Designing and implementing an electronic system to control moving orthosis virtual mechanical system to emulate lower limb

Figures & data

Figure 1. A single leg with relative coordinates for each joint.

Table 1. D-H link parameter

Link number	θ i	αi	di	Ai
1	θ 1	0	0	a1
2	θ 2	0	0	a2
3	θ 3	0	0	a3

Table 2. 4-lower limb leg model parametres

Symbol	Quantity
θ	Manipulator joint leg
α	Link twist
d	Link offset
a	Link length
T i,j	Transformation matrices from an initial coordinate system i to a final coordinate system j
R i,j	Three by three rotation transformation from coordinate frame i to j
o i,j	Coordinate vector from coordinates i to j
$\xi$	Manipulator’s end velocity
$\dot{q}$	Vector of joint velocities
J	Jacobian matrix
τ	Vector of joint torques
K	Kinetic energy
m	Link mass
v	Linear velocity of the link at the center of mass
w	Rotational velocity of the link
$\mathfrak{T}$	Inertia matrix for the link
g	Gravity vector in terms of the base coordinate frame
r ci	Provides the coordinates of the center of mass of link i from the base to the center of mass of link i
Inertia matrix for the link: $\mathfrak{T}=RI{R}^T$
$I=\left[\begin{array}{ccc}{\left({\ell }_h^2+{\ell }^2\right)}^{\frac{m}{12}}& 0& 0\\ 0& {\left({\ell }_h^2+{\ell }_w^2\right)}^{\frac{m}{12}}& 0\\ 0& 0& {\left({\ell }^2+{\ell }_w^2\right)}^{\frac{m}{12}}\end{array}\right]$

Figure 2. Control system scheme for lower limb.

Figure 3. Lab hardware system design.

Table 3. values of controller matrices Q & R gains

Joint	Q & R Matrices	Gains
Hip joint	$Q_1=\left[\begin{array}{ccc}85& 0& 0\\ 0& 2,320& 0\\ 0& 0& 18,601\end{array}\right]$, R11 = 0.001	Ko1 = 507.2
		Kw1 = 304.3
		Kξ1 = −4066.7
Knee joint	$Q_2=\left[\begin{array}{ccc}85& 0& 0\\ 0& 2,500& 0\\ 0& 0& 18,980\end{array}\right]$, R11 = 0.001	Ko2 = 539.4
		Kw2 = 292.7
		Kξ2 = −4095.2
Ankle joint	$Q_3=\left[\begin{array}{ccc}90& 0& 0\\ 0& 2,501& 0\\ 0& 0& 18,790\end{array}\right]$, R11 = 0.001	Ko3 = 542
		Kw3 = 300.2
		Kξ3  =  −4072.2

Figure 4. Reference angle & open loop exoskeleton angle of hip joint.

Figure 5. Reference angle & open loop exoskeleton angle of knee joint.

Figure 6. Reference angle & open loop exoskeleton angle of ankle joint.

Figure 7. Reference angle & exoskeleton angle of hip joint using controller.

Figure 8. Reference angle & exoskeleton angle of knee joint using controller.

Figure 9. Reference angle & exoskeleton angle of ankle joint using controller.

Table 4. A comparison study between the average of the percentage error for both the proposed optimal controller strategy and open loop control system response for each joint

Joint	Average of percentage error optimal control	Average of percentage error open loop sys.
Hip	±5.07%	±61.45%
Knee	±1.8%	±29.4%
Ankle	±4.57%	±8.26%

Figure 10. Comparing bioloid steps with normal gait phases.