This document presents research on bi-articular muscle actuation design for robot arms. It discusses how bi-articular actuators can distribute output force homogeneously and transfer power between joints, as seen in human muscles. It also addresses the actuator redundancy problem that arises with bi-articular systems and proposes solving it with a 1-norm approach to maximize end effector force compared to the traditional 2-norm pseudo-inverse method. An experimental bi-articular robot arm called BiWi is described along with feedforward control testing that validates the 1-norm approach increases output force by 30% over the 2-norm.

1. Bi-Articular Muscle Actuation Design
for Robot Arms
V. Salvucci Y. Kimura S. Oh Y. Hori
Hori-Fujimoto Lab, The University of Tokyo
ICRA 2011 Workshop on Biologically-inspired Actuation, Shanghai

2. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy Problem
Traditional: Pseudo-inverse Matrix (2 norm)
Our Solution: The 1 norm Approach
3 Experimental Setup
BiWi:Bi-Articularly Actuated Wire Driven Robot Arm
Feedforward Control Strategy
4 Experimental Results
5 Conclusions
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 2/24

3. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy Problem
Traditional: Pseudo-inverse Matrix (2 norm)
Our Solution: The 1 norm Approach
3 Experimental Setup
BiWi:Bi-Articularly Actuated Wire Driven Robot Arm
Feedforward Control Strategy
4 Experimental Results
5 Conclusions
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 3/24

4. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
What are Bi-articular Actuators?
Multi-articular actuators produce torque in 2 (or more) consecutive joints
Biceps brachii
Coracobrachialis Brachialis
Simpli

5. ed model of human musculo-skeletal structure
f1 e1: antagonistic pair of mono-articular muscles
f2 e2: antagonistic pair of mono-articular muscles
f3 e3: antagonistic pair of bi-articular muscles
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 4/24

6. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Why Bi-Articular Actuators?
1 Homogeneous Maximum Force at End Eector [Fujikawa 1999]
2 Impedance control without FB [Hogan 1985]
3 Power transfer from proximal to distal joints [Schenau 1989]
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 5/24

7. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Why Bi-Articular Actuators?
2 actuators
of 10 Nm
each
3 actuators
of 6.6 Nm
each
Safety: smaller peak force (in case of controller failure)
Vertical balance: greater ground horizontal force [Salvucci 2011b]
1 Homogeneous Maximum Force at End Eector [Fujikawa 1999]
2 Impedance control without FB [Hogan 1985]
3 Power transfer from proximal to distal joints [Schenau 1989]
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 6/24

8. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Why Bi-Articular Actuators?
2 actuators
of 10 Nm
each
3 actuators
of 6.6 Nm
each
Safety: smaller peak force (in case of controller failure)
Vertical balance: greater ground horizontal force [Salvucci 2011b]
1 Homogeneous Maximum Force at End Eector [Fujikawa 1999]
2 Impedance control without FB [Hogan 1985]
3 Power transfer from proximal to distal joints [Schenau 1989]
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 7/24

9. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy Problem
Traditional: Pseudo-inverse Matrix (2 norm)
Our Solution: The 1 norm Approach
3 Experimental Setup
BiWi:Bi-Articularly Actuated Wire Driven Robot Arm
Feedforward Control Strategy
4 Experimental Results
5 Conclusions
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 8/24

10. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Actuator Redundancy Problem
Model
(
T1 = (f1 e1)r + (f3 e3)r
T2 = (f2 e2)r + (f3 e3)r
Statics
(
T1 = 1 + 3
T2 = 2 + 3
Given desired T1 and T2 ) 1=?, 2=?, 3=?
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 9/24

11. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Pseudo-inverse Matrix (2 norm)
Moore Penrose is the simplest pseudo inverse matrix = 2 norm [Klein 1983]
2 norm optimization criteria
minimize
q
2
1 + 2
2 + 2
3 (1)
subject to
(
T1 = 1 + 3
T2 = 2 + 3
(2)
Closed form solution
8
:
3T1 1
3T2
1 = 2
2 = 1
3T1 + 2
3T2
3T1 + 1
3T2
3 = 1
(3)
T = [2:0; 1:5] ) = [1:66; 0:33; 0:83]
Given F ) T =
JT
F
T ) using (3)
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 10/24

12. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Our Solution: The 1 norm Approach [Salvucci 2010]
1 norm optimization criteria
minimize maxfj1j; j2j; j3jg (4)
subject to
(
T1 = 1 + 3
T2 = 2 + 3
(5)
Closed form solution [Salvucci 2010]
if T1T2 0 )
8
:
1 = T1T2
2
2 = T2T1
2
3 = T1+T2
2
(6)
if T1T2 0
and jT1j jT2j
)
8
:
1 = T1 T2
2
2 = T2
2
3 = T2
2
(7)
if T1T2 0
and jT1j jT2j
)
8
:
1 = T1
2
2 = T2 T1
2
3 = T1
2
(8)
T = [2:0; 1:5] ) = [1:0; 0:5; 1:0]
Given F ) T =
JT
F
T ) using (6), (7), or (8)
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 11/24

13. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy Problem
Traditional: Pseudo-inverse Matrix (2 norm)
Our Solution: The 1 norm Approach
3 Experimental Setup
BiWi:Bi-Articularly Actuated Wire Driven Robot Arm
Feedforward Control Strategy
4 Experimental Results
5 Conclusions
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 12/24

14. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
BiWi: Bi-Articularly Actuated Wire Driven Robot Arm [Salvucci 2011a]
+ Human-like actuation structure
+ Wire Transmission ) low link
inertia (safety, energy eciency)
+ Mono-/bi- articular torque
decoupling (statics)
- Not intrinsically compliant, but
solvable with springs
- Transmission loss in the wires
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 13/24

15. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Feedforward Control Strategy
x ; F
y ]T and T = [T
F = [F
2 ]T : desired output forces and input
1 ;T
torque.
[
1 ,
2 ,
3 ]: desired actuator joint torques
[e
1 , f
1 , e
2 , f
2 , e
3 , f
3 ]: motor reference torques calculated as:
e
i =
Ktli
i if
i 0
0 otherwise
f
i =
Ki
i if
i 0
0 otherwise
(9)
where Ktl2=1.33 (thrust wire transmission lost), Ktl1 = K3 = 0.
Fx and Fy : measured forces at the end eector.
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 14/24

16. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy Problem
Traditional: Pseudo-inverse Matrix (2 norm)
Our Solution: The 1 norm Approach
3 Experimental Setup
BiWi:Bi-Articularly Actuated Wire Driven Robot Arm
Feedforward Control Strategy
4 Experimental Results
5 Conclusions
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 15/24

17. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
In

18. nity Norm VS Pseudo-inverse matrix (2 norm) [Salvucci 2011c]
1 = 60
2 = 120
1 = 25
2 = 50
Measured maximum output force Relative dierence in output force
Fdi =
jF1nj jF2nj
jF2nj
(10)
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 16/24

19. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy Problem
Traditional: Pseudo-inverse Matrix (2 norm)
Our Solution: The 1 norm Approach
3 Experimental Setup
BiWi:Bi-Articularly Actuated Wire Driven Robot Arm
Feedforward Control Strategy
4 Experimental Results
5 Conclusions
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 17/24

20. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Conclusions
Bi-articular muscles key points
1 Homogeneous distribution of output force
2 Power transfer proximal to distal joints
3 FF impedance control
BiWi, Bi-articularly actuated and Wire driven Robot Arm
Human-like actuation structure
Low link-inertia ) Safety, eciency
Perfect decoupling between mono- and bi- articular actuator (statics)
The 1 norm approach for actuator redundancy resolution
Closed form solution based on a piecewise linear function continuous in
all the domain D = fT1;T2g
Maximization of force at the end eector: +30% than 2 norm
Applicable to systems with 3 inputs and 2 outputs
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 18/24

21. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Conclusions
Bi-articular muscles key points
1 Homogeneous distribution of output force
2 Power transfer proximal to distal joints
3 FF impedance control
BiWi, Bi-articularly actuated and Wire driven Robot Arm
Human-like actuation structure
Low link-inertia ) Safety, eciency
Perfect decoupling between mono- and bi- articular actuator (statics)
The 1 norm approach for actuator redundancy resolution
Closed form solution based on a piecewise linear function continuous in
all the domain D = fT1;T2g
Maximization of force at the end eector: +30% than 2 norm
Applicable to systems with 3 inputs and 2 outputs
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 19/24

22. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Conclusions
Bi-articular muscles key points
1 Homogeneous distribution of output force
2 Power transfer proximal to distal joints
3 FF impedance control
BiWi, Bi-articularly actuated and Wire driven Robot Arm
Human-like actuation structure
Low link-inertia ) Safety, eciency
Perfect decoupling between mono- and bi- articular actuator (statics)
The 1 norm approach for actuator redundancy resolution
Closed form solution based on a piecewise linear function continuous in
all the domain D = fT1;T2g
Maximization of force at the end eector: +30% than 2 norm
Applicable to systems with 3 inputs and 2 outputs
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 20/24

23. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Thank you for your kind attention
V. Salvucci Y. Kimura S. Oh Y. Hori
www.hori.k.u-tokyo.ac.jp www.valeriosalvucci.com
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 21/24

24. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
2 norm Vs 1 norm in 2D
Equation with in

25. nite solutions
k = x +

26. y
k, and

27. are constant
x and y represent the motor torques ) bounded
2 norm
minimize
p
x2 + y2
1 norm
minimize max fjxj; jyjg
Comparison
Solutions comparison
maxfy1; x1g maxfy2; x2g
Smaller solution space for 2 norm
no solution for 2 norm!!
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 22/24

28. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
The Best Norm
Output Force for 2 2 f30; 60; 90; 120; 150g j1j + j2j + j3j for 2 = 90
norm 1 norm 2 norm 1
min (j1j + j2j + j3j) min (
p
2
1 + 2
2 + 2
3 ) min maxfj1j; j2j; j3jg
j1j + j2j + j3j of 1 norm j1j + j2j + j3j of 2 norm
j1j + j2j + j3j of 2 norm j1j + j2j + j3j of 1 norm
The best norm: switching between 1 norm, 2 norm and 1 norm
. . . but the system could not be stable due to discontinuity in torque
patterns
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 23/24

29. Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
References
T. Fujikawa, T. Oshima, M. Kumamoto, and N. Yokoi. Output force at the endpoint
in human upper extremities and coordinating activities of each antagonistic pairs of
muscles. Transactions of the Japan Society of Mechanical Engineers. C, 65(632):
1557{1564, 1999.
N. Hogan. The mechanics of multi-joint posture and movement control. Biological
Cybernetics, 52(5):315{331, 1985.
V. Salvucci, S. Oh, and Y. Hori. In

30. nity norm approach for precise force control of
manipulators driven by bi-articular actuators. In IECON 2010 - 36th Annual
Conference on IEEE Industrial Electronics Society, pages 1908{1913, 2010.
V. Salvucci, Y. Kimura, S. Oh, and Y. Hori. BiWi: Bi-Articularly actuated and wire
driven robot arm. In IEEE International Conference on Mechatronics (ICM), 2011a.
V. Salvucci, Y. Kimura, S. Oh, and Y. Hori. Disturbance rejection improvement in
Non-Redundant robot arms by bi-articular actuators. In Industrial Electronics
(ISIE), IEEE International Symposium on, 2011b.
V. Salvucci, Y. Kimura, S. Oh, and Y. Hori. Experimental veri

31. cation of in

32. nity norm
approach for force maximization of manipulators driven by bi-articular actuators. In
American Control Conference (ACC), 2011c.
G. J. V. I. Schenau. From rotation to translation: Constraints on multi-joint
movements and the unique action of bi-articular muscles. Human Movement
Science, 8(4):301{337, Aug. 1989.
V. Salvucci, Y. Kimura, S. Oh, Y. Hori Hori-Fujimoto Lab, The University of Tokyo
Bi-Articular Muscle Actuation Design for Robot Arms 24/24