Controlling a bipedal robot that walks on a dynamic rigid surface (DRS) is a challenging task due to the complexity of the associated robot dynamics. We introduce a hybrid linear inverted pendulum (LIP) model
for underactuated bipedal walking on a DRS. We also propose a discrete-time stepping controller to provably stabilize the periodic gait of the hybrid LIP.
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Analytical solution to a time-varying LIP model for quadrupedal walking on a vertically oscillating surface
This paper introduces an analytically tractable and computationally efficient model for legged robot dynamics during locomotion on a dynamic rigid surface (DRS), along with an approximate analytical solution and a real-time walking pattern generator synthesized based on the model and solution. By relaxing the static-surface assumption, we extend the classical, time-invariant linear inverted pendulum (LIP) model for legged locomotion on a static surface to dynamic-surface locomotion, resulting in a time-varying LIP model termed as “DRS-LIP”. Sufficient and necessary stability conditions of the time-varying DRS-LIP model are obtained based on the Floquet theory. This model is also transformed into Mathieu’s equation to derive an approximate analytical solution that provides reasonable accuracy with a relatively low computational cost. Using the extended model and its solution, a walking pattern generator is developed to efficiently plan physically feasible trajectories for quadrupedal walking on a vertically oscillating surface. Finally, simulations and hardware experiments from a Laikago quadrupedal robot walking on a pitching treadmill (with a maximum vertical acceleration of 1 m/s
) confirm the accuracy and efficiency of the proposed analytical solution, as well as the efficiency, feasibility, and robustness of the pattern generator, under various surface motions and gait parameters.
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- PAR ID:
- 10468053
- Editor(s):
- Sun, Weichao; Yao, Bin
- Publisher / Repository:
- ELSEVIER
- Date Published:
- Journal Name:
- Mechatronics
- Edition / Version:
- 1.0
- Volume:
- 96
- Issue:
- C
- ISSN:
- 0957-4158
- Page Range / eLocation ID:
- NA
- Subject(s) / Keyword(s):
- Legged locomotion reduced-order modeling motion planning nonlinear control
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.mechatronics.2023.103073
