## 5 Conclusions  
This paper proposes an adaptive control strategy including system identification and gain scheduling. The system identification is conducted by parameter estimation based on least-squares method, and it estimates the unknown parameters of the dynamic equation of the loading device. In the simulation, the root-mean-square error between the motions of a predefined system and the estimated system is almost 0. This means that the least-squares method-based system identification technique estimates the dynamic equation that moves in equal motion with the real loading device. The accuracy of the parameter estimation of the system identification technique is improved using a null-space solution. Compared to the parameter estimation of the normal system identification technique showing error rates of 31.960%, 399.427%, 399.479%, the improved system identification technique shows error rates of 0.928%, 0.925%, 0.925%. In the proposed adaptive control strategy, the weights for the null-space solution are determined by the motor torque. Therefore, the parameter estimator can respond appropriately to the demanded torque in the gain scheduling process. The PID gain scheduling for the frames of the pitch axis and the roll axis uses independent gain schedulers for each axis. Each gain scheduler consists of surface functions using the estimated unknown parameters in the system identification process as the variables. The surface functions are constructed in advance by interpolating the optimized gains. The gain scheduler can adapt the controller by assigning the unknown parameters to the scheduling surface functions in real-time. In the case of the structure of the controller, it includes not only a system identification and a gain scheduler but also a smoothing filter and anti-wind-up technique. The experiments using a motion platform are conducted. In the results of the experiments, the root-mean-square error between the angular accelerations of the real loading device and the estimated system is 0. The gain scheduler properly adapts the controller depending on the motor torque in real-time. In the case of the balancing control of the loading box, every overshoot and settling time of 5% error rate of all experiments are 2 degrees and 2.45 s or less. The 2-axes gimbal loading device is well balanced by the proposed adaptive control strategy despite the tilting of the motion platform and system change caused by the luggage. The next step of this study is to apply the loading device to a stair-climbing delivery robot. The loading device should be lighter, and carefully adjust the position of the center of gravity for the stable operation of the delivery robot. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**The Empty Loading Device**} & **Load 3 kg in Offset Position** & **Load 5 kg** \\ \hline \multirow{2}{*}{Pitch} & \multicolumn{1}{c}{Overshoot (degree)} & 1.7 & 1.21 & 1.77 \\ \cline{2-4}  & \multicolumn{1}{c}{Settling time (s)} & 0.64 & 2.11 & 2.19 \\ \hline \multirow{2}{*}{Roll} & \multicolumn{1}{c}{Overshoot (degree)} & 1.18 & 1.45 & 2 \\ \cline{2-4}  & \multicolumn{1}{c}{Settling time (s)} & 1.67 & 2.45 & 2.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Largest overshoot and longest settling time of each experiment. **Author Contributions:** Conceptualization, S.J. ; methodology, Y.S. ; software, Y.S. ; validation, S.J. and Y.S. ; formal analysis, S.J. ; data curation, Y.S. ; writing--original draft preparation, Y.S. ; writing--review and editing, S.J. ; visualization, Y.S. ; supervision, S.J. ; project administration, S.J. ; All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the Korea Agency for Infrastructure Technology Advancement (KAIA) grant funded by the Ministry of Land, Infrastructure and Transport (Grant 2 ICTAP-C164242-01). **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author.