# A Method of Estimating an Object's Parameters Based on Simplication with Momentum for a Manipulator
## 5 Conclusions  
This paper presents a method for accurately estimating the parameters of a manipulated object using minimal motion. By leveraging momentum, the estimation model is simplified to focus on key parameters, including the object's mass, the position of its center of mass (COM) relative to the robot's end-effector, and elements of the object's inertia tensor matrix. The effectiveness of the proposed method is validated through simulations that compare its results with those of previous research. Unlike earlier approaches that rely on high \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Motion** & **Joint** & \begin{tabular}{c} **Method in** \\ [13] \\ \end{tabular} & \
\begin{tabular}{c} **Method in** \\ [18] \\ \end{tabular} &
\begin{tabular}{c} **Method in** \\ [26] \\ \end{tabular} \\ \hline \multirow{8}{*}{Range of joint angles (rad)} & \(q_{1}\) & 1.57 & 1.22 & 2.59 \\ \cline{2-5}  & \(q_{2}\) & 1.05 & 0.52 & 1.44 \\ \cline{2-5}  & \(q_{3}\) & 1.57 & 1.22 & 1.14 \\ \cline{2-5}  & \(q_{4}\) & 3.14 & 0.70 & 1.17 \\ \cline{2-5}  & \(q_{5}\) & 1.57 & 2.44 & 3.24 \\ \cline{2-5}  & \(q_{6}\) & 1.57 & & 1.84 \\ \cline{2-5}  & \(q_{7}\) & & & 0.84 \\ \hline \multirow{8}{*}{Maximum joint velocity (rad/s)} & \(q_{1}\) & 2.94 & 2.29 & 2.21 \\ \cline{2-5}  & \(q_{2}\) & 1.96 & 0.98 & 2.21 \\ \cline{2-5}  & \(q_{3}\) & 2.94 & 2.29 & 1.20 \\ \cline{2-5}  & \(q_{4}\) & 5.89 & 1.31 & 2.10 \\ \cline{2-5}  & \(q_{5}\) & 2.94 & 4.58 & 2.30 \\ \cline{2-5}  & \(q_{6}\) & 2.94 & & 2.10 \\ \cline{2-5}  & \(q_{7}\) & & & 2.50 \\ \hline \multirow{8}{*}{Maximum joint acceleration (rad/s\({}^{2}\))} & \(q_{1}\) & 4.53 & 3.85 & 3.77 \\ \cline{2-5}  & \(q_{2}\) & 3.03 & 1.65 & 6.81 \\ \cline{2-5}  & \(q_{3}\) & 4.53 & 3.85 & 2.53 \\ \cline{1-1} \cline{2-5}  & \(q_{4}\) & 9.06 & 2.20 & 7.54 \\ \cline{1-1} \cline{2-5}  & \(q_{5}\) & 4.53 & 7.70 & 3.26 \\ \cline{1-1} \cline{2-5}  & \(q_{6}\) & 4.53 & & 4.80 \\ \cline{1-1} \cline{2-5}  & \(q_{7}\) & & & 14.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Range of joint angles and maximum joint velocity and acceleration during the estimation in previous studies. acceleration motions for parameter estimation, the proposed method uses a momentum-based approach with smaller motions. The results indicate that the proposed method achieves accuracy comparable to previous studies while requiring significantly smaller motions. As a result, the inertial forces generated during estimation are lower, enhancing safety. Additionally, the reduced motion range allows the proposed method to be applied to manipulators with less power. This improvement stems from the simplified estimation model, which effectively addresses the underconstrained nature of the problem by incorporating momentum. Furthermore, in environments with higher noise levels than those considered in this study, increasing the estimation motion range to 0.2 radians or slightly higher could potentially improve accuracy. However, the proposed method has two limitations. First, it requires more time for estimation compared to previous methods. Second, it necessitates the robot to grasp and shake one side of the object, adding to the payload and potentially limiting the robot's maximum payload capacity during manipulation. While parameter estimation during collaborative manipulation with a human or another robot could help overcome this limitation, it introduces new challenges due to disturbances from external forces and torques generated by the collaborating partner. Future research will explore solutions to these challenges. Conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing--original draft preparation, visualization, J.J.; writing--review and editing, supervision, J.H.P. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.