Hybrid Lyapunov-based feedback stabilization of bipedal locomotion based on reference spreading
<|reference_start|>Hybrid Lyapunov-based feedback stabilization of bipedal locomotion based on reference spreading: We propose a hybrid formulation of the linear inverted pendulum model for bipedal locomotion, where the foot switches are triggered based on the center of mass position, removing the need for pre-defined footstep timings. Using a concept similar to reference spreading, we define nontrivial tracking error coordinates induced by our hybrid model. These coordinates enjoy desirable linear flow dynamics and rather elegant jump dynamics perturbed by a suitable extended class ${\mathcal K}_\infty$ function of the position error. We stabilize this hybrid error dynamics using a saturated feedback controller, selecting its gains by solving a convex optimization problem. We prove local asymptotic stability of the tracking error and provide a certified estimate of the basin of attraction, comparing it with a numerical estimate obtained from the integration of the closed-loop dynamics. Simulations on a full-body model of a real robot show the practical applicability of the proposed framework and its advantages with respect to a standard model predictive control formulation.<|reference_end|>
@article{bertollo2024hybrid,
    title={Hybrid Lyapunov-based feedback stabilization of bipedal locomotion based
  on reference spreading},
    author={Riccardo Bertollo and Gianni Lunardi and Andrea Del Prete and Luca
  Zaccarian},
    journal={arXiv preprint arXiv:2405.02184},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.02184},
    primaryClass={eess.SY cs.SY math.DS}
}