It is a.

Distinct pleasure for me to be
introducing and welcoming her to this for

you know what's good for us to do good
days I'm really happy and all Irish.

You know we're trying to leave.

Off with all the audience strong.

Feelings for the robot the boy systems
of today we're going to be free

to have Cyber a human interactions
with a good first thing.

Rather than the border a lot of the stuff
that goes on here on campus who are.

Not only looks at cyber human systems but
the U.S.

is really a not only a control
guy at heart as far as I know

meaning is higher has been the norm in
your control think he's throughout my

career we've been able being
various incarnations all

the water systems all the way from when he
was a fifty two students he got a Ph D.

from.

A class a university and.

He already cracked something small I
feel guilty for years morning but.

I think her birthday.

That happily graduated went to all group
stuff a lot and I think that he went to

University of Florida going back to the
data golden era phase the part where he's

basically go through the ranks and
he's now a and then doubtful professor in.

This department and his work has been
both practically relevant theoretically

elegance is one of the few people that
truly can struggle this finds in the fact

that matter in his work has been highly
recognized and rewarded correctly so so

I got tired of reading his bio
because they're worth every If he

is a fellow told tales of the I
simply this one the future.

More.

Yes a career of more science from
the early career of the work for

all that I see a lot of.

US will still call the commanders
of the service of war.

US Air Force so that's where the salt
really got going ordered field by.

And in fact this is more of committees
vote only with resources but from the.

Always when I feel that I got to do
that I look at it when I go yeah

why it won't work because
you see me is ridiculous.

When he sleeps we don't know you
know he never shapes nobody.

This is a more rugged us a little bit more
of we're delighted to have you there for

sure thanks for having us it's a real
pleasure to be here in fact today's talk.

In some ways has its roots here in Atlanta
when I worked at National Laboratory

we were doing a lot of some of
the early days exoskeleton work and.

I imagined how exoskeletons could
be used for rehabilitation and

I took it from a very naive
roboticists approach where

hey robots can do things more repetitive
and more precise than people can.

And it's a lot of physical labor for
physical therapist to move the limbs of

people to do physical therapy so why can't
we just replace the physical therapist for

the robot and I visited
the Shepherd Center here in Atlanta

because it's one of the largest
rehab centers in the Southeast and

I was in mightn't how naive that
impression of physical therapy was and

that there will always be a person
in the loop a physical therapist in

the loop there because of
the interactions with the person.

And also with.

The exoskeleton work at the time having
a small portable power supply was

really one of the limiting factors for
having soldiers

carry three hundred pound packs and sprint
through the mountains of Afghanistan.

And that was part of my motivation for
looking at rehabilitation because you

could be in a lab and
just tethered to the wall.

But was it a Shepherd Center I saw for

the first time muscle stimulation and
it instantly dawned on me while

we are to have nature's power plant
right there waiting for us to use.

Its low power we eat you know just
give us soldiers some to read O's and

then they've got the fuel that they
need to to actuate their muscles and

then I saw the rehabilitation
aspect of it and.

From that experience here at
the Shepherd Center in Atlanta I then

wrote my career proposal almost topic and
I've been working on it ever since so

in some ways my trip to
the Shepherd Center really inspired.

The initial development in the Syria.

I want to think my students first and

foremost because really it's their
creative ideas and hard labor

I actually do get a lot of sleep as these
guys who don't get to sleep very much.

And I give a lot of credit to these
guys we've had a number of formal

muscle guys in the group who have
gone on to faculty positions

several of them have started their
companies one of the companies has been

they've received some multi-million
dollar buyout offers and

they've said no which I think
is crazy great for them.

And so it's been a real success for
me or pleasure for

me to kind of see people who work in this
area go on to do great things as well and

so this is my current group of students
some of which work on this problem others

of which work on some other problems.

That's new.

The different colored T.

shirts don't mean anything it's
just some people want to blue and

some people want to black ones.

I don't know what's happening with my
second slide here seconds ago it was fine

would move on past that it basically was
just showing what is muscle stimulation

and if you if you've watched late night
T.V. And you've seen these as seen on T.V.

ads where you apply stimulation
to a muscle it'll contract.

I don't know necessarily to give
you the six pack abs it certainly

I don't own one but I don't think it
would have helped in my case anyway.

But it is a commonly
clinically prescribed.

Rehabilitative treatment and.

And that's exactly it you apply
a potential across a muscle and

it will contract and so
this whole art of closed loop control

of the muscle is how to intelligently
stimulate the muscle so

that actuates the limb and
moves the limb in a desired way.

There are a number of challenges
associated with this from the controls

community and while the clinical community
has been doing muscle stimulation for

one hundred years the controls community
really hasn't embraced it until

maybe the last twenty years and
even there it's really been

the adoption of controls
tools without necessarily

understanding the underpinnings of
those tools in order to kind of use

them maybe in the most optimal way or
to develop them further and

so whenever I give this talk I really
it's really a call to arms for

people from the control systems
robotics background to maybe

think about this is an application that
application outlet for your research.

So in the upper videos.

See that the muscle contracts differently
depending on what frequency worse

we're stimulating it at this video seen
on the left seems to stop playing but

you probably saw it bumping around that
was if you had a low frequency you could

actually see the low frequency stimulation
in the right approach most video this

is a higher frequency stimulation was just
a constant contraction we'll talk a little

bit more about that later and then in
this bottom picture which will also talk

about later you see the geometry of
the muscle changed quite a bit so

where you may have electrodes placed and
you stimulate when the arms at

a certain angle at a different angle the
muscle has moved and now you're going to

get a different response from the muscle
and so how can we compensate for that.

Muscles are inherently nonlinear and
dynamic systems they

also have a large number of uncertainties
associated with them my muscles and

your muscles will be very different
to have a different response to them.

It's a function of your hydration of
the person the fat content of the person

different people have different muscle
fiber types are different compositions

of muscle fiber types some people are more

inclined to sprinter muscles some people
are more inclined to more marathon muscle.

And so and the muscle fatigue is very
rapidly when we externally stimulate

it one of the questions that people often
have is well are you stimulating it like

the brain stimulates it and we can't
because the nervous system innervates

the muscle fibers in a way that
we just don't have access to so

we we don't have access to the individual
muscle fibers to stimulate them in a way

that would would be akin to
the way the brain would do it and

we don't know the brain
knows when it stimulating.

Marathon muscle fibers versus sprinter
muscle fibers for example and

we wouldn't have that information so
when I talk to school kids

you know describe this is we just put
stickers on your legs and then re and.

Enable your legs to do things and
especially for

kids who have spinal cord injuries or
a variety of neurological disorders

these stickers can and they will them
to do things they couldn't before.

And so based on the fact that.

Muscle fatigue rapidly because of the way
that we have to externally stimulate

them the fact that there's the sense
certainties the fact that there is these

non-linearities.

And other factors that we'll get into in
a few moments these cause real fundamental

challenges for
us to examine from a controls perspective

So some interesting questions that
come up when thinking about this area

more from a controls a control
systems perspective some of the things

that we've been thinking about in my lab
are how do we develop an overall stable

subsystem when we switch between modes
where we're controlling a person and

when we're not controlling a person or
when we are controlling the system

the stabilize the ball and a system that
is unstable and we want to be unstable so

so developing controllers for
that is is a question.

If we're switching between controlled
systems and uncontrolled systems for

those of you who are maybe familiar
with hybrid systems theory and

those that that means you have to develop
as well time for how long you spend in

the controlled system versus how long
you spend in the uncontrolled system and

to develop these these twelve times you
have to know how fast you converge but

what happens when you want to use adaptive
control for example because adaptive

control is really amenable to this kind of
problem because we want to compensate for

the uncertainties in the system but
with adaptive control you typically

are dealing with a non
strictly optimal function and

you don't know how fast you converge
you're just converging asymptotically So

how do you develop a time when you're
only converging asymptotically.

How can you and
how can you compensate for.

Uncertain input delays I'll talk
about that problem in just a moment.

And a recent thing that we've been
thinking about is is as a human

robot system two different systems that
are interconnected in some way and

if so then maybe passive a theory is the
best way to look at those kind of problems

where you want the robot to be passive
with respect to the human for example or

is the human robot system one continuous
time Amec system that just has

a logical switches between the two and
in that case maybe hybrids which systems

theory is the best theories to kind
of approach the problem from and

we're kind of looking at it from both
perspectives and exploring the pluses and

minuses of both of those and
then related to the functional

electrical stimulation question and
functional stimulation

is when you're applying electric field
to do a functional Pasch like cycling or

bicep curls or those kinds of things
that you'll see in the presentation.

And.

Traditionally electrical stimulation
was applied as a means to just

build the muscle mass or to keep the
muscle from atrophying you just don't want

the muscle mass to decay because of disuse
and that was fine you can use open loop

stimulation trains and you can put the
muscle under load and you can do that but

if you want coordinated limb motions
to perform functional tasks and

modern rehabilitation theory has shown
that if you can do a repetitive task

with some cueing that that
helps the neural system.

Reestablish itself and
achieve was called neural plasticity.

And so in order to achieve those kind of
gains we want to be able to not fatigue.

The muscle purposely just to build
muscle mass now fatigue is our enemy and

we want to be able to prolong
the experiment as long as possible so

how can we come up with new
stimulation methods to maybe offset.

The muscle fatigue that happens.

Also you want to maximize
the person's contribution and

there are a lot of rehabilitation robots
that are out there exit Skelton's and

others where the person is strapped to
a robot the robot moves around the person

can take a nap or watch T.V. and
just have their muscles moving around and

that's not very beneficial others there
are rehabilitation cycles where there's

a motor that keeps the the desired cadence
all the time and we have people who

work out on those cycles and then try and
do experiments in our lab they'll come and

tell well we maximize our T three
hundred I mean we I do train on that all

the time but unfortunately they're being
duped by the fact that the motor is doing

all the work they're not really doing
the work and they come in our lab and

we're really making their muscles do
the work all the sudden there's a sense of

disappointment because they understand
that before it wasn't their muscles

that was doing the work it was really
the machine that was doing all the work so

we're really interested in questions
like How can we maximize the person's

active participation in the therapy and
then you know we've now gotten to

a point where we've done experiments on
a wide range of people with a wide range

of neurological conditions and some people
are hypersensitive to the stimulation

I mean you get near an electric field and
they say this is pins and needles and

I can't stand it and then there's just no
way you're going to produce enough torque

to do anything then you get to
other people who they just say you

know give me as much as possible it
doesn't hurt in fact it's kind of a.

Kind of sensation you know and
and I'm doing these things

that's cool Give me give me you know
increases stimulation some people.

Have Different their conditions cause
their muscles to behave in a different way

so we're kind of thinking of things now
different torte production capabilities

for example some people have a lot of fat
content compared to their muscle to their

their muscle fibers some people have have
been long past their their injury and

they just don't have the capabilities that
they do compared to someone who's just

recent past an injury for example and so
we're now looking out talk to this about

I'll talk about this at the end of the
presentation on how can we accommodate for

these changes in a person and how can
we set it up to allow the person to do

whatever they can do which is kind
of coupled to the second question so

maximizing what they can do but then.

Building in allowances for
what they can't do.

So.

Since we're controls and robotics people
have the slide which is basically two sets

of dynamics that are involved here one
is the body segment on dynamics this is

simple mass times acceleration kind
of stuff or arranged dynamics and

then you also have actually dynamics this
is the electro chemical process that

some bald there's only like
phenomenological models for

how the application of
electric field causes chemical

changes causes the production of
force within the muscle fibers.

So some of the phenomena that happen in
there there are delays that are involved

there nonlinear recruitment curves for
how the muscle will start to contract

there's fatigue so you can think
of that as as a state dependent or

time dependent controlled influence
matrix if you will whereas over

time you have less ability as the muscle
fatigues the same input is less output.

There are calcium dynamics
that kind of are involved.

In this whole process with fatigue and
the generation of force and so

we we have both sets of dynamics that

are in play here when we're when we're
doing muscle stimulation one of those.

Things that talked about was the way and
when you apply an electric field and

you're expecting you know I apply my
input I want to output immediately but

there is this complex electrochemical
process that happens in their body

that causes the torque production and
that yields this delay and

the delay is on the order of like fifty
to eighty milliseconds which may or

may not sound a lot to you depending
on your application field but

I'll show you that it does
make a difference in people.

And so this is an input delay and

input the Lays are an area that
as a non-linear systems community

there's still a lot of open questions and
the problem is if you think about

strategically if you know there's going
to be a delay in the system well what can

you do about it well as an engineer you
would say OK well I'm just going to.

Give the input now that
I want to have happen T.

seconds later where T.

is the lay in the process so
that then after the delay the control

I want to apply happens at that time which
is exactly the strategy everyone uses

However if you have a linear system and
you can predict how long it delays going

to be because it's a linear system great
then you can do that but what happens if

it's a non-linear system and what happens
if it's an uncertain on the your system it

becomes much more complicated to predict
when that delay is going to happen and

in fact we found out through some
experiments studies in our lab that as

your muscle fatigues that
delay gets larger Right so

not only is it a uncertain delay
in a non-linear system but

it also changes in time and so.

That becomes a very complicated for
get muscles in the application domain

that's a very complicated problem just
from the calls at the vexed he kind of.

Examination.

So we've developed some controllers
this is basically a component here and

then this term is an interview
all over the past and

puts And one of the I guess
interesting things that we did is that

we integrate over a window
where we don't know that.

You would want to integrate over
the window of the length of the delay

in the system but
we don't know the delay in the system so

we're just approximating that
delay with some estimate.

And we were able to show.

That we have exponential
convergence to a residual error

whenever we use these kind of controllers.

Here's the lead up on our function for
those controllers so

you can see that we have some standard
sum of squares kind of terms in there but

then we have some other These are
typically referred to as a functionals but

there's a lot of innovation that comes
in the design of these OK functionals in

order to compensate or

to enable us to design the controllers
that can compensate for that delay.

Here our experiment results where we
implemented so the controller is a P.D.

controller plus a still a compensation
term and if we implement the P.D.

controller you see a lot of bumpy behavior
it's not it's not very smooth and

the errors are you know they're getting
to like fifteen degrees of error whereas

if we implement the exact same controller
on the same person with the same control

gains everything's held the same except
for now we turn on the delayed compensator

term now you see a much smoother
behavior by the controller the errors

are much less the him put to
the muscle is much smoother and.

What it means in practice so
this is an example of US applying the P.D.

controller without the delay
compensator and you see this jerky

horrible this is an unstable behavior
really it's not comfortable either by

the way because you're going to shocked
shocked shocked in a very sporadic way.

Whereas same person saying gains same
everything we just turn on the delay

compensation term for this simple you know
fifty to eighty millisecond delay and

now you look nice smooth contractions
which are also much more comfortable

they also fatigue the muscle much less and

we get much better behavior as we stall
in those plots earlier so it really does.

Make a difference in the application.

We also are are looking at ways
to adaptively compensate for

the delay in the previous work we had
a robust strategy to compensate for

that on certain input delay here
we're using a neural network we turn

it into a partial differential
equation where the delay is a spatial

variable is transformed into a spatial
variable and we do control on that.

You also see kind of a sum of squares
terms some neural network adaptation

terms and then here's our functional
which again there was a lot of

innovation that came into the design of
a functional the compensate for the delay.

And then we've implemented that and
we also get some nice results where we're

actively compensating for
the uncertain delay.

And we've been working on that area for
quite some time but

I want to move on to some some other
characteristics here is a is a reasonably

good plot that describes muscle fatigue so
in this I'm giving the same inputs

throughout this three hundred second
window but the axis on the left.

It is torque output and you can see you
know initially we were getting twenty five

meters of torque but by the end we were
getting like fifteen meters of torque So

this is the time varying
control influence if you

will that's due to the muscle fatigue and
we want

to stimulate the muscle at a high enough
frequency to get a smooth contraction.

But the higher we stimulate the muscle
the more rapidly we fatigue the muscle.

And so what are some strategies that
we can employ to get good results and

effectively get high
stimulation frequencies but

not fatigue the muscle as quickly.

And one idea is this idea of asynchronous
stimulation so in a conventional

single channel stimulation you know we
would descend a pulse train to the muscle.

But the idea between asynchronous
stimulation is to spatially divide that

channel up across the leg so here is
someone who has a spinal cord injury and

they have a single channel electrode So
just one stimulation Pad

whereas here we have
multiple channels set up and

we break this effective amount of energy
up across different muscle fibers and

there's going to be some crossover Yes but
we at least try to

spatially distribute the energy
that we're putting in and

the idea there is that you reduce
the duty cycle that individual muscle

fibers would receive but you're still
these effectively of the same amount

of energy is just distributed across
multiple inputs and these are some

experiments done on individuals with
spinal cord injury these are error bars so

you can see the results are pretty tight
pretty pretty consistent in fact and

the black curve is one where we stimulated
a high frequency with the standard thing.

Channel and that's comparable to
the red curve which is the same

effective stimulation frequency but
distributed asynchronously and

then the blue is the asynchronous curve
that corresponds to the green one and so

you can see the difference between almost
exponential fatigue versus almost linear

fatigue so that's a big deal for someone
because and is statistically significant

across a number of subjects that's
what the slide shows the time

for fatigue when you compare
conventional like sixteen seconds mean

in fifty seconds meaning to over one
hundred seconds I mean that's a big deal

in rehabilitation because if I can
extend the number of repetitions that

I do from fifteen seconds worth of
repetitions to one hundred seconds

repetition worth of repetitions the that's
a lot more repetitions for my therapy.

Now in order to do that asynchronous
stimulation I distributed

energy across the number of different
channels and so that means that I am.

I am switching between different actuators
effectively is what's going on and we're

discretely switching across the actual
waiters and so my input is a discrete

input switches from the different
channels and then I have an input

matrix that's also discretely changing
between the different muscle fibers.

In fact let me go ahead and
go to this slide where.

These are the torque out
the torque output per input.

Modulation signal for the different
channels and you can see that not all

channels across or not all spatial
regions across the quadriceps in this

case the same torque output and so
you have to compensate for that as well.

So going back we developed a P.I.
the kind of air system.

This is the.
Open the bear system for that so

you have the non-linear all arranged kind
of dynamics in here a lot of the actuator

dynamics are particular to the muscle or
are captured in some a good term here.

Some terms can be upper bound
by constants others by.

Higher order or
quadratic functions of the state.

And so for this controller we disagree is
a simple sliding mode controller where we

have a discontinuity there and then this
is our resulting closed loop dynamics.

And we were able to show
exponential convergence.

When switching across these different
actuators Now one of the reasons why and

we use the commonly a one off function
to do that and one of the reasons why

we're able to do this is we were always
switching between a stable subsystem

we were just each actuator was
switching but each actuator was

able to stabilize the system and so
that made the problem a bit more simple.

In the stability analysis though because
we have discussed newbies on the right

hand side you know we had a set value
derivative and we went through all

the mathematics in the details of that
in order to get our exponential decay.

And this is an implementation of

the switching across
the different channels of the.

You see it's a nice smooth
contraction even though there is

the switching strategy across
the channels to reduce the fatigue but

we get very nice results when we when
we stimulate the muscle in this way.

In fact the same controller we
implemented with a conventional

single channel on a person same
control gains everything and

then we implement it just by dividing
the channels asynchronously and

here you can see the R.M.S. air goes down.

But then it eventually
creeps up because and

here you can see the air are growing and
the reason for

the error growth is that we're just
not able to have enough energy so

the red curve which is the actual leg
extension the height of the leg extension

doesn't meet our desired blue you
know leg extension trajectory

Whereas when we stimulate asynchronously
you see the error goes down and

it doesn't increase because the muscle
the fatigue over this period of time and

our tracking errors are remaining constant
and we're able to keep the same level

of range of motion because
we're not fatiguing the muscle.

So again and is statistically
significant across a number of subjects

as what that shows So again by using
switch systems theory and using those

ideas to develop enough analysis of the
controller to switch across the muscles we

had a real physical impact in terms
of the in terms of the therapy so

here we also divide the muscle
into a number of channels but for

a different reason and this reason
reason again you can see the muscle

geometry changes significantly
through the range of motion and

if we had static pads which
I mean there static pads.

Then we would really see the effect
of that changing muscle geometry and

so to accommodate for
that we are switching across the different

stimulation paths to different
channels state dependently as

the function of the angle of
the elbow in order to be able to

maximize the torque production
throughout the range of motion and

I have another plot here in a moment but
you can maybe see the different

colors along this plot the different
colors are when we need to switch to.

Different stimulation channels in order

to maximize the contraction
the force by the bicep.

And you can see you see kind of
like some some wiggling there and

it doesn't quite look like a natural
contraction and that's caused by

the electrical stimulation so we wrote one
paper where we had three electrodes and

we were switching discretely across
the different electrodes to try and

maximize the force and so
these were plots of the force

output as a function of
the electrode position and so

over here the blue electrode is going to
give us more force production whereas over

here the green electrode configuration is
going to give us more force production so

we switch across them and then we wrote
a different paper where we blended

the inputs in the time that a channel
could give us some torque that was

above a threshold then we blended that in
with all the channels that could yield

toward production and order to maximize
the torque throughout the range of motion.

But now I want to move
on to cycling which is

predominantly where our
work is moving now.

This person is not cycling on her own

free will I mean her free will is just
that she's going to sit there and

allow us to stimulate her legs and let her
be the be controlled by a computer but

she's just passively sitting there in the
computer is coordinating the stimulation

across the different muscle groups in
order to coordinate her limbs in order to

have this nice cycling trajectory if I
didn't tell you that it was a lie she's

just peddling a bicycle and now imagine
a child who had a spinal cord injury and

is not able to ever ride a bicycle and
then you give them this kind

of technology and all the sudden they're
able to ride a mobile bicycle it is a huge

It's what I love about this field is
that it combines both deep theory.

Challenges as well as
significant outcome and

sense of accomplishment and
impact in people's lives.

In order to yield this kind of cycling

we also have to switch across
different muscle groups.

Because in some parts of the cycle

we would stimulate with our
left leg versus our right leg.

And when we're stimulating with a leg
sometimes we will use our quadriceps more

sometimes the user hamstrings more
sometimes will use our glutes more and

so there are different
regions of the can the magic

date when we would want
to switch to different.

Muscle groups and there's also a part of
the gate basically when when the feet

in the pedals are like this where I can

stimulate the muscle really hard
trying to generate torque but

there's just not a lot of torque to
generate when I'm in this configuration

versus say in this configuration work and
really apply a lot of torque right and so

we don't want to stimulate
the muscle when it's in these non.

Favorable torque producing regions and
so our and

which of these grays shaded areas here so
our options there are just not stimulate

at all and stimulate enough when we can
the kind of get through those regions and

we do that and I'll show you some of that
and then another way to do that is when

I'm in these regions that it's not
fruitful to cause the muscles to

yield the sufficient amount to work well
let's just put a motor in the loop and

let the motor turn but not all the time to
maintain cadence let's just intermittently

use the motor in these regions when
it's not efficient to use the muscle.

So it's a closed loop kinematic chain
you know what angle you know them all.

The dynamics of the system you have
torques produced by the cycle which

are just standard mass times
acceleration kind of things you have to.

Work associated with a rider which is
a passive torque which are kind of all

arranged dynamics you have an active
torque which is due to the electrical

stimulation is also due to the person
what they can voluntarily contribute if

anything and if they can Boy we sure want
them to because that's part of the therapy

and then maybe there's some
disturbances in each of those dynamics.

And so the active torque This is where
we can stimulate the muscles and

we can yield cycling by by inducing
torques through the muscles.

Here you basically see that
we have a switch system again

it'll be state dependent switching across
different muscle groups the right and

left glute squads and hamstrings and

then here is a state dependent again
control influence matrix if you will.

Where we have this torque
transfer ratio this T.M. and

basically if I were in a region where that
tort transfer is above some threshold

then we say that's a region where it's
OK to stimulate that muscle otherwise we

should stimulate that muscle because
it's not going to produce useful torque.

So we set up a switching
scenario between switching

between different muscle
groups within the.

Within the person and that's where we
have our electrical stimulation input and

then if we have a motor in the loop then
we also have a switching condition for

when to cut on the motor or not.

In this one of our first experiments with
cycling our control objective was just

to maintain a desired cadence if you set
your control objective up that way then

you can write your open loop dynamics in
this way with this term I just has a buy.

Of.

Linear non-linear terms in it but they can
all be upper bound by a linear bound and

that turns out to be very
helpful mathematically.

We have again controller and
I'll come back to why all

these controllers aside the controllers
towards the end of the talk.

And we're able to show.

That when we're in the controlled
regions with more stimulating

the muscle where there's no motor
in the loop here we're able to get

exponential convergence that's no surprise
we're using a slide in the controller.

And then when we're in the uncontrolled
regions where we just were just going to

not stimulate the muscle we actually
can have exponential growth and

that's what you see here where this
Lambie use a positive constant and

this exponential growth is actually
due to the fact that we can

upper bound those collection
of terms by a linear beyond.

And here's kind of a plot
of the strategy so

when we are in regions where
we're stimulating the muscle.

Up in our function is convergent and
when we're in regions where we're not

stimulating the muscle then we
can have exponential rise but

as long as we're switching
sufficiently fast.

Then overall the magnitude of our all
the up and all function is detaining and

over all we can decay to

ultimate ball or residual error and
that's just going to

be the be the case always because if
you're switching to regions where you're

not controlling it all you're always going
to have some amount of growth and so

you're always going to have this
residual amount of error every cycle.

And because we're switching between
a stable controlled system and an unstable

uncontrolled system we have to develop
a time and that's what this condition.

Here is which just says that based on
how fast we converge when we're in

the controlled region and how fast we blow
up when we're in the uncontrolled region.

And given ratios of the amount of time
that were in those regions you can develop

this overall region which says you
have to converge at least this fast

given knowledge of how long you're going
to spin each of those regions OK So

this is how a typical
to all time condition.

So we did experiments on
a number of different people

this is a healthy normal person and
again it looks like they're peddling

by themselves but but
the machine is entirely paddling for

them in fact sometimes we get
people in with disabilities or

neurological conditions and
they're just so eager to help and

to like calls this thing to work that
they will they will try to control early

on when we were naive in and told them
just let the machine do everything I let

let let us to me let your muscles in the
appropriate way they would try to sneak in

some contribution but we could instantly
tell when they were doing that and

in fact it would it would kind of
disturb things which calls us to rethink

the way we approach the problem which our
show you and some of the later stuff so

we had that just cadence
tracking objective.

We had this weird D.C. offset in our
cadence is always behind a little bit and

so and this picture just shows
how we in one crank cycle how we

distribute between switching between
the different muscle groups and

this is what it looks like with
the whole thing normal person.

Then when we stimulated someone
with Parkinson's disease.

One of the effects of their
disease is that they were hyper

sensitive to the stimulation so much so

that we could not stimulate
them enough to generate enough.

Work for then be able to cycle and so
with this person when we stimulate our

healthy normals they don't know the desire
to inject or they don't see any plots or

anything we usually try to talk with
them and distract them in fact but

when this person could not just couldn't
tolerate the amount of energy that we

needed to put in to generate enough
torque we showed him the trajectory and

we said try to pedal and
try to contribute so

that you know you are producing
some contributive torque so

we don't have to stimulate you so
hard and we did that he was able

when he was contributing also there
was no D.C. offset these gray boxes or

when we also added in a lot of we
changed gears on the bike basically on

the fly and so it made it harder to paddle
but you didn't really see too much of

an effect on the error you see there's a
little bit more energy that has to go and

overcome the added resistance but here's
someone with Parkinson's disease and

you can tell that this side
of his body was affected and

you can see these curves look very
some water to the person that's

the healthy normal control but but

these curves look very different from
from the standard healthy normal.

So when we compare you know what
how good can you do right so

we had people volitionally pedal
you see that is our trajectory.

You see your desired actual and you try
to peddle the best you can to minimize

the air and healthy normals they
could get to you know less than two

to R.P.M.'s of air with about in
a desire to carry about fifty R.P.M..

And with electrical stimulation
with them doing nothing

we were a lie you know five plus or
minus two rpm so

he looks pretty good these are pretty
reasonable results as far as it goes.

But then when we look at the person
with Parkinson's disease.

It turns out they can also tell
pretty good because you can cheat and

you can one legged paddle right and
so kind of one legged paddling or

just doing the best he could possibly do.

It wasn't as good as the healthy
normal but it wasn't too bad but

then when we took what he
could do voluntarily and

we added in the electrical stimulation
on top of it I mean that's that's

a pretty nice we can improve his ability
to pedal when we're simultaneously

stimulating him so that was kind of
a nice result then we changed the control

checked it to a position and velocity
control objective now these terms in this

bucket here now it contains some quadratic
terms so we're not able to upper bound

those linearly anymore we still use
controller to control the muscles

in the controlled regions we still
get exponential stability but

in the uncontrolled regions now because
of those quadratic terms this quadratic

nonlinearities now we have
faster than exponential growth

OK so this calls a lot of
mathematics to have to deal with

time conditions have things like
natural logs of tangent functions.

But really what it meant at the end
of the day is the same scenario but

because the escape is faster we
just have to be more aggressive

in our convergence when we're
in the controlled regions and

we can do well less time and
uncontrolled regions.

And again we converge to a ball and

there's a lot of mathematics to
dictate the size of the ball.

And when we change the control objective
it made the math a lot harder but

then the results are better now
we don't have these D.C. offset.

Anymore in when we have our our
people do the experiments so

we still get you know within
five R.P.M.'s of error but

no D.C.
offset then we did experiments where we

added in the motor so so
now our open loop dynamics

contain both the electrical stimulation
input and the motor and put.

And then we have switching conditions for
the electrical stimulation we

have electrical stimuli we have
a switch in conditions for the motor.

And now we just always get
exponential stability why because

now there is no uncontrolled regions in
the more because either we are controlling

it through the muscle or we're controlling
it through the machine either way we're

just converging converging converging so
in this way we were able to get

overall exponential convergence and here's
a picture of a strategy so now there's

no uncontrolled region where we have
the growth so we're just always decaying

and here is a plot of
the distribution of the control input

between the different muscles
in the different colors and

in the black is when we
needed to cut on the motor so

you can see intermittently we're filling
in for the muscles with the motor.

Then we started to think about OK
we want to do adaptive control and

here was a big problem because all
the previous controllers that you saw were

also controllers because we had these
twelve time conditions that we needed to

me and
we have to know how fast were converging

in order to develop those
dwell time conditions and so.

You know unless you are doing some very
exotic things to get parameter to in

effect cation simultaneously it's hard to
know how fast you're converging if you're

using an adaptive controller because
typically you have a knowledge strictly

off and off function and you're only
going to get asymptotic convergence but

with a motor in the loop then
you know there is no trial time

condition because you're always
switching between a stable subsystem and

so with the motor in the loop and
always switching between stable

subsystems we said OK well now maybe this
opens the door for us to be able to do

our first adaptive control result and
so the first Africa troll result that

we tried was a repetitive learning
controller So this is a type of

a data control result that exploits
the repetitive nature of the problem and

with cycling it's very repetitive right
I mean it's not exactly periodic.

And so when we develop our controller.

We segregate out some dynamics this W.D.
Not coincidentally with more index and.

We collect a bunch of terms in this
this bucket which are functions of our

desire trajectory which is very periodic
And so now the strategy is to design our.

Troll or this this new here to
compensate for the for the periodic.

Near terms that are uncertain the rest
of the terms we crush with live in most

control and robust feedback terms so here
you see the adaptive feed for component

proportional derivative feedforward
term and then some sliding mode terms

to compensate for the other uncertainties
in disturbances in the system and we've

developed this kind of a learning term
which has a saturation function on it.

In order to keep our
repetitive estimate bounded.

And then here now for the first time we
have not an exponential convergence but

now we have the limit as time goes
to infinity we have this ass and

product convergence of
our cadence error system.

The advantage that.

Is that we're not having to dominate we're
not having to use all of our controller

to dominate the disturbances and
uncertainties in the system

with high gain high frequency feedback
which over stimulates the muscle and

fatigues it more rapidly we're able to
offset some of the control energy to this

feed forward term which is typically
a lower frequency term which is typically

a lower magnitude term it doesn't have
these high gains multiplied by noisy

sensor measurements and so has a lower
frequency content in it and therefore

the idea here is Stickley is that it would
lead to lower muscle fatigue we haven't

had enough time to test that out so right
now is to remains a heuristic notion.

And so here we have our sum of squares
terms only up in a function and

then here is our.

Integral over the past period for
our periodic learning terms.

So we've implemented this controller
on various people with different

neurological conditions.

We also implemented on our first
person who is quadriplegic and so

from my perspective it was a big step for
us to move into a situation where we're

doing experiments on someone who has no
control of their body below the neck.

And here is the repetitive learning
controller on a healthy normal person

again looks like cycling

you can see this is the stimulator if
you can see that little light coming on

this little light of mine is when
we're stimulating the muscle.

And then this is a video that on
one hand is like fantastic for

me to see on the other hand I want
to strangle the student who made it

this is the person who's a quadriplegic
you see them pet on the cycle this is

an amazing triumphant video for
us to record in the lab you can see is

fingers they kind of just move based
on rubbing against this other hand so

he doesn't have any control over his
body at all yet he's cycling but for

some reason my student that is the hand
in the video on the on the paddle and

I just got this the other day and I said
why did you put your hand on the pedal and

I said well you know he has the sation and
he said that is new is heard

in a mobile bit and I said So why did
you have your head on the pedal and

I said I would like it
made him feel better.

Yeah but you killed my baby.

So there's no reason for
it in the have his hand on the paddle and

I almost strangled him yesterday
when I found out he did that but

they he this guy's paddling
completely through the computer

making him part of the cycle which
is which is just really nice to see.

Kind of moving on and
I know we're running out of time but

some of our recent results.

Kind of on this idea of let the person
do as much as they can possibly do

now we're setting up the switching
zones where we have an aside.

Distance region where we say here's
the minimum speed that you should go in

the cycle and in that region we're
switching between electrical stimulation

and maybe using a motor then we have
this voluntary region where we say hey

look if you can pedal beyond the pail and
speed knock yourself out

you should in fact we encourage you
to pedal faster if you want to and

then we reach an upper limit that says hey
look some of these people who come in for

these experiments again have a lot of
enthusiasm and a lot of energy so much so

that they could maybe be you know
cause safety issues for themself or

potential damage the equipment so they
had a set of upper bound and on the upper

bound now we have the motor fighting
against them and basically increasing

the resistance in the bike to a point
where they're not going to fast anymore.

But what's nice about it is that we have
some just very preliminary experiments

here where here's an assistive
mode where the person is not

pedaling fast enough and here you see lots
of muscle stimulation going on in that

region we also are steaming are switching
back and forth on the on the motor.

In some of the kinetic
regions to also help and

then the person paddles
faster voluntarily then

the desired objective now from a controls
perspective it's hard to design this

because you know a controller says
we want to go to zero and if they're

peddling faster than the desired speed
that means ease not zero anymore and so

the controller would want to fight against
that but we've designed this in a way that

it won't and we disallow them to stay in
this uncontrolled region as long as they

want to doing as much as they can and then
we told this was a healthy normal person

said OK now pedal pedal too fast and
we set a threshold and now the motor cuts

on and you can see the motor is providing
resistance to fight against them so.

I think this was either a C.D.C.
paper or an A.C.C. paper.

In the last cycles that we submitted
really excited about this kind of war.

We're also doing more work where
we're looking at the human and

the machine is coupled
interconnected systems and

we're taking a passive eighty
based approach in the analysis and

this is an admittance controller where
the robot desire to inject lags behind.

The person's trajectory
by about ten degrees and

we have the person is being
electrically stimulated to

fight against the machine and
the machine is providing a desired and

adaptive resistive force against
the person but it's also admitting

to the person so you develop this this
passive ity base that mittens controller

that allows the two the two
systems to interact in a way

to kind of optimize the work out here so
here's the motor providing the resistance.

And then here's the we're
following the curves.

As an explanation and then last slide.

We're also moving into now upright
walking kind of experiments

where we have this step or treadmill we
have instrumented a motorized so that we

can do everything in close of control we
also have a body weight support system and

it's essentially a cycle that's
upright but with having the person's

body weight involved and having their
arms involved that opens the door for

new therapeutic outcomes and so

we're kind of moving in this
direction as well so it's a the three

kind of directions that we're moving in
are this kind of switching between these

passive zones and allowing the person
to decide to do as much as they can.

Developing adaptive controllers.

Even though we're switching
among different subsystems.

And these admittance.

Kind of force control problems
where we're looking at

passive interactions or pass it using
passively theory to look at the at mittens

interactions between the person and
the robot so that concludes my top.

One hundred three.

Questions.

Where were using P.

i D.

plus something else.

The only neural network controller
that we implemented was on the time

delay stuff and the role of the neural
network was to learn what is

the delay that the input
delay which is uncertain.

Yeah so that is you know kind of trial and

error ad hoc tuning during
the experiments so.

You can increase the workload.

And it is a real a robot exercise

I mean if you're I got on the cycle Well
if I go on a cycle maybe you're better and

better say that I am if I own
the cycle and they did experiments on

me over the course of half an hour
the next day I would feel as if

I did a lot of a robotic exercise and
I would have that kind of muscle soreness.

So there is the potential to and
in terms of like lifting stuff

there's if you if you did the maximum
amount that you could possibly lift and

then you add electrical stimulation
you can that's a lot more so

it's interesting how much your mind
limits what your body can do so.

There.

Are.

I don't have any numbers but
my guess would be horribly inefficient and

that's not due to the fault of
the muscle because the body

does things incredibly efficiently but
the way that the our

window into using the muscle
just externally and

some people do internal stimulation
they implant electrodes and

they and their the group at Northwestern
does this for example Case Western.

But we don't want to get involved
in the invasive experiments so

we destabilize Turnley and
when you stakes turn only and

you're grabbing all the muscle fibers
at once when you're stimulating

you're really fatiguing
the muscle rapidly and so

this is probably the biggest
problem to overcome in this area.

Yeah I think that could be beneficial for

sure you know we're right
now we're just using.

The joint angles which are easy
to measure and then we

developed a map that related say
torque output based on the angle and.

If we knew muscle length and
muscle shortening velocity

those kinds of things could improve our
model and I'm a firm believer the more

you know about the system you're trying to
control the better job you can control it.

OK.

OK yeah that could be useful I mean we
have read some literature about that

at one time we also tried to
use like a thermal camera to

like blood flow in the muscle
to maybe correlate that.

I thought was a great idea the student
really didn't completely buy into it and

it kind of fizzled out but.

Maybe they were like.

The thing with you that
the whole human with.

The better part.

So yeah I think that there's
a cycle that goes on where

we start with a theory that we know and
we apply it to the application and

then in in the in the practice of
applying it we see things like

I mentioned before where we were initially
telling the people well hey don't tell

just let us do let us actually it's your
muscles and then we realized how dumb that

was to do that because and we should
other people tell as best they can and

contribute as much as they can so then we
went back to the drug drawing board and

we said OK well how can we design
a controllers now where that we allow

the person to contribute as much as they
can even if then contributing will cause

our control errors to be non-zero can
we develop the control structure to let

that happen and so I think there's
this perpetual cycle between

doing the experiments and learning from
the experiments thing going back and

maturing theory and then and
then repeat and repeat sound.

Good.

Is that a brass Tiger.

Now maybe a bumble bee.

Thank you.