Bi-articular Muscle Actuation Design for Robot Arms
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Transcript of Bi-articular Muscle Actuation Design for Robot Arms
Bi-Articular Muscle Actuation Designfor 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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy ProblemTraditional: Pseudo-inverse Matrix (2− norm)Our Solution: The ∞− norm Approach
3 Experimental SetupBiWi:Bi-Articularly Actuated & Wire Driven Robot ArmFeedforward 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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy ProblemTraditional: Pseudo-inverse Matrix (2− norm)Our Solution: The ∞− norm Approach
3 Experimental SetupBiWi:Bi-Articularly Actuated & Wire Driven Robot ArmFeedforward 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
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
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
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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Why Bi-Articular Actuators?
1 Homogeneous Maximum Force at End Effector [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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Why Bi-Articular Actuators?
2 actuatorsof 10 Nmeach
3 actuatorsof 6.6 Nmeach
Safety: smaller peak force (in case of controller failure)Vertical balance: greater ground horizontal force [Salvucci 2011b]
1 Homogeneous Maximum Force at End Effector [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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Why Bi-Articular Actuators?
2 actuatorsof 10 Nmeach
3 actuatorsof 6.6 Nmeach
Safety: smaller peak force (in case of controller failure)Vertical balance: greater ground horizontal force [Salvucci 2011b]
1 Homogeneous Maximum Force at End Effector [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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy ProblemTraditional: Pseudo-inverse Matrix (2− norm)Our Solution: The ∞− norm Approach
3 Experimental SetupBiWi:Bi-Articularly Actuated & Wire Driven Robot ArmFeedforward 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
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 = τ1 + τ3
T2 = τ2 + τ3
Given desired T1 and T2 ⇒ τ1=?, τ2=?, τ3=?
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
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√τ 2
1 + τ 22 + τ 2
3 (1)
subject to
{T1 = τ1 + τ3
T2 = τ2 + τ3
(2)
Closed form solutionτ1 = 2
3T1 − 1
3T2
τ2 = − 13T1 + 2
3T2
τ3 = 13T1 + 1
3T2
(3)
T = [2.0, 1.5]⇒ τ = [1.66, 0.33, 0.83]
Given F ⇒ T =(JT)
FT ⇒ τ 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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Our 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−T22
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)
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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy ProblemTraditional: Pseudo-inverse Matrix (2− norm)Our Solution: The ∞− norm Approach
3 Experimental SetupBiWi:Bi-Articularly Actuated & Wire Driven Robot ArmFeedforward 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
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 linkinertia (safety, energy efficiency)
+ Mono-/bi- articular torquedecoupling (statics)
- Not intrinsically compliant, butsolvable 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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
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 < 0
0 otherwisef ∗i =
{Kiτ∗i if τ∗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.
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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy ProblemTraditional: Pseudo-inverse Matrix (2− norm)Our Solution: The ∞− norm Approach
3 Experimental SetupBiWi:Bi-Articularly Actuated & Wire Driven Robot ArmFeedforward 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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Infinity Norm VS Pseudo-inverse matrix (2− norm) [Salvucci 2011c]
θ1 = −60◦
θ2 = 120◦
θ1 = −25◦
θ2 = 50◦
Measured maximum output force Relative difference in output force
F diff =|F∞−n| − |F 2−n|
|F 2−n| (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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
Outline
1 Bi-articularly Actuated Robot Arms
2 Actuator Redundancy ProblemTraditional: Pseudo-inverse Matrix (2− norm)Our Solution: The ∞− norm Approach
3 Experimental SetupBiWi:Bi-Articularly Actuated & Wire Driven Robot ArmFeedforward 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
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, efficiency
Perfect decoupling between mono- and bi- articular actuator (statics)
The ∞− norm approach for actuator redundancy resolution
Closed form solution based on a piecewise linear function continuous inall the domain D = {T1,T2}Maximization of force at the end effector: +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
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, efficiency
Perfect decoupling between mono- and bi- articular actuator (statics)
The ∞− norm approach for actuator redundancy resolution
Closed form solution based on a piecewise linear function continuous inall the domain D = {T1,T2}Maximization of force at the end effector: +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
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, efficiency
Perfect decoupling between mono- and bi- articular actuator (statics)
The ∞− norm approach for actuator redundancy resolution
Closed form solution based on a piecewise linear function continuous inall the domain D = {T1,T2}Maximization of force at the end effector: +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
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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
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 |}
Comparison
Solutions comparison
max{y∞, x∞} ≤ max{y2, x2}
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
Bi-articularly Actuated Robot Arms Actuator Redundancy Problem Experimental Setup Experimental Results Conclusions References
The Best Norm
Output Force for θ2 ∈ {30, 60, 90, 120, 150◦} |τ1|+ |τ2|+ |τ3| for θ2 = 90
norm 1 norm 2 norm ∞min (|τ1|+ |τ2|+ |τ3|) min (
√τ 2
1 + τ 22 + τ 2
3 ) min max{|τ1|, |τ2|, |τ3|}
|τ1|+ |τ2|+ |τ3| of ∞− norm > |τ1|+ |τ2|+ |τ3| of 2− norm|τ1|+ |τ2|+ |τ3| of 2− norm > |τ1|+ |τ2|+ |τ3| of 1− normThe best norm: switching between 1− norm, 2− norm and ∞− norm. . . but the system could not be stable due to discontinuity in torquepatterns
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
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 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.
N. Hogan. The mechanics of multi-joint posture and movement control. BiologicalCybernetics, 52(5):315–331, 1985.
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. Disturbance rejection improvement inNon-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 verification of infinity normapproach for force maximization of manipulators driven by bi-articular actuators. InAmerican Control Conference (ACC), 2011c.
G. J. V. I. Schenau. From rotation to translation: Constraints on multi-jointmovements and the unique action of bi-articular muscles. Human MovementScience, 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