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Controller design for bipedal walking on dynamic rigid surfaces (DRSes), which are rigid surfaces moving in the inertial frame (e.g., ships and airplanes), remains largely underexplored. This paper introduces a hierarchical control approach that achieves stable underactuated bipedal walking on a horizontally oscillating DRS. The highest layer of our approach is a real-time motion planner that generates desired global behaviors (i.e., center of mass trajectories and footstep locations) by stabilizing a reduced-order robot model. One key novelty of this layer is the derivation of the reduced-order model by analytically extending the angular momentum based linear inverted pendulum (ALIP) model from stationary to horizontally moving surfaces. The other novelty is the development of a discrete-time foot-placement controller that exponentially stabilizes the hybrid, linear, time-varying ALIP. The middle layer translates the desired global behaviors into the robot’s full-body reference trajectories for all directly actuated degrees of freedom, while the lowest layer exponentially tracks those reference trajectories based on the full-order, hybrid, nonlinear robot model. Simulations confirm that the proposed framework ensures stable walking of a planar underactuated biped under different swaying DRS motions and gait types.
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Design of smooth hybrid controllers for a class of non‐linear systems
Symbolic planning techniques rely on abstract information about a continuous system to design a discrete planner to satisfy desired high‐level objectives. However, applying the generated discrete commands of the discrete planner to the original system may face several challenges, including real‐time implementation, preserving the properties of high‐level objectives in the continuous domain, and issues such as discontinuity in control signals that may physically harm the system. To address these issues and challenges, the authors proposed a novel hybrid control structure for systems with non‐linear multi‐affine dynamics over rectangular partitions. In the proposed framework, a discrete planner can be separately designed to achieve high‐level specifications. Then, the proposed hybrid controller generates jumpless continuous control signals to drive the system over the partitioned space executing the discrete commands of the planner. The hybrid controller generates continuous signals in real‐time while respecting the dynamics of the system and preserving the desired objectives of the high‐level plan. The design process is described in detail and the existence and uniqueness of the proposed solution are investigated. Finally, several case studies are provided to verify the effectiveness of the developed technique.
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- Award ID(s):
- 1832110
- PAR ID:
- 10570711
- Publisher / Repository:
- DOI PREFIX: 10.1049
- Date Published:
- Journal Name:
- IET Control Theory & Applications
- Volume:
- 14
- Issue:
- 19
- ISSN:
- 1751-8644
- Format(s):
- Medium: X Size: p. 3251-3259
- Size(s):
- p. 3251-3259
- Sponsoring Org:
- National Science Foundation
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