Functional Electrical Stimulation Induced Cadence Control ... · neurological conditions such spinal cord injury or stroke. FES is the direct application of electrical current across

Abstract—Functional electrical stimulation (FES) has become a

popular and successful form of rehabilitation for people with

neurological conditions such spinal cord injury or stroke. FES is

the direct application of electrical current across the motor

neurons of a muscle to generate artificial muscle contractions to

perform functional tasks. Arm-cycling is a beneficial

rehabilitation activity and motivation exists to use FES in arm-

cycling. It has previously been shown that closed-loop FES control

can be designed to achieve accurate, repetitive motion. In a

previous study, a robust sliding-mode controller was used to track

a desired crank cycle cadence (crank velocity) on a decoupled hand

cycle. For this thesis the hand-cycle was modified to yield an

improved tracking performance. Using a combination of FES and

volition, experimental results from three able-bodied participants

are presented for the developed control system. Two protocols

were ran, one of which activated the motor for all time and

demonstrated an average cadence tracking error of -0.04 ± 2.83 revolutions per minute (RPM) for a desired cadence of 40 RPM.

The second protocol deactivated the motor when the bicep was

stimulated and demonstrated an average cadence tracking error

of -0.02 ± 5.35 RPM.

Index Terms—Functional electrical stimulation (FES),

Lyapunov, rehabilitation robotics, switched systems, stability

I. INTRODUCTION

UNCTIONAL electrical stimulation (FES) has been used

for decades as a form of rehabilitation for individuals with

upper motor neuron lesions, caused by an event such as a stroke

or spinal cord injury (SCI) [1]. Neuromuscular electrical

stimulation (NMES) is called FES when it is used to perform

functional tasks [2]. NMES is the application of electrical

current across muscle fibers to yield artificial muscle

contractions [2]. FES has commonly been used for

rehabilitation because it helps restore voluntary muscle

function, increases bone mineral density and muscle mass,

improves cardiovascular health, and decreases spasticity [1].

This can also lead to psychological benefits such as improved

independence and self-esteem [1]. Enhancing a person’s

physiological (skeletal, cardiopulmonary and muscular

systems) and psychological well-being may enable them to

improve their ability to perform activities of daily living [3].

In research, FES applied to the lower extremities is generally

divided into three categories: cycling, standing, and walking.

FES-cycling has an advantage over standing and walking

exercises since people with paralysis can perform cycling [3].

Regular FES cycling has been shown to improve general health,

decrease the possibility of cardiovascular disease, and diminish

the effects of secondary complications of SCIs [4].

The FES stimulation intensity, in past studies, has been

controlled using proportional-derivative feedback or open-loop

control to obtain a desired cycling cadence (crank velocity) [1].

Cadence tracking was used as the primary control objective

because it is one of the most important factors in cycling

rehabilitation [1]. Furthermore, the stimulation was switched

between multiple muscle groups to achieve a predetermined

stimulation pattern throughout the crank cycle [1]. Thus, FES

cycling systems can be seen as switched control systems with

autonomous, state-dependent switching.

In addition, FES control input is commonly not applied

during kinematic dead zones in the crank cycle, where only a

small portion of the torque produced by the cyclist’s muscles is

transferred as torque about the crank axis [5]. In a previous

study, electric motors were used throughout the entire crank

cycle to help maintain the desired cadence and account for the

kinematic dead zones [4]. Recent studies have also

implemented Lyapunov-based nonlinear control techniques to

improve the performance and effectiveness of FES cycling [1].

A recent study successfully developed a controller that switches

the control input between an electric motor and FES of various

muscle groups [5]. Using the electric motor only during

kinematic dead zones when FES control input is not used, can

maximize the contribution of the cyclist’s muscles [5].

However, there are several challenges with using FES

control. One challenge is that stimulated muscles fatigue at a

higher rate than muscles that contract voluntarily [4]. The

muscles fatigue at a high rate because the stimulation only

engages small portions of each muscle, which also makes

controlling the muscles difficult [6]. Electric motors can be

used to compensate for muscle fatigue so that the person can

continue performing the exercise even while fatigued and

without stimulation [4]. Another challenge that exists relates to

the repeatability of the stimulation because the effectiveness of

the stimulation is influenced by many factors such as muscle

fatigue, body fat, body hydration, and the correlation between

stimulation and muscle reaction [6]. Electrode placement is

another factor because there is no guarantee the electrode will

be placed at the same location every time or in the best position

for stimulation [2].

Based on the success of FES cycling for the lower

extremities, there is evidence that FES cycling can also be

applied to the upper extremities. Individuals with SCIs above

Functional Electrical Stimulation Induced

Cadence Control of a Hand Cycle Michael Woc, Christian Cousin, Brendon Allen, Warren E. Dixon

F

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Th1 (thoracic vertebrae 1) suffer from upper extremity

impairments and would benefit from upper limb rehabilitation

[7]. The aforementioned methods for FES cycling in the lower

extremities can be applied to FES cycling with the upper limbs.

Preliminary work such as characterizing the dynamics of an

arm-cycle system and defining the arm stimulation regions have

been performed in [6], [8]. This thesis seeks to improve the

performance (crank cycle cadence tracking) of the controller

developed in [6] by improving the cycle hardware (i.e., the

electric motor).

In this thesis, a switched-systems sliding mode controller

was developed and used on a FES arm-cycle system with

electric motor assistance. The cadence was tracked during

experiments and the cadence tracking error was used to quantify

the performance of the controller. Preliminary experiments

were conducted on three able-bodied individuals to evaluate the

performance of the controller. FES cycling rehabilitation is

intended for people with neurological conditions (NCs), but for

their safety the arm-cycle system was first tested on able-bodied

individuals. Two different protocols were implemented for the

experiments, Protocol 1 and Protocol 2. Both protocols had

each participant cycle at a specific RPM (revolutions per

minute). In Protocol 1, the motor was on during the entire crank

cycle and the participant only added volition if the cadence error

exceeded ±5 RPM. In Protocol 2, the motor was deactivated during bicep stimulation and the participant was never allowed

to add volition. In the subsequent sections the arm-cycle

dynamic model, the developed switched-systems sliding mode

controller, and the resulting stability analysis are provided.

II. MODEL

A. Arm-Cycle Dynamic Model

A person pedaling a motor assisted arm-cycle can be

modeled as single degree-of-freedom system [6], [8], which can

be expressed as:

𝑀(𝑞)�̈� + 𝑉𝑚(𝑞, �̇�)�̇� + 𝐺(𝑞) + 𝑃(𝑞, �̇�) + 𝑐𝑑�̇� + 𝑑(𝑡)

= 𝜏𝑚(𝑞, �̇�, 𝑡) + 𝜏𝑒(𝑞, �̇�, 𝑡) (1)

where 𝑞 and �̇� denote the measured crank angle and velocity of the cycle, respectively; �̈� denotes the unmeasured crank acceleration; 𝑀 is the inertia matrix; 𝑉𝑚 represents the centripetal and Coriolis effects; 𝐺 denotes the gravitational effects; 𝑃 accounts for the viscoelastic tissue forces; 𝑐𝑑 is the coefficient of viscous damping, and 𝑑 accounts for time-varying disturbances. The torque produced by the upper limb

muscle contractions of the individual is expressed as:

𝜏𝑚(𝑞, �̇�, 𝑡) = ∑ 𝐵𝑚𝑢𝑚𝑚∈ℳ

(2)

where 𝐵𝑚 denotes the uncertain, nonlinear control effectiveness term that relates the stimulation input to the torque output of a

muscle group. The term 𝑢𝑚 is the input stimulation intensity applied to each muscle group. The subscript 𝑚 indicates the muscle group and is defined as 𝑚 ∈ ℳ ≜{𝑅𝐵𝑖, 𝐿𝐵𝑖, 𝑅𝑇𝑟𝑖, 𝐿𝑇𝑅𝑖}. 𝐵𝑖 and 𝑇𝑟𝑖 represent the biceps brachii and triceps brachii muscle groups, respectively; 𝑅 and 𝐿 correspond to right and left arm, respectively. The torque

applied about the crank cycle axis by the electric motor is

represented by:

𝜏𝑒(𝑡) = 𝐵𝑒𝑢𝑒 (3) where 𝐵𝑒 is a known positive constant term that relates the motor’s applied current to the resultant torque. 𝐵𝑒 can be bounded as 0 < 𝐵𝑒 ≤ 𝑐𝑒. The current applied to the motor is represented by 𝑢𝑒.

B. Switched System Model

As previously mentioned, the stimulation needs to switch

between different muscle groups in many FES applications to

produce coordinated motion, such as cycling. Switched systems

have additional control challenges since switching between

subsystems, such as muscles and electric motors, can generate

instabilities in the overall system and it is necessary to prove

the stability of the overall switched system, even if the

subsystems are stable. The stability analysis for the arm-cycle

system used in this thesis was developed similar to that of

previous studies done on a recumbent stationary cycle [1], [5].

In both studies, the stimulation was not applied during

kinematic dead zones. In [5], it was shown that coupling a

motor to the cycle increased the controllability of the dead

zones. As a result, the arm-cycle system was analyzed as a

switched system with control input switching between

stimulation of the biceps and triceps muscle groups and the

electric motor.

The stimulation regions for each muscle were defined by a

range of crank angles in the crank cycle that allow for that

muscle to produce positive torque about the crank axis. The

motor-controlled regions are the kinematic dead zones or

kinematically inefficient regions for any of the muscles to

produce positive torque. Let the set of crank angles (ℚ ) vary from [0, 2π), the crank cycle regions where stimulation is

applied to each muscle be represented by ℚ𝑚 ⊂ ℚ, and the regions of the crank cycle where the electric motor is used be

ℚ𝑒 ⊂ ℚ. The union of crank regions where FES is applied is denotes as 𝑄𝐹𝐸𝑆 is defined as:

ℚ𝐹𝐸𝑆 ≜ ⋃ ℚ𝑚𝑚∈ℳ

(4)

The 𝑄𝑒 regions can be expressed as: ℚ𝑒 ≜ ℚ\QFES (5) A graphical representation of the kinematic dead zones (also

known as ℚ𝑒 regions in this thesis) and the stimulation regions, ℚ𝑚, using crank angles over the crank cycle is in Fig. 1.

Fig. 1. Sample schematic showing the arm muscle stimulation regions for the biceps (red region) and the triceps (green region). The kinematic dead zones

(KDZ) are also displayed with the gray areas [6].

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The control inputs for the muscle stimulation (𝑢𝑚) and current input (𝑢𝑒) for the electric motor are represented as:

𝑢𝑚 ≜ 𝑘𝑚𝜎𝑚𝑢𝑠 (6)

𝑢𝑒 ≜ 𝑘𝑒𝜎𝑒𝑢𝑐 (7)

where 𝑢𝑠, 𝑢𝑐 are subsequently designed control inputs and 𝑘𝑚, 𝑘𝑒 are positive, constant control gains. A switching signal for the muscle groups (𝜎𝑚) and the motor (𝜎𝑒) are defined as:

𝜎𝑚 ≜ {

1,0,

𝑖𝑓 𝑞 ∈ ℚ𝑚 𝑖𝑓 𝑞 ∉ ℚ𝑚

(8)

𝜎𝑒 ≜ {

1,0,

𝑖𝑓 𝑞 ∈ ℚ𝑒 𝑖𝑓 𝑞 ∉ ℚ𝑒

(9)

Switched control effectiveness terms 𝐵𝑀 and 𝐵𝐸 are introduced to rewrite the dynamics of the overall arm-cycle

system. 𝐵𝑀 is defined as:

𝐵𝑀 = ∑ 𝐵𝑚𝑘𝑚𝜎𝑚𝑚∈ℳ

(10)

and 𝐵𝐸 is defined as:

𝐵𝐸 = ∑ 𝐵𝑒𝑘𝑒𝜎𝑒𝑚∈ℳ

(11)

The arm-cycle system dynamics can be rewritten, accounting

for the switching signals, as:

𝑀�̈� + 𝑉𝑚�̇� + 𝐺 + 𝑃 + 𝑐𝑑�̇� + 𝑑 = 𝐵𝑀𝑢𝑠 + 𝐵𝐸𝑢𝑐 (12)

Finally, the overall switched system adheres to the following

properties:

Property 1: The inertia matrix (𝑀) is positive-definite and can be bounded as 𝑐𝑚 ≤ 𝑀 ≤ 𝑐𝑀, where 𝑐𝑚 and 𝑐𝑀 are known constants.

Property 2: The centripetal and Coriolis matrix (𝑉𝑚) can be upper bounded as |𝑉𝑚| ≤ 𝑐𝑣|�̇�|, where 𝑐𝑣 is a known constant.

Property 3: The gravitational effects matrix (𝐺) can be upper bounded as |𝐺| ≤ 𝑐𝐺, where 𝑐𝐺 is a known constant.

Property 4: The passive and viscoelastic tissue effects (𝑃) can be bounded as |𝑃| ≤ 𝑐𝑃1 + 𝑐𝑃2|�̇�|, where 𝑐𝑃1 and 𝑐𝑃2 are known constants.

Property 5: The time-varying disturbance term (𝑑) can be upper bounded as |𝑑| ≤ 𝑐𝑑, where 𝑐𝑑 is a known constant.

Property 6: The lumped muscle control effectiveness term

(𝐵𝑀) can be upper and lower bounded as 𝑐𝐵1 ≤ 𝐵𝑀 ≤ 𝑐𝐵2, where 𝑐𝐵1 and 𝑐𝐵2 are known constants.

Property 7: The motor control effectiveness term (𝐵𝐸) can be upper and lower bounded as 𝑐𝐸1 ≤ 𝐵𝐸 ≤ 𝑐𝐸2, where 𝑐𝐸1 and 𝑐𝐸2 are known constants.

Property 8: The inertia and centripetal and Coriolis matrices

follow the skew-symmetry relationship: 1

2�̇� − 𝑉𝑚 = 0.

III. CONTROL DEVELOPMENT

The control objective of the arm-cycle system is to track a

desired crank cadence. Two tracking errors are measured and

the error signals are expressed as:

𝑒1 ≜ 𝑞𝑑 − 𝑞 (13)

𝑒2 ≜ �̇�1 + 𝛼𝑒1 (14)

where 𝑒1 is the position tracking error, 𝑒2 is an auxiliary filtered tracking error that considers errors in position and cadence

tracking, and 𝛼 is a user-defined positive gain. The desired crank position (𝑞𝑑) is designed so that its derivatives exist and are bounded as �̇�𝑑, �̈�𝑑 ∈ ℒ∞ . Additionally, the tracking errors are combined to generate an error vector (𝑧):

𝑧 ≜ [𝑒1 𝑒2]𝑇 (15)

The open-loop error system is calculated by taking the time

derivative of (14), multiplying the derivative by the inertia

matrix (𝑀), and using (12)-(14) to yield:

𝑀�̇�2 = 𝜒 − 𝑒1 − 𝑉𝑚𝑒2 − 𝐵𝑀𝑢𝑠 − 𝐵𝐸𝑢𝑐 (16)

where 𝜒 represents a group of constant and state-dependent terms that can be bounded using Properties 1-8 by a known

function of the states. Equation 16 and the Lyapunov-based

stability analysis from the subsequent section are used to design

the robust sliding mode controllers for the stimulation (𝑢𝑠):

𝑢𝑠 ≜ 𝑘1𝑒2 + (𝑘2 + 𝑘3‖𝑧‖ + 𝑘4(‖𝑧‖)2)𝑠𝑔𝑛(𝑒2) (17)

and the current supplied to the motor (𝑢𝑐):

𝑢𝑐 ≜ 𝑘5𝑒2 + (𝑘6 + 𝑘7‖𝑧‖ + 𝑘8(‖𝑧‖)2)𝑠𝑔𝑛(𝑒2) (18)

where 𝑘1, 𝑘2, 𝑘3, 𝑘4, 𝑘5, 𝑘6, 𝑘7, and 𝑘8 are selectable positive control gains and sgn( ̇ ∙) is the signum function. The control inputs in (17)-(18) are substituted into the open-loop error

system in (16) to generate the closed-loop system dynamics:

𝑀�̇�2 = 𝜒 − 𝑒1 − 𝑉𝑚𝑒2 − 𝐵𝑀[𝑘1𝑒2 + (𝑘2 + 𝑘3‖𝑧‖

+𝑘4(‖𝑧‖)2)𝑠𝑔𝑛(𝑒2)]- 𝐵𝐸[𝑘5𝑒2 + (𝑘6 + 𝑘7‖𝑧‖ +

𝑘8(‖𝑧‖)2)𝑠𝑔𝑛(𝑒2)]

(19)

IV. STABILITY ANALYSIS

The stability analysis begins by defining 𝑉𝐿, a positive-definite, continuously differentiable common Lyapunov

function candidate, denoted as:

𝑉𝐿 ≜

1

2𝑀𝑒2

2 +1

2𝑒1

2 (20)

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where 𝑉𝐿 can be bounded as:

𝜆1(‖𝑧‖)2 ≤ 𝑉𝐿 ≤ 𝜆2(‖𝑧‖)

2 (21)

where 𝜆1 and 𝜆2 are known constants. Taking the derivative of (20) and substituting in (14) and (16) results in:

�̇�𝐿 = 𝑒2(𝜒 − 𝑒1 − 𝑉𝑚𝑒2 − 𝐵𝑀𝑢𝑠 − 𝐵𝐸𝑢𝑐)

+1

2�̇�𝑒2

2 + 𝑒1(𝑒2 − 𝛼𝑒1) (22)

For the case when 𝜎𝑚 = 1 and 𝜎𝑒 = 0, (22) can be simplified by using Properties 6-8, (17)-(18), cancelling terms, upper

bounding, and assuming certain gain conditions are met to

produce:

�̇�𝐿 ≤ −𝑐𝐵1𝑘1𝑒22 − 𝛼𝑒1

2 (23)

For the case when 𝜎𝑚 = 0 and 𝜎𝑒 = 1, (22) can be simplified by using Properties 6 and 8, (17)-(18), cancelling terms, upper

bounding, and assuming certain gain conditions are met to

produce:

�̇�𝐿 ≤ −𝑐𝐸1𝑘5𝑒22 − 𝛼𝑒1

2 (24)

The bounds in (23) and (24) can be expressed in terms of the

error vector (𝑧) and a known constant (𝜆3) for all time as:

�̇�𝐿 ≤ −𝜆3(‖𝑧‖)2 (25)

Knowing that 𝑉𝐿 is bounded by (21), then �̇�𝐿 can be expressed as a first order differential equation:

�̇�𝐿 ≤ −

𝜆3𝜆2

𝑉𝐿 (26)

The bound in (26) was solved for 𝑉𝐿 in terms of the initial condition of 𝑉𝐿 (𝑉𝐿,0), 𝜆2, 𝜆3, and 𝑡 to yield:

𝑉𝐿 ≤ 𝑉𝐿,0exp (−𝜆3(𝑡−𝑡0)

𝜆2) (27)

Using (21) and the initial condition of the error vector (𝑧0), (27) can be rewritten as:

‖𝑧‖ ≤ √𝜆2𝜆1

‖𝑧0‖exp (−𝜆3(𝑡 − 𝑡0)

𝜆2) (28)

Hence, the error system is bounded by an exponentially

decaying envelope. As a result, the stability analysis shows that

the closed-loop error system in (19) is globally, exponentially

stable for all 𝑡 ∈ [𝑡0, ∞), where 𝑡0 is initial time.

V. EXPERIMENTS

For simplicity, the performance of the controllers in (17)-(18)

were assessed using preliminary experiments on the right arm.

The goal of the experiments was to track a desired crank

velocity of 40 RPM. In the experiments, only the biceps and

triceps muscles of the right arm were stimulated. Experiments

were performed on three able-bodied individuals (three male)

23-27 years old. Prior to the experiment, each individual gave

written informed consent approved by the University of Florida

Institutional Review Board.

A. Arm-Cycle Testbed Setup

The arm-cycle system, shown in Fig. 2, consists of two

independently controlled arm-cycles. Each arm-cycle has its

own electric motor, shaft, handle, torque sensor, and encoder.

The motor is a 250 Watt, brushed, 24 VDC electric motor

(Unite Motor Co. Ltd. MY1016Z) mounted to the system frame

and coupled to the handle. The torque sensor is located on the

same shaft as the handle. The encoder (US Digital H1) is used

to provide crank position feedback. The handle has straps to

ensure the user’s arm remains fixed to the cycle. There is also

an emergency stop button that enables the user to stop the

experiment immediately, if necessary.

Fig. 2. Right arm-cycle testbed setup. (A) Electric motor. (B) Handle. (C)

Encoder. (D) Torque Sensor.

The current supplied to the motor was controlled with data

acquisition hardware (Quanser QPIDe) and an Advanced

Motion Controls motor driver. A desktop computer was used to

run real-time control software (QUARC 2.5,

MATLAB/Simulink, Windows 10) at a sampling rate of 500

HZ to implement the controller. A current-controlled stimulator

(Hasomed RehaStim) and PALS electrodes were used to deliver

stimulation to the biceps and triceps; the same computer and

control software were used to control the stimulation.

B. Experimental Setup

Each participant was seated in a chair in front of the arm-

cycle testbed at a distance that allowed the entire crank cycle to

be completed without fully extending the right arm. Electrodes

were placed on the individual’s right biceps and triceps, as seen

in Fig. 3. The top biceps and triceps electrodes were placed high

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enough on the arm to ensure there was enough space for the

bottom electrodes, but low enough that the shoulder would not

be stimulated. The individuals were instructed to remain

passive throughout the entire exercise, unless otherwise

instructed such as in Protocol 1, and to stay fixed in the chair;

this was done to minimize the volitional effort in the

experiment.

Fig. 3. Arm-cycle testbed with an individual. (A) PALS electrodes for Biceps.

(B) PALS electrodes for Triceps.

Two different protocols were performed on the arm-cycle

testbed, identified as Protocol 1 and Protocol 2. In Protocol 1,

the motor was always on and muscle stimulation was applied in

the muscle stimulation regions. Individuals were shown a

monitor with the actual and desired cadence; they were also

instructed to briefly apply volitional effort if the cadence error

began to exceed ±5 RPM. Protocol 1 was conducted to evaluate the performance of the modified arm-cycle testbed. In

Protocol 2, the motor was on in all regions except the bicep

stimulation region. Protocol 2 was conducted without the motor

during the bicep stimulation region to explore the possibility of

only having the motor on during kinematic dead zones.

Each experiment was designed to last 180 seconds. The

experiment began by using the motor to bring the arm-cycle to

40 RPM before starting the switching between muscle

stimulation and motor. The arm cycle speed was increased

exponentially to 40 RPM before leveling out. The switching

signal was designed to start at 20 seconds and from that point

on the participant received stimulation until the end of the

experiment when in FES regions of the crank cycle.

Furthermore, the motor had a current offset of 0.05 A to

ensure smooth cycling in the muscle stimulation regions, since

the motor was never completely turned off in Protocol 1. The

stimulation regions were found experimentally and identified

as:

5.06 𝑟𝑎𝑑 < 𝑄𝑏𝑖 < 5.76 𝑟𝑎𝑑 (28)

1.75 𝑟𝑎𝑑 < 𝑄𝑡𝑟𝑖 < 2.44 𝑟𝑎𝑑 (29)

where 𝑄𝑏𝑖 and 𝑄𝑡𝑟𝑖 represent the regions where the biceps and triceps were stimulated, respectively. Multiple experiments

were performed to adjust the gains in (14) and (17)-(18) to

ensure that the controller tracked the desired cadence

effectively. Once the controller was tuned, a final experiment

was performed to collect data.

C. Results

Protocol 1

The cadence, cadence error, motor current input, and pulse

width stimulation for each subject for Protocol 1 are seen in

Fig. 4-9.

Fig. 4. Plots of Subject 1 (S1) results. The top graph compares the actual

cadence (blue) to the desired cadence (red). The bottom graph shows the

cadence and position errors, where 𝑒1̇ (blue) is the cadence error in RPM and 𝑒1 (red) is the position error in rad. The plots start at 20 seconds since the rider starts at rest and ramps up to the desired cadence (40 RPM) in 20 seconds, after

which the controllers in (17)-(18) turn on.

Fig. 5. Plots of Subject 1 (S1) results. The top graph shows the amount of

current sent to the motor. The bottom graph shows the pulse width stimulation

over the course of the experiment. The vertical black line indicates when the controllers in (17)-(18) were activated.



cadence and position errors, where 𝑒1̇ (blue) is the cadence error in RPM and 𝑒1 (red) is the position error in rad. The plots start at 20 seconds since the rider starts at rest and ramps up to the desired cadence (40 RPM) in 20 seconds, after which the controllers in (17)-(18) turn on.

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Fig. 7. Plots of Subject 2 (S2) results. The top graph shows the amount of current sent to the motor. The bottom graph shows the pulse width stimulation

over the course of the experiment. The vertical black line indicates when the

controllers in (17)-(18) were activated.





Fig. 9. Plots of Subject 3 (S3) results. The top graph shows the amount of

current sent to the motor. The bottom graph shows the pulse width stimulation

over the course of the experiment. The vertical black line indicates when the controllers in (17)-(18) were activated.

Protocol 2

The cadence, cadence error, motor current input, and

pulse width stimulation for each subject for Protocol 2 are

seen in Fig. 10-15.

Fig. 10. Plots of Subject 1 (S1) results. The top graph compares the actual cadence (blue) to the desired cadence (red). The bottom graph shows the










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Fig. 14. Plots of Subject 3 (S3) results. The top graph compares the actual cadence (blue) to the desired cadence (red). The bottom graph shows the






The mean and standard deviation of the cadence error (𝑒1̇) and cadence were calculated for each subject in Protocols 1-2 and

the results are shown in Table I-II.

TABLE I

PROTOCOL 1 ANALYSIS

Subject 1 Subject 2 Subject 3 Averages

𝑒1̇ Mean (RPM) -0.04 -0.06 -0.04 -0.04 𝑒1̇ STD (RPM) 2.69 3.43

2.35 2.83

Cadence Mean (RPM)

40.04 40.06 40.04 40.04

Cadence STD

(RPM) 2.69 3.43 2.35 2.83

TABLE II

PROTOCOL 2 ANALYSIS

Subject 1 Subject 2 Subject 3 Averages

𝑒1̇ Mean (RPM) -0.02 -0.03 -0.04 -0.03 𝑒1̇ STD (RPM) 4.74 5.37

5.94 5.35

Cadence Mean

(RPM) 40.02 40.03 40.04 40.03

Cadence STD

(RPM) 4.74 5.37 5.94 5.35

VI. DISCUSSION

A. Experimental Results

The experimental results from Protocol 1 demonstrate the

ability of the controllers in (17)-(18) to distribute current to the

electric motor and apply FES to the rider’s muscles on the

modified arm-cycle. The experiment in [6] had the same

protocol as Protocol 1 except for the cadence tracked. In [6], a

cadence of 65 RPM was tracked, while the experiments

performed in this thesis had a cadence of 40 RPM. A cadence

of 65 RPM was deemed too fast to be an effective arm cycling

cadence and was reduced to 40 RPM. In addition, participants

were not allowed to apply volition in [6] and Protocol 2 was

also not performed in the previous study [6]. The experiment in

[6] had a cadence error of -0.06 ± 7.96 RPM and the experiments in this thesis had an average cadence error of -0.04

± 2.83 RPM. The standard deviations of the cadence error (𝑒1̇) and cadence

for each subject in Protocol 1 were all under 4 RPM. However,

the standard deviations approximately double in Protocol 2

compared to Protocol 1. The average cadence error in Protocol

2 was -0.03 ± 5.35 RPM, which is also smaller than the error in [6]. Thus, these results display the arm-cycle testbed’s

potential for future experiments.

A challenge associated with decoupled cycling, such as the

arm-cycle in this thesis, is that for a portion of the crank cycle

the participant must fight against gravity. With a coupled cycle,

when one side is being resisted by gravity, the other is being

aided to assist in offsetting the gravitational effect. However,

this is not the case with a decoupled cycle. This results in a

portion of the cycle having an increased difficulty, which is

partially responsible for the worse cadence error when the

participant provides no voluntary input. To improve this result,

a more advanced controller will be necessary, such as an

adaptive controller to learn these periodic dynamics that occur

throughout the crank cycle.

8

8

B. Arm-cycle Testbed Design

The arm-cycle testbed used for this thesis is similar to the one

used in [6]; Fig. 16 shows the left arm-cycle testbed used in [6].

The arm-cycle testbed in this thesis used the same arm-cycle

frame, handle, shaft couplers, encoder, and torque sensor. The

direct drive electric motor was replaced with the chain driven

electric motor mentioned before. The existing direct drive

motor lacked resolution resulting in an inability to effectively

control the system using a robust sliding-mode controller.

Fig. 16 Original left arm-cycle testbed.

To accommodate the new motor, a motor mount was designed

and machined so that the motor was mounted to the existing

arm-cycle testbed structure. A new shaft was machined to

couple the handle, sprocket driven by the motor, and the gear

connected to the encoder. The chain used to drive the sprocket

was fed through a non-spring-loaded chain tensioner to

maintain tension in the chain.

Furthermore, a sleeve bearing was mounted near the encoder

to provide stability at the end of the shaft and to ensure accurate

measurements were recorded by the encoder. The previous

sleeve bearing near the handle was replaced with one that only

had a 5° shaft misalignment capability; the existing bearing had

a 23° misalignment capability. This sleeve bearing was replaced

to reduce disturbances seen by the system during cycling.

C. Future Design Improvements

The arm-cycle testbed can be improved for future

experiments by increasing the rigidity of the system. The

system currently flexes a visible amount along the coupling

shaft. Flexible couplers were initially chosen to help account

for misalignment but have proven to be detrimental. The

flexible couplers can be replaced with rigid couplers. In

addition, an aluminum shaft was used to couple the sprocket

and encoder gear which can be replaced with a steel shaft.

Lastly, the coupling shaft portion of the system can be

shortened.

VII. CONCLUSION

This thesis discussed the challenges and benefits of

controlling FES systems, particularly for rehabilitation

applications. The application discussed in this thesis was for an

arm-cycle system and the thesis sought to improve the

performance (cadence tracking) of the arm-cycle system in a

previous study. The changes included implementing new

hardware (i.e. electric motor) and software (i.e. modified robust

sliding-mode controller). The results from the preliminary

experiments indicate the controllers’ ability to sufficiently track

a desired cadence; the results also showed that the new system

is an improvement over the previous system.

The improved arm-cycle testbed will enable future research

in FES rehabilitation for upper extremities. There is potential

for restoring muscle function in individuals with NCs using

arm-cycling; however, experimental results from experiments

conducted on able-bodied individuals do not represent how

individuals with NCs would perform. Moreover, additional

experiments, especially on individuals with NCs, will need to

be performed to further refine the controller and investigate

how this system would affect people with NCs. Future research

will involve characterizing the stimulation regions analytically

using upper arm kinematics and implementing adaptive control

schemes to account for unknown disturbances. Finally, future

experiments will involve simultaneous, independent cycling of

the left and right arms.

ACKNOWLEDGMENT

I would like to acknowledge my advisor, Dr. Warren E.

Dixon for allowing me to work in his lab the last three years,

my committee members and colleagues at the Nonlinear

Controls and Robotics Laboratory. I would also like to

acknowledge my mentors: Christian Cousin, Courtney Rouse,

and Brendon Allen for all the help and knowledge they have

provided me throughout the years. I would not be the engineer

I am today without everyone’s help and for that I will be

eternally grateful.

REFERENCES

[1] M. J. Bellman, T. -H. Cheng, R. J. Downey, C. J. Hass, and W. E. Dixon, "Switched Control of Cadence During Stationary Cycling Induced by Functional Electrical Stimulation," IEEE Transactions on Neural Systems

and Rehabilitation Engineering, vol. 24, no. 12, pp. 1373-1383 (2016).

[2] W. E. Dixon and M. J. Bellman, "Cycling Induced by Functional Electrical Stimulation: A Control Systems Perspective," ASME Dynamic

Systems & Control Magazine, vol. 4, no. 3, pp. 3-7 (2016).

[3] C.-W. Peng, S.-C. Chen, C.-H. Lai, C.-J. Chen, C.-C. Chen, J. Mizrahi, and Y. Handa, “Review: Clinical benefits of functional electrical

stimulation cycling exercise for subjects with central neurological

impairments,” J. Med. Biol. Eng., vol. 31, pp. 1-11, 2011. [4] K. Hunt, B. Stone, N.-O. Negard, T. Schauer, M. Fraser, A. Cathcart, C.

Ferrario, S. Ward, and S. Grant, “Control Strategies for Integration of

Electric Motor Assist and Functional Electrical Stimulation in Paraplegic

Cycling: Utility for Exercise Testing and Mobile Cycling,” IEEE

Transactions on Neural Systems and Rehabilitation Engineering, vol. 12,

no. 1, pp. 89–101, Mar. 2004. [5] M. J. Bellman, R. J. Downey, A. Parikh and W. E. Dixon, "Automatic

Control of Cycling Induced by Functional Electrical Stimulation with

Electric Motor Assistance," IEEE Transactions on Automation Science and Engineering, vol. 14, no. 2, pp. 1225-1234 (2017).

[6] M. H. Cohen, V. H. Duenas, C. A. Cousin, and W. E. Dixon, “Control of the Upper LImbs for Rehabilitative Arm-Cycling via Functional Electrical Stimulation,” Journal of Undergraduate Research, University

of Florida, vol. 20, no. 1, 2018.

[7] G. J. Snoek, M. J. Ijzerman, H. J. Hermens, D. Maxwell, and F. Biering-Sorensen, “Survey of the needs of patients with spinal cord injury: impact

and priority for improvement in hand function in tetraplegics,” Spinal

Cord, vol. 42, no. 9, pp. 526–532, 2004. [8] A. Carraha, C. Cousin, V. Duenas, C. Rouse, and W. Dixon, “Stationary

Arm Cycling Induced by Functional Electrical Stimulation – Muscle Zone

Characterization,” Journal of Undergraduate Research, University of Florida, vol. 18, no. 3, 2017.

[9] V. H. Duenas, C. A. Cousin, A. Parikh, P. Freeborn, E. J. Fox, and W. E. Dixon, "Motorized and Functional Electrical Stimulation Induced Cycling via Switched Repetitive Learning Control," IEEE Transactions on

Control Systems Technology, to appear.

Functional Electrical Stimulation Induced Cadence Control ... · neurological conditions such spinal cord injury or stroke. FES is the direct application of electrical current across

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