[PPT] - Strategy to lock the knee of exoskeleton stance leg: study in the PowerPoint Presentation

SLIDE 1

Strategy to lock the knee of exoskeleton stance leg: study in the framework of ballistic walking model

Yannick Aoustin, Alexander Formalskii 1

Mesrob 2015, Nantes

July 10, 2015

1Supported Ministry of Education and Science of Russian Federation, Project No.

7.524.11.4012, and by Région des Pays de la Loire, Project LMA and Gérontopôle Autonomie Longévité des Pays de la Loire.

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 2

Motivation

To design a wearable assist device for human.

To improve daily life for patients or elderly To avoid the musculoskeletal disorders for industrial workers

Desired performances: To be able to compensate a part of the loads due the human’s weight. To have an assist device with an energetic autonomy. Good adaptation to the shape of human’s body.

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 3

Statement of the problem

To consider a five-link planar Biped with a strapped exoskeleton. There are not any actuators in our exoskeleton. To define a ballistic walking gait of the biped alone without any assist device for the transport of a load. During ballistic walking of the biped with exoskeleton the knee of the stance leg of the exoskeleton (and as a consequence of the biped) is locked. Walking of the biped consists of alternating single- and instantaneous double-support phases. At the instant of this phase, the knee of the previous swing leg is locked and the knee of the previous stance leg is unlocked. To compare the energy consumption of the biped alone and with its exoskeleton.

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 4

The geometrical structure of the biped and its wearable assist device.

(a)

sT st ss sp

(b)

Γ1 Γ2 Γ3 Γ4 q1 q3 q3 q4 q5

seven generalized coordinates x = [q1, q2, q3, q4, q5, x, y]⊤.

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 5

Physical parameters.

Mass (kg) Length (m) Inertia moment center of (kg.m2) mass (m) Human shin

ms = 4.6 ls = 0.55 I s = 0.0521 ss = 0.324

Human thigh

mt = 8.6 lt = 0.45 I t = 0.75 st = 0.18

Human trunk

mT = 48.6 lT = 0.75 I T = 11.3 sT = 0.386

Exoskeleton shin

m1 = 1.0 l1 = 0.497 I 1 = 0.0260 ss = 0.324

Exoskeleton thigh

m2 = 2.0 l2 = 0.41 I 2 = 0.0354 st = 0.18

Exoskeleton trunk

m3 = 8.0 l3 = 0.75 I 3 = 0.3817 sT = 0.386

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 6

Matrix equations

Equations of the motion of the biped in single support A(x)¨ x + h(x, ˙ x) = DΓ + J⊤

r1r1 + J⊤ r2r2,

(1) with the constraint equations, Jri ¨ x + ˙ Jri ˙ x = 0 for i = 1 or/and 2. (2) The joint variables θi for i = (1, 2, 3, 4) as functions of the generalized coordinates are: θ1 = q2 − q1, θ2 = q5 − q2, θ3 = q5 − q3, θ4 = q3 − q4. (3)

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 7

Definition of the ballistic motion

Statement of the problem Let x(0) be an initial configuration t = 0. Let x(T) be an final configuration t = T.

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 8

Definition of the ballistic motion

ballistic motion be in single support: Γ = 0. A(x)¨ x + h(x, ˙ x) =

D1

D2 D3 D4 Γ1 03×1

+ J⊤

r1r1,

with the constraint equation for the stance leg tip fixed on the ground: Jr1¨ x + ˙ Jr1 ˙ x = 0, and with the constraint equation for the knee of the stance leg locked in the swing phase: D⊤

1 ¨

x = 0. problem: Which velocity vector ˙ x(0) such that x(t) starting from x(0) reaches x(T) ⇒ A boundary value problem solved using a Newton method

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 9

Impulsive control

decomposition of the impulsive impact. After impact the velocity of the biped has to be equal to the founded initial velocity. ⇒ impulsive impact. Let ˙ xb be the final velocity vector of the current ballistic swing, Let ˙ xa be the initial velocity vector of the next ballistic swing.

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 10

The structure of the instantaneous double support

First sub-phase: Impulsive phase. A[x(T)](˙ x− − ˙ xb) =

D1

D2 D3 D4 I −

1

I−

3×1

+ J⊤

r1I− r1.

(4) Jr1 ˙ x− = 02×1 (5) The velocity of the inter-link angle of the stance (hind) leg after first sub-phase remains zero, therefore D⊤

1 ˙

x− = 0. (6) I−

3×1 applied by human.

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 11

The structure of the instantaneous double support

Second sub-phase: Passive impact. Knee of the leg 1 is unlocked, knee of the leg 2 is locked with I4. The second sub-phase: passive impact. The stance leg lifts off the ground (Hypothesis). A (˙ x+ − ˙ x−) =

D1

D2 D3 D4 03×1 I4

+ J⊤

r2Ir2

(7) The associate equation: Jr2 ˙ x+ = 02×1 (8) To take into account the locking of the knee of the leg 2, we have to complete equations (7) and (8) with equation: D⊤

4 ˙

x+ = 0. (9)

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 12

The structure of the instantaneous double support

Third sub-phase: Impulsive impact. A (˙ xa − ˙ x+) = D1 D2 D3 D4 I+

3×1

I +

4

+ J⊤

r2I+ r2

(10) There are 27 scalar equations to find 29 unknown variables, which are the components of the vectors and scalars: ˙ x−(7 × 1), I −

1 , I− 3×1(I − 2 , I − 3 , I − 4 )⊤, I− r1(2 × 1) (for the first

sub-phase), ˙ x+(7 × 1), I4, Ir2(2 × 1) (for the second sub-phase), I+

3×1(I + 1 , I + 2 , I + 3 )⊤, I + 4 and I+ r2(2 × 1) (for the third sub-phase).

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 13

Cost functional 1/3

With the impulsive torques, the cost functional is W =

4

i=2

T

T−
Γ−

i (t) ˙

θi(t)

dt +

3

i=1

T+

T
Γ+

i (t) ˙

θi(t)

dt

W =

4

i=2

W −

i

+

3

i=1

W +

i

(11)

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 14

Cost functional 2/3

The energy due to the impulsive torques becomes [Formal 82] W =

4

i=2

W −

i

+

3

i=1

W +

i

with: Values W −

i

(i = 2, 3, 4) are calculated as follows: W −

i

=

I −

i

=

I −

i

( ˙ θb

i )2 + ( ˙

θ−

i )2

2

˙

θ−

i − ˙

θb

i

if

SLIDE 15

Cost functional 3/3

The energy due to the impulsive torques becomes [Formal 82] W =

4

i=2

W −

i

+

3

i=1

W +

i

with: Values W +

i

(i = 1, 2, 3) are calculated using analogous formulas: W +

i

=

I +

i

˙ θ+

i + ˙

θa

i

2

if

˙ θ+

i ˙

θa

i ≥ 0 i = 1, 2, and 3,

W +

i

=

I +

i

( ˙ θ+

i )2 + ( ˙

θa

i )2

2

˙

θa

i − ˙

θ+

i

if

SLIDE 16

Energy cost as a function of T. (1/2)

0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 40 60 80 100 120 140 160 180 200 220 240

W

T

For human with the exoskeleton (diamond), and for human alone (circle). The step length is 0.5 m.

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 17

Energy cost as a function of L. (2/2)

0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 40 60 80 100 120 140 160 180 200 220 240

W

L

For human with the exoskeleton (diamond), and for human alone (circle). The step time is 0.45 s

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram

SLIDE 18

Conclusion and perspectives 1/2

Conclusion The planar five-link anthropomorphic bipedal mechanism is considered as a mechanical model of a human walking. The links of the exoskeleton are strongly strapped to the corresponding links of the biped. A passive exoskeleton without any sources of energy and actuators; the knee of the stance leg of our exoskeleton (and as consequence of the human) is locked using mechanical brake device, but the knee of the swing leg is unlocked. It is shown theoretically the efficiency of mentioned above passive exoskeleton for human carrying a load. Perspectives To add feet to our biped. to extend to 3D motions. To extend this work with optimal walking gaits.

Yannick Aoustin, Alexander Formalskii Strategy to lock the knee of exoskeleton stance leg: study in the fram