emg sliding mode finger joint synergy control of a
TRANSCRIPT
Abstract—From observation of human data, a set of
sinusoidal trajectories were developed to mimic the human
motion of unscrewing a bottle cap with the thumb and index
finger. These trajectories were then implemented on a
dexterous robotic hand in the form of a robustly stable sliding
mode control algorithm. With the developed synergies, a single
myoelectric input was used to control multiple finger joints
simultaneously. This controller was then compared to a one
degree of freedom prosthetic hand also under sliding mode
control. The two hands were used to complete an unscrewing
task as quickly as possible. The synergy controller produced a
statistically significant reduction in task completion time and
also reduced the required workspace.
Index Terms—Dexterous Hands, Distributed Parameter
Systems, Electromyogram, Grasp Synergy, Prosthetic Hands
I. INTRODUCTION
he introduction of dexterous robotic hands into industry
will permit the possibility of replacing humans with
robots in complex, tedious, or dangerous tasks.
Manipulators such as the Dexterous Shadow Hand [1] and
Gifu Hand have a high level of dexterity, approaching that
of the human hand. These manipulators have suffered from
the large number of actuators required to provide such
dexterity. This shortcoming typically requires the motors to
be placed outside the hand. The motors are then connected to
the joints through a tendon routing system. A recent advance
in this regard is the SmartHand transradial prosthesis, which
contains four actuators inside the hand and is similar in size
and weight to the human hand [2]. The SmartHand possesses
16 joints actuated by four motors, and is capable of multiple
grasps. Because this manipulator is completely self-
contained, it has a large potential to be fitted to upper limb
amputees.
However, most prosthetic hands contain only a single
degree of freedom (DOF) that opens and closes in a pinch
grasp [3]. Even the more advanced prosthetic hands
commercially available today, such as the i-Limb, contain
only five active degrees of freedom (DOFs) and one passive
DOF at the thumb [4]. While this disparity between
Manuscript received April 27, 2012. This work was supported in part by
the University of Akron Faculty Research Grant FRG1708.
B. Kent*, N. Karnati, and E. Engeberg are with the Mechanical
Engineering Dpt. at the University of Akron, Akron, OH 44325 USA (B.
Kent contact; phone: 330-998-4122; e-mail: [email protected]. N.
Karnati email: [email protected] , E. Engeberg email:
prostheses and human hands is in part due to the increased
mechanical constraints, it is also because of the limited
number of available control inputs.
Prosthetic hands are often controlled by two
electromyogram (EMG) signals placed on an antagonistic
muscle pair [5]. The signals from these two antagonistic
muscle groups are then differenced to produce a dual
polarity control signal for the motor of the prosthesis [3].
There have been many techniques proposed to improve
EMG control; feature extraction, neural networks, and
wavelet transforms have been previously utilized to classify
EMG signal patterns and obtain greater accuracy in
decoding the user’s intended movement [6]. However, these
methods suffer from their own set of drawbacks such as an
increased number of EMG recording sites and additional
time delays to process EMG signals.
Despite differences in the proposed EMG control
techniques for multiple DOF systems, the problem remains
that the mapping of control inputs to outputs is typically less
than one to one. This makes it difficult to control multiple
functions simultaneously without requiring an expensive
number of inputs or high cognitive demands from the
amputee.
The prime contribution of this paper is a synergy
controller which allows a dexterous robotic hand, described
in Section II, to produce unscrewing motions of the finger
and thumb with a single EMG input. This was accomplished
by analyzing the finger joint motions of humans performing
the unscrewing task and approximating these motions with
sinusoids, as outlined in Section IV. The proposed sinusoidal
synergy controller for the dexterous hand is derived in
Section V. For comparison, the synergy controller is
compared to a one DOF prosthetic hand, described in
Section VI. Both artificial hands were then evaluated
through a timed unscrewing task, and compared to results
obtained with the human hand. Experimental methods and
results are contained in Section VII and Section VIII,
respectively.
II. THE SHADOW DEXTEROUS HAND
The Shadow Dexterous Hand is a 24 joint, 20 DOF
underactuated tendon-driven anthropomorphic manipulator.
Hall effect sensors within the hand provide joint angle data
for all 24 joints of the hand, with a resolution < 1˚. The
index, middle and ring finger each have four joints and three
DOFs. The distal interphalangeal (DIP) joints of each finger
are kinematically coupled to the proximal interphalangeal
EMG Sliding Mode Finger Joint Synergy
Control of a Dexterous Artificial Hand
Benjamin A. Kent, Student Member, IEEE, Nareen Karnati, and Erik D. Engeberg, Member, IEEE
T
The Fourth IEEE RAS/EMBS International Conferenceon Biomedical Robotics and BiomechatronicsRoma, Italy. June 24-27, 2012
978-1-4577-1198-5/12/$26.00 ©2012 IEEE 87
(1)
(2)
(3)
(PIP) joints. All 24 joints are driven by 20 motors located
below the wrist joints, with a pair of antagonistic tendons
connecting each motor to the corresponding joint. However,
only the index finger and thumb are used in the experiments
presented in this paper. The considered kinematic models of
these digits are given in Fig. 1(a).
Since the DIP and PIP joints of the index finger are
coupled, a virtual joint is defined as the sum of the DIP and
PIP angles. This relationship can also be described by the
following piecewise linear equations:
where is the position of the virtual joint and
x1a and x1b are the angular positions of the DIP and PIP,
respectively (Fig. 1(a)). This is a mechanical constraint
because the DIP and PIP joints of the index finger are both
controlled by a single motor. The extension/flexion of the
metacarpophalangeal (MCP) joint is x2, and
abduction/adduction of the MCP joint is x3 (Fig. 1(a)). The
system model for the seven DOFs of the Shadow Hand
thumb and first finger can be written as
where , and are matrices that
respectively contain the inertia, damping and stiffness terms
of the seven DOFs within the thumb and first finger.
is a vector of torques applied by the seven motors.
III. CYBERGLOVE II
A. Sensors
The hand motion profiles of nine human test subjects were
recorded using the ver. 2.2 22 sensor CyberGlove II (Fig.
1(b)) (Immersion Corporation, San Jose, CA). The
CyberGlove uses bend-sensing resistive technology to
convert hand motions into digital joint angle data. The index
finger of the CyberGlove contains four sensors, two of
which record joint angle data for DIP and PIP joints (FJ1a
and JF1b). The remaining two measure the extension/flexion
(FJ2) and abduction/adduction (FJ3) of the MCP joint.
For the thumb, TJ1 and TJ2 measure the flexion/extension
of the DIP and MCP, respectively. Sensors TJ3 and TJ4 of
the CyberGlove respectively record the abduction and roll
angles of the carpometacarpal (CMC) joint of the thumb
(Fig. 1(b)). Abduction of the index finger is calculated as a
weighted difference between sensors FJ3 and TJ3.
B. CyberGlove-Shadow Hand Joint Angle Correlation
The correlation of the thumb joints from the CyberGlove to
the Shadow Hand is such that sensors TJ1 and TJ2 of the
CyberGlove (Fig. 1(b)) correspond to angles x7 and x6 of the
Shadow Hand (Fig. 1(a)). These represent the
flexion/extension of the DIP and MCP joints of the thumb,
respectively. Sensors TJ3 and TJ4 of the CyberGlove are
respectively mapped to angles x5 and x4 of the Shadow Hand
(Fig. 1(a)). The mapping of the index finger from
CyberGlove to Shadow Hand is such that sensors FJ1a,
FJ1b, FJ2, and FJ3 correspond to angles x1a, x1b, x2, and x3
respectively.
IV. HUMAN HAND MOTION ANALYSIS
A. Experimental Methods
Nine human test subjects gave informed consent prior to
experiments in accordance with IRB protocol. After signing
the consent forms, they underwent a brief CyberGlove
calibration procedure. After the glove was calibrated, the test
subjects performed the following steps: first, each subject
was asked to place his or her right hand flat on the table.
After two seconds, the participant was asked to grasp the
neck of a bottle using the middle, ring, and pinky fingers.
Using only the index and thumb, the bottle cap was then
unscrewed and screwed back on. This procedure was
repeated three times for each test subject. After data
collection, the hand motion profiles of the individual trials
were analyzed in Simulink. A principal component analysis
(PCA) was performed on the data to determine the impact of
each joint during the task using the princomp function in
MATLAB. As will be further explicated, the periodic nature
of the human finger joint angles to produce the unscrewing
motion allowed the human joint position profiles to be
Fig. 2. Results of PCA analysis for individual subjects while unscrewing.
(a) (b)
Fig. 1. (a) The seven DOF kinematic diagram of the thumb and index finger
of the Shadow Hand; the DIP and PIP of the first finger are kinematically
coupled. Axes of rotation are visualized as black arrows. Axes of rotation
perpendicular to the page are designated by an (X). (b) The CyberGlove II
has 22 sensors to measure the motions of human hands.
88
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(5)
(7)
approximated well by a set of sinusoidal trajectories.
B. Principal Component Analysis Results
A PCA was performed on the data obtained from human
experiments. PCA is commonly used as a data reduction
method to eliminate redundant variables in high dimension
problems. Results of the PCA show that the first principal
component (PC) for each test subject accounts for 83% of
the variance on average. The scalar coefficients of the first
PC for each test subject were converted to percentages to
determine the contribution of each joint variable to that PC
(Fig. 2). Results show that joint FJ2, TJ1, and TJ2 have the
largest impact on the motion.
C. Sinusoidal Approximation of Finger Joint Trajectories
The joint angle data from the experiments were filtered
and normalized with respect to time. Observation of the data
revealed two tendencies: first, that the individual finger
joints exhibited a periodic motion while unscrewing the
bottle cap. Second, the frequency of this periodic motion
remained relatively constant for all joints throughout the
duration of each trial. This trend was consistent with all nine
test subjects for each finger and thumb joint (Fig. 3(a)).
Because of the periodic nature of the joint angle motions
used by the test subjects to complete the task, these joint
trajectories were approximated by sine waves. This has been
done in previous work, where the developed sinusoidal
trajectories allowed the Shadow Hand to successfully
unscrew and screw a bottle cap [7]. Due to kinematic
differences between the Shadow Hand and human hand (see
(1) and (2)), the developed trajectories for the index finger
could not be directly implemented on the Shadow Hand.
To achieve this, the forward kinematics were derived and
used to find the resulting fingertip trajectories in Cartesian
space [7]. From there, solution of the inverse kinematics
problem for the index finger produced a new set of
sinusoidal parameters which could be implemented on the
Shadow Hand (TABLE I). The sinusoid parameters obtained
from the inverse kinematics solution were then implemented
on the physical Shadow Hand, explained further
subsequently. The sine wave parameters are given in
TABLE I; these include the amplitudes, phase angles, and
offsets for each joint.
In Cartesian space, these fingertip and thumbtip
trajectories form elliptical trajectories that are periodic on 2
(Fig. 3(b)). For the purposes of the present work, the
elliptical trajectories are considered in two halves. In the
first half of the sinusoid cycle, the finger is considered to be
in the “contact stroke” of the synergy, where both the index
and thumb will make contact with the bottle cap, causing
rotation. In the second half of the cycle, the finger is
considered to be in the “return stroke” where neither finger
is in contact and no rotation of the bottle cap occurs (Fig.
3(b)).
V. SHADOW HAND SYNERGY CONTROLLER
A. Synergy Controller
By utilizing the joint synergies described above, all DOFs
involved in the unscrewing motion (or the screwing motion
[7]) can be controlled by a single input. The desired position
(xD ) for the synergy controller involving n joints is of
the form
where A is a constant diagonal matrix:
.
The quantities A1-An represent the amplitudes of the
sinusoidal trajectories for the index finger and thumb joints
(TABLE I). is a vector of sinusoids
T.
is a vector of joint angle offsets:
T.
The phase shift ( ) and joint angle offset (bK) for any joint
k, are determined from the observations of the human data
(Fig. 3, Fig. 3a) and are included in TABLE I.
(a)
(b)
Fig. 3. (a) The unscrewing finger joint motions of the nine test subjects
recorded by the CyberGlove were periodic and resembled sinusoids. (b)
Elliptical trajectory of the index finger in Cartesian space when driven by
sinusoids in the joint space. is a switching term used to map the generated
trajectories to the EMG signals of the test subject, as explained in Section
V.
TABLE I
SINE WAVE SCALING PARAMETERS FOR SHADOW HAND (RAD)
Joint x1b x2* x4 x6 x7
Gain 0.62 0.22 0.31 0.25 0.43
Phase Offset 4.712 1.571 3.66 1.571 4.712
* Reference Joint (RJ)
89
(9)
(10)
(8)
Fig. 4. PID sliding mode control diagram for the Shadow Hand synergy controller. The switching function (δ) determines which half of the synergy the
input (EE) is mapped to. This is decided by the position of the reference joint ( ). This scaled single input (E) is then sent to the synergy controller. A, b,
and are vectors of joint amplitudes, position offsets, and phase offsets, respectively. These are used to scale each joint individually from one input. ε is
used to change the slope of the sliding manifold.
The control architecture for the Shadow Hand finger joint
synergy controller (Fig. 4) enables all of the DOFs involved
in the synergy to be controlled by a single input, E, which is
defined to be
EE is the amplified EMG signal measured from the
extensor digitorum communis (EDC) muscles of the human
test subjects, and saturates at 1 according to (8). The
switching term, δ, is defined to be 0 or 1 based on whether
or not the synergy is in the contact stroke or return stroke
portion of the synergy (Fig. 3(b)). This is determined by the
measured position of a reference joint ( . This joint is
given an initial phase offset of rad, with the remaining
joints being scaled in phase relative to this joint [8]. With
this offset, the joint position increases/decreases through the
first/second half of the synergy. Because the sine wave
parameters are known prior to implementation, the
maximum and minimum joint positions are known, and
these correspond to the endpoints of the fingertip trajectories
in Cartesian space. The value of δ is initially zero, causing a
contraction of the EDC to drive the fingers of the Shadow
Hand along the contact stroke of the synergy. When the
input E reaches , the reference joint (x2) is at its maximum
position. Once this condition is reached, the value of δ
switches to 1, and the signal is mapped to the return stroke
of the synergy as the muscle is relaxed. As E reaches zero, x2
reaches its minimum point, and the value of δ switches back
to zero. To facilitate proper behavior of the Synergy
Controller, relays are employed near the δ switching points.
This ensures that the controller switches properly in the
presence of noise or if E does not exactly reach 0 or 1.
The experimental setup of the Shadow Hand, explained
further in Section VII, is shown in Fig. 5(a). The
manipulator was securely mounted in the shown orientation,
while a single turn potentiometer attached to a cylinder acted
as the object that human operators used the Shadow Hand to
unscrew. Example data of the Shadow Hand performing the
unscrewing task under the EMG Synergy Controller are
shown in Fig. 6.
B. PID Sliding Mode Synergy Controller
Sliding mode control is a nonlinear technique that is often
used to robustly control nonlinear systems like the Shadow
Hand [9]. The benefit is that excellent error minimization
attributes are guaranteed within certain bounds even though
nonlinear disturbances are applied. This is a particularly
useful trait for this application to track the desired sinusoidal
angular position trajectories as the intermittent contact with
the object to be screwed or unscrewed will apply torques to
the motors involved in the synergy. To facilitate sliding
mode control, an error state is defined as
.
The sliding manifold for the system is written as
Fig. 6. Sample data from the Synergy Controller performing the
unscrewing task. The top graph illustrates the mapping of the amplified and
filtered EMG signal to the controller input . The middle graph
depicts the change in potentiometer position (α) and velocity as the Shadow
Hand is executing the contact stroke.
(a) (b)
Fig. 5. (a) Experimental setup of the Shadow Hand driven by the Synergy
Controller. The cap rotates about the axis α and has a range of motion of
6rad. (b) Experimental setup of the Motion Control Hand.
(b) Experimental setup of the Motion Control Hand.
90
(13)
(14)
(11)
(12)
(15)
KI , KP , and KD are the diagonal
integral, proportional and derivative gain matrices,
respectively. The KI, KP, and KD gain terms are chosen so
that the poles of the system are in the left hand plane.
The PID sliding mode control law is then written as
,
where is the voltage input vector to the motors
(Fig. 4). is a diagonal matrix that is chosen as an
upper bound estimate on the motor voltages required to
overcome the torques applied to the joints of the Shadow
Hand that are involved in the synergies. The sat term is the
vector saturation function such that
T.
The sat function is used instead of the signum function
because it is piecewise continuous. The sat function partially
linearizes the control law to alleviate the chattering
phenomenon that is common with mechanical systems that
use a fully nonlinear control law associated with the signum
function. Incorporation of the integral error state ensures
zero steady state error.
VI. MOTION CONTROL HAND
A. Mechanism
The Motion Control Hand has a single DOF. Differential
equations to describe the system are given by
In these equations, represents the angular position and
is the angular velocity. Z, d, and I are the stiffness,
damping and inertia of the system, respectively. Z is
negligible before an object is grasped and xC is the angular
position when contact is initially established with the
environment. VM is the voltage input to the motor; N is a
factor based on the gear ratio, armature resistance, and
torque constant of the motor. D is the sum of unknown
internal and external disturbances applied to the hand which
may be nonlinear in nature.
The Motion Control Hand used in this paper is equipped
with an A1321 Hall effect sensor to measure the position
( ). Strain gauges mounted on the thumb measure the
normal force (FN).
B. Motion Control Hand Sliding Mode Controller
The sliding mode controller for the Motion Control Hand
has been described elsewhere [10] and is of the form
where VM is the voltage control law, R is a positive constant
and S1 is the sliding manifold comprised of position, velocity
and force feedback. The sliding mode controller is used to
improve the control of force and velocity for the prosthesis.
See [10] for a stability and robustness analysis of hybrid
force-velocity sliding mode control for this particular
system.
The sliding mode controller for the Motion Control Hand
requires two EMG inputs, placed on the EDC (EE) and flexor
carpi radialis (FCR) muscles of the forearm (EF). The two
signals are differenced to create a dual polarity signal which
is used to control the prosthesis. The fingertips from a
commercially available cosmetic glove are placed on the
Motion Control Hand to replicate frictional characteristics
that would be encountered during daily use by amputees
(Fig. 5(b)). Example data from a human operator using the
Motion Control Hand to perform the unscrewing task are
shown in Fig. 7. The difference in the measured EMG
signals (EE and EF) of the left arm is used to open or close
the gripper by alternating the relative contraction strength of
each muscle (Fig. 7, top). When the Motion Control Hand
has the potentiometer in grasp FN increases and the
prosthesis is manually turned with the right hand to induce a
change in the potentiometer angle α (Fig. 5(b)).
VII. EXPERIMENTAL METHODS: ARTIFICIAL HAND
CONTROL
Ten human test subjects gave informed consent prior to
participation in the experiments in accordance with IRB
protocol. An experimental apparatus consisting of a single
turn potentiometer attached to a 40mm diameter cylinder
was constructed to record the cylinder angle with respect to
time. Initially, each subject was asked to unscrew the
potentiometer with their own hand 10 times, with the
additional instruction to complete the task as quickly as
possible.
After this procedure was completed, the participants
then performed the task ten times using both the Motion
Control Hand and the Shadow Hand with the Synergy
controller (Fig. 5). Two EMG preamplifiers were placed on
the EDC and FCR of the subjects’ forearms prior to testing.
EMG signals were rectified, filtered and amplified using
Myolab II (Motion Control, Inc.). These filtered EMG
Fig. 7. The Motion Control Hand under sliding mode control. A contraction
of the EDC (EE) causes the Motion Control Hand to open, while a
contraction of the FCR (EF) causes the Motion Control Hand to close.
α α
91
signals were used to control the Motion Control Hand with
MATLAB/Simulink using the real time windows target
kernel. In the case of the Shadow Hand, the EMG signals
were output from Simulink to a 12-bit oversampled analog-
to-digital converter.
Half of all test subjects began with the Motion Control
Hand first (Group 1), and the other half performed the task
with the Shadow Hand first (Group 2). Each participant
performed the unscrewing task 10 times with each system,
with the time to complete the task being tabulated. A single
factor ANOVA test was performed between the controllers
to determine if a statistical improvement was offered by the
Synergy Controller in regard to the time to complete the
task.
VIII. EXPERIMENTAL RESULTS
After data collection, the average time to complete the task
from the ten trials per person using each system was
calculated (Fig. 8). These values represent the average time
each subject took to complete the task with each system. The
composite averages and standard deviations across all
subjects was also tabulated (TABLE II). As expected,
subjects using their own hands completed the task in the
shortest time, with an average of 0.99s. Results between the
Motion Control Hand and Shadow Hand were more mixed,
with six of the ten subjects having a lower average
completion time with the Synergy Controller. The task was
completed (on average) in 6.21s and 5.17s using the Motion
Control Hand and Shadow Hand, respectively. The average
of all ten test subjects shows that the Synergy Controller
offered a 16.7% improvement in task completion time. This
improvement was substantially larger for Group 1, who
completed the task 28.2% faster with the Synergy
Controller. Subjects in Group 2 showed a 7.4%
improvement with the Synergy Controller (TABLE II).
A single factor ANOVA test was performed on these
values to determine if there existed a statistical difference in
the performance of each controller. Both the Shadow Hand
Synergy Controller and the Motion Control Hand were
compared to the human data and each other. The completion
time of each trial for each subject was used for the ANOVA
test, resulting in 100 data points each for the Motion Control
Hand, the Shadow Hand and the human hand. As expected, a
statistical difference between each of the robotic systems
and the human hand exists with a very high level of
confidence (p < 0.001). Between the two robotic systems,
the ANOVA test yields a value of p = 0.014. This indicates a
statistical improvement in the time to complete the
unscrewing task with the Shadow Hand Synergy Controller
with a 95% confidence interval (p < 0.05).
Due to the inherent differences (i.e. mechanical) between
the two systems, the improvement in completion time may
not be attributed fully to the difference in control methods.
More importantly however, the Synergy Controller offers a
novel method of coordinating multiple joint motions via a
single EMG input. This concept can be extended to other
synergistic motions, with a large potential for creating
complex motions with a low number of inputs.
IX. CONCLUSION
From observation of human data, a set of sinusoidal
trajectories were developed to mimic the human motion of
unscrewing a bottle cap with the thumb and index finger.
These trajectories were then implemented on a dexterous
robotic hand in the form a robustly stable sliding mode
algorithm driven by a single EMG signal. This synergy
controller was then evaluated against a one DOF prosthetic
hand also under sliding mode control to complete a timed
task in the minimum required time. In addition to
completing the task in a shorter amount of time (on average),
the developed Shadow Hand synergy controller has the
additional benefit of a greatly reduced workspace required to
complete the unscrewing task. Also, the Synergy Controller
requires only a single EMG input, while the Motion Control
Hand requires two for this task.
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Fig. 8. Averaged results of ten trials per test subject from each of the three
timed unscrewing tasks. Test subjects 1-5 began with the Motion Control
Hand first (Group 1). Test subjects 6-10 began with the Shadow Hand with
the Synergy Controller first.
TABLE II
TASK COMPLETION TIME (SECONDS)
System Group 1 Group 2 Average
Human Hand 1.04 ± 0.64 0.93 ± 0.30 0.99 ± 0.48
Motion Control
Hand 5.57 ± 1.83 6.85 ± 3.31 6.21 ± 2.61
Shadow Hand
Synergy Controller 3.99 ± 0.56 6.34 ± 2.23 5.17 ± 1.92
92