2017/11/06 by Xingye Da, Da, Xingye, Jessy W. Grizzle +1 · 2 citations
Engineering · Physics and Astronomy · #Biomimetic flight and propulsion mechanisms #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Robotic Locomotion and Control
paper · pdf · doi:10.48550/arxiv.1711.02223
openalex publication_date 2017/11/06 · openalex created_date 2017/11/17 · openalex updated_date 2026/07/28
To overcome the obstructions imposed by high-dimensional bipedal models, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The process begins with trajectory optimization to design an open-loop periodic walking motion of the high-dimensional model and then adding to this solution, a carefully selected set of additional open-loop trajectories of the model that steer toward the nominal motion. A drawback of trajectories is that they provide little information on how to respond to a disturbance. To address this shortcoming, Supervised Machine Learning is used to extract a low-dimensional state-variable realization of the open-loop trajectories. The periodic orbit is now an attractor of the low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable. The design procedure is first developed for ordinary differential equations and illustrated on a simple model. The methods are subsequently extended to a class of hybrid models and then realized experimentally on an Atrias-series 3D bipedal robot.