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Reduced Order Model Inspired Robotic Bipedal Walking: A Step-to-step Dynamics Approximation based Approach


Xiong, Xiaobin (2021) Reduced Order Model Inspired Robotic Bipedal Walking: A Step-to-step Dynamics Approximation based Approach. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/9bz9-x102.


Controlling bipedal robotic walking is a challenging task. The dynamics is hybrid, nonlinear, high-dimensional, and typically underactuated. Complex physical constraints have to be satisfied in the walking generation. The stability in terms of not-falling is also hard to be encoded in the walking synthesis. Canonical approaches for enabling robotic walking typically rely on large-scale trajectory optimizations for generating optimal periodic behaviors on the full-dimensional model of the system; then the stabilities of the controlled behaviors are analyzed through the numerically derived Poincaré maps. This full-dimensional periodic behavior based synthesis, despite being theoretically rigorous, suffers from several disadvantages. The trajectory optimization problem is computationally challenging to solve. Non-trivial expert-tuning is required on the cost, constraints, and initial conditions to avoid infeasibilities and local optimality. It is cumbersome for realizing non-periodical behaviors, and the synthesized walking can be sensitive to model uncertainties.

In this thesis, we propose an alternative approach of walking synthesis that is based on reduced order modeling and dynamics approximation. We formulate a discrete step-to-step (S2S) dynamics of walking, where the step size is treated as the control input to stabilize the pre-impact horizontal center of mass (COM) state of the robot. Stepping planning thus is converted into a feedback control problem. To effectively and efficiently solve this feedback stepping planning problem, an underactuated Hybrid Linear Inverted Pendulum (H-LIP) model is proposed to approximate the dynamics of underactuated bipedal walking; the linear S2S dynamics of the H-LIP then approximates the robot S2S dynamics. The H-LIP based stepping controller is hence utilized to plan the desired step sizes on the robot to control its pre-impact horizontal COM state. Stable walking behaviors are consequently generating by realizing the desired step size in the output construction and stabilizing the output via optimization-based controllers. We evaluate this approach successfully on several bipedal walking systems with an increase in the system complexity: a planar five-linkage walker AMBER, an actuated version of the Spring Loaded Inverted Pendulum (aSLIP) in both 2D and 3D, and finally the 3D underactuated robot Cassie. The generated dynamic walking behaviors on these systems are shown to be highly versatile and robust. Furthermore, we show that this approach can be effectively extended to realizing more complex walking tasks such as global trajectory tracking and walking on rough terrain.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Bipedal robots; reduced order model; step-to-step dynamics; walking synthesis; feedback control;
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ames, Aaron D.
Thesis Committee:
  • Burdick, Joel Wakeman (chair)
  • Murray, Richard M.
  • Sreenath, Koushil
  • Ames, Aaron D.
Defense Date:25 May 2021
Non-Caltech Author Email:xiaobinisawesome (AT)
Funding AgencyGrant Number
Record Number:CaltechTHESIS:06022021-035141903
Persistent URL:
Related URLs:
URLURL TypeDescription
https://xiaobinxiong.infoAuthorPersonal website adapted for Chapter 6 and 10 adapted for Chapter 6 and 9 adapted for Chapter 7 adapted for Chapter 11 adapted for Chapter 3, 4, 7, 8 and 12 adapted for Chapter 9 B A
Xiong, Xiaobin0000-0002-6275-3900
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14230
Deposited By: Xiaobin Xiong
Deposited On:04 Jun 2021 18:31
Last Modified:11 Jun 2021 15:49

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