Predictive control methods for walking commonly use low dimensional models, such as a Linear Inverted Pendulum Model (LIPM), for simplifying the complex dynamics of legged robots. This paper identifies the physical limitations of the modeling methods that do not account for external disturbances, and then analyzes the issues of numerical stability of Model Predictive Control (MPC) using different models with variable receding horizons. We propose a new modeling formulation that can be used for

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... oth gait planning and feedback control in an MPC scheme. The advantages are the improved numerical stability for long prediction horizons and the robustness against various disturbances. Benchmarks were rigorously studied to compare the proposed MPC scheme with the existing ones in terms of numerical stability and disturbance rejection. The effectiveness of the controller is demonstrated in both MATLAB and Gazebo simulations.