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This work aims to enhance the linear inverted pendulum model (LIPM) for bipedal robot control. While the LIPM simplifies the dynamics by assuming homogeneity, it fails to capture important nonlinear dynamics observed in real-world scenarios. To address this limitation, we propose the non-homogeneous LIPM (NH-LIPM), which incorporates a non-homogeneous term in the traditional LIPM dynamics. The NH-LIPM is augmented with controllable inputs, allowing for greater parameter control compared to the LIPM. Through regression analysis and the use of the Recursive Least Squares algorithm with forgetting, we extract and adaptively tune the NH-LIPM parameters. Evaluation through high-fidelity simulation and experimentation on a 30-degree-of-freedom humanoid demonstrates that the NH-LIPM offers improved velocity tracking control, particularly when ankle torque with damping control is added. This model provides a flexible framework for simultaneously controlling the center of mass velocity and position, enabling precise reference tracking and enhanced bipedal locomotion. A video is linked here: http://tiny.cc/NHLIPM
Hinojosa et al. (Tue,) studied this question.