# Online Control for Biped Robot with Incremental Learning Mechanism
## 4 Experiment Results and Analysis
### Experiment: Walking on Flat Ground  
As illustrated in Figure 1 and Table 1, the biped robot BRZ-4 is set up as test bed. Roughly, the test bed consists of two parts, which are the ground workstation and BRZ-4. We apply the proposed control algorithm to BRZ-4. Specifically, our scheme contains off-line and online learning parts. To improve the efficiency, the off-line training is carried out in matlab while the online learning is implemented by using C language. Moreover, the control commands and the states of robot can be transmitted through RS485 bus. To visually present the basic components of hardware system, a graphical result is provided in Figure 4.  
One of the goals of the experiment is to control the biped robot to track the desired gait, such that stable walk is achieved. Under the new constructed control framework, desired gait is planned by using a spline-based parametric optimization technique [31], which contains start gait, period normal gait, and stop gait. In addition, the generation of planned gait is implemented in the ground workstation and specific control command will be transmit to BRZ-4 through RS485 bus in real time. To visually illustrate the planned results, the stick animation is presented in Figure 5, in which the CoM trajectory is highlighted in red. Figure 4: Basic components of hardware system. In the construction of the proposed IT2 FWI, we take the Gaussian function with fixed standard deviation \(\sigma\) and uncertain mean as the primary membership functions. By applying the trial-and-error procedure, the designed parameters of membership functions of ZMP stability margin and yaw moment are chosen as follows  
\[\sigma_{z}=0.12;\sigma_{y}=0.18\] \[[\underline{c}_{ij}^{z},\overline{c}_{ij}^{z}]_{j=1}^{5}= \{[-0.02,0.02],[0.23,0.27],[0.48,0.52],\] \[[0.73,0.77],[0.98,1.02]\}\] \[[\underline{c}_{ij}^{y},\overline{c}_{ij}^{y}]_{j=1}^{5}= \{[-1.02,-0.98],[-0.52,-0.48],[-0.02,0.02],\] \[[0.48,0.52],[0.98,1.02]\}\]  
A comparison between the proposed control scheme and the one in [26] is carried out on the platform of BRZ-4. The ZMP response trajectories are plotted in Figure 6. As indicated in this figure, all the ZMP trajectories are observed to be within the convex boundaries of the supporting foot, which implies that both methods can ensure the locomotion stability in horizontal direction. On the other hand, undesired yaw moment has an significant impact on locomotion stability of biped robot, as pointed out in [16; 17; 18]. Now we test the effectiveness of our control scheme in compensating for yaw moment. The evolutions of yaw moment, with our method and the one in [26] are visualized in Figure 7. As seen from the comparison, with the above two methods, the yaw moment is successfully suppressed. Apart from these, the root-mean-square (RMS) errors of x-axis/y-axis ZMP stabilities and yaw moment are recorded in Table 2. It is noted that, with the proposed scheme, the RMS errors of x-axis,y-axis ZMP trajectories and yaw moment are around 5.9%, 9.9%, and 20.7% lower than those in [26], respectively. Moreover, comparing with the method in [26], the online learning time is dramatically reduced from 1.56 s to 0.23 s. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Proposed Method** & **Method in [26]** \\ \hline RMS error (\(x_{zmp}\)) & 0.0322 & 0.0341 \\ RMS error (\(y_{zmp}\)) & 0.0251 & 0.0276 \\ RMS error (\(M_{z}\)) & 0.0617 & 0.0745 \\ Learning time of each cycle (s) & 0.23 & 1.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of control performance. Figure 5: Animation of planned gait. **Remark 1**. : _Comparing with [26] which also focuses on the optimization-based learning control design, the learning mechanism in our scheme can be divided into two parts including off-line learning and online learning. By employing a flat network structure and deriving an weight matrix updating Equation (14), the proposed method successfully avoids the entire retraining from beginning. As a result, the online learning time is dramatically reduced as shown in Table 2._