actuation and control design for safe wearable robotic arms
DESCRIPTION
Actuation and Control Design for Safe Wearable Robotic ArmsTRANSCRIPT
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Actuation and Control Design
for Safe Wearable Robotic Arms
V. Salvucci Y. Kimura S. Oh T. Koseki Y. Hori
The University of Tokyo
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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
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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
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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
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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
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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
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Why Bi-Articular Actuators?
1 Homogeneous Maximum Force at End Effector [Fujikawa 1999]
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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
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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=?
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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)
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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)
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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
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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.
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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)
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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
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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
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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
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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|}
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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.