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Published June 2018 | public
Book Section - Chapter

Observer-Based Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Underactuated Bipedal Walking

Abstract

This paper presents a systematic approach to design observer-based output feedback controllers for hybrid dynamical systems arising from bipedal walking. We consider a class of parameterized observer-based output feedback controllers for local exponential stabilization of hybrid periodic orbits. The properties of the Poincaré map are investigated to show that the Jacobian linearization of the Poincaré map takes a triangular form. This demonstrates the nonlinear separation principle for periodic orbits. In particular, the exponential stabilization of hybrid periodic orbits under dynamic output feedback control can be achieved by solving separate eigenvalue placement problems for the nonlinear state feedback and the observer. The paper then solves the state feedback and observer design problems by employing an iterative algorithm based on a sequence of optimization problems involving bilinear and linear matrix inequalities. The theoretical results are confirmed by designing a nonlinear observer-based output feedback controller for underactuated walking of a 3D humanoid model with 18 state variables, 54 state feedback parameters, and 271 observer parameters.

Additional Information

© 2018 AACC. This material is based upon work supported by the National Science Foundation under Grant Number 1637704. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NSF. R. D. Gregg holds a Career Award at the Scientific Interface from the Burroughs Wellcome Fund.

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023