# Online Control for Biped Robot with Incremental Learning Mechanism
## 1 Introduction  
In recent years, biped robot has received considerable attention owing to its unique bipedal movement, excellent suitability to human society and theoretical importance. Up to date, a number of active control approaches have been proposed, e.g., stability-criterion-based method [1; 2; 3], model-based method [4; 5; 6], and optimization-based method [7; 8; 9]. In addition to these, many real robot platforms have been successfully developed, including Atlas, MABEL, ASIMO, and NAO [10; 11]. To achieve the bipedal locomotion stability, zero-moment-point (ZMP) was proposed and have become the most popular stability criteria. In [12], [PERSON] et al. designed a ZMP tracking servo controller and proposed a bipedal walking pattern generation algorithm based on cart-table model. In [13], a modified walking pattern method was presented by utilizing allowable ZMP variation and both step length and walking period can be independently adjusted without any extra step. Subsequently, [PERSON] et al. [14] further proposed a practical gait synthesis algorithm by optimizing gait parameters, and the locomotion stability was guaranteed. Moreover, [PERSON] et al. [15] defined the pendular support area and presented a whole-body controller for locomotion across arbitrary multicontact stances. Despite these contributions, the stability established in [12; 13; 14; 15] depends on an assumption that the effect on stability caused by yaw moment can be ignored, which is in fact a restrictive condition. As pointed out in [16; 17; 18], yaw moment is inevitably generated by the motion of swing leg, which may lead to slippage or falling down. To remove such limitation, much effort has been paid in this field and some interesting results were reported in [16; 17; 18; 19; 20; 21]. In particular, [PERSON] et al. [16] proposed a waist-rotation-based yaw moment compensation algorithm, while a biped robot was modeled as a 3D inverted pendulum. In [22], with the fusion of waist joint control techniqueand optimized swing leg reference generation method, a fast walking pattern generation approach was presented to counteract the effect of yaw moment. Inspired by human walking experience, [PERSON] et al. (2018) designed an arm-swing-based control scheme to cancel the factors which produce the yaw moment. To further improve the control performance, in ([PERSON] et al., 2018), the angular momentum rate changes were smoothly integrated into yaw moment equation and the locomotion stability was ensured by utilizing a Eulerian ZMP resolution approach. Moreover, [PERSON] et al. (2018) constructed a practical control scheme to compensate yaw moment by controlling lower limb. Although much progress has been made in dynamic balance control field, some challenging difficulties still remain open. In most of existing control schemes on yaw moment compensation for biped robot, such as those mentioned above, only a few joints are involved which bring much burden to driving motors and may result in unnatural gaits. In practice, it is difficult to generate natural and efficient gaits in real time according to external disturbance from circumstance. To address this problem, a series of optimization-based methods were proposed. In ([PERSON] et al., 2018), a spline-based estimation of distribution algorithm was proposed by formulating the gait pattern generation into a multiobjective optimization problem. In ([PERSON] et al., 2018), besides ensuring the ZMP stability, the performance of energy efficiency was also well guaranteed by the fusion of moving ZMP criterion with the fourier series approximation technique. With the recourse of Newton-Raphson iteration, the locomotion stability was achieved and the walking speed of robot was successfully regulated online in ([PERSON] et al., 2018). Furthermore, [PERSON] et al. (2018) presented a SVM-based learning control system for biped robots, in which a novel SVM objective function with energy-related slack variables was proposed.