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A biped with its wearable assist device: Numericalstudy of the efficiency for an optimal walking gait
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian 1
France Nantes, IRCCyN, University of Nantes
June 30, 2014
1This work is supported by Région des Pays de la Loire, Project LMA andGérontopôle Autonomie Longévité des Pays de la Loire.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Motivation
To design a wearable assist device for human.
To improve daily life for patients or elderlyTo avoid the musculoskeletal disorders for industrial workers
Desired performances:
To be able to compensate a part of the loads due the human’sweight.
To have an assist device with a energetic autonomy.
Good adaptation to the shape of human’s body.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Several realisations 1/2
prototype honda
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Several realisations 2/2
ARGO Medical Technologies
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Statement of the problem
Preliminary studies about a simple mechanical:
To consider a seven-link planar Biped with a wearable assist device.
To define a cyclic walking gait with for the biped without any assistdevice.
To compare the energy consumption of the biped with its wearableassist device for four cases.
The assist device is fully actuated.The hips of the assist device are actuated only.The knees of the assist device are actuated only.The ankles of the assist device are actuated only.
A each sampling time of the trajectory an optimal distribution of thetorques for the assisted biped are found.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
The geometrical structure of the blped and its wearable
assist device.
(a) (b)
Γ1
Γ2
Γ3Γ4
Γ5
Γ6
Γ7
Γ8
Γ9
Γ10Γ11
Γ12
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Generalized coordinates and torques
Both geometrical closed structures can be cut in any point.
The generalized coordinates is introduced, assuming a treegeometrical structure.
15 generalized coordinatesx = [q1, q2, q3, q4, q5, q6, q7, q8, q91, q92, q101, q102, q11, x , y ]
⊤.
q8, q91, q92, q101, q102, and q11 are devoted to the wearable assistdevice.
Torque vector, Γ number of components between six (no assistance)and 12 (fully assisted).
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Physical parameters.
Mass (kg) Length (m) Inertia (kg .m2) center of mass (m)
Foot mf = 0.678 Lp = 0.207 I f = 0.012 spx = 0.0135and lp = 0.072 spy = 0.0321shoe Hp = 0.064Shin ms = 4.6 ls = 0.497 I s = 0.0521 ss = 0.324Thigh mt = 8.6 lt = 0.41 I t = 0.7414 st = 0.18Trunk mT = 16.5 lT = 0.625 IT = 11.3 sT = 0.386
Seat m3 = 2.0 l3 = 0.1 IT = 0.3 s3 = 0.05Upper m1 = 3.0 l1 = 0.392 I 1 = 0.04 s1 = 0.1127frameLower m2 = 2.0 l2 = 0.3645 I 2 = 0.02 s2 = 0.169link
Table : Physical parameters of the seven-link biped and of its walking assistdevice.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Matrix equations
Equations of the motion of the biped in single support
A(x)x + h(x, x) =[
D J⊤1 J⊤2
]
[
Γfc
]
+ J⊤
r1
[
r1
m1z
]
+ J⊤
r2
[
r2
m2z
]
, (1)
with the constraint equations,
Jrix + Jri
x = 0 for i = 1 to 2[
J1
J2
]
x +
[
J1
J2
]
x = 0.(2)
[
ri miz
]⊤, with i = 1 to 2, : resultant wrenches of the contact efforts
λi = fci=[fxi
, fyi,mzi
]⊤ : the wrench, for each loop closure.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
The walking reference gait 1/3
An optimal cyclic walking gait
Each step: a single support phase and an impact.
The swing foot impacts the ground the other foot takes off theground
Biped’s joints are prescribed with third order polynomial functions
Definition of the coefficients of these polynomial functions takes intoaccount:
The cyclic propertiesThe impact equations
Parametric optimization algorithm is used to determine the neededcoefficients −→ optimization variables with constraints.
Non linear constraints (limits on ZMP, ground reaction, Torques).
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Optimal distribution of the torques for the biped with the
wearable assist device 1/4
The biped equipped with its wearable assist device tracks the referencetrajectory defined previously.
Three cases
The biped is fully assisted There are 12 torques.
The biped is partially assisted: There are 6 torques + 2 provided bythe assit device in the hips.
The biped is partially assisted: There are 6 torques + 2 provided bythe assit device in the knees.
The biped is partially assisted: There are 6 torques + 2 provided bythe assit device in the ankles.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Optimal distribution of the torques for the biped with the
wearable assist device 2/4
The optimization statement at each sampling period
A sampling period ∆ is defined such as: ∆ =T
N.
At each sampling period a new optimal process is stated to get anoptimal distribution of the torques.
Let matrix J⊥(12× 15) be such that [r1 m1z]⊤ belongs to the kernel
of the linear map represented with J⊥(12 × 15) J⊤r1
, (in singlesupport on leg 1: r2 = 0, m2z
= 0)
The dynamic equation of the biped and assist device is multipliedwith J⊥(12 × 15), we get
J⊥A(x)x + J
⊥h(x, x) = J
⊥[
D J⊤1 J⊤2
]
[
Γfc
]
. (3)
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Optimal distribution of the torques for the biped with the
wearable assist device 3/4
Definition of the optimization variables
The left handle side J⊥A(x)x + J⊥h(x, x) is well-known because itdepends on the walking reference gait and the physical parametersof the mechanical systems only.
The rank of this J⊥[
D J⊤1 J⊤2
]
is equal to 12.
Biped fully assisted in stance phase: There are 12 equations for 18unknown variables −→ 6 optimization variables.
Biped partially assisted: There are 12 equations for 14 −→ 2optimization variables.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Optimal distribution of the torques for the biped with the
wearable assist device 2/3
The optimization statement
A sampling period ∆ is defined such as: ∆ =T
N.
At each sampling period a new optimal process is stated to get anoptimal distribution of the torques.
The criteria for k = 1, · · · ,N are:
C1k = m⊤
k mk .
with mk the vector torques of the bipedand
C2k = Γ⊤
k Γk .
with Γk the vector torques of the biped and its assist device.
Constraints: to limit the efforts of each loop closure for biped andits assist advice, vertical component of the ground reaction positiveand no rotation of the stance foot.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Reference walking gait
Numerical data
N = 50. Walking trajectory defined in 50 points.
Time of a step: 0.55 s.
Length of one step: 0.3575 m.
The velocity of the biped −→ : 0.65 m/s or 2.34 km/h
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Three distributions for the impulsive torques 1/3
Fully
assisted
Hipsassisted
Kne
esassisted
Ank
lesassisted
200
400
600
Cost
Funct
ional
Part for Biped
Part for Assist device
Biped with Assist device
Biped without Assist device
Figure : The torques of the biped are minimized (Cost C1k): Histogram as afunction of different distributions for the torques.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Three distributions for the impulsive torques 1/3
Fully
assisted
Hipsassisted
Kne
esassisted
Ank
lesassisted
100
200
Cost
Funct
ional
Part for Biped
Part for Assist device
Biped with Assist device
Biped without Assist device
Figure : The torques of the biped and walking assist device are minimized (costC2k): Histogram as a function of different distributions for the torques.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Criteria as functions of the velocity 0.4 m/s and 0.9 m/s
(1.44 km/h and 3.24 km/h). (1/2)
(a)
0.4 0.5 0.6 0.7 0.8 0.90
100
200
300
400
500
600
700
800
900
(b)
0.4 0.5 0.6 0.7 0.8 0.90
100
200
300
400
500
600
700
(a) Fully assisted biped with C1k , and (b) Fully assisted biped with C2k .
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Criteria as functions of the velocity 0.4 m/s and 0.9 m/s
(1.44 km/h and 3.24 km/h). (2/2)
(c)
0.4 0.5 0.6 0.7 0.8 0.90
50
100
150
200
250
300
350
400
(d)
0.4 0.5 0.6 0.7 0.8 0.90
50
100
150
200
250
300
350
400
450
500
(c) Biped with assistance in the hips with C1k and (d) Biped withassistance in the hips with C2k .
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Conclusion and perspectives 1/2
Conclusion
Preliminary study with a simple bipedal robot and a simplegeometrical structure for the wearable assit device.
Full actuation of actuation at hip only are two interesting proposals.
actuation at the knee or ankle only are ineffective.
A study for several velocities confirm these properties.
In joints, which are not assisted, we can observe the torques of thebiped can increase little.
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
Conclusion and perspectives 2/2
Perspectives
Added research on the design of the assist device and the trajectoriesare necessary to get null torques with full actuation (paralyzedhuman subjects).
To use a walking gait with double support phases, single supportphases and impact as reference gait.
To insert flexible elements between human and its wearable assitdevice.
To deal with a 3D biped.
Climbing stairs
Yannick Aoustin, Christine Chevallereau and Vigen Arakalian A biped with its wearable assist device: Numerical study of the efficiency
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