The document discusses actuation and control design for safe wearable robotic arms. It proposes using redundant biarticular actuators and an infinity norm approach to actuator redundancy resolution. This allows the controllable force at the end effector to match the maximum human force, improving safety. Experimental validation with a bi-articularly actuated and wire-driven robot arm shows the infinity norm approach increases the controllable output force compared to the conventional pseudo-inverse matrix 2-norm approach.

1. Actuation and Control Design
for Safe Wearable Robotic Arms
V. Salvucci Y. Kimura S. Oh T. Koseki Y. Hori
The University of Tokyo

2. Outline
1 Maximum Output Force in Wearable Robotic Arms: Safety Problem
2 Wearable Robotic Arms with Redundant Biarticular Actuators
Actuator Redundancy Problem
Conventional Solution: Pseudo-inverse Matrix (2 − norm)
Proposed Solution: The 1− norm Approach
Experimental Validation
3 Conclusions

3. Outline
1 Maximum Output Force in Wearable Robotic Arms: Safety Problem
2 Wearable Robotic Arms with Redundant Biarticular Actuators
Actuator Redundancy Problem
Conventional Solution: Pseudo-inverse Matrix (2 − norm)
Proposed Solution: The 1− norm Approach
Experimental Validation
3 Conclusions

4. Maximum Output Force in Wearable Robotic Arms: Safety Problem
robot max force
human max force
MGA Exoskeleton [Carignan 2009] (qualitative representation of max forces)
Robotic Arms: one motor in the shoulder and one in the elbow produce a
maximum force with quadrilateral shape
Human Arms: due to the presence of redundant biarticular muscles
produce a maximum force with hexagonal shape
The difference in shape is not safe in case of controller failure
) Biarticular actuation is a solution

5. Outline
1 Maximum Output Force in Wearable Robotic Arms: Safety Problem
2 Wearable Robotic Arms with Redundant Biarticular Actuators
Actuator Redundancy Problem
Conventional Solution: Pseudo-inverse Matrix (2 − norm)
Proposed Solution: The 1− norm Approach
Experimental Validation
3 Conclusions

6. What are Bi-articular Actuators?
Multi-articular actuators produce torque in 2 (or more) consecutive joints
Biceps brachii
Coracobrachialis Brachialis
Simplified 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

7. Why Bi-Articular Actuators?
1 Homogeneous Maximum Force at End Effector [Fujikawa 1999]

8. Wearable Robotic Arms with Redundant Biarticular Actuators
hu human max force
robot max force
controllable max force (2-n)
Saitama University (qualitative representation of max forces)
Maximum human force and maximum robot force match
However, using the conventional redundancy resolution controller
(2-norm), the controllable force is smaller than the realizable force
) Our solution is an Infinity Norm based Resolution Controller

9. 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=?

10. Conventional Approach: 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


1 = 2
3T1 − 1
3T2
2 = −1
3T1 + 2
3T2
3 = 1
3T1 + 1
3T2
(3)
T = [2.0, 1.5] ) = [0.83, 0.33, 1.17]
Given F ) T =
JT
F
T ) using (3)

11. Proposed Solution: The 1− norm Approach [Salvucci 2010]
1− norm optimization criteria
minimize max{|1|, |2|, |3|} (4)
subject to
(
T1 = 1 + 3
T2 = 2 + 3
(5)
Closed form solution [Salvucci 2010]
if T1T2 0 )
8:
1 = T1−T2
2
2 = T2−T1
2
3 = T1+T2
2
(6)
if T1T2 0
and |T1| |T2|
)
8:
1 = T1 − T2
2
2 = T2
2
3 = T2
2
(7)
if T1T2 0
and |T1| |T2|
)
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)

12. BiWi: Bi-Articularly Actuated Wire Driven Robot Arm [Salvucci 2011a]
+ Human-like actuation structure
+ Wire Transmission ) low link
inertia (safety, energy efficiency)
+ Mono-/bi- articular torque
decoupling (statics)
- Not intrinsically compliant, but
solvable with springs
- Transmission loss in the wires

13. Feedforward Control Strategy
F∗ = [F∗
y ]T and T∗ = [T∗
x , F∗
1 ,T∗
2 ]T : desired output forces and input
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 =
i if ∗
i 0
0 otherwise
Ktli ∗
f ∗
i =
i if ∗
Ki ∗
i 0
0 otherwise
(9)
where Ktl2=1.33 (thrust wire transmission lost), Ktl1 = K3 = 0.
Fx and Fy : measured forces at the end effector.

14. Infinity Norm VS 2-norm [Salvucci 2011b]
1 = −60◦
2 = 120◦
1 = −25◦
2 = 50◦
Measured maximum output force Relative difference in output force
Fdiff =
|F∞−n| − |F2−n|
|F2−n|
(10)

15. Outline
1 Maximum Output Force in Wearable Robotic Arms: Safety Problem
2 Wearable Robotic Arms with Redundant Biarticular Actuators
Actuator Redundancy Problem
Conventional Solution: Pseudo-inverse Matrix (2 − norm)
Proposed Solution: The 1− norm Approach
Experimental Validation
3 Conclusions

16. Conclusions
robot max force
human max force
hu human max force
robot max force
controllable max force (2-n)
controllable max force (i-n)
Biarticular Actuation + Infinity Norm Resolution Controller
+
Increased safety in wearable robotic arms

17. Thank you for your kind attention
V. Salvucci Y. Kimura S. Oh T. Koseki Y. Hori
www.hori.k.u-tokyo.ac.jp www.koseki.t.u-tokyo.ac.jp
www.valeriosalvucci.com

18. 2 − norm Vs 1− norm in 2D
Equation with infinite solutions
k = x +

19. y
k, and

20. are constant
x and y represent the motor torques ) bounded
2 − norm
minimize
p
x2 + y2
1− norm
minimize max {|x|, |y|}
Solutions Comparison
max{|y∞|, |x∞|} max{|y2|, |x2|}

21. References
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interface for virtual task training. In Intelligent Robots and Systems, 2009. IROS
2009. IEEE/RSJ International Conference on, pages 3697–3702, 2009.
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.
V. Salvucci, S. Oh, and Y. Hori. Infinity 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. Experimental verification of infinity norm
approach for force maximization of manipulators driven by bi-articular actuators. In
American Control Conference (ACC), 2011b.