Actuation and Control Design

for Safe Wearable Robotic Arms

V. Salvucci Y. Kimura S. Oh T. Koseki Y. Hori

The University of Tokyo

Outline

1 Maximum Output Force in Wearable Robotic Arms: Safety Problem

2 Wearable Robotic Arms with Redundant Biarticular ActuatorsActuator Redundancy ProblemConventional Solution: Pseudo-inverse Matrix (2− norm)Proposed Solution: The ∞− norm ApproachExperimental Validation

3 Conclusions

Outline

1 Maximum Output Force in Wearable Robotic Arms: Safety Problem

2 Wearable Robotic Arms with Redundant Biarticular ActuatorsActuator Redundancy ProblemConventional Solution: Pseudo-inverse Matrix (2− norm)Proposed Solution: The ∞− norm ApproachExperimental Validation

3 Conclusions

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 amaximum force with quadrilateral shape

Human Arms: due to the presence of redundant biarticular musclesproduce a maximum force with hexagonal shape

The difference in shape is not safe in case of controller failure⇒ Biarticular actuation is a solution

Outline

1 Maximum Output Force in Wearable Robotic Arms: Safety Problem

2 Wearable Robotic Arms with Redundant Biarticular ActuatorsActuator Redundancy ProblemConventional Solution: Pseudo-inverse Matrix (2− norm)Proposed Solution: The ∞− norm ApproachExperimental Validation

3 Conclusions

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

Why Bi-Articular Actuators?

1 Homogeneous Maximum Force at End Effector [Fujikawa 1999]

Wearable Robotic Arms with Redundant Biarticular Actuators

huhuman max forcerobot max forcecontrollable 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

Actuator Redundancy Problem

Model

{

T1 = (f1 − e1)r + (f3 − e3)r

T2 = (f2 − e2)r + (f3 − e3)r

Statics

{

T1 = τ1 + τ3

T2 = τ2 + τ3

Given desired T1 and T2 ⇒ τ1=?, τ2=?, τ3=?

Conventional Approach: Pseudo-inverse Matrix (2− norm)

Moore Penrose is the simplest pseudo inverse matrix = 2− norm [Klein 1983]

2− norm optimization criteria

minimize√

τ 21 + τ 2

2 + τ 23 (1)

subject to

{

T1 = τ1 + τ3

T2 = τ2 + τ3(2)

Closed form solution

τ1 =23T1 −

13T2

τ2 = − 13T1 +

23T2

τ3 =13T1 +

13T2

(3)

T = [2.0, 1.5] ⇒ τ = [0.83, 0.33, 1.17]

Given F ⇒ T =(

JT)

F

T ⇒ τ using (3)

Proposed Solution: The ∞− norm Approach [Salvucci 2010]

∞− norm optimization criteria

minimize max{|τ1|, |τ2|, |τ3|} (4)

subject to

{

T1 = τ1 + τ3

T2 = τ2 + τ3(5)

Closed form solution [Salvucci 2010]

if T1T2 ≤ 0 ⇒

τ1 =T1−T2

2

τ2 =T2−T1

2

τ3 =T1+T2

2

(6)

if T1T2 > 0

and |T1| ≤ |T2|⇒

τ1 = T1 −T22

τ2 =T22

τ3 =T22

(7)

if T1T2 > 0

and |T1| > |T2|⇒

τ1 =T12

τ2 = T2 −T12

τ3 =T12

(8)

T = [2.0, 1.5] ⇒ τ = [1.0, 0.5, 1.0]

Given F ⇒ T =(

JT)

F

T ⇒ τ using (6), (7), or (8)

BiWi: Bi-Articularly Actuated & Wire Driven Robot Arm [Salvucci 2011a]

+ Human-like actuation structure

+ Wire Transmission ⇒ low linkinertia (safety, energy efficiency)

+ Mono-/bi- articular torquedecoupling (statics)

- Not intrinsically compliant, butsolvable with springs

- Transmission loss in the wires

Feedforward Control Strategy

F∗ = [F ∗

x ,F∗

y ]T and T∗ = [T ∗

1 ,T∗

2 ]T : desired output forces and input

torque.

[τ∗

1 ,τ∗

2 , τ∗

3 ]: desired actuator joint torques

[e∗1 , f∗

1 , e∗

2 , f∗

2 , e∗

3 , f∗

3 ]: motor reference torques calculated as:

e∗

i =

{

Ktliτ∗

i if τ∗

i < 00 otherwise

f∗

i =

{

Kiτ∗

i if τ∗

i > 00 otherwise

(9)

where Ktl2=1.33 (thrust wire transmission lost), Ktl1 = K3 = 0.

Fx and Fy : measured forces at the end effector.

Infinity Norm VS 2-norm [Salvucci 2011b]

θ1 = −60◦

θ2 = 120◦

θ1 = −25◦

θ2 = 50◦

Measured maximum output force Relative difference in output force

Fdiff =

|F∞−n| − |F 2−n|

|F 2−n|(10)

Outline

1 Maximum Output Force in Wearable Robotic Arms: Safety Problem

2 Wearable Robotic Arms with Redundant Biarticular ActuatorsActuator Redundancy ProblemConventional Solution: Pseudo-inverse Matrix (2− norm)Proposed Solution: The ∞− norm ApproachExperimental Validation

3 Conclusions

Conclusions

robot max force

human max force

huhuman max forcerobot max forcecontrollable max force (2-n)controllable max force (i-n)

Biarticular Actuation + Infinity Norm Resolution Controller

⇓

Increased safety in wearable robotic arms

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

2− norm Vs ∞− norm in 2D

Equation with infinite solutions

k = αx + βy

k, α and β are constant

x and y represent the motor torques ⇒ bounded

2− norm

minimize√

x2 + y 2

∞− norm

minimize max {|x |, |y |}

Solutions Comparison

max{|y∞|, |x∞|} ≤ max{|y2|, |x2|}

References

C. Carignan, J. Tang, and S. Roderick. Development of an exoskeleton hapticinterface for virtual task training. In Intelligent Robots and Systems, 2009. IROS2009. IEEE/RSJ International Conference on, pages 3697–3702, 2009.

T. Fujikawa, T. Oshima, M. Kumamoto, and N. Yokoi. Output force at the endpointin human upper extremities and coordinating activities of each antagonistic pairs ofmuscles. 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 ofmanipulators driven by bi-articular actuators. In IECON 2010 - 36th AnnualConference on IEEE Industrial Electronics Society, pages 1908–1913, 2010.

V. Salvucci, Y. Kimura, S. Oh, and Y. Hori. BiWi: Bi-Articularly actuated and wiredriven robot arm. In IEEE International Conference on Mechatronics (ICM), 2011a.

V. Salvucci, Y. Kimura, S. Oh, and Y. Hori. Experimental verification of infinity normapproach for force maximization of manipulators driven by bi-articular actuators. InAmerican Control Conference (ACC), 2011b.