Title:
Time Dependent Control Lyapunov Functions and Hybrid Zero Dynamics for Stable Robotic Locomotion
Time Dependent Control Lyapunov Functions and Hybrid Zero Dynamics for Stable Robotic Locomotion
Author(s)
Kolathaya, Shishir
Hereid, Ayonga
Ames, Aaron D.
Hereid, Ayonga
Ames, Aaron D.
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Abstract
Implementing state-based parameterized periodic
trajectories on complex robotic systems, e.g., humanoid robots,
can lead to instability due to sensor noise exacerbated by
dynamic movements. As a means of understanding this phenomenon,
and motivated by field testing on the humanoid
robot DURUS, this paper presents sufficient conditions for the
boundedness of hybrid periodic orbits (i.e., boundedness of
walking gaits) for time dependent control Lyapunov functions.
In particular, this paper considers virtual constraints that
yield hybrid zero dynamics with desired outputs that are a
function of time or a state-based phase variable. If the difference
between the phase variable and time is bounded, we establish
exponential boundedness to the zero dynamics surface. These
results are extended to hybrid dynamical systems, establishing
exponential boundedness of hybrid periodic orbits, i.e., we
show that stable walking can be achieved through time-based
implementations of state-based virtual constraints. These results
are verified on the bipedal humanoid robot DURUS both in
simulation and experimentally; it is demonstrated that a close
match between time based tracking and state based tracking
can be achieved as long as there is a close match between the
time and phase based desired output trajectories.
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Date Issued
2016-07
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Proceedings