A Passive 2-DOF Walker: Hunting for Gaits Using Virtual Holonomic Constraints

A planar compass-like biped on a shallow slope is one of the simplest models of a passive walker. It is a 2-degree-of-freedom (DOF) impulsive mechanical system that is known to possess periodic solutions reminiscent of human walking. Finding such solutions is a challenging computational task that ha...

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Bibliographic Details
Published in:IEEE transactions on robotics 2009-10, Vol.25 (5), p.1202-1208
Main Authors: Freidovich, L.B., Mettin, U., Shiriaev, A.S., Spong, M.W.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Compasses
Computer science
control theory
systems
Control system synthesis
Control theory. Systems
Differential equations
Dynamics
Exact sciences and technology
Gait
Humans
Legged locomotion
Limit cycles
Mathematical models
Mechanical systems
Motion control
Physics
Regulators
Robot control
Robot kinematics
Robotics
State-space methods
underactuated mechanical systems
virtual holonomic constraints
Walking
walking robots
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Summary:A planar compass-like biped on a shallow slope is one of the simplest models of a passive walker. It is a 2-degree-of-freedom (DOF) impulsive mechanical system that is known to possess periodic solutions reminiscent of human walking. Finding such solutions is a challenging computational task that has attracted many researchers who are motivated by various aspects of passive and active dynamic walking. We propose a new approach to find stable as well as unstable hybrid limit cycles without integrating the full set of differential equations and, at the same time, without approximating the dynamics. The procedure exploits a time-independent representation of a possible periodic solution via a virtual holonomic constraint. The description of the limit cycle obtained in this way is useful for the analysis and characterization of passive gaits as well as for design of regulators to achieve gaits with the smallest required control efforts. Some insights into the notion of hybrid zero dynamics, which are related to such a description, are presented as well.
ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2009.2028757