# Online Control for Biped Robot with Incremental Learning Mechanism
## 1 Introduction
This objective function followed the principle that the slack variables were determined by energy cost, which means the sample with lower energy consumption contributes more to SVM regression. This provided an interesting clue to learn biped walking locomotion. However, this method generally depends on a well-trained model, which may not always be achieved in practical applications. Motivated by such an observation, in this paper, we make an attempt to further address the online control problem for biped robot. To remove the restrictions just mentioned, the main challenging difficulty that obstructs the design of our control scheme lies in the development of a protocol to compensate yaw moment and at the same time maintain zero-moment-point stability. To overcome the difficulty, an online walking control approach is presented. In summary, the work of this paper has the following novelties and contributions:  
1. As compared with the control scheme developed in ([PERSON] et al., 2018), ours newly equips with a neural-network estimator and an incremental mechanism, with which those newly coming data can be used straightforwardly to update the original well-trained model in real time. This implies that it is possible for a robot to achieve better locomotion stability in dynamic environment, e.g., from flat ground to uneven terrain;
2. Traditional optimization-based methods, such as those in ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018) are involved in many adaption laws to be updated or computed online, which may result in a computation burden during control implementation. To remove this restriction, we achieve the fusion of the random vector functional-link neural network with an incremental mechanism, so that the entire retraining from beginning can be effectively avoided. Furthermore, by designing an interval type-2 fuzzy weight identifier (IT2 FWI), both horizontal and vertical locomotion stabilities are successfully taken into account in training procedure. The rest of this paper is organized as follows. In Section 2, the kinematics and dynamics of the biped robot are given and some preliminaries are presented. In Section 3, we propose an online control scheme based on incremental learning Algorithm 1, and a neural-network mechanism is established. In Section 4, simulation and experiment are carried out to verify the effectiveness of our scheme. In Section 5, the conclusions are given. ```
1: incoming new samples \(\mathbf{Q}_{l}=(\mathbf{q}_{i},\mathbf{\dot{q}}_{i},\mathbf{\dot{q}}_{i},\Delta X _{z}^{i},M_{z}^{i})\);
2:
3:\(\mathbf{T}=(t_{1},...,t_{N})=(\Delta\mathbf{q}_{1},...,\Delta\mathbf{q}_{N})\)
4: Randomly initiate \(\mathbf{W}_{e}\), \(\mathbf{W}_{h}\), \(\mathbf{\dot{\rho}}_{e}\), \(\mathbf{\dot{p}}_{h}\), set training error \(e=0\);
5: Calculate the matrix \(\mathbf{A}=[\mathbf{K}^{n}\ \mathbf{H}^{m}]\);
6: Calculate \((\mathbf{A}^{m})^{+}\) with Equation (11);
7:while\(e\leq threshold\); do
8: Randomly initiate \(\mathbf{W}_{p}\), \(\mathbf{\beta}_{p}\);
9: Set \(\mathbf{Y}_{p}=\varphi(\mathbf{Q}\mathbf{W}_{p}+\mathbf{\dot{\rho}}_{p})\) and \(\mathbf{A}^{m+1}=[\mathbf{A}^{m}|\mathbf{Y}^{p}]\)
10: Calculate \((\mathbf{A}^{m+1})^{+}\) and \(\mathbf{W}^{m+1}\) by Equations (12)-(14);
11:endwhile
12:Calculate \(\mathbf{T}=(\mathbf{A}^{m+1})^{+}\mathbf{W}^{m+1}\)
```  
**Algorithm 1** Online Updating with increment learning algorithm