# A Safe Admittance Boundary Algorithm for Rehabilitation Robot Based on Space Classification Model
## 4 Conclusions  
In this paper, a morphological model construction method of HRI workspace is proposed and a safety detection control algorithm is constructed by integrating the variable stiffness admittance strategy. Finally, the safe admittance boundary of the rehabilitation robot HRI process is established. Space verification experiments and out-of-bounds simulation experiments are conducted in the simulation system using DAS. As indicated by the experimental results, when the side length of the voxel grid for voxel center filtering is set to 0.06 m, the accuracy of the space definition is 98.40%. The average maximum response time for out-of-bounds behaviors is 165.62 ms. These experiments verify the accuracy of the virtual constraints imposed on the HRI space and the feasibility of this method in improving the HRI safety in robot-assisted training.  
Our research lays the groundwork for using mass-produced, low-cost collaborative robots to provide safe physiotherapy for patients. However, before the proposed algorithm is put into practice, some limitations must be overcome. One is the scientificity of the kinematic model of the human upper arm. The introduction of DAS can improve the scientificity and accuracy of determining the space accessible by the upper arm using the proposed algorithm. However, a key issue affecting the definition of the safe admittance boundary is the question of how to more correctly determine the space accessible by the upper arms of different patients. The second is concerned with the application of collaborative robots in upper arm rehabilitation in real-world settings. We have already made efforts to avoid safety hazards caused by mismatches between robots and patients or misoperation of robots during active rehabilitation training. However, the collaborative robot needs to be empowered as a mediator for the scenario of active rehabilitation training. In the future, we will improve on the method for determining the space accessible by the upper arms based on clinical investigations. Forward kinematics of the human musculoskeletal system may be employed for robotic motion planning so that the robot can become a qualified mediator to offer professional and scientific rehabilitation guidance for patients. We will further verify the possibilities of using collaborative robots in assisting active rehabilitation training.  
Conceptualization, Y.T. and Y.J.; methodology, Y.T. and Y.J.; software, Y.J. and D.H.; validation, Y.J. and H.G.; formal analysis, D.H.; investigation, Y.J. and D.H.; resources, H.G.; data curation, H.G.; writing-original draft preparation, Y.J. and D.H.; writing-review and editing, Y.T. and T.W.; visualization, Y.J.; supervision, H.G.; project administration, Y.T. and T.W.; All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tester** & **Number of** & **Maximum Response Time** & **Average Response Time** \\
**Number** & **Experiments** & **(ms)** & **(ms)** \\ \hline
1 & 4 & 165.63 & 161.54 \\
2 & 4 & 162.59 & 159.64 \\
3 & 4 & 170.84 & 161.91 \\
4 & 4 & 167.12 & 162.80 \\
5 & 4 & 161.91 & 158.44 \\ Average & 4 & 165.62 & 160.87 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Out-of-bounds simulation results.  
**Funding:** This research was funded by the Sichuan Science and Technology Planning Project. Grant number: 2021 YFSY003.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.