Wearable Robot Design Optimization Using ClosedForm Human–Robot Dynamic Interaction Model
Abstract
:1. Introduction
 (a)
 Defining assistive objectives of the robot in terms of unknown forces and torques in the humanrobot system of equations of equilibrium to keep it statically determinate, allowing to solve it directly without optimization.
 (b)
 Using the technique developed by Shahabpoor and Pavic [16] to estimate the walking GRFs from the reference measured kinematic data, avoiding the need to measure walking GRFs.
 (1)
 Computational efficiency: the combination of a simplified link segment model and directly solving the system of equations for joint and interaction forces and torques without optimization makes the process highly computationally efficient. This, not only allows for effortless offline design optimization of the robot, but also allows the framework to be used online as part of the robot controller for realtime calculation of assistive torques.
 (2)
 Transparency: the clear mathematical formulation of the human–robot system allows for direct analysis of the relationship between the robot interventions and the consequent changes in human kinematics and kinetics.
 (3)
 Less prone to input errors due to the limited number of assumptions and uncertain inputs used.
2. Experimental Measurements
3. HRI Modelling Framework
 A.
 Human and robot are each modelled with an appropriate link segment (LS) model with lumped masses at each segment’s CoM and linked together based on the actual HRI configuration.
 B.
 Inverse Kinematics analysis is carried out to calculate the movements of human and robot segments from the measured marker trajectories.
 C.
 The contact forces between the human–robot system and the environment are estimated/measured.
 D.
 The system of equations of equilibrium for the human–robot LS model is formulated and solved for the net joint/interaction forces and torques (ID analysis). To make the system of equations statically determinate, the robot should have the same number of passive or active DoFs as the degree of indeterminacy of the human–robot system. Torque at each passive joint is set to zero. Assistive objectives of the robot are then used to define extra force/torque constraints, equal to the number of robot’s active DoFs, to make the system statically determinate.
4. Application of the HRI Framework to an Assistive LowerLimb Exoskeleton
4.1. Step A
4.2. Step B
4.3. Step C
4.4. Steps D
5. Design Optimization
5.1. Center of Rotation of Hip Joint
5.2. Center of Rotation of Ankle Joint
 (a)
 the magnitude of ${F}_{R,x}$ and ${F}_{R,z}$ that the robot with a passive ankle can provide at the user’s CoM over the gait cycle (Figure 9a,b);
 (b)
 the magnitude of torque at the human ankle ${M}_{HA,y}$ for the robot with a passive ankle (Figure 9c);
 (c)
 the ankle torque ${M}_{RA,y}$ required in a robot with active ankle joints (Figure 9d).
5.3. Joint Torque–Velocity Requirements
6. Discussion and Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
CDF  cumulative distribution function 
CoM  center of mass 
CoP  plantar center of pressure 
D  distal 
DoF  degree of freedom 
DS  doublesupport phase of the walking gait 
e  mean efficiency 
${F}_{P1P2,P3}$ ${M}_{P1P2,P3}$  force (f) or moment (m) at

g  gravitational constant 
GRF  ground reaction forces 
HAT  head–arms–trunk 
HRI  human–robot interaction 
I  rotational inertia 
ID  inverse dynamics 
LS  link segment 
m  mass 
P  proximal 
S  human subject 
SS  singlesupport phase of the walking gait 
${v}_{w}$  walking speed 
w  walking 
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Honda walking assist: 1 active DoF per leg: hip 15 unknowns and 15 equations and constraints In each leg link segment model:
 
Ascend robotic knee brace (Roam Robotics): 1 active DoF per leg: knee 18 unknowns and 18 equations and constraints In each leg link segment model:
 
Fall prevention robot developed by the authors: 1 active DoF per leg: hip 15 unknowns and 15 equations and constraints In each leg link segment model:
 
Samsung walking assist robot: 2 active DoFs per leg: hip and knee 18 unknowns and 18 equations and constraints In each leg link segment model:
 
Honda weight support robot: 1 active DoFs per leg: knee 18 unknowns and 18 equations and constraints In each leg link segment model:

${\mathit{F}}_{\mathit{R},\mathit{x}}$ Conf (a)  ${\mathit{F}}_{\mathit{R},\mathit{x}}$ Conf (b)  ${\mathit{F}}_{\mathit{R},\mathit{x}}$ Conf (c)  ${\mathit{F}}_{\mathit{R},\mathit{z}}$ Conf (a)  ${\mathit{F}}_{\mathit{R},\mathit{z}}$ Conf (b)  ${\mathit{F}}_{\mathit{R},\mathit{z}}$ Conf (c)  

$e$  92%  97%  99%  68%  73%  80% 
${\mathit{M}}_{\mathit{H}\mathit{A},\mathit{y}}$ Unassisted  ${\mathit{M}}_{\mathit{H}\mathit{A},\mathit{y}}$ Conf (a)  ${\mathit{M}}_{\mathit{H}\mathit{A},\mathit{y}}$ Conf (b)  ${\mathit{M}}_{\mathit{H}\mathit{A},\mathit{y}}$ Conf (c)  ${\mathit{M}}_{\mathit{R}\mathit{A},\mathit{y}}$ Conf (a)  ${\mathit{M}}_{\mathit{R}\mathit{A},\mathit{y}}$ Conf (b)  ${\mathit{M}}_{\mathit{R}\mathit{A},\mathit{y}}$ Conf (c)  

$\mathrm{max}\left(\left{M}_{y}\right\right)$  0.09  0.10  0.12  0.16  0.09  0.07  0.10 
$\raisebox{1ex}{$\sum \left{M}_{y}\right$}\!\left/ \!\raisebox{1ex}{$100$}\right.$  0.028  0.025  0.032  0.038  0.028  0.022  0.023 
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Shahabpoor, E.; Gray, B.; Plummer, A. Wearable Robot Design Optimization Using ClosedForm Human–Robot Dynamic Interaction Model. Sensors 2024, 24, 4081. https://doi.org/10.3390/s24134081
Shahabpoor E, Gray B, Plummer A. Wearable Robot Design Optimization Using ClosedForm Human–Robot Dynamic Interaction Model. Sensors. 2024; 24(13):4081. https://doi.org/10.3390/s24134081
Chicago/Turabian StyleShahabpoor, Erfan, Bethany Gray, and Andrew Plummer. 2024. "Wearable Robot Design Optimization Using ClosedForm Human–Robot Dynamic Interaction Model" Sensors 24, no. 13: 4081. https://doi.org/10.3390/s24134081