Stability analysis and control for bipedal locomotion using energy methods

Moon, Jae-Sung

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https://hdl.handle.net/2142/24253 Copy

Description

Title

Stability analysis and control for bipedal locomotion using energy methods

Author(s)

Moon, Jae-Sung

Issue Date

2011-05-25T15:01:54Z

Director of Research (if dissertation) or Advisor (if thesis)

Spong, Mark W.

Doctoral Committee Chair(s)

Stipanović, Dušan M.

Committee Member(s)

• Spong, Mark W.
• Hsiao-Wecksler, Elizabeth T.
• Hutchinson, Seth A.
• Sreenivas, Ramavarapu S.

Department of Study

Industrial&Enterprise Sys Eng

Discipline

Systems & Entrepreneurial Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Passive dynamic walking
• Bipedal locomotion
• Walking robots
• Energy portrait analysis
• Multiple switching control
• Bifurcations and chaos
• Gait asymmetries
• Six stages of bifurcations

Abstract

In this thesis, we investigate the stability of limit cycles of passive dynamic walking. The formation process of the limit cycles is approached from the view of energy interaction. We introduce for the first time the notion of the energy portrait analysis originated from the phase portrait. The energy plane is spanned by the total energy of the system and its derivative, and different energy trajectories represent the energy portrait in the plane. One of the advantages of this method is that the stability of the limit cycles can be easily shown in a 2D plane regardless of the dimension of the system. The energy portrait of passive dynamic walking reveals that the limit cycles are formed by the interaction between energy loss and energy gain during each cycle, and they are equal at equilibria in the energy plane. In addition, the energy portrait is exploited to examine the existence of semi-passive limit cycles generated using the energy supply only at the take-off phase. It is shown that the energy interaction at the ground contact compensates for the energy supply, which makes the total energy invariant yielding limit cycles. This result means that new limit cycles can be generated according to the energy supply without changing the ground slope, and level ground walking, whose energy gain at the contact phase is always zero, can be achieved without actuation during the swing phase. We design multiple switching controllers by virtue of this property to increase the basin of attraction. Multiple limit cycles are linearized using the Poincare map method, and the feedback gains are computed taking into account the robustness and actuator saturation. Once a trajectory diverges from a basin of attraction, we switch the current controller to one that includes the trajectory in its basin of attraction. Numerical simulations confirm that a set of limit cycles can be used to increase the basin of attraction further by switching the controllers one after another. To enhance our knowledge of the limit cycles, we performed sophisticated simulations and found all stable and unstable limit cycles from the various ground slopes not only for the symmetric legs but also for the unequal legs that cause gait asymmetries. As a result, we present a novel classification of the passive limit cycles showing six distinct groups that are consecutive and cyclical.

Graduation Semester

2011-05

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http://hdl.handle.net/2142/24253

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Copyright 2010 Jae-Sung Moon

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