Identification Procedure for McKibben Pneumatic Artificial Muscle Systems

490 views
404 views

Published on

Kogiso, Sawano, Itto, and Sugimoto, "Identification Procedure for McKibben Pneumatic Artificial Muscle Systems." presented in IROS 2013

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
490
On SlideShare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Identification Procedure for McKibben Pneumatic Artificial Muscle Systems

  1. 1. IEEE/RSJ International Conference on Intelligent Robots and Systems October 7-12, 2012 Vilamoura, Algarve, Portugal Identification Procedure for McKibben Pneumatic Artificial Muscle Systems K. Kogiso, K. Sawano, T. Itto, and K. Sugimoto Nara Institute of Science and Technology (NAIST), Japan Oct. 10, 2012 @ WedBT5, 9:30 to 9:45 am, Regular Session, Gemini 2, Tivoli Marina Vilamoura13年1月30日水曜日
  2. 2. Outline Introduction Modeling of PAM system Identification Procedure Experimental Validation Extension Conclusion Active Link, Co. 213年1月30日水曜日
  3. 3. Introduction McKibben Pneumatic Artificial Muscle (PAM) rubber tube mesh Advantage for application Disadvantage for modeling & control high power/weight ratio complex & nonlinear system (hydrodynamics) flexibility empirical approximation or linearization 313年1月30日水曜日
  4. 4. Introduction Motivation Mathematical modeling of PAM is a challenging issue. L0 L l nonlinearities such as hysteresis, hydrodynamics, friction,... solenoid PDC valve valve difficulty to explain validity of approximation or linearization. dependence on what kind of a valve you use. air compressure M M PAM system = PAM + proportional directional control (PDC) valve 0.3 Mathematical modeling of PAM system w/ constant weight. 0.2 [Itto, Kogiso: Hybrid modeling of McKibben pneumatic artificial muscle systems, IEEE ICIT&SSST, 2011] ε formulates model structure based on dynamics, but 0.1 M = 3 [kg] requires complete try and errors for identifying parameters. M = 6 [kg] M = 9 [kg] 0 hysteresis loop 100 200 300 400 500 600 700 pressure [kPa] 413年1月30日水曜日
  5. 5. Introduction Motivation Mathematical modeling of PAM is a challenging issue. L0 L l nonlinearities such as hysteresis, hydrodynamics, friction,... solenoid PDC valve valve difficulty to explain validity of approximation or linearization. dependence on what kind of a valve you use. air compressure M M PAM system = PAM + proportional directional control (PDC) valve 0.3 Mathematical modeling of PAM system w/ constant weight. 0.2 [Itto, Kogiso: Hybrid modeling of McKibben pneumatic artificial muscle systems, IEEE ICIT&SSST, 2011] ε formulates model structure based on dynamics, but 0.1 M = 3 [kg] requires complete try and errors for identifying parameters. M = 6 [kg] M = 9 [kg] 0 hysteresis loop Outcomes 100 200 300 pressure 400 [kPa] 500 600 700 a parameter identification procedure supported by analysis of the mathematical model, which contributes to reduce the cost for try and errors. an identified model validated by comparison with several experimental data, which well simulates behaviors of a practical PAM system. an extension to a model expressing the PAM system over a specified weight range, which is realized by interpolation of some dominant parameters in terms of a weight. 413年1月30日水曜日
  6. 6. Modeling Dynamics of PAM system [Itto, Kogiso, IEEE ICIT&SSST 11] switched system with 64 nonlinear subsystems x(t) = f (x(t), u(t)) if x(t) 2 S ˙ y(t) = h(x(t)) T x := [✏ ✏ P ]T y := [✏ F ] ˙ S := {x 2 <3 | (x)  0} 2 {1, 2, · · · , 64} 513年1月30日水曜日
  7. 7. Modeling Dynamics of PAM system [Itto, Kogiso, IEEE ICIT&SSST 11] switched system with 64 nonlinear subsystems x(t) = f (x(t), u(t)) if x(t) 2 S ˙ y(t) = h(x(t)) T x := [✏ ✏ P ]T y := [✏ F ] ˙ S := {x 2 <3 | (x)  0} 2 {1, 2, · · · , 64} dynamic equation (w/ friction [Kikuue, IEEE TRO 06] ) 8 > F (P, ✏, t) M g Ff (t) > < M L¨(t) = ✏ K(L0 L(1 ✏(t)))3 , if ✏(t)  L LL0 , > > : F (P, ✏, t) M g F (t), f otherwise, 8 > cv L✏(t) + cc sgn(✏(t)), ˙ ˙ if ✏(t) 6= 0, ˙ > > < c , if ✏(t) = 0 and Fo (t) > cc , ˙ c Ff (t) = > Fo (t), if ✏(t) = 0 and Fo (t) 2 [ cc , cc ], > ˙ > : cc , if ✏(t) = 0 and Fo (t) < cc , ˙ 513年1月30日水曜日
  8. 8. Modeling Dynamics of PAM system PAM volume [Kagawa, CEP 97], [Minh, Mechatronics 10] [Itto, Kogiso, IEEE ICIT&SSST 11] V (t) = D1 ✏(t)2 + D2 ✏(t) + D3 switched system with 64 nonlinear subsystems x(t) = f (x(t), u(t)) if x(t) 2 S ˙ y(t) = h(x(t)) T x := [✏ ✏ P ]T y := [✏ F ] ˙ S := {x 2 <3 | (x)  0} 2 {1, 2, · · · , 64} dynamic equation (w/ friction [Kikuue, IEEE TRO 06] ) 8 > F (P, ✏, t) M g Ff (t) > < M L¨(t) = ✏ K(L0 L(1 ✏(t)))3 , if ✏(t)  L LL0 , > > : F (P, ✏, t) M g F (t), f otherwise, 8 > cv L✏(t) + cc sgn(✏(t)), ˙ ˙ if ✏(t) 6= 0, ˙ > > < c , if ✏(t) = 0 and Fo (t) > cc , ˙ c Ff (t) = > Fo (t), if ✏(t) = 0 and Fo (t) 2 [ cc , cc ], > ˙ > : cc , if ✏(t) = 0 and Fo (t) < cc , ˙ 513年1月30日水曜日
  9. 9. Modeling Dynamics of PAM system PAM volume [Kagawa, CEP 97], [Minh, Mechatronics 10] [Itto, Kogiso, IEEE ICIT&SSST 11] V (t) = D1 ✏(t)2 + D2 ✏(t) + D3 switched system with 64 nonlinear subsystems contraction force [Tondu, IEEE CSM 00], [Kang, ICRA 09] x(t) = f (x(t), u(t)) if x(t) 2 S ˙  n ⇣ ⌘ o2 Cq2 Pg (t) F (P, ✏, t) = APg (t) at a C q1 1 + e ✏(t) as y(t) = h(x(t)) T x := [✏ ✏ P ]T y := [✏ F ] ˙ S := {x 2 <3 | (x)  0} 2 {1, 2, · · · , 64} dynamic equation (w/ friction [Kikuue, IEEE TRO 06] ) 8 > F (P, ✏, t) M g Ff (t) > < M L¨(t) = ✏ K(L0 L(1 ✏(t)))3 , if ✏(t)  L LL0 , > > : F (P, ✏, t) M g F (t), f otherwise, 8 > cv L✏(t) + cc sgn(✏(t)), ˙ ˙ if ✏(t) 6= 0, ˙ > > < c , if ✏(t) = 0 and Fo (t) > cc , ˙ c Ff (t) = > Fo (t), if ✏(t) = 0 and Fo (t) 2 [ cc , cc ], > ˙ > : cc , if ✏(t) = 0 and Fo (t) < cc , ˙ 513年1月30日水曜日
  10. 10. Modeling Dynamics of PAM system PAM volume [Kagawa, CEP 97], [Minh, Mechatronics 10] [Itto, Kogiso, IEEE ICIT&SSST 11] V (t) = D1 ✏(t)2 + D2 ✏(t) + D3 switched system with 64 nonlinear subsystems contraction force [Tondu, IEEE CSM 00], [Kang, ICRA 09] x(t) = f (x(t), u(t)) if x(t) 2 S ˙  n ⇣ ⌘ o2 Cq2 Pg (t) F (P, ✏, t) = APg (t) at a C q1 1 + e ✏(t) as y(t) = h(x(t)) T pressure change in a PAM [Richer, JDSMC 00] x := [✏ ✏ P ]T y := [✏ F ] ˙ ˙ ˙ RT V (t) S := {x 2 <3 | (x)  0} 2 {1, 2, · · · , 64} P (t) = k1 m(t) ˙ k2 P (t) V (t) V (t) dynamic equation (w/ friction [Kikuue, IEEE TRO 06] ) 8 > F (P, ✏, t) M g Ff (t) > < M L¨(t) = ✏ K(L0 L(1 ✏(t)))3 , if ✏(t)  L LL0 , > > : F (P, ✏, t) M g F (t), f otherwise, 8 > cv L✏(t) + cc sgn(✏(t)), ˙ ˙ if ✏(t) 6= 0, ˙ > > < c , if ✏(t) = 0 and Fo (t) > cc , ˙ c Ff (t) = > Fo (t), if ✏(t) = 0 and Fo (t) 2 [ cc , cc ], > ˙ > : cc , if ✏(t) = 0 and Fo (t) < cc , ˙ 513年1月30日水曜日
  11. 11. Modeling Dynamics of PAM system PAM volume [Kagawa, CEP 97], [Minh, Mechatronics 10] [Itto, Kogiso, IEEE ICIT&SSST 11] V (t) = D1 ✏(t)2 + D2 ✏(t) + D3 switched system with 64 nonlinear subsystems contraction force [Tondu, IEEE CSM 00], [Kang, ICRA 09] x(t) = f (x(t), u(t)) if x(t) 2 S ˙  n ⇣ ⌘ o2 Cq2 Pg (t) F (P, ✏, t) = APg (t) at a C q1 1 + e ✏(t) as y(t) = h(x(t)) T pressure change in a PAM [Richer, JDSMC 00] x := [✏ ✏ P ]T y := [✏ F ] ˙ ˙ ˙ RT V (t) S := {x 2 <3 | (x)  0} 2 {1, 2, · · · , 64} P (t) = k1 m(t) ˙ k2 P (t) V (t) V (t) net mass flow rate of PDC valve dynamic equation (w/ friction [Kikuue, IEEE TRO 06] ) m(t) = ↵(t)mi (t) (1 ↵(t))mo (t) ˙ ˙ ˙ 8 8 r ⇣ ⌘k 1 > F (P, ✏, t) M g Ff (t) > > > A Pp k > 0 tank R k+1 2 k+1 < > > > > T ⇣ ⌘ kk 1 > M L¨(t) = ✏ K(L0 L(1 ✏(t)))3 , if ✏(t)  L LL0 , > > < if P (t)  2 k+1 Ptank , > > mi (t) = ˙ r : > > > q ⇣ ⌘k 1 ⇣ ⌘ kk 1 F (P, ✏, t) M g F (t), f otherwise, > A0 Pp > > > tank T 2k P (t) R(k 1) Ptank 1 P (t) Ptank > > ⇣ ⌘ kk 1 > 8 : if P (t) > 2 Ptank , > cv L✏(t) + cc sgn(✏(t)), ˙ ˙ if ✏(t) 6= 0, ˙ 8 r k+1 > > > ⇣ ⌘k 1 k+1 < c , if ✏(t) = 0 and Fo (t) > cc , ˙ > A P (t) k > 0p > > 2 R k+1 c > > T ⇣ ⌘ kk 1 Ff (t) = > > > 2 > Fo (t), if ✏(t) = 0 and Fo (t) 2 [ cc , cc ], > ˙ < if P (t) k+1 Pout , > : mo (t) = ˙ > q ⇣ ⌘1 r ⇣ ⌘ kk 1 > > cc , if ✏(t) = 0 and Fo (t) < cc , ˙ > A0 P (t) > > p 2k Pout k R(k 1) P (t) 1 Pout P (t) > > T ⇣ ⌘ kk 1 > > : if P (t) 2 < Pout . k+1 513年1月30日水曜日
  12. 12. Analysis     Dominant parameters switched system with 64 nonlinear subsystems x(t) = f (x(t), u(t)) if x(t) 2 S ˙ y(t) = h(x(t)) x := [✏ ✏ P ]T y := [✏ F ]T ˙ 613年1月30日水曜日
  13. 13. Analysis     Dominant parameters M : mass of weight [kg] D0 : natural diameter of PAM [m] switched system with 64 nonlinear subsystems L0 : natural length of PAM [m] x(t) = f (x(t), u(t)) if x(t) 2 S ˙ D1 D2 D3 : coefficients for PAM volume [m^3] y(t) = h(x(t)) Ptank : source absolute pressure [Pa] x := [✏ ✏ P ]T y := [✏ F ]T ˙ Pout : atmospheric pressure [Pa] k : specific heat ratio for air [-] R : ideal gas constant [J/kg K] T : absolute temperature [K] K : coefficient of elasticity [N/m^3] ✓ : initial angle btw braided thread & cylinder long axis [deg] Cq1 : correction coefficient [-] Cq2 : correction coefficient [1/Pa] cc : Coulomb friction [N] A0 : orifice area of PDC valve [m^2] k1 k2 : polytropic indexes [-] cv : viscous friction coefficient [Ns/m] 613年1月30日水曜日
  14. 14. Analysis     Dominant parameters M : mass of weight [kg] D0 : natural diameter of PAM [m] switched system with 64 nonlinear subsystems L0 : natural length of PAM [m] x(t) = f (x(t), u(t)) if x(t) 2 S ˙ D1 D2 D3 : coefficients for PAM volume [m^3] y(t) = h(x(t)) Ptank : source absolute pressure [Pa] x := [✏ ✏ P ]T y := [✏ F ]T ˙ Pout : atmospheric pressure [Pa] k : specific heat ratio for air [-] R : ideal gas constant [J/kg K] Analysis result: T : absolute temperature [K] For the PAM system model, : coefficient of elasticity [N/m^3] K its steady-state behavior is characterized by : initial angle btw braided thread ✓ & cylinder long axis [deg] parameters: K ✓ Cq1 Cq2 cc : correction coefficient [-] Cq1 and its transient behavior is characterized by Cq2 : correction coefficient [1/Pa] cc : Coulomb friction [N] parameters: A0 k1 k2 cv A0 : orifice area of PDC valve [m^2] k1 k2 : polytropic indexes [-] Hint: as t ! 1 , then params left or not. cv : viscous friction coefficient [Ns/m] 613年1月30日水曜日
  15. 15. Analysis     Dominant parameters M : mass of weight [kg] D0 : natural diameter of PAM [m] switched system with 64 nonlinear subsystems L0 : natural length of PAM [m] x(t) = f (x(t), u(t)) if x(t) 2 S ˙ D1 D2 D3 : coefficients for PAM volume [m^3] y(t) = h(x(t)) Ptank : source absolute pressure [Pa] x := [✏ ✏ P ]T y := [✏ F ]T ˙ Pout : atmospheric pressure [Pa] k : specific heat ratio for air [-] R : ideal gas constant [J/kg K] Analysis result: T : absolute temperature [K] For the PAM system model, : coefficient of elasticity [N/m^3] K its steady-state behavior is characterized by : initial angle btw braided thread ✓ & cylinder long axis [deg] parameters: K ✓ Cq1 Cq2 cc : correction coefficient [-] Cq1 and its transient behavior is characterized by Cq2 : correction coefficient [1/Pa] cc : Coulomb friction [N] parameters: A0 k1 k2 cv A0 : orifice area of PDC valve [m^2] k1 k2 : polytropic indexes [-] Hint: as t ! 1 , then params left or not. cv : viscous friction coefficient [Ns/m] 613年1月30日水曜日
  16. 16. Analysis     Dominant parameters M : mass of weight [kg] D0 : natural diameter of PAM [m] switched system with 64 nonlinear subsystems L0 : natural length of PAM [m] x(t) = f (x(t), u(t)) if x(t) 2 S ˙ D1 D2 D3 : coefficients for PAM volume [m^3] y(t) = h(x(t)) Ptank : source absolute pressure [Pa] x := [✏ ✏ P ]T y := [✏ F ]T ˙ Pout : atmospheric pressure [Pa] k : specific heat ratio for air [-] R : ideal gas constant [J/kg K] Analysis result: T : absolute temperature [K] For the PAM system model, : coefficient of elasticity [N/m^3] K its steady-state behavior is characterized by : initial angle btw braided thread ✓ & cylinder long axis [deg] parameters: K ✓ Cq1 Cq2 cc : correction coefficient [-] Cq1 and its transient behavior is characterized by Cq2 : correction coefficient [1/Pa] cc : Coulomb friction [N] parameters: A0 k1 k2 cv A0 : orifice area of PDC valve [m^2] k1 k2 : polytropic indexes [-] Hint: as t ! 1 , then params left or not. cv : viscous friction coefficient [Ns/m] Note, no couplings btwn the two param groups. 613年1月30日水曜日
  17. 17. Achievement Identification procedure -5 x 10 7 PAM volume: PAM volume 6 measurable or known in advance V (t) = V [m ] 3 5 D1 ✏(t)2 + 4 M D0 L0 D1 Ptank Pout k T R D2 ✏(t) + D3 3 2 contraction ratio 0 0.1 0.2 0.3 ε steady-state behavior transient behavior Determines the parameters value: Determines the parameters value: K ✓ Cq1 Cq2 cc A0 k1 k2 cv until model maker satisfies. until model maker satisfies. 713年1月30日水曜日
  18. 18. Achievement Identification procedure -5 x 10 7 PAM volume: PAM volume 6 measurable or known in advance V (t) = V [m ] 3 5 D1 ✏(t)2 + 4 M D0 L0 D1 Ptank Pout k T R D2 ✏(t) + D3 3 2 contraction ratio 0 0.1 0.2 0.3 ε steady-state behavior transient behavior Determines the parameters value: Determines the parameters value: K ✓ Cq1 Cq2 cc A0 k1 k2 cv until model maker satisfies. until model maker satisfies. When satisfied? Since determination of values is subjective, observe a trend by parameter variation. 713年1月30日水曜日
  19. 19. Info.  for  observing Trend by parameter variation 0.3 0.3 0.3 0.2 0.2 0.2 cq  increases cc increases ε ε ε cq  increases 0.1 0.1 0.1 cc = 0 cq  = 0.8 cq  = - 1/0.01 x10-6 cc = 4.875/P (oo) x105 cq  = 0.99 cq  = - 1/0.083 x10-6 0 cc = 9.75 / P (oo) x105 0 0 cq  = 1.2 cq  = - 1/0.2 x10-6 100 200 300 400 500 600 700 100 200 300 400 500 600 700 100 200 300 400 500 600 700 pressure [kPa] pressure [kPa] pressure [kPa] param in contraction force param in contraction force Coulomb friction coefficient 0.26 0.26 0.26 ε εε 0.24 0.24 0.24 k  increases k  increases c v increases A increases 0.22 0.22 0.22 0 10 20 0 10 20 0 10 20 pressure [kPa] pressure [kPa] 550pressure [kPa] 550 550 -6 k = 1.0, k = 1.0 c v = 10 A = 0.058 x10 -6 k = 1.0, k = 1.4 A increases A = 0.099 x10 500 k = 1.4, k = 1.0 500 c v = 500 500 -6 c v = 1000 A = 0.176 x10 k = 1.4, k = 1.4 450 k  increases k  increases 450 450 0 10 20 0 10 20 0 10 20 time [s] time [s] time [s] polytropic indexes viscous friction coefficient max orifice area 813年1月30日水曜日
  20. 20. Experimental  Validation PAM system setup for model validation proportional directional control valve How to validate: Input a step signal to the PDC valve, and check steady-state and transient responses of simulation and experiment. 913年1月30日水曜日
  21. 21. Experimental  Validation Comparison: steady state behavior in e vs P 0.30 0.30 0.25 M = 4.0 [kg] 0.25 M = 5.0 [kg] 0.20 0.20 0.15 0.15 ε ε 0.10 0.10 0.05 0.05 experiment experiment model fixed at M=4 model fixed at M=5 0 0 model parametried by M model parametried by M 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 P [kPa] P [kPa] experiment 0.30 experiment 0.30 model fixed at M=7 model fixed at M=8 0.25 model parametried by M 0.25 model parametried by M 0.20 0.20 0.15 0.15 ε ε 0.10 0.10 0.05 0.05 0 M = 7.0 [kg] 0 M = 8.0 [kg] 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 P [kPa] P [kPa] 1013年1月30日水曜日
  22. 22. Experimental  Validation Comparison: transient behavior in e vs t & P vs t M = 4.0 [kg] 1113年1月30日水曜日
  23. 23. Extension  to  M-‐‑‒parameterized  Model Interpolation over [1, 9] in weight 1.15 18 1.1 16 1.05 14 1 12 Cq1 [-] 10 cc [N] 0.95 8 0.9 6 0.85 4 0.8 Cq1 (M ) = 0.1573 log M + 0.7974 2 cc (M ) = 1.7353M + 0.1422 0.75 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 M [kg] M [kg] x 10 7 8 40 7 38 0.7915M 0.2296 K(M ) = 109600 exp 36 ✓(M ) = 39.984M 6 34 5 K [N/m] 32 θ [rad] 4 30 3 28 2 26 1 24 0 22 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 M [kg] 12 M [kg]13年1月30日水曜日
  24. 24. Extension  to  M-‐‑‒parameterized  Model Interpolation over [1, 9] in weight 1.15 18 1.1 16 1.05 14 1 12 Cq1 [-] 10 cc [N] 0.95 8 0.9 6 0.85 4 0.8 Cq1 (M ) = 0.1573 log M + 0.7974 2 cc (M ) = 1.7353M + 0.1422 0.75 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 M [kg] M [kg] x 10 7 8 40 7 38 0.7915M 0.2296 K(M ) = 109600 exp 36 ✓(M ) = 39.984M 6 34 5 K [N/m] 32 θ [rad] 4 30 3 28 2 26 1 24 0 22 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 M [kg] 12 M [kg]13年1月30日水曜日
  25. 25. Extension  to  M-‐‑‒parameterized  Model Comparison: steady state behavior in e vs P 0.30 0.30 0.30 0.25 M = 4.0 [kg] 0.25 M = 4.5 [kg] 0.25 M = 5.0 [kg] 0.20 0.20 0.20 0.15 0.15 0.15 εε ε 0.10 0.10 0.10 0.05 0.05 0.05 experiment experiment model fixed at M=4 experiment model fixed at M=5 0 0 model parametried by M 0 model parametried by M model parametried by M 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 P [kPa] P [kPa] P [kPa] experiment 0.30 experiment 0.30 experiment 0.30 model fixed at M=7 model parametried by M model fixed at M=8 0.25 model parametried by M 0.25 0.25 model parametried by M 0.20 0.20 0.20 0.15 0.15 0.15 ε εε 0.10 0.10 0.10 0.05 0.05 0.05 0 M = 7.0 [kg] 0 M = 7.5 [kg] 0 M = 8.0 [kg] 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 P [kPa] P [kPa] P [kPa] 1313年1月30日水曜日
  26. 26. Extension  to  M-‐‑‒parameterized  Model Comparison: transient behavior in e vs t & P vs t M = 4.5 [kg] M = 7.5 [kg] 1413年1月30日水曜日
  27. 27. Conclusion Summary a mathematical model of a PAM system (PAM + PDC valve) with a constant weight, which involves 11 measurable parameters and 9 need-to-be-identified parameters. a parameter identification procedure supported by analysis of the mathematical model, which contributes to reduce the cost for try and errors in finding the 9 parameter values. an identified model validated by comparison with several experimental data, which well simulates behaviors of a practical PAM system. a mathematical model expressing the PAM system over a specified weight range, which is also identifiable by using the proposed procedure plus interpolation. Future works an automatic identification procedure that appropriately determines parameter values based on experimental sample data. an antagonistic layout of PAMs as an actuator to realize position/force controls appropriate for applications of power-assist systems or rehabilitation/training exoskeleton systems. a model reduction technique in case of practical use of many PAMs. 1513年1月30日水曜日
  28. 28. Thank you for your kind attention. 1613年1月30日水曜日

×