# Whole-Body Motion Generation for Balancing of Biped Robot
## 1 Introduction
In [19], push recovery was implemented through optimization based on the analytical solution of the CP concept. Depending on how the optimization problem is formulated, MPC can be applied to modify the ZMP [20]. A cascaded structure combining CP control with MPC allows for robust walking control, where the CP feedback stabilizes the divergent dynamics and adjusts ZMP, MPC generates feasible COM trajectories based on the adjusted ZMP. In [21], the DCM concept was utilized along with a single MPC that combines ZMP manipulation, footstep adjustment, and centroidal moment pivot (CMP) modulation, enabling robust walking on irregular terrain. In [22], the ZMP modification through CP control from [18] was combined with the modified LMPC approach used in [20] to maintain balance in the presence of disturbances. Despite these advancements, most previous works neglect angular momentum. Angular momentum plays an essential role in enhancing the balance of a walking humanoid. However, most studies assume a point mass model without consideration of angular momentum. The upper body of a humanoid robot usually takes a large proportion of momentum due to its dominant inertia proportion [23]. In [24; 25], the momentum equations were expressed in a linear form, and resolved momentum control was proposed to modify the movements of the body and free joints to track the reference momentum. In [26], inverse dynamics were used to generate upper body rotation for balance maintenance. In [27], the angular momentum generated by the lower body movements was calculated to compensate for it using the upper body, compensating for the yaw direction angular momentum. However, existing studies still have limitations in flexibly responding to unexpected disturbances or adjusting balance using the arms, as humans do. Research on enhancing dynamic stability using robot arms has been pursued through various approaches. Some studies have focused on imitating human arm motions or learning their characteristics based on motion capture [28; 29]. Other works have involved maintaining balance through reactive upper-body movements within a whole-body momentum control framework [26], and studies have also explored planning predictive arm responses to disturbances using model hierarchy predictive control (MHPC) [30]. However, these approaches often utilize arm motions as a secondary consequence of specific tasks or complex integrated control systems. The method proposed in this paper generates arm motions in real time through an optimization-based, decoupled momentum controller designed specifically to minimize whole-body angular momentum. This approach establishes a direct objective for angular momentum management and proposes a decoupled framework for arm motion generation, which can enhance the generality and flexibility of application. In this paper, we propose an arm motion generation through an optimization-based momentum controller. Unlike the lower limbs, the arms of a humanoid robot are not constrained by ground contact, making them particularly suitable for generating compensatory angular momentum. This characteristic becomes especially critical when footstep adjustment is limited or infeasible. Building upon this idea, we propose a whole-body motion generation framework that integrates CP control, MPC, and an optimization-based momentum controller for arm motion. This integrated approach directly addresses the limitations of conventional lower-body-centric control frameworks. These frameworks often struggle with effective angular momentum management, particularly when facing unexpected disturbances or constraints on foot placement. The CP was used to modify the pre-planned ZMP in order to stabilize the dynamics of LIPM. To track the modified ZMP and generate the COM trajectory, MPC was used. While inheriting the CP and MPC structure, our approach extends it by incorporating a decoupled arm control module based on angular momentum minimization.