Hybrid Lyapunov-based feedback stabilization of bipedal locomotion based on reference spreading
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911865263620096 |
|---|---|
| author | Bertollo, Riccardo Lunardi, Gianni Del Prete, Andrea Zaccarian, Luca |
| author_facet | Bertollo, Riccardo Lunardi, Gianni Del Prete, Andrea Zaccarian, Luca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid Lyapunov-based feedback stabilization of bipedal locomotion based on reference spreading Bertollo, Riccardo Lunardi, Gianni Del Prete, Andrea Zaccarian, Luca Systems and Control Dynamical Systems 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. |
| title | Hybrid Lyapunov-based feedback stabilization of bipedal locomotion based on reference spreading |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2405.02184 |