In this paper we present the Model Predictive Control (MPC) with dynamic constraints for generating dynamic walking for the compliant humanoid COMAN. The dynamics of the robot are modeled using the cart-table model which allows the generation of a dynamically balanced gait given a planned walking pattern based on the Zero Moment Point (ZMP). Our simulation study of the MPC's implementation on bipedal walking finds out that a large receding and control horizons are needed to track a predefined walking pattern, leading to numerical instability. Therefore, the Extended Prediction Self-Adaptive Control (EPSAC) approach for MPC has been used and a method based on the analysis of the Singular Value Decomposition (SVD) is presented as new contribution to guarantee feasibility, robustness and stability of the MPC formulation. Study on an inverted pendulum and the COMAN humanoid prove that the proposed strategy improves the robustness and stability of the original EPSAC controller, in both well or ill conditioned systems. The simulation results finally demonstrate that the proposed methodology is well suited to smoothly track a dynamic walking pattern.
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