# Human–Exoskeleton Interaction Force Estimation in Indego Exoskeleton

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Interaction Torque Modeling

#### 2.2. System Identification

#### 2.3. Experimental Estimation of Human–Exoskeleton Interaction Torque

## 3. Results and Discussion

#### 3.1. Tuning the Network Structure and Hyperparameters

#### 3.2. N9 Performance on Test Dataset

#### 3.3. Human–Exoskeleton Interaction Torque Estimation

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**A**) The exoskeleton coordinates and joint angles. The global, trunk, and thigh frames are denoted by 0, 1, and 2 indices, respectively. The trunk and thigh angles with respect to the gravity vector are denoted by $\theta $ and $\gamma $, respectively. ${q}_{h}$ and ${q}_{k}$ represent the hip and knee joint angles, respectively. ${\mathit{p}}_{1}$ and ${\mathit{p}}_{2}$ show the position of the trunk and thigh coordinated in the global frame ((${x}_{0},{y}_{0}$)). In blue, the acceleration vector ($\mathit{a}$) measured by the accelerometer embedded in the exoskeleton’s thigh is plotted against the thigh frame. In red, we plotted the interaction force vector (${\mathit{f}}_{\mathit{int}}$) calculated from the linear spring’s deflection measured by motion capture. The distance from the trunk frame origin to the hip joint rotation axis and from there to the accelerometer location on the exoskeleton’s thigh is indicated by ${l}_{1}$ and ${l}_{2}$, and the gravity axis is illustrated by dashed lines. (

**B**) The exoskeleton in hung position during data collection for dynamics identification. Joints are excited during the experiment while the exoskeleton interaction with the environment is limited to the force applied through a linear spring with reflective markers on both ends enabling us to measure the spring deflection using a motion capture system and, consequently, the applied force.

**Figure 2.**The hip and knee excitation torques applied to the left and right exoskeleton legs, as well as the interaction force on the y axis. During the generation of each of the training, validation, and test datasets, exoskeleton joints were activated with unique and different chirp commands resulting in different exoskeleton–environment interaction profiles.

**Figure 3.**(

**A**) Block diagram of the exoskeleton dynamic identification experiment. The interaction force (${f}_{\mathrm{int}}$) is applied to the exoskeleton through a linear spring through which the exoskeleton is hung. Exoskeleton joints are controlled by chirp position commands using PD controllers applying the excitation torques (${\tau}_{\mathrm{act}}$) to the exoskeleton. Measurements of the exoskeleton (x), containing joint angles and their derivatives as well as the thigh angle with respect to the gravity vector and its linear acceleration, are fed to a neural network for the estimation of the interaction force (${\widehat{f}}_{\mathrm{int}}$) and motor torques (${\widehat{\tau}}_{\mathrm{act}}$), which are then compared to their actual values. The estimation error is then used to update the neural network weights to improve its estimation accuracy. (

**B**) Structure of a time–delay neural network with 10 input delays and 3 hidden layers with 50, 50, and 20 neurons, respectively, with a $tanh$ activation function.

**Figure 4.**(

**A**) Validation performance of ANNs with 10 different structures in terms of RMSE and adjusted ${R}^{2}$ computed on the Z–normalized data. The training procedure was repeated 5 times for each structure to study the sensitivity of the training procedure to the network’s initial weight for each structure. Each validation performance is denoted by a black dot while the average performance is denoted by bars. The training was conducted with 5 input delays and no regularization. N3 (denoted by red) and N9 (denoted by blue) demonstrated a better performance compared to the other networks. N9, however, exhibited more variability across training repetitions. Those networks were selected for further analysis to investigate the effect of regularization factor and the number of input delays. (

**B**) Comparison of N3 and N9 performance across different selections of regularization factors. The variation of the N9 performance across training repetitions is unaffected by regularization. (

**C**) Effect of the number of input delays on the N3 and N9 networks’ performance. N3 has the best performance with 5 input delays while N9 reaches the best performance at 10 input delays.

**Figure 5.**The Test performance of N9 for each output channel. In the top row, the distribution of the estimation error of external force or joint applied torques relative to their peak–to–peak range is depicted. Interaction forces in the y and x direction exhibit a higher estimation error compared to those of the exoskeleton active joints. Applied torques to the hip joints, in particular, are estimated with a higher accuracy and smaller standard deviation. Even though knee joint applied torques are estimated with similarly small errors (small bias), they show a higher standard deviation associated to the more prominent role of static friction. The bottom row shows the correlation between the measured data and the N9 estimation for each output channel. The estimated outputs have a relatively lower coefficient of determination in case of interaction forces, while they show ${R}^{2}$ > 0.9 for the active joints of the exoskeleton.

**Figure 6.**The estimated interaction torques at (

**A**) the hip and (

**B**) the knee joints of the right leg for three participants walking at different speeds (ranging from 0.4 m/s to 0.8 m/s) are shown. The values represent the average across different steps. The solid lines represent the median of the estimated interaction torque, while the shaded area represents the torques that fall within the 5th to 95th percentile. Positive torque values are in favor of joint flexion while negative values are in favor of joint extension.

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**MDPI and ACS Style**

Shushtari, M.; Arami, A.
Human–Exoskeleton Interaction Force Estimation in Indego Exoskeleton. *Robotics* **2023**, *12*, 66.
https://doi.org/10.3390/robotics12030066

**AMA Style**

Shushtari M, Arami A.
Human–Exoskeleton Interaction Force Estimation in Indego Exoskeleton. *Robotics*. 2023; 12(3):66.
https://doi.org/10.3390/robotics12030066

**Chicago/Turabian Style**

Shushtari, Mohammad, and Arash Arami.
2023. "Human–Exoskeleton Interaction Force Estimation in Indego Exoskeleton" *Robotics* 12, no. 3: 66.
https://doi.org/10.3390/robotics12030066