JSME), Fellow
•Robotics Society of Japan (RSJ), Fellow
Int. J. of Automation Technology Vol.10 No.4, 2016 493
