Vishalini Bundhoo, Edmund Haslam, Benjamin Birch and Edward J. Park*
Department of Mechanical Engineering, University of Victoria, PO Box 3055 STN CSC, Victoria, British Columbia, Canada, V8W 3P6
Summary
Keywords: Artificial finger; Biomimetic design; Tendondriven mechanism; Shape memory alloy.
1. Introduction
In this paper, a new biomimetic tendon-driven actuation
system for prosthetic and wearable robotic hand applications
is presented. It is based on the combination of compliant
tendon cables and one-way shape memory alloy (SMA) wires
that form a set of agonist–antagonist artificial muscle pairs
for the required flexion/extension or abduction/adduction of
the finger joints. The performance of the proposed actuation
system is demonstrated using a 4 degree-of-freedom (three
active and one passive) artificial finger testbed, also
developed based on a biomimetic design approach. A
microcontroller-based pulse-width-modulated proportionalderivation
(PWM-PD) feedback controller and a minimum
jerk trajectory feedforward controller are implemented and
tested in an ad hoc fashion to evaluate the performance of
the finger system in emulating natural joint motions. Part
II describes the dynamic modeling of the above nonlinear
system, and the model-based controller design.
Rehabilitation robotics1-4 has grown significantly in the
last two decades. Rehabilitation robotics is a special branch
of robotics that aims at building robotic devices as a way
to rehabilitate, assist, replace, or enhance impaired human
motor control capabilities. This field includes a wide variety
of systems ranging in complexity, from simple adaptive tools
to advanced microcontroller-driven mechanisms, such as
upper-limb myoelectric prostheses and lower-limb powered
orthoses.
However, although tremendous technological progress has
been made in the state-of-the-art of orthoses and prostheses,
current devices cannot yet perform as well as their biological
counterparts.5 In order to find a solution to this problem, engineers
and scientists are turning to nature for inspiration and
guidance. Nowadays, more researchers are focused on not
only at building mechanical systems that will aid the disabled,
but strive toward the development of biomimetic (i.e., lifelike)
systems having the same adaptability, functionality, and
cognitive abilities as biological systems. The trend in reverse
engineering of nature is justified by the fact that, with millions
of years of evolution, biological systems have evolved into
very efficient and effective mechanisms. It is believed that
imitating these systems represent enormous potential to
improve the tools that we use. The continued advances in
human–machine interfaces, muscle-like actuators, artificial
sensors, and biomimetic control schemes promise to lead
us to more sophisticated human-like artificial devices in
the next several decades.6 As these biomimetic devices
become more affordable, lighter in weight, and their ability
to autonomously aid human motor functions increases due to
the advances in the above component technologies, the range
of applications in theworld of physical therapy, orthotics, and
prosthetics will increase exponentially.
In the field of industrial robotics, significant advancements
have already been made in terms of actuation transmission
mechanism design, sensing, and control in the development
of multifingered dexterous hands: e.g., the Belgrade/USC
Hand, Stanford/JPL Hand, and Utah/MIT Hand.7-8 Some of
the more recent developments include the NTU Hand,9 DLR
Hand,10 NASA’s Robonaut Hand,11 and the commercially
available Shadow Hand (from Shadow Robot Company).
However, the problem of building similar hand devices for rehabilitation
robotics differs considerably from the industrial
robotics context, where the industrial hands typically operate
in a structured environment with predefined tasks and, often,
with no considerations to the human–hand interaction.12
Successful rehabilitation robots cannot be realized with
direct application of only industrial robotic technologies; and
rehabilitation robotics has many technical as well as nontechnical
challenges.3 The following issues become more sensitive
in rehabilitation robotics: (i) low cost, (ii) low weight,
(iii) noiseless actuation, (iv) anthropomorphic size and
appearance, (v) user safety, (vi) human–machine interface;
hence, any device or component technology developed needs
to be geared toward solving these issues. In addition, future
rehabilitation robotics needs to be more human-friendly, i.e.,
not only on cosmetic alone but in function as well. Rehabilitation
robots should be highly intelligent systems that would
recognize the physical and cognitive abilities of the users so
as to provide a higher level of comfort and functionality.4 For
instance, it is a known fact that in the prosthetic hand field,
commercially available devices (e.g., the OttoBock Sensor
Hand or the Vasi Hand) have faced high user rejection rates
owing to the rigidity of the artificial hands, their low grasping
stability, heavy weight, the noisy operation of actuators, as
well as the unnatural feel and robot-likemotion of the fingers.
In this paper, we present a biomimetic tendon-driven actuation
system for artificial fingers employed in rehabilitation
robots, particularly useful to wearable robotics (e.g., robotic
exoskeletons and orthoses) and prosthetics. The proposed
actuation system, which uses shape memory alloy (SMA)
artificial muscles in a spring-biased agonist–antagonist (i.e.,
differential-type13 which is made of two opposing SMA
elements) configuration, is demonstrated on a 4 degree-offreedom
(DOF) biomimetic artificial finger testbed. The testbed
itself is anthropomorphically and kinematically accurate
physical model of the natural hand. Note that the above industrial
dexterous hands mostly utilize the conventional electric
or pneumatic actuation methods. However, the more strict
considerations on size, appearance, weight, noise, and cost
requirements14 of prosthetic or rehabilitation devices hamper
the free use of conventional actuators that are bulky and noisy,
and the use of complex motion transmission mechanisms. In
an effort to improve the actuation system, a number of promising
“artificial muscle” actuators that exhibit life-likemuscle
behaviors have appeared, most notably McKibbon pneumatic
artificial muscles15 and SMA artificial muscles. This paper
is focused on the latter type, which have been successfully
implemented in many biomedical applications.16
In the literature, SMA muscle wires have been proposed
as actuators for a number dexterous hand and finger design,
including the Hitachi Hand.17 This is another industrial robotic
hand—a four-fingered (three fingers and a thumb) that
utilizes multiple 0.02mm and 0.035mm diameterSMA wires
to actuate its finger and wrist, respectively. De Laurentis and
Mavroidis18 proposed a combined use of SMA wires and
tendon cables for dexterous prosthetic hand applications,
focusing on the mechanical design and fabrication of a finger
using the selective laser sintering (SLS) rapid prototyping
technique to facilitate the routing of the cables through it
(the cables are then to be crimped to differential-type SMA
wires in the palm). Very recently, Price et al.19 proposed a
three-fingered SMA-based prosthetic hand, with bias-type
SMA wires (i.e., composed of an SMA element and a
bias spring) directly routed through the finger joints in a
traversing arrangement. The main advantage of SMAs is that
they can be used in direct-drive configuration eliminating
the need for complex transmission systems. Furthermore,
they possess a high power to weight ratio enabling the
design of compact, lightweight systems without too much
compromising power capabilities. Moreover, SMAs only
use the phase transformation for actuation which permits
silent operation. However, actuation rates are dependent on
the cooling capacity of the wire which limits the actuator
bandwidth. Other limitations are: limited life cycle, nonlinear
operation owing to hysteretic behavior and still low actuation
strains. The pros and cons of using SMAs for prosthetics are
summarized in Kyberd et al.14 — who suggest that, due to the
comparably low actuation bandwidth and forces, they could
be more appropriate for a child’s prosthesis than an adult’s.
In order to design the proposed biomimetic tendon-driven
actuation system, and the artificial finger testbed for the subsequent performance evaluation, the natural finger and
its physiology—the muscle and tendon architecture and
the sensory abilities—were studied and mimicked in a
practically efficient manner. A novel contribution of this
paper is the integration of a compliant tendon (via a springslack
element) to each one-way SMA muscle wires. This
allows the formation of true three agonist–antagonist (or
differential) artificial muscle pairs for the actuation of the
flexion/extension and abduction/adduction of the metacarpophalangeal
(MCP) joint and the flexion/extension of the
proximal interphalangeal (PIP) joint of the artificial finger.
As a result, the proposed actuation system produces similar
manipulative and functional abilities found in the natural
finger. Tactile feedback is provided by the use of a simple
resistive force sensor placed on the fingertip surface, while
joint position feedback is obtained by embedding miniature
potentiometers and a resistive bend sensor into the finger
joints. A combined pulse-width-modulated proportionalderivation
(PWM-PD) feedback controller and minimum jerk
trajectory feedforward controller are implemented for each
active joint via on-board microcontrollers to enable closedloop
biomimetic control of the artificial finger. The resulting
system is a low-cost, lightweight, stand-alone system suitable
for ambulatory applications in rehabilitation robotics.
2. Human Finger Physiology
This section describes the key features of the human finger
anatomy that we have considered to design an artificial finger
that can be characterized as biomimetic.
2.1. Bones and joints of the human finger
The fingers of the human hand consist of three intercalated
bony segments: the proximal, middle, and the distal
phalanges. The proximal phalange is located at the base
of the finger, connected to the metarcarpal bones in the
palm of the hand, while the distal phalange is located at
the fingertip. The finger joints are the MCP, the PIP, and DIP
(distal interphalangeal) joints. Fig. 1 illustrates the location
of the finger joints and phalanx. The MCP joint of the hand
can be considered as a 2 DOF universal joint that allows
for adduction/abduction and flexion/extension. The PIP and
DIP joints are both single DOF revolute joints that are only
capable of extension and flexion. However, the PIP and DIP
joints are interdependent, i.e. the DIP is a passive DOF that
is driven by the rotation at the PIP. Hence, the natural finger
can be considered as a 4 DOF mechanism with three active
and one passive joints.
Fig. 1. Anatomy of the index finger.
Table 1. Range of motion (ROM) of index finger23.
The range of motion (ROM) at the joints varies from finger
to finger. Although the joint surface geometry defines the
joint ROM, the effective range is also limited by the tendon
network and ligaments of the fingers. The typical ROMof the
index finger,which has the greatest range of extension/flexion
amongst the fingers, is shown in Table I.
2.2. Muscles and tendons of the human finger
The tendons of the natural finger are collagen-based with
nonlinear stiffness characteristics. Since the tendons get
stiffer as they are stretched, they allow finger joints to flex
or extend within a limited range. They also permit the finger
to return to its original position after flexion/extension or
abduction/adduction. The dynamic and highly redundant
nature of the tendon structure renders the finger-actuating
anatomy complex and difficult to fully comprehend and
model. As such, only the tendons essential for the index
finger flexion/extension and abduction/adduction are studied
and mimicked in our design.
The muscles of the natural finger can be categorized into
two groups: (i) extrinsic muscles, which are heavy lifting
muscles located in the forearm, and (ii) intrinsic muscles,
which are weaker muscles originating from the palm and
used for precision movements of the fingers. Finger flexion
is produced by the action of two extrinsic flexors: flexor
digitorum superficialis (FDS), flexor digitorum profundus
(FDP). The FDS tendon attaches the base of the middle
phalanx, while the FDP attaches to the distal phalanx as
shown in Fig. 1. Finger extension occurs through the action
of a web-like structure referred to as the extensor hood
that rides on the dorsal surface of the finger. Two main
extrinsic extensors are the extensor digitorum (EDC) and
extensor indicis (EI). The EDC and EI tendons merge with
the extensor hood at the MCP. Beyond the hood, the EDC
and EI separate into three bands: the central band that inserts
dorsally at the base of the middle phalanx and the two
lateral bands that rejoin as a terminal tendon at the base
of the distal phalanx. Besides the above extrinsic flexors and
extensors, three intrinsic muscles are necessary for finger
motion. These are the lumbricals (LU), the dorsal and the
palmar interosseous (IOs). The attachment of the LU and IOs
are also shown in Fig. 1. The two IOs are connected to the
sides of the proximal phalange. They work in opposition and
control the adduction and abduction motions of the finger.
2.3. Finger senses
Besides its primary prehensile and manipulative functions,
each finger also acts as a sense organ. The finger senses can be
grouped into internal and external senses. The external finger
senses, or tactile senses, refer to the tiny receptors embedded
in the skin that capture and relay sensations of contact, pain,
and temperature to the brain through the central nervous
system.20 The internal senses, or proprioceptive senses,
refer to receptors that are found within the human body,
attached to joints, tendons, and muscles. The proprioceptors
enable humans to perceive body movements, position and
orientation in space, as well as assessing the external force
the human body is subjected to, when muscles and joints
undergo movements.21
3. Design of Biomimetic Artificial Finger Testbed
The design of a biomimetic artificial finger requires a
profound understanding of the biological features of the
human hand. However, the essential design goal is to
accurately represent the important biological functions of
the natural finger. In this work, the degree of emulation
was limited to the following key factors, which were
deemed essential characteristics of a biomimetic artificial
finger: (i) anthropomorphically accurate size and appearance;
(ii) kinematically accurate motion, (iii) tendon-driven
agonist–antagonist biomimetic actuation, and (iv) biomimetic
sensory feedback. Our key design constraints were
to achieve these characteristic in a cost-effective and
lightweight manner for rehabilitation robotic applications
(e.g., prosthetics/orthotics or wearable exoskeletons). This
section describes our biomimetic design philosophy behind
the design of the artificial finger testbed, which is used to test
the proposed tendon-driven actuation mechanism.
3.1. Anthropomorphically accurate size and appearance
Firstly, an anthropometric size was desired as our design
goal was to maintain the physical attributes of the natural
finger, while matching it functionality at the same time. Data
pertaining to hand dimensions are available from Buccholz
et al.22, where finger anthropomorphic data was conveniently
expressed in terms of statistically derived coefficients that
enabled for phalangeal lengths, phalangeal breadths/depths,
and joint centers to be estimated from data on hand length,
hand breadth, and bone length, respectively. The resulting
dimensional values are summarized in Tables II, III, and IV.
The artificial finger was designed within the boundaries of
the physical dimensions given in the above tables to closely
resemble the contours of the natural finger. Figures 2(a) and
2(b) are the CAD representations of the resulting artificial
finger design, which is anthropomorphically consistent with
the natural finger.
Table 2. Phalangeal length estimates
Table 3. Phalangeal depth and breadth estimates.
Table 4. Joint center location estimates.
3.2. Kinematically accurate motion
To enable a biological motion resemblance, the artificial
finger was modeled after the natural hand’s kinematics. As
shown in Fig. 3, our biomimetic artificial finger is hence made
up of three links corresponding to the proximal, middle, and
distal phalanges of the natural finger. Joint movement in the
natural finger is described by the movement of the finger bone
segments along articular surfaces. The convex and concave
topologies of the contacting bone extremities characterize
the human finger joint as ball-type joints. However, the
finger joints are spanned by muscles, tendons, and ligaments
which restrain the latter from having a 6 DOF motion.
These kinematic constraints allow simplifications to be made
when modeling the finger movement. Hence, the 2 DOF
articulations at the MC Pare replicated using a universal joint,
which mimics the biaxial nature of this joint. The PIP and DIP
joints are modeled as hinge joints, since they are 1 DOF joits
with articulation in the sagittal plane (plane perpendicular to
the palmar surface) only. Buccholz et al.22 further suggested
that an anatomical estimate of the joint center location can be
defined at the head of the bone proximal to the given joint and
that these joint centers remain fixed along the entire range of
motion of the phalanges. Transferring these features to our
model, fixed axes of rotation were implemented at the head
of the proximal and middle phalanges for the PIP and DIP
joints, respectively. In these joints, rotation occurs about a
shaft common to the head of the proximal phalange and the
base of the middle phalange for the PIP joint, and the head
of the middle phalange and the base of the distal phalange
for the DIP. A four-bar linkage mechanism mounted into
the finger structure coordinates the PIP and DIP in flexion
and extension replicating the natural motion of the two finger
joints. In the natural finger, however, the lateral bands (which
originate from the extensor hood) couple the DIP and PIP
joints, enforcing their passive interdependence.
Fig. 2. CAD models for the proposed biomimetic artificial finger for the experimental testbed. (a) Nominal resting state. (b) Flexed state.
Fig. 3. Kinematic architecture of the artificial finger.
The ROM in the artificial finger joints reflect those of the
natural index finger shown in Table I. A flexion/extension
range of 90° and adduction/abduction of 40° is modeled at
the MCP. Similarly, flexions/extensions of 100° at the PIP
joint and 80° at the DIP joint are modeled. The flexion and
extension limits of all joints are achieved by mechanical
stops, incorporated within the structure of the links. In
summary, Fig. 3 illustrates the kinematic architecture of the
artificial finger.
A significant consideration in emulating the human finger
is that, in its nominal resting position, the finger is not
in a rigidly straight position along the palmar plane. The
proximal phalange is at an angle to the palmar plane,
while the finger segments are also at an angle to each
other. Goniometric measurements of finger joint angles were
subsequently performed on a test sample consisting of six
subjects. Based on these measurements, it was determined
that the proximal link’s resting position is at about 40° with
respect to the palmar plane, while the middle link rests at an
angle of about 20° with respect to the proximal link phalange.
Figure 2(a) shows the nominal resting positions of the joints
implemented in the artificial finger. In an extended position,
however, the centers of rotation of the three joints lie in the
same plane as the palmar plate (see Fig. 4). Note that in both
resting and extended positions, the middle and distal links of
the finger maintain a slightly bent (but at varying) position to
each other, as they are connected at angles (using the internal
four-bar linkage mechanism) to replicate the natural posture
of the corresponding segments.
Fig. 4. Alignment of MCP, PIP, and DIP joints in the extended position.
Fig. 5. Motion analysis on the MCP joint of the index finger to verify the minimum jerk model. (a) Placement of LEDs for Visualeyez system. (b) Comparison between the minimum jerk model and natural joint motion obtained using Visualeyez.
Minimum jerk approximation of natural finger motion. Jerk,
which is the time derivative of acceleration, is a universally
accepted quantity of evaluating motor smoothness of human
limbs. If we apply Hogan’sminimum jerkmotor coordination
theory24 to the motion of the natural finger joints, each
joint should move smoothly from one position to another
following a joint trajectory that minimizes the sum of the
squared jerk, that is,
where θ(t) is the jerk of the joint trajectory θ(t). Hence, in
order to create a truly biomechanically accurate artificial
finger, its joint motion should follow a minimum jerk
trajectory as well. The general solution to Eq. (1) is given
by:
In order to verify the validity of the above minimum jerk
joint trajectory model of the natural finger, a motion analysis
was performed using a Visualeyez motion tracking system
(from PheoniX Technologies Inc.). As shown in Fig. 5(a),
four LED sensors were placed on a subject’s hand for the
Visualeyz system, two on the metarcarpar bone and two on
the proximal bone of the index finger. This setup allows the
measurement of the MCP joint angle between the two bones,
and the subject was asked to move the index finger from
a nominal resting position to a flexed position at the MCP
joint level. The dotted grey line in Fig. 5(b) is an average of
10MCP flexion trials, while the black line is the minimum
jerk approximation over the same range of motion. It can be
seen from the figure that the natural MCP flexion motion indeed
follows a very similar trajectory to that of the minimum
jerk model of Eq. (3). The model was found to be acceptable
and was subsequently implemented as a biomimetic feedforward
controller for the proposed artificial finger (Section 5.4).
Fig. 6. A CAD representation of potentiometers and bend sensor embedded in the artificial finger. Contact force sensor is located at the fingertip (not shown). Inset shows the actual force (top) and bend (bottom) sensors.
3.3. Biomimetic sensory feedback
Resistive sensors, which offer a cost-effective solution
for implementing sensory feedback in the artificial finger,
use variable resistive characteristics of some conductive
materials (e.g., conductive rubber, carbon, or polymer)
to relay information about mechanical motions or forces.
These sensors were chosen based on a number of factors—
compactness, lightweight, good repeatability, and sensitivity
and, of course, low price. As shown in Fig. 6, three different
types of resistive sensors were chosen: thin-film flexible
bend sensors, miniature rotary potentiometers, and thick-film
flexible force sensors.
The commercially available flexible bend sensors (from
Flexpoint Sensor System Inc.) consist of a thin polymide
film coated with a carbon/polymer-based ink. When the
film is bent, the micro separation of the coated ink changes
the electrical resistance of the film. Among commercially
available resistive bend sensors, Simone et al.25 suggested the
Flexpoint bend sensors to be the most accurate and repeatable
for measuring the natural finger flexion. For the present
work, we chose a sensor with no polyester overlaminate,
and mounted it within the upper inner layer of the artificial
finger structure to act as internal proprioceptive sensors,
providing positional feedback of the PIP flexion/extension
movements. Note that the motions of the DIP and PIP
joints are interconnected through the planar four-bar linkage
mechanism; hence, given the position of the PIP joint, the
position of the DIP joint can be easily determined.
While the bend sensors proved to be highly sensitive and
reliable formonitoring the PIP flexion/extension movements,
two miniature rotational potentiometers (Panasonic EVWAE4001B14)
were employed for measuring the MCP
flexion/extension and adduction/abduction movements,
respectively. The 2 DOF motion requirement for the MCP
joint prohibited the use of the bend sensors, as these can be
allowed to bend only in one direction.
Although many different types of biomimetic tactile
sensors have been proposed in the literature,26-28 it is still
very difficult to replicate the multifaceted functionalities of
the biological skin that is capable of multiple tactile sensing
modes (see Section 2.3). In thiswork, only one tactile sensing
mode—contact force—was attempted for practical reasons.
The sensor is a commercially available polymeric thick-film
force sensitive resistor (FSR) from Interlink Electronics. The
force sensorwas applied only to the fingertip (proven sensory
input location for finger dexterity) of the artificial finger,
then covered it with a layer of elastomeric foam to evenly
distribute any applied force and improve the repeatability
of the measurements. Although this type of sensor is
generally appropriate for qualitative rather than precision
measurements, the performance was found to be sufficiently
accurate for measuring fingertip forces (see Section 5.4).
4. Biomimetic Tendon-Driven Actuation Mechanism
4.1. Biomimetic tendon architecture
Human finger joint motion is produced by contracting
muscles in the forearm and palm that are attached to the finger
bones through a convoluted network of interdependently
acting tendons and ligaments. The emulation of this complex
architecture is, to date, an unattained benchmark. A partial
physical modeling of the finger anatomy, namely the extensor
mechanism, was achieved byWilkinson et al.29 However, the
representation of this anatomical complexity is unnecessary
for general rehabilitation robotic applications. In our work,
large simplification of the complex tendon architecture is
made possible due to the fact that we have mechanically
represented the natural finger joints as simple 2 DOF
universal (MCP) and 1 DOF hinge (PIP) joints. Hence,
the multifunctionality nature of the natural tendons and
ligaments that, as well as producing motion, also restricts
the finger joint to 1 DOF or 2 DOF, was not fully replicated.
Fig. 7. (a) Extensor and adductor tendon cable configuration. (b) Flexor and abductor tendon cable configuration.
Fig. 8. Differential spring-biased SMA joint actuation mechanism. The insets show the actual SMA actuator and spring-slack element implemented.
4.2. Biomimetic actuation mechanism using compliant tendons and SMA artificial muscles
As shown in Fig. 7, flexible cables were attached directly
to the artificial finger structure, mimicking the tendon-driven
configuration of the natural finger. Two flexor cables were
attached to the proximal and middle links emulating the FDS
and FDP tendons. Two extensor cables were attached on the
dorsal surface of the proximal and middle links, emulating
the EDC and EI tendons. Finally, two adductor/abductor
cables were connected to the ulnar and radial sides of the
proximal joint mimicking the IO and LU tendons. The flexor,
extensor, and adductor/abductor cables act as antagonist
muscles enabling flexion/extension at the MCP and PIP and
adduction/abduction at the MCP. As already mentioned, the
DIP joint flexion/extension is coupled to that of the PIP joint
by the implementation of the miniature four-bar linkage
mechanism between those two joints inside the artificial
finger structure. The four-bar linkage mimics the action
of the natural finger’s lateral bands, coupling the PIP and
DIP joints so that both joints attain their maximum flexion
angles (100° at the PIP and 80° at the DIP) simultaneously.
While the natural finger has no direct flexor and extensor
attachment points to the proximal phalange (i.e., the MCP
flexion/extension occurs through the action of the sliding
extensor hood), the proposed tendon configuration allows
the mimicking of the finger kinematics. Note that the exact
attachment locations of the tendon cables on the finger
structure were obtained in our previous work30 through
kinematic and static torque analyses, which were omitted
in this paper for the sake of brevity.
A spring-biased SMA mechanism is one where a spring is
used to oppose the contraction of a SMA such that, when
the wire cools, the spring’s opposing force helps the wire
return to its original length. Typically, SMA-based robotic
actuation systems, e.g., Elahinia and Ashrafiuon,31 consist of
a single SMA spring-biased mechanism where link rotation
is produced by the action of a one-way SMA actuator and the
link’s return to the original position is made by a bias spring
(either linear or torsional) connected in opposition to that
actuator. However, when the human finger is in its natural
resting position, it maintains a nominally flexed position
(Fig. 2(a)). Full range of motion can be achieved by moving
the finger in both flexion and extension directions about its
nominal resting position. Since a spring-biased, one-way
SMA actuation mechanism can only be used to pull the
artificial finger in one direction (e.g. flexion or abduction)
and not in the other direction (e.g., extension or adduction),
we required an actuation mechanism that would permit
biomimetic bi-directional (or differential) agonist–antagonist
pulling motion about each finger joint. Furthermore, the
elasticity of the natural muscle–tendons is a crucial characteristic
of the finger’s kinematic architecture and needed
to be replicated. In robotics, such compliance is a necessary
element in providing stabilizing effect during contact tasks
(e.g., gripping), especially in an unstructured environment.32
A schematic diagram of the proposed biomimetic
compliant differential actuation mechanism is shown in
Fig. 8. One end of the tendon cable is attached to the artificial
finger structure, mimicking the attachment of the natural
tendon to the finger bones, while the other end of the tendon
cable is tied to the SMA actuator (from Miga Motors
Company). The actuators are placed remotely to the finger
joint, similar to the natural finger’s extrinsic musculature.
Joint rotation is produced by the contractile action of two
SMAactuators, placed in opposition to each other in a double
spring-biased fashion. As shown in the lower inset of Fig. 8,
passive compliance is introduced in the tendon cables of
the artificial finger by connecting a spring in parallel to a
slack portion of each tendon cable such that, as the SMA
actuator contracts, the spring in the corresponding tendon
elongates until the slack is absorbed and the tendon is taut.
At this point, the tendon can be considered to have “infinite”
stiffness and furtherSMAactuator contraction causes tension
to be transferred to the finger for link rotation. This simple
spring-slack artificial tendon effectively mimics the nonlinear
stiffness of the natural tendon whose stiffness tends to infinity
as it approaches its natural limit of extension. The dual
spring-biased configuration permits the two SMA actuators
to work as an agonist–antagonist pair, enabling both active
extension and flexion of the joint.
In the proposed differential spring-biased actuation
mechanism shown in Fig. 8, the spring S1 biases the SMA
actuator A2, while the spring S2 biases the SMA actuator
A1. Flexion occurs by the contraction of A1 on the finger
while extension occurs by the contraction of A2. As an SMA
actuator contracts, the spring in the tendon cable to which
the actuator is connected to (we will refer this tendon as the
“active tendon”) expands, absorbing the slack in the active
tendon until the cable is fully stretched and taut. While the finger
can rotate simultaneously during the absorbing of the
slack (depending on the spring stiffness), at this point any
further contraction of the SMA actuator acts directly on the
finger along, rotating it about the joint axis. Simultaneously,
as the finger flexes or extends, the spring in the opposing
tendon (we will refer this tendon as the “passive tendon”)
expands and the slack in the passive tendon is also absorbed.
Note that the springs in both the active and passive tendons
need to be stretched whether the artificial finger is in a
flexed or extended state with respect to its resting position.
When an SMA actuator (A1 or A2) is deactivated and the
contraction force is removed, the springs will go back to
return to their original positions; and the spring in the active
tendon recreates the slack. The spring in the opposing passive
tendon reverse-biases the SMA actuator, exerting a pulling
force on the artificial finger structure, and returns the joint to
its original position. While the nonlinear stiffness property
of the biological tendons limits the flexion/extension range
of the natural finger, the limit on the range of motion of the
artificial finger is dependent on the following two factors:
(i) SMA actuator’s contraction range—the SMA actuator’s
stroke range must be sufficiently large to first absorb the
slack in the active tendon to which it is connected in order
to produce joint rotation, and (ii) slack length in the passive
tendon opposing the motion—the link cannot rotate beyond
the elastic limit of the opposing tendon. As such, the proposed
actuation mechanism demands a careful balance between the
allowable tendon slack and the SMA contraction range to
generate the desired range of motion.
One of the practical limitations of the chosen differential
SMA actuation configuration is that, due to the presence of
the slacks in the tendons, only a portion of the SMA strain
ranges are available to cause the effective joint rotation.
However, because of the fact that two SMA actuators are
employed for active bi-directional rotation of each joint DOF,
its overall range of motion is still greater than that of an
equivalent single spring-biased SMA actuation mechanism
(with no slack). Furthermore, the combined action of the
spring and SMA in the tendon cable mimics the characteristics
of the natural muscle–tendon, providing power only
during contraction, yet providing compliance to deal with an
opposing load as well. Also note that SMA actuators can be
controlled in partial contraction, allowing finger links to be
partially flexed and extended. The use of the two opposing
SMA actuators per DOF allows the additional benefit of
more precise finger positioning, as the direction of motion
can be quickly reversed at any point during joint rotation.
Dynamic modeling and control design of the proposed
actuation system will be addressed in Part II of this work.
5. Experimental Evaluation
5.1. Experimental setup
The experimental setup consisted of a biomimetic artificial
finger, which was constructed using a Stereolithography
rapid prototyping system (SLA-3500),mounted on an optical
breadboard (see Fig. 9). The SMA actuators (DM01-15-
PULL), which are off-the-shelf products from Miga Motor
Company, were mounted on the breadboard as well. The
patented internal architecture of MigaMotor’s SMA actuator
produces a relatively large stroke length in a compact,
lightweight housing. It is capable of producing a half inch
linear stroke with a maximum contracting force of 20 N.
In addition to providing a mounting surface, the aluminum
breadboard also acted as a heat sink, improving the cooling
rate of the actuators (however, this advantage would not be
available in a real prosthesis/orthosis). The artificial tendon
cables were attached to the finger structure, routed through
the finger core and connected to their corresponding SMA
actuators. A Teflon-coated microfibre line (SpiderWire’s
Stealth) was chosen for the tendon cables. This allowed
the creation of strong tendons that were also resistant to
twisting and abrasions, so that they could easily be routed
and fitted within the finger structure, without risking failure
through frictional contacts or sharp bends. More importantly,
the material’s teflon coating provided a very low coefficient
of friction—an important consideration where the tendons
had to pass through several guides and traveled in directions
at various angles.
A microcontroller (PIC16F917) from Microchip Technologies
was used to control the finger motion. For preliminary
evaluation purposes, the microcontroller was programmed
with a simple ad hoc proportional derivative (PD) controller
as described in Section 5.3 and generated a pulse-widthmodulation
(PWM) control signal based on a set reference
value (which can be a desired joint positional angle or
fingertip force) entered by the user. The PWM control signal
operated power MOSFET transistors, acting as switches to
modulate the voltage applied to the SMA actuators. The
microcontroller’s built-in analog-to-digital (A/D) converter
translated analog feedback information from the finger
sensors to a digital form suitable for handling by the
microcontroller. Serial configuration data sent by a host PC
(through an RS232 port) were processed by the microcontroller’s
built-in UART that performed serial to parallel and parallel
to serial data conversion to and from the microcontroller.
A terminal program running on the host PC was used for
communication with the finger’s microcontroller. The user
interface was based on a menu structure with all text prompts
generated by the microcontroller’s firmware.Once all control
gains and desired final finger positions (or a fingertip force)
were entered, the finger was capable of operation as a standalone
device. The microcontroller’s firmware sampled the
position of the finger in space by reading the appropriate
sensors at 100 Hz, and generated appropriate closed-loop
PWMcontrol signals until the desired finger position or force
value was reached.
Fig. 9. Artificial finger testbed with six tendon cables routing through the finger core and attached to the corresponding six remotely placed SMA actuators. (a) Artificial finger prototype constructed using SLA-3500 RP machine loaded with Vantico CibaTool SL5510 resin. (b) Artificial finger and six SMAs mounted on optical breadboard.
Fig. 10. Sensor response plots for the MCP abduction/adduction and MCP flexion/extension potentiometers. (a) MCP abduction/adduction potentiometer calibration curve. (b) MCP flexion/extension potentiometer calibration curve.
5.2. Sensor calibration
To provide valid experimental results, it was necessary
to calibrate the various angle sensors and fingertip force
sensor employed in the system. For all sensors used,
calibration was done in terms of the number of A/D counts
reported by the microcontroller’s built-in A/D converter.
Calibration of the various joint angle sensors was performed
using a goniometer designed for human finger joint angle
measurement. Calibration of the fingertip force sensor was
performed by static loading of the sensor using a series of
weights of known mass and a load cell.
The rotary potentiometer selected for the measurement of
the MCP flexion/extension and MCP adduction/abduction
is an inherently linear device and, beyond simply correlating
joint angles with the resulting A/D count values and applying
a basic straight line fit, no further manipulation of the
data was required. The resistive bend sensor used for
the PIP flexion/extension measurements and the resistive
force sensor used for measuring the fingertip forces are,
however, nonlinear in their responses. It was found that
the embedded control algorithms were sufficiently robust
that the linearization of the output from these sensors was
unnecessary. However, it was necessary to plot the sensor’s
response and find a fourth-order polynomial fit to the
response curves to facilitate the creation of a look-up table
for the microcontroller. Figures 10 and 11 showthe responses
obtained from the various sensors.
5.3. Control strategy
SMAs are inherently nonlinear and hysteretic in nature and,
as such, pose a challenge as far as the implementation of an
accurate and robust controller is concerned. Furthermore,
the dynamic behavior of SMAs is highly dependent on
the fabrication process, alloy content, and training. High
parametric uncertainty accompanies the nonlinear SMA
models31,33 available in the literature, further complicating
the design of a controller. A robust controller is required
in order to account for all nonlinearities and allow precise
control of the proposed spring-biased differential SMA
actuation system—this will be addressed in Part II of
this work. In this paper, the focus was placed on quick
testing and evaluation of the actuation mechanism with
a simple and practical embedded pulse-width-modulated
proportional-derivative (PWM-PD) controller.
During SMA actuation, the martensitic and austentic
transformation rates of the SMA wire are controlled solely
by the rate at which heat is transferred to and removed
from the wire. In the case of electrical (or joule) heating,
heat transfer is dictated by the level of current applied.
While electrical heating using direct current (DC) is very
effective in rapidly increasing the material’s temperature,
merely turning the current off once the desired actuator
position is reached is not a solution, since the actuators return
to their initial extended position upon cooling. Therefore, a
means of varying the amount of heating power supplied to
the actuator SMA wire is required. Direct control of the
actuator’s DC voltage would be one way to vary the amount
of heating that the SMA wire experiences, and therefore the
degree to which a state change progresses. Direct control
is, however, wasteful of energy, with whatever fraction of
the power not required by the actuator load being simply
dissipated as waste heat. PWM is a more practical approach,
where the relatively slow response time of an SMA element
serves to average the duty cycle of PWM signals, enabling
uniform heating and effective control over the transformation
process.33 Little heat is generated with this method of control
and rechargeable batteries can be used to provide power to
theSMAactuators in stand-alone, ambulatory applications in
rehabilitation robotics. In addition, PWM has the advantage
of being easily implemented using microcontrollers.
Hence, PWM voltage signals were used as the control
variable and integrated with a PD feedback controller
possessing a satisfactory stability margin for standalone
operation of the biomimetic artificial finger. The
required controller was implemented completely in firmware
programmed into the system’s microcontroller. In addition,
an integral feedback term was also calculated although not
used in this Part I of the work. However, the end result was
a microcontroller-based system capable of controlling finger
joint motion under fully embedded PWM-PID control, and
the proportional (Kp), integral (Ki), and derivative (Kd) gain
terms were all user-programmable.
The PWM signals applied are voltage signals of uniform
height and variable duration. Varying the duty cycle of the
PWMsignal varies the average control energy that is directed
to the SMA actuator. Increasing the duty cycle increases the
applied energy, causing the temperature of the actuator to
increase, thus increasing the rate of actuator contraction. If
the duty cycle is reduced below the actuation threshold, the
wire cools below the actuation temperature, and a reverse
bias force will then cause the SMA wire to stretch toward
its original prestrained length. If the duty cycle is, on the
other hand, maintained at just the threshold actuation value,
the SMA wire maintains its existing length without any
change in strain. The actuator contraction rate is, thereby,
controlled by varying the duty cycle of the applied voltage
until the desired angular position is achieved. Note that the
maximum applicable voltage is 28 V for the chosen Miga
Motor’s SMA actuator. However, this voltage level reduces
the SMA actuator life and may cause overheating. As such,
a voltage level of 8 V was chosen for the PWM signal, since
this voltage level yields adequate actuator response without
compromising actuator life. A constant PWM frequency of
225 Hz was used with the duty cycle capable of being varied
from 0 to 100%. Experimental identification showed that a
minimum 20% threshold duty cycle was required to maintain
the SMA actuator in a steady activated state.
The set point for the controller is a desired angular
position (θd) (or desired fingertip force for closed-loop
force control). The positional sensors (the bend sensor and
potentiometers) measure the actual angular position (or the
force sensor measures fingertip force), which is fed back
to the controller. The error signal, which is the difference
between the desired and measured values, is fed into the
controller and a proportional error term and a derivative
error term are calculated. The proportional and derivative
error terms are then added to produce the final control signal.
The resulting value is then scaled to provide a corresponding
PWM signal with a value somewhere between 0 and 100%
duty cycle.
Fig. 11. Sensor response plots for the PIP bend sensor and fingertip force sensor. (a) PIP flexion/extension bend sensor calibration curve with a fourth order polynomial fit. (b) Fingertip force sensor calibration curve.
Fig. 12. Open-loop MCP adduction and abduction motion profiles. (a) MCP adduction: open loop. (b) MCP abduction: open loop.
5.4. Experimental results
The controller gains (Kp and Kd) used in this paper are
obtained and tuned using direct experimental observations
rather than a complex nonlinear mathematical model of the
system, which will be derived in Part II. The resulting gain
values varied depending on the particular joint DOF being
activated and the direction of actuation (e.g., flexion versus
extension), ranging typically from 500 to 10,000. It was
found that the response time of the controller, which had
an update rate of 10 ms, and large gain values were possible
without instability or overshoot problems.
The purpose of the following experimentswas to demonstrate
the 3 DOF active motion (excluding the 4th passive DOF)
of the biomimetic artificial finger via the proposed springbiased
differential SMA-based tendon-driven actuation
system. Open-loop tests were first performed to assess the
effectiveness of the actuation mechanism designed, most
specifically with respect to the agonist–antagonist motion of
each active finger joint. Closed-loop tests were then carried
out to assess the performance of incorporating feedback
control into the system.
As shown in Fig. 9(a), the artificial finger was placed in the
nominal resting position to mimic the natural posture of the
human finger when at rest. The springs and the slacks in the
tendons were adjusted under slight tension to always maintain
the finger in this initial position when the SMA actuators
are inactive. The MCP joint was thus positioned at 40° to
the metacarpal link and the PIP joint at 20° relative to the
proximal link. The passive DIP was automatically positioned
by the four-bar linkage coordinating the PIP and DIP joint
motion. Joint motion was initiated by a user request to move
the link into a desired position. The controller generated a
PWM signal of fixed duty cycle for open-loop motions and
variable duty cycle for closed-loop motions. The open-loop
duty cycle was limited to 50% to avoid overheating of the
SMAwires inside the actuator, and hence permanent damage.
Given the points of attachment of the elastic tendons from
the finger’s joint centers and the slack required in each
tendon, the required minimum SMA contraction length was
calculated to be at least 1 inch as per Eq. (8). However,
although the tendon slacks were set up to enable full ranges of
joint motion (i.e., 50° flexion, -40° extension, and +/-20°
adduction/abduction at the MCP; 80° flexion and -20°
extension at the PIP joint about the resting position), the
actual range of motion tested was restricted due to the limited
stroke of the Miga Motor’s SMA actuators that we employed
(i.e., 0.5 inch; 1 inch stroke SMAactuators are being custombuilt
as our ongoing work). Our preliminary experimental
testing showed that only the following joint ranges could be
obtained repeatedly in the closed-loop configuration without
damaging the SMA actuators: MCP adduction/abduction of
+/-15°,MCP flexion/extension of +/-20°, and PIP flexion
of +25° and extension of -15° about the resting position.
Since SMA contraction responds to temperature changes
caused by joule heating, the average current delivered to
the SMA wire was measured. Open-loop tests showed that
an average of about 0.7 to 0.8 A was sufficient to produce
joint motion. This was achieved by setting the PWM to a
50% duty cycle. The open-loop graphs (Figs. 12–14) indicate
satisfactory but slow (at certain joints) agonist–antagonist
motion of the finger link. For instance, the rate of motion for
MCP abduction/adduction as well as MCP flexion/extension
was much slower than that for PIP flexion/extension. The
relatively high joint settling times at the MCP are related to
the high torques required to move the entire finger structure
at that joint, while at the PIP, the SMA actuator acts on
the middle and distal links only. The double spring-biased
mechanism successfully returned each joint to its original
position. However, the return process was slow and unsteady
in all open-loop cases, with an unacceptable return period in
the 20- to 30-s range. This behavior is due to the high cooling
times associated with the Miga Motor SMA actuators that
prevent their fast return. Furthermore, once actuator power
was applied, a time delay of approximately 2–8 s (depending
on duty cycle) was observed before joint motion occurred.
This delay corresponds to the SMA actuation time (about 1
s at a constant 8 VDC), as well as the time required for some
initial slack to be absorbed from the tendon cables before the
actuator affects joint motion.
Fig. 13. Open-loop MCP flexion and extension motion profiles. (a) MCP flexion: open loop. (b) MCP extension: open loop.
Fig. 14. Open-loop PIP flexion and extension motion profiles. (a) PIP flexion: open loop. (b) PIP extension: open loop.
The closed-loop plots (Figs. 15–17) showed that the
feedback control incorporated into the system significantly
improved the performance of the joint motion of the finger.
The controller produced signals of variable duty cycle based
on the current link’s position (as measured by the bend
sensors) with respect to the desired position. The current
graphs indicate a sharp increase in the current level to a peak
value of approximately 1.4 to 1.5 A at the beginning of the
joint motion. The current then tapered to a lower level as
the desired joint angle was approached. Finally, the current
reduced to a still lower value sufficient to hold the finger
in position once the desired joint angle was reached. This
current profile behavior suggests that aPWMsignal with high
duty cycle was initially generated, enabling the SMA wire to
heat up rapidly. The PWM duty cycle was then reduced to a
value yielding a constant actuator position that corresponds
to a desired joint position.
The embedded PWM-PD controller was highly effective
in reducing the response time of the system, enabling final
positions to be achieved within a matter of seconds. Once the
desired angular position was achieved, the finger maintained
a steady posture. Although the closed-loop position control
produced rapid and steady finger motion, spring-biased
return to the original resting position was observed to be
still slow in the closed-loop configuration as well, which is
expected, since the return to a neutral position was effected
simply by removing actuator power, as in the open-loop
case. Powering the opposing actuator during the joint’s return
phase to its resting position would be an obvious solution to
this problem, which will be addressed in Part II. Also, adding
some sort of an active heat sink to the SMA actuator should
increase the SMA cooling rate and improve the rate at which
the finger joints return to their resting position.
Next, the biomimetic feedforward controller (i.e., the
minimum jerk trajectory) that was developed in Section 3.2
was added to the PWM-PD feedback controller of the
artificial finger. The minimum jerk path was calculated for
the range of motion of the finger at the MCP (from relaxed to
flexed) and was implemented as a look-up table in the microcontroller.
The artificial finger was driven to follow the lookup
table and its resulting motion was analyzed using the
Visualeyez system, which showed a satisfactory agreement
between the actual motion and the minimum jerk reference
motion (Fig. 18).
Fig. 15. Closed-loop MCP adduction and abduction motion profiles and the current profiles of the corresponding SMA actuators. Starting from a nominal position of 0°, the set values of 11° for both adduction and abduction were successfully achieved. (a) MCP adduction: closed loop. (b) MCP abduction: closed loop.
Fig. 16. Closed-loop MCP flexion and extension motion profiles and the current profiles of the corresponding SMA actuators. Starting from a nominal position of 40°, the set values of 55° and 25° for flexion and extension, respectively, were successfully achieved. (a) MCP flexion: closed loop. (b) MCP extension: closed loop.
One of the main functional tasks of the human hand is the
grasping of objects, and the amount of force applied while
holding an object must be precisely controlled. Therefore,
once the ability to move finger joints to set positions had
been evaluated, a subsequent experiment was performed to
ascertain howsuccessfully closed-loop force control could be
applied to the fingertip. It was decided that closed-loop force
control of the PIP joint would be the most logical approach,
since that joint is directly linked to the fingertip’s DIP joint.
The fingerwas oriented to allowthe fingertip pressure sensor,
mounted near the end of the underside of the DIP joint,
to transfer force to a load cell for force measurement. A
desired fingertip force (an A/D count value corresponding
to approximately 0.2 N force) was input to the controller
and the PIP flexion actuator began applying force that was
transferred to the load cell and the fingertip force sensor. The
results of this experiment are shown in Fig. 19.
Due to the particular circuit configuration for this
force sensor, decreasing A/D count readings correspond
to increasing force values. It can be seen that the finger
reaches a steady-state value where approximately the desired
fingertip force is applied to the load cell. However, one
potential issue of consequence can be seen in looking at
the plot: over time, the actual measured fingertip force
decreases while the force reported by the fingertip force
sensor stays relatively constant. This is due to the type of
sensor (i.e., FSR) chosen to measure the fingertip force.
When compressed for long periods of time (more than a
few seconds) the resistance of the thick-film sensor slowly
changes. All sensors of this type exhibit this shift to a degree,
with some manufacturer’s sensors being better than others in
this regard. However, this effect is reversible once pressure
is removed from the sensor. The low cost and lightweight
advantages of this type of sensor made its use attractive for the
artificial finger, and incorporation into rehabilitation robots
might still be practical given the relatively small magnitude
of the phenomenon, and the fact that the human hand is not
generally required to grasp objects for long periods of time
with significant accuracy.
Fig. 17. Closed-loop PIP flexion and extension motion profiles and the current profiles of the corresponding SMA actuators. Starting from a nominal position of 20°, the set values of 40° and 10° for flexion and extension, respectively, were successfully achieved. (a) PIP flexion: closed loop. (b) PIP extension: closed loop.
Fig. 18. Comparison between reference and actual minimum jerk flexion trajectories of artificial finger’s MCP using Visualeyez motion tracking system. (a) Placement of LEDs for Visualeyez system. (b) Closed-loop MCP joint following minimum jerk flexion trajectory.
Fig. 19. Sensor A to D counts and measured fingertip force while attempting to apply 0.2 N force using PIP joint force control.
6. Conclusion
The aim of this work was to emulate the biological features
of the natural muscle–tendon arrangement in the human hand
in developing a new actuation mechanism for a biomimetic
artificial finger. It is based on the integration of compliant
tendon cables and one-way shape memory alloy (SMA) wires
in an agonist–antagonist artificial muscle pair configuration
for the required flexion/extension or abduction/adduction
of the finger joints. An anthropomorphically and biomechanically
accurate artificial finger was also developed as a
platform to test the proposed actuation mechanism. The main
features of the proposed biomimetic actuation and finger
system can be summarized as: (i) anthropomorphically
accurate size and appearance; (ii) kinematically accurate
joint motion, (iii) compliant and tendon-driven muscle-like
actuation, and (iv) biomimetic sensory feedback. The entire
system is a compact, low-cost, lightweight, stand-alone
system suitable for ambulatory applications (e.g., prosthetic
and wearable robotics) in rehabilitation robotics, while
capable of producing similar manipulative and functional
abilities found in the natural finger. A microcontroller-based
pulse-width-modulated proportional-derivation (PWMPD)
feedback controller and a minimum jerk trajectory
feedforward controller were implemented in an ad hoc
fashion to evaluate the performance of the finger system in
producing closed-loop biomimetic joint motions.
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