## 4 Experiments
### Results of Experiments  
Figures 9 and 10 show the experimental results. Figure 9 is for the frame of the pitch axis and Figure 10 is for the frame of the roll axis. Figures 9a and 10a show the tilt of the loading box and the motion platform in one graph. Figures 9b and 10b show the \(\breve{\mathscr{O}}_{\text{real}}\) of the real loading device and the \(\breve{\mathscr{O}}_{\text{estimated}}\) of the system identification. Figure 8: Experiment of the loading device: (**a**) the experiment with the empty loading device; (**b**) the experiment with luggage (5 kg). Figure 7: Design of the loading device for stair-climbing delivery robot. Figure 9: Experimental result for the frame of the pitch axis: (**a**) the tilt of the loading device and the motion platform: (**a.1**) the empty loading device experiment; (**a.2**) load 3 kg luggage in the offset position; (**a.3**) load 5 kg luggage; (**b**) the angular accelerations of the real loading device and the estimated system by the system identification: (**b.1**) the empty loading device experiment; (**b.2**) load 3 kg luggage in the offset position; (**b.3**) load 5 kg luggage; (**c**) the scheduled gains of controller of each experiment: (**c.1**) P gain; (**c.2**) I gain; (**c.3**) D gain. Figure 10: Experimental result for the frame of the roll axis: (**a**) the tilt of the loading device and the motion platform; (**a.1**) the empty loading device experiment; (**a.2**) load 3 kg luggage in the offset position; (**a.3**) load 5 kg luggage; (**b**) the angular accelerations of the real loading device and the estimated system by the system identification: (**b.1**) the empty loading device experiment; (**b.2**) load 3 kg luggage in the offset position; (**b.3**) load 5 kg luggage; (**c**) the scheduled gains of controller of each experiment: (**c.1**) I gain; (**c.2**) D gain. Figure 9a.1,b.1 and Figure 10a.1,b.1 are the results of the experiment with the empty loading device. Figure 9a.2,b.2 and Figure 10a.2,b.2 are the graphs of experiment with 3 kg luggage in an offset position, the back of the loading box. Figure 9a.3,b.3 and Figure 10a.3,b.3 are from the experiment with 5 kg luggage. Figures 9c and 10c compare the scheduled PID gains of each experiment in one graph. Figure 9c.1 shows P gains, Figure 9c.2 shows I gains, and Figure 9c.3 shows D gains. Figure 10c.1 shows I gains and Figure 10c.2 shows D gains. The P gain of the frame of the roll axis is fixed at 1.2 derived as the optimized gain by the experimental results in advance. All of the root-mean-square errors of the angular acceleration of the real loading device and estimated dynamic equation in Figures 9b and 10b are 0. The parameter estimator by the least-squares method-based system identification technique works properly and estimates the dynamic equation of equal motion with the real loading device. In Figures 9c and 10c, the gains of the experiments are scheduled by the estimated \(X_{2}\) and \(X_{3}\), and adapt to the system of the loading device in real-time. The luggage of each experiment has fixed properties like mass, moment of inertia, and position of center of gravity during the experiments. In Figures 9c and 10c, all PID gains change during each experiment. It means the estimated parameter in system identification changes although the system has fixed properties. As end of Section 2.2 explained, the reason is that the estimating parameter of Equation (11) in system identification has countless solution. The main goal of the proposed control strategy is not to estimate the system correctly, but to optimize the controller for balancing loading device. Therefore, in the system identification process, the weights for a null-space solution are determined by the motor torque to derive appropriate PID gains for the required torque. As shown in Figure 9a,c and Figure 10a,c, the change in the gains occurs when the motion platform changes the tilt.