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Addressed Leila's comments.
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moorepants committed Oct 3, 2024
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\usepackage{amsmath}
\usepackage{booktabs} % nice tables
\usepackage[margin=25mm]{geometry}
\usepackage[natbib=true,style=numeric,sorting=none]{biblatex}
\usepackage[natbib=true,style=numeric,sorting=none,giveninits=true]{biblatex}
% NOTE : this file is automatically generated from Zotero, do not edit
% manually!
\addbibresource{references.bib}
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\abstract{
Uncontrolled bicycles are generally unstable at low speeds. We add an
automatically controlled steering motor to a consumer electric bicycle that
has a stabilizing effect down to about 4~\si{\kph}. We hypothesize that a
stabilized bicycle will reduce the probability of falling. To test the
stabilizes the riderless bicycle down to about 3~\si{\kph}. We hypothesize
that a stabilized bicycle will reduce the probability of falling. To test the
motor's possible assistance during falls, we apply varying magnitude external
handlebar perturbations to twenty-six participants who rode on a treadmill
with the balance assist system activated and deactivated. The probability of
recovering from a handlebar perturbation significantly increases when the
balance assist is activated at a travel speed of 6~\si{\kph}. This positive
effect is most prominent at and around the individual riders' perturbation
resistance threshold. We conclude that use of a balance assist system in real
world bicycling would reduce the number of falls that occur near riders'
control authority limits.
with the balance assist system both activated and deactivated. The
probability of recovering from a handlebar perturbation significantly
increases when the balance assist is activated at a travel speed of
6~\si{\kph}. This positive effect is most prominent at and around the
individual riders' perturbation resistance threshold. We conclude that use of
a balance assist system in real world bicycling would reduce the number of
falls that occur near riders' control authority limits.
}

\section*{Affliation}
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Correspondence: [email protected]

\section*{Keywords}
bicycle, fall, prevention, automatic control, stability
bicycle, fall prevention, automatic control, stability

\section*{Highlights}
%
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successfully demonstrated balancing a robotic bicycle on a treadmill with both
steering control and a laterally moving mass. \citet{Ruijs1986} followed this
breakthrough by demonstrating an automatically balanced motorcycle and they did
so solely with a steering motor. Ruijs and Pacejka clearly showed that steer
torque driven by roll angle feedback stabilizes the capsize mode, by roll
angular rate feedback stabilizes the weave mode, and by steer angular rate
feedback stabilizes the wobble mode.~\footnote{These motorcycle (and bicycle)
eigenmodes are defined in \citep{Sharp1971}.} They also showed how the control
gains must change with respect to vehicle speed for favorable control across
all speeds. This roll motion feedback enables the simplest controller that can
stabilize a single-track vehicle above a minimum speed when one is not
concerned with wobble instabilities. But Ruijs and Pacejka's work was not
particularly concerned with low speed stability and their vehicle was fully
automatic, i.e no human rider was involved.
so solely with a steering motor. Ruijs and Pacejka showed that steer torque
driven by roll angle feedback stabilizes the capsize mode, by roll angular rate
feedback stabilizes the weave mode, and by steer angular rate feedback
stabilizes the wobble mode.~\footnote{These motorcycle (and bicycle) eigenmodes
are defined in \citep{Sharp1971}.} They also showed how the control gains must
change with respect to vehicle speed for favorable control across all speeds.
This roll motion feedback enables the simplest controller that can stabilize a
single-track vehicle above a minimum speed when one is not concerned with
wobble instabilities. But Ruijs and Pacejka's work was not particularly
concerned with low speed stability and their vehicle was fully automatic, i.e
no human rider was involved.

Many more automatically balanced single-track vehicles have been demonstrated
over the last 40 years, but none have demonstrated that increasing low speed
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Participants wore a helmet and they were attached to the ceiling via a fall
safety harness, Figure~\ref{fig:participant-in-set-up}. The harness allowed
free movement pre-fall. The participants practiced riding on the treadmill
until they indicated they were comfortable enough to have perturbations
applied. For most, this was less than a 10~\si{\minute} warm up. We then asked
the rider to ride for 90~\si{\second}, while attempting to maintain the
location of their front wheel on the center line of the treadmill as a baseline
measure before the perturbations. We then applied perturbations in random
directions (clockwise or counter-clockwise), starting at 20~\si{\newton} and
increasing the magnitude by 30~\si{\newton} until the participants fell. We
defined a ``fall'' on the treadmill by two criteria: 1) the rider removes their
foot from the pedal and places it on the ground or 2) the bicycle wheel exceeds
the width of the treadmill belt. Figure~\ref{fig:perturbation-sequence} shows
an example resulting motion from a perturbation. We logged the force magnitude
that caused the first fall to characterize that participant's
\emph{perturbation resistance threshold}.
natural free movement pre-fall. The participants practiced riding on the
treadmill until they indicated they were comfortable enough to have
perturbations applied. For most, this was less than a 10~\si{\minute} warm up.
We then asked the rider to ride for 90~\si{\second}, while attempting to
maintain the location of their front wheel on the center line of the treadmill
as a baseline measure before the perturbations. We then applied perturbations
in random directions (clockwise or counter-clockwise), starting at
20~\si{\newton} and increasing the magnitude by 30~\si{\newton} until the
participants fell. We defined a ``fall'' on the treadmill by two criteria: 1)
the rider removes their foot from the pedal and places it on the ground or 2)
the bicycle wheel exceeds the width of the treadmill belt.
Figure~\ref{fig:perturbation-sequence} shows an example resulting motion from a
perturbation. We logged the force magnitude that caused the first fall to
characterize that participant's \emph{perturbation resistance threshold}.
%
\begin{figure}
\centering
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At 6~\si{\kph} the riders could often recover in the allotted treadmill width
due to the smaller lateral deviations. We believe our results are very much
dependent on the two modes of falling, i.e. exit the treadmill width or foot is
placed on the belt. On the other hand, Cycle paths are a similar width as the
placed on the belt. On the other hand, cycle paths are a similar width as the
treadmill, so rider's are often limited in width when recovering from a fall
thus exiting the treadmill width may be an appropriate measure for indicating a
fall.
fall. While the treadmill simulates narrow cycle paths, real-world paths may
offer more lateral recovery space, providing riders with additional
opportunities to regain balance after a perturbation. However, testing in such
narrow conditions is still highly relevant, as system design and validation
should focus on extreme conditions like narrow paths, because even in wider
paths, obstacles such as parked cars or barriers can limit lateral space.

\subsection{On Rider Bicycling Skill and Experience}
%
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