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A. System overview of a virtual prosthetic hand with a biorealistic neuromorphic reflex controller, whose inputs are α motor command, γs and γd commands. B.
Block diagram of the integrated virtual hand system. It consists of a tendon-driven virtual hand, a pair of antagonistic muscles with the biorealistic controller and
a sensory feedback system. Force perturbations can be applied at the fingertip, or at the tendon of flexor/extensor muscles in perturbation experiments. C. Simulation
results unveil that the virtual hand has acquired human-like ability of compliant control as follows. (1) The virtual hand can switch control modes between position
and force naturally according to external loads. (2) The variability of fingertip force increases with the mean force in proportion (R2=0.99, p=0.0000). It implies
the capability for fine force manipulation with low levels of muscle activation. (3) The virtual hand can achieve stable control of finger equilibrium positions and
reflex regulation of muscle stiffness via Ia afferent, which enhances fingertip and muscle stiffness. (4) Muscle stiffness can be modulated by α command linearly
and adaptively adjusted with object stiffness for a given background activation. The length-tension curve and reflex compensation underscore the neuromechanical
mechanism of stiffness adaptation.
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ABSTRACT Objective: Human neuromuscular reflex control provides a biological model for a compliant hand prosthesis. Here
we present a computational approach to understanding the emerging human-like compliance, force and position control, and
stiffness adaptation in a prosthetic hand with a replica of human neuromuscular reflex model. Methods: A virtual twin of prosthetic
hand was constructed in the MuJoCo environment with a tendon-driven anthropomorphic hand structure. Biorealistic mathematic
models of muscle, spindle, spiking-neurons and monosynaptic reflex were implemented in neuromorphic chips to drive the virtual
hand for real-time control. Results: Simulation showed that the virtual hand acquired human-like ability to control fingertip position,
force and stiffness for grasp, as well as the capacity to interact with soft objects by adaptively adjusting hand stiffness. Conclusion:
The biorealistic neuromorphic reflex model restores human-like neuromuscular properties for hand prosthesis to interact with soft
objects.
INDEX TERMS Prosthetic Hand, Compliant Control, Neuromuscular Reflex, Computational Modeling, Stiffness Adaptation
IMPACT STATEMENT Results elucidate the emerging human-like properties of adaptive compliant control endowed with the biorealistic
neuromorphic reflex model for next-generation hand prosthesis.
I. INTRODUCTION
n spite of remarkable advances in the design, manufacture
and control of myoelectric bionic hand prosthesis [1]–[4],
performance of these devices is acceptable at best when
compared to the dexterity of human hand [5]–[7]. Research
on restoring the functions of lost limbs in past decades has
motivated several generations of neural prosthesis [2], [8]–
[10]. A primary challenge for existing bionic hand prosthesis
is to execute precision tasks, such as grasping deformable or
brittle objects. A major limitation of present prosthetic hands
is that its motor control does not behave similarly as human
sensorimotor control. This may lead to frustration in
amputees who could not adapt to the alien behaviors of the
prosthetic hand, therefore, hesitating using it to perform
activities in daily living [7], [11], [12].
The importance of compliant control has been recognized
in robotics. Recently, soft robotic hands with pneumatic
actuation have demonstrated compliant property and robust
grasp of soft objects [13]–[15]. Their compliance is derived
from pneumatic actuation, soft materials and/or flexible
structures. But the range of compliance in soft robotic hands
may still be limited compared to that of human hand driven
by muscles [16], [17].
Alternatively, we developed a biorealistic approach for
hand prosthesis leveraging computational models to restore
human-like neuromuscular control [18]. Real-time
reanimation of human neuromuscular reflex for prosthetic
hand was achieved with neuromorphic models of
biologically realistic elements [18]–[23]. Functional benefits
have been demonstrated in tests with amputees-in-the-loop
controlling the biorealistic prosthesis. The capacity of finger
force control was found comparable to that of an intact hand
finger, but significantly better than that of a conventional
prosthetic controller [24]. The ability to complete delicate
tasks was revealed in tests to grasp slipping or brittle objects,
such as picking up golf balls or potato chips [25]. However,
this prototype of biorealistic hand still lacked antagonistic
muscle control of finger movements. Specifically, its
biorealistic properties were not fully understood with regard
to the origin of compliance and the maneuverability of hand
A Biorealistic Computational Model Unfolds
Human-Like Compliant Properties for
Control of Hand Prosthesis
Zhuozhi Zhang2, Jie Zhang2, Qi Luo2, Chih-Hong Chou1,2, Anran Xie2, Chuanxin M. Niu1,2
Member, IEEE, Manzhao Hao1,2 and Ning Lan*,1,2 Senior Member, IEEE
1 Institute of Medical Robotics, Shanghai Jiao Tong University, Shanghai, China
2 Laboratory of Neurorehabilitation Engineering, School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China
CORRESPONDING AUTHOR: Ning Lan (e-mail: ninglan@sjtu.edu.cn)
This work was supported in part by grants from the National Key R&D Program of China (No. 2017YFA0701104), the National Natural
Science Foundation of China (No. 81630050), and the Science and Technology Commission of Shanghai Municipality (No. 20DZ2220400).
This article has supplementary downloadable material
I
This article has been accepted for publication in IEEE Open Journal of Engineering in Medicine and Biology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/OJEMB.2022.3215726
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stiffness via myoelectrical signals from amputees.
The objective of this study was to unveil the underlying
human-like compliant properties embedded in the
biorealistic hand prosthesis. A virtual twin of the prosthetic
hand with antagonistic muscle control for finger flexion and
extension movements was constructed for real-time
simulation. The main goal was to elucidate the adaptive
mechanism of prosthetic hand stiffness during interacting
with a soft object. We hypothesized that the biorealistic
modelling approach can restore human-like compliant
properties for hand prosthesis. Tests unveiled that the
neuromorphic-based computational model displayed similar
behaviors of stiffness regulation and the capacity of force
control as those of humans qualitatively. Results indicated
that the biorealistic controller acquired a wide range of
stiffness/force control ability, as well as adaptive adjustment
of hand stiffness when interacting with a soft object. The
similarity with human sensorimotor control may lead to a
superior neural compatibility for amputees to better control
the biorealistic hand prosthesis [24], [25]. Preliminary result
was presented in a conference proceeding [26].
II. RESULTS
A virtual twin of the biorealistic hand prosthesis was
developed in the MuJoCo environment with tendon-driven
actuation, fingertip tactile sensors and neuromorphic reflex
model (for details, see Fig. 5(b) in Methods). The virtual twin
was integrated with a pair of neuromorphic antagonistic
muscles emulating neuromuscular reflex control [23] and a
sensory feedback system via electrically evoked tactile
sensation (ETS) [27]. To simplify the control issue of whole
virtual hand, we investigated the control problem of a
prosthetic index finger by a pair of antagonistic muscles. A
comprehensive evaluation on virtual hand properties was
conducted to reveal its human-like behaviors with a
qualitative comparison to the corresponding features of
human neuromuscular reflex control.
A. Control of fingertip force and position
Figure. 1(a) presents an overview of prosthetic control
system. α motor commands activated a pair of antagonistic
muscles with neuromorphic reflex model controlling the
index finger. Muscle outputs drove two motors pulling the
index finger of the virtual hand.
Central to control the system was the Hill’s muscle model
in Fig. 1(b). The α motor command was converted to an
activation signal through a motoneuron pool (MP) and a
twitch model (TM). The latter acted as a low-pass filter and
converted a spiking activation to a muscle twitch signal to
drive the Hill-type muscle. Muscle force was generated
through an activation-contraction process [28]–[32], in
which three factors determined force generation, i.e.
activation factor, fascicle length factor and contraction
velocity factor [29]. The most important element of muscle
force production was the modulation by length-tension effect
in Fig. 1(c) [29], [31]. It was described by a parabolic shape
with a positive stiffness segment and a plateau followed by a
negative stiffness range [29]. In this study, the range of
muscle fascicle length (Lce) was set to operate in the positive
stiffness part of length-tension property to assure stability
during external perturbations. Therefore, Lce range for flexor
was chosen between 0.80 ~ 0.95 Lo and for extensor was
between 0.75 ~ 0.90 Lo. The parallel, serial and tendon
elastic elements worked together to transform
musculotendon length (Lmtu) from externally coupled device
into internal muscle fascicle length (Lce) for force
computation [23], [33]. The active stiffness arising from
length-tension relation along with passive elastic
components in the model contributed to total muscle stiffness
or compliance.
Three tests were performed to verify control capacity of
the virtual prosthetic hand. First, the fingertip forces in
flexion and extension were evaluated and found to vary
linearly with α command (Fig. 1(d)). It revealed that the α
commands of flexor and extensor could produce a well-
behaved fingertip force in a given finger configuration.
Second, force variability of the biorealistic control system
was assessed. The index finger was controlled to press a
wooden block by co-activated α commands embedded with
signal-dependent noise (SDN) [34], as shown in the first
panel of Fig .1(e). The variability of fingertip force increased
with the mean force in proportion. This indicated that the
virtual prosthetic hand had the capability of fine force control
at low levels of muscle activation.
In the third test, the index finger was driven to press a
spring plate with 30 N/m stiffness with a ramp α command
to each muscle. Results in Fig. 1(f) showed three phases of
control: (1) fingertip position (prior to t1), (2) combination of
position and force (between t1 and t2), and (3) force (after t2).
It clearly illustrated that the biorealistic controller could
stably handle switch from position control to force control,
or both without having to explicitly identify the states. This
revealed an important human-like compliant property of
biorealistic control. This nature could allow intuitive control
of fingertip position and force amid changes in external load
during grasping an object.
B. Control of fingertip compliance
Endpoint perturbation test was used to evaluate compliant
property of the tendon-driven virtual prosthetic hand. When
the index finger was stabilized at an equilibrium position (EP)
by activating a pair of constant α motor commands, a vector
of perturbation force was applied to the fingertip, and
system’s response was shown in Fig. 2(a). The endpoint of
finger deviated from the initial EP, then reached to a new EP.
The musculotendinous length (Lmtu) and fascicle length (Lce)
of flexor were shortened and the flexor force was reduced,
while the Lmtu and Lce of extensor were lengthened and the
extensor force was increased according to the length-tension
curve (Fig. 1(c)).
Endpoint stiffness ellipses of the index finger and muscle
stiffness of flexor and extensor were calculated in Fig. 2(b)
and Fig. 2(c). At each EP, the area of endpoint stiffness
This article has been accepted for publication in IEEE Open Journal of Engineering in Medicine and Biology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/OJEMB.2022.3215726
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Fig. 1. (a) The virtual hand was driven by a pair of biorealistic reflex models. Inputs of the models are α motor commands, γs and γd commands. (b) A
Hill-type muscle model. The active component is activated by a motoneuron pool (MP) via a twitch model (TM). Kpe, Kse and Kt represent the stiffness of
parallel elastic element, series elastic element and tendon. Lmtu, Lt, Lm and Lce represent the musculotendinous unit length, tendon length, muscle length
and muscle fascicle length. (c) The relationship between measured muscle force and normalized fascicle length in our model. The normalized range of
flexor Lce is 0.80 ~ 0.95 Lo, while the range of extensor Lce is 0.75 ~ 0.90 Lo. (d). Force generation in flexion and extension. It shows the experimental
scenario and the force responses to α command. (e). Force variability test. It shows the change of α command, muscle force, fingertip force when the
signal-dependent noise added and the relationship between SD force and mean force. (f) System responses under α ramp commands to flexor and extensor
that control the index finger to press a spring plate of 30 N/m. t1 is the time of finger contact with the spring plate and t2 is the time that the spring plate
was pressed to its limit position.
ellipse increased with the increasing level of antagonistic co-
contraction (AC) (Fig. 2(b)). The shape and orientation of
endpoint stiffness ellipses were qualitatively similar to those
in human multi-joint arm postures [35], [36]. Long axis of
the ellipse represented the maximum stiffness direction, and
short axis signified the minimum stiffness direction, which
corresponded to the direction of finger movement.
Muscle stiffness represented the relation between changes
in muscle force and fascicle length. Muscle stiffness was
proportional to α motor command (Fig. 2(c)), as well as
muscle force produced as in Fig. 2(d). These properties were
similar to those observed in physiological measurements in
mammalian animals and humans [28], [37]. These findings
confirmed that the virtual hand encompassed the similar
compliant property of human neuromuscular system.
C. Reflex contribution to muscle and endpoint stiffness
In the biorealistic reflex model, Ia afferent from spindle
model regulated the activation of motoneuron pools, closing
the loop of reflex. Here we evaluated to what extent Ia
afferent may affect muscle stiffness and endpoint
compliance.
Endpoint stiffness ellipses in open-loop and closed-loop at
the same levels of AC were illustrated in Fig. 3. Compared
to stiffness ellipses in closed-loop, the area of stiffness
ellipses in open-loop appeared smaller with no change in
shape and orientation at each EP. Thus, Ia afferent altered
mainly the magnitude of stiffness ellipses.
Specifically, the contribution of reflex pathway was
assessed with a set of perturbation tests under four different
levels of AC at EP_B. Changes in eigenvalues and area of
ellipses of endpoint stiffness matrix, as well as the change in
This article has been accepted for publication in IEEE Open Journal of Engineering in Medicine and Biology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/OJEMB.2022.3215726
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Fig. 2. Results of closed-loop perturbation experiments at equilibrium positions. (a) An example of profiles of variables in closed-loop perturbation
experiments. (b) Stiffness ellipses of endpoint with four increasing levels of muscle antagonistic co-contraction (AC) at equilibrium position (EP) EP_A,
EP_B and EP_C on the x-y horizontal plane. Four ellipses are superimposed at each EP, and each level of AC is identified by a different color. The
calibration of the ellipse is provided by a standard circle on the top right corner, which represents an isotropic stiffness of 500 N/m. (c) Muscle stiffness
of flexor and extensor at EP_A, EP_B and EP_C under four increasing AC levels. (d) Muscle stiffness in response to muscle force at EP_A, EP_B and
EP_C.
Fig. 3. Contribution of stretch reflex on endpoint and muscle stiffness. (a) Presents stiffness ellipses of endpoint at three EPs in open-loop and closed-loop
perturbation experiments. Red dashed line represents open-loop stiffness ellipses and blue solid line represents those in closed-loop. (b-c) Effects on
stiffness ellipse change of reflex feedback at EP_B. The magnitude, shape and orientation of endpoint stiffness are shown in (b) and (c). (d) Depicts the
change of muscle stiffness of flexor and extensor caused by the reflex contribution.
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content may change prior to final publication. Citation information: DOI 10.1109/OJEMB.2022.3215726
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muscle stiffness were calculated using eq. (3). Results were
summarized in Fig. 3(b-d). Compared to open-loop model,
changes in closed-loop model were manifested mainly as an
increase in the major axis of endpoint stiffness ellipses at
10.84 ± 3.94 % and the minor axis at 11.34 ± 3.13 % (Fig.
3(b)), increase in the total area of endpoint stiffness ellipse at
23.50 ± 7.80 % (Fig. 3(b)), and increase in muscle stiffness
at 16.16 ± 12.33 % for flexor and 8.79 ± 9.54 % for extensor
(Fig. 3(d)). But there was little or no influence on the shape
and orientation of endpoint stiffness ellipses (Fig. 3(c)). This
may be due to the fact that joint configurations dominated
the influence to shape and orientation of endpoint stiffness.
These showed that Ia afferent in neuromorphic reflex model
did enhance fingertip and muscle stiffness to a certain extent
consistent with experimental findings [38]–[40].
D. Adaptive regulation of compliance in grasping a soft
spring
Compliant operation of the virtual hand interacting with a
soft object (spring) was further evaluated. At steady state of
grasping a spring in Fig. 4(b), a perturbation force was
applied to the tendon of flexor or extensor, respectively, and
the stiffness of fingertip and muscle was calculated. Fig. 4(a)
depicted a representative trial of variables of the finger
moving from the original EP to a new EP with a perturbation
force (17 N) applied to flexor tendon. The Lmtu and Lce of
flexor were shortened and flexor force was reduced; while
the Lmtu and Lce of extensor were lengthened and extensor
force was increased. The index fingertip force was greater
due to added perturbation force, pressing the spring further
in.
It was observed that fingertip stiffness matched to the
spring stiffness at the finger-spring contact as in Fig. 4(c)
(R2=1, p=0.0000). This was consistent with the mechanical
constraint of impedance matching between objects at the
interacting interface in the vertical direction [41] based on
the physical law of action and reaction in opposing forces.
Muscle stiffness varied linearly with muscle activation levels,
and external spring stiffness as shown in Fig. 4(d).
Spring stiffness determined the degree of spring
deformation, which affected muscle length Lce, hence,
muscle force/stiffness at equilibrium with a given muscle
activation. Fig. 4(d) illustrated an adaptive adjustment of
muscle force and stiffness with changes in Lce from length-
tension curve and reflex compensation for a given
background activation of flexor and extensor. The range of
stiffness adjustment was represented by the variability, or
standard deviation (SD), in muscle stiffness (Fig. 4(e)). It
was noted that the flexor SD appeared to have an upward
trend (R2=0.90, p=0.0523), while the trend in extensor was
Fig. 4. Results of perturbation experiments in grasping spring plates of different stiffness. (a) An example of profiles of variables in perturbation
experiments when grasping a spring plate. (b) The experimental scenario that the index finger presses a soft spring plate. The coordinate system indicates
the direction of the horizontal plane. (c) Depicts endpoint stiffness when grasping objects of different stiffness under four levels of AC. Linear correlation
between endpoint stiffness and object stiffness is y=0.9999*x+0.002 (R2=1, p=0.0000). (d) 3-D curve in muscle stiffness of flexor and extensor under
different AC levels when grasping various compliant spring plates. (e) The standard deviation (SD) of muscle stiffness in grasping springs of various
stiffness at different α commands.
This article has been accepted for publication in IEEE Open Journal of Engineering in Medicine and Biology. This is the author's version which has not been fully edited and
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not apparent (R2=0.07, p=0.7434) due to little change of α
command, implying that background activation may also
affect the range of stiffness adjustment. This was
corroborated with the fact that the length-tension curve in the
model was a quadratic curve scaled with activation level.
III. DISCUSSION
Human hand control presents a perfect model for
prosthetic control. Humans achieve dexterous grasp through
compliant actuation of muscles and rich sensory afferents
from proprioceptors and cutaneous receptors [18]. The
compliant control can adjust hand stiffness when grasping
brittle or soft objects without violating them. The
viscoelasticity of skeletal muscle arises from length-tension
and force-velocity properties of muscular fiber [28], [29],
[42], [43], and the dynamic property of muscle results from
activation and contraction dynamics of muscle fibers [30],
[43]. The monosynaptic stretch reflex compensates muscle
length changes and regulates to a certain degree the
compliance of neuromuscular system [40], [44]–[46]. A
large body of empirical data are available for comparison of
biorealistic controller properties [30], [35], [38], [41], [47]–
[50].
In this study, a virtual twin of a biorealistic prosthetic hand
is developed with computational models of neuromuscular
reflex control. The prosthetic controller incorporated a Hill’s
muscle model [51], a spindle model [19], spiking
motoneuron models [52], and a monosynaptic stretch reflex
model [32] in neuromorphic hardware chips [53]. Contact
sensors embedded at fingertips of the hand allow tactile
information to be delivered to amputees through a non-
invasive neural interface using evoked tactile sensations
(ETS) [27]. The purpose here is to reveal that the virtual
prosthetic hand exhibits qualitatively similar behaviors to
human neuromuscular reflex system. To our knowledge, this
is the first computational model that can capture human-like
compliant properties emerging from biologically realistic
models.
Switching force and position control according to external
load is a natural ability of human motor control [54]. Results
in Fig. 1 verify that the biorealistic hand prosthesis captures
this nature of human compliant control. The fingertip force
in flexion and extensor can be well controlled by the α
commands (or surface EMGs) through the muscle model
with modulation of muscle fascicle length and reflex (Fig.
1(d)). Fingertip force variability with signal-dependent noise
(SDN) in the input illustrates a linear scaling with respect to
the mean force (Fig. 1(e)). This property allows for more
delicate grasp tasks of brittle objects that requires precise and
low levels of fingertip force and stiffness. Since muscle (or
fingertip) stiffness was proportional to muscle (or fingertip)
force (Fig. 2(d), 4(d)), the ability to regulate stiffness in the
muscle or by co-contracting antagonistic muscles is crucial
for dexterous functions of the prosthetic hand. For example,
in grasping a soft spring plate as shown in Fig. 1(f), the finger
underwent switching in three phases of control according to
external load conditions, i.e. initial position control before
contact, both position and force control after contact, and
then force control with the spring fully pressed. This ability
to naturally switch its control mode according to external
loads is similar to that of human [54]. The natural compliant
control is advantageous over conventional prosthetic/robotic
hands that require sensors to detect external loading
conditions in order to switch control modes [41], [54], [55].
Fingertip stiffness regulation by co-contracting
antagonistic muscles is mainly manifested in magnitude,
while joint configuration plays a significant factor for the
shape and orientation of endpoint stiffness ellipse as
illustrated in Fig. 2. These results were qualitatively similar
to those in observed humans in magnitude, shape and
orientation [22], [35], [50], [56]. Specially, muscle force and
stiffness were proportionally to each other and with α motor
commands (Fig. 2(d), Fig. 4(d)) as observed in animal and
human studies [28], [37], [38], [57]. It is noted that the value
of muscle stiffness calculated in the model was smaller than
that measured in humans [58]. This discrepancy is due to the
fact that the maximum muscle force set in the model (at 100
N [24]) was an order of magnitude smaller than actual
maximal force in human muscle [58]. It is also observed that
in free-moving conditions, fingertip positions could be
maintained by co-varying activations of a pair of antagonistic
muscles (Fig. 2(b)). This suggests that equilibrium position
could emerge as a result of length-dependent forces
generated by agonist-antagonist muscles [59].
Spindle model used here was constructed using data
collected from animal studies [19], and was verified to
generate reflex behaviors as those of human spindle [22],
[60], [61], as well as those from microneurography [62], [63].
The contribution of monosynaptic reflex to enhance muscle
stiffness in the model was estimated at 16.16 ± 12.33 % and
8.79 ± 9.54 % for flexor and extensor, respectively (Fig.
3(d)), which was close to the range of measured values at 18-
44 % of total stiffness in the first dorsal interosseous muscle
in humans [38]. The lower contribution may be due to the
fact that reflex gain in our model was moderate (about 10%)
to avoid instability [23]. The three parameters of endpoint
stiffness ellipses (area, major and minor axes) could not be
modulated independently by reflex, since it changed α
commands of flexor and extensor. This was evident with
results in Fig. 2&3. Therefore, α commands determined
magnitudes of stiffness ellipse (Fig, 2(b)), while joint
configuration affected mainly orientation and shape of the
stiffness ellipse (Fig. 3(c)). These properties are a necessary
consequence of mechanics in the model.
A striking new revelation comes from investigation of
interaction of the virtual hand with a spring object as
demonstrated in Fig. 4. At steady state of grasp, the finger
stiffness at contact point matched to the spring stiffness at
the finger-spring interface as in Fig. 4(c), consistent with the
requirement at mechanically interacting interface [41]. The
process of matching fingertip stiffness is adaptively
regulated by the muscle model (also see a video
demonstration in Supplementary Materials).
This article has been accepted for publication in IEEE Open Journal of Engineering in Medicine and Biology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/OJEMB.2022.3215726
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For a given spring stiffness, a constant α command may
be issued to the flexor muscle with a strength not calculated
exactly to produce a matching fingertip stiffness. But the
matching is achieved with adaptive adjustment of muscle
stiffness endowed by the muscle model. If the fingertip
stiffness initially produced is greater than the spring stiffness,
the spring will be pressed in further, and the Lce of flexor
muscle will be shortened. According to the length-tension
curve, the force and stiffness of the muscle/fingertip will be
reduced. This adjustment process will continue until the
force and stiffness at the fingertip equal to those of the spring.
An opposite process in the extensor muscle takes place to aid
the adjustment of fingertip force and stiffness. On the other
hand, if the initial fingertip stiffness is smaller than the spring
stiffness, the length-tension curve of flexor and extensor will
make concerted adjustments to increase fingertip force and
stiffness until a balance at fingertip-spring is reached. This
automatic adjustment mechanism depicts the process of
“adaptive stiffness regulation” (see video demonstration in
the Supplementary Materials). With this mechanism, one
does not have to calculate an exact α command to flexor and
extensor when grasping a soft object. An estimate of rough α
command may be issued, and the adaptive mechanism will
allow fine tuning of muscle force and stiffness to match those
of the spring. This is one of the advantages of compliant
control in humans.
A secondary mechanism via reflex will also participate in
the adaptive stiffness regulation process through Ia afferent
induced by Lce changes. However, its effect may be limited
due to low reflex gain [23] and a delay (about 200 ms [61])
in afferent signal transmission. Nevertheless, the two
adaptive mechanisms work in concert to fine tune muscle or
fingertip stiffness to match the spring stiffness. The range of
stiffness modulation by the length-tension curve and reflex
under a given background activation showed an increasing
range with the AC level (Fig. 4(e)). This is consistent with
fact that the length-tension curve in the muscle model is
scaled with α command. This property of adaptive stiffness
regulation will be beneficial for the biorealistic prosthetic
hand to handle soft objects.
We showed here that comprehensive model exhibits
compliant properties qualitatively similar to those obtained
in human or animal physiological experiments. The
emerging behaviors originate from the physiologically
realistic sub-models, i.e. neurons, muscles and spindle,
which constitute the biorealistic neuromorphic reflex control.
Second, the muscle model was coupled to the prosthetic hand
with anatomically realistic parameters. This ensures the
physiological plausibility for amputees to operate the
prosthetic hand. This in turn substantiated our previous
findings of improved performance in human experiments
[25]. It is interesting to note that this modeling approach can
be further combined with a surgical procedure that creates a
better agonist-antagonistic residual muscle pair for prosthetic
control [64]. But replacing our model of intact muscle with
one of residual muscle [65] would still preserve the
compliant properties of the prosthetic hand.
There are limitations, however, in this study. First, we
simplified simultaneous control of multiple degrees of
freedom in prosthetic fingers [1], [66] to a single tendon
force control, and reduced decoding multi-channel EMG
signals for commands [4], [66] to intuitive control by flexor
and extensor sEMGs. Second, the neuromorphic model is
still preliminary compared to biological neuromuscular
reflex system. The neural transmission delay of the spindle
was about 200 ms [61], and the overall computational delay
between α command input to force output was about 400 ms.
Ib reflex of the Golgi tendon organ (GTO) was omitted in
this model for its low gain in physiological condition [22],
[67], despite significant roles in lower limb weight bearing
[68]. Nevertheless, human-like neuromuscular reflex control
was demonstrated necessary and sufficient to provide a good
neural compatibility with the sensorimotor system and
superior task performance by amputees using the biorealistic
prosthetic hand [24], [25].
There are several implications for future advances. (1)
This study along with our previous work [24], [25] leads to
a novel direction for developing a new generation of
prosthetic hand with human-like properties i.e., a
comprehensive replica of human’s neuromuscular control
that can adjust stiffness over a wide range of operating
conditions [69]; (2) the biorealistic hand can be seamlessly
neural compatible with the human sensorimotor system, thus,
facilitate amputees for more dexterous control using an
antagonistic muscle pair as command sources [64]; (3) the
virtual hand developed here may establish a useful training
platform for amputees to familiarize control of biorealistic
prosthetic hands; and (4) the computational modeling
approach can promote reverse engineering to understand
neural mechanisms of brain control for hand movements in
humans.
IV. CONCLUSIONS
In this study, a virtual hand with a pair of neuromorphic
muscles and a sensory feedback system was integrated in
MuJoCo environment. The model incorporated biorealistic
elements of human neuromuscular reflex. A comprehensive
evaluation indicated that the virtual twin of the biorealistic
prosthetic hand could maintain a stable hand opening for
grasp, adjust control mode according to the external loading
condition, and adaptively regulate hand stiffness to match the
stiffness of grasped object. This study confirms that the
virtual hand is capable of recapturing human-like
neuromuscular properties of compliance, adaptative stiffness
regulation, and fine control of fingertip force. These findings
lead to new insights into how human-like neuromuscular
reflex may facilitate prosthetic control of the virtual hand and
suggest a teleological correlation between human-like
neuromuscular control and neural compatibility in hand
prosthesis.
V. MATERIALS AND METHODS
A. Virtual prosthetic hand definition
MuJoCo is a virtual environment using a physics engine
that has fast and accurate computational power to calculate
contact interactions between objects. It runs the simulation at
This article has been accepted for publication in IEEE Open Journal of Engineering in Medicine and Biology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/OJEMB.2022.3215726
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/
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a frequency of 500 Hz. We developed a tendon-driven virtual
prosthetic hand (Fig. 5(a)) in the MuJoCo (Version 2.0)
environment of real-time computation. Tendon-driven
structure was added on the virtual prosthetic hand based on
the provided vMPL hand (Johns Hopkins Applied Physics
Lab, Laurel, MD) to fit the neuromorphic control (Fig .5(a)).
The added ten tendons started from the forearm and passed
through fixed anchor points to the tip of each finger
according to the anatomy of hand musculature [70]. On the
palmar and dorsal side of each joint, an anchor point was set
on the joint, which rotated with joint movement. The rotation
axis of each joint was parallel to the palmar side of the hand
to make the joint flex or extend. All anchor points on the
palmar side were coupled by the flexor tendon, while those
on the dorsal side were coupled by the extensor tendon. The
tendon compliance was considered in the muscle model with
a serial tendon stiffness Kt (Fig. 1(b)), and the stiffness
parameter of the elastic components was shown in Table S1.
The value of Kt was much greater that of Kse, and Kt still
contributed to the overall stiffness at the fingertip. Tendons
were actuated by ten muscles (actuators). Here the maximum
force of each muscle generated was set to 100 N.
Overall, the modified virtual hand as in Fig. 5(a) has 5
contact sensors: one on the distal phalangeal segment of each
finger; 14 joints: two joints in the thumb and three joints in
other fingers; 10 tendons: two for each finger; and 10
actuators: five pulling flexion tendons and five pulling
extension tendons. Each tendon wrapped around all joints of
the digit.
B. Integration of virtual prosthetic hand system
The virtual prosthetic hand system was integrated with a
pair of biorealistic controllers and a sensory feedback system.
The biorealistic reflex models replaced the original agonist-
antagonist muscle pair in situ to compute muscle forces to
actuate virtual tendons to produce movements in the MuJoCo
environment. The physiological plausibility of this model
was achieved by physiologically realistic properties included
and anatomically realistic parameters specified according to
the anatomy of target muscles in situ. Contact sensors at
fingertips delivered force information to amputees using a
sensory feedback system when interacting with objects (Fig.
5(b)).
The biorealistic controller emulated a monosynaptic
stretch reflex loop by modeling essential elements in the
neuromuscular system, which was implemented on a
programmable Very-Large-Scale-Integration (VLSI) in real-
time using FPGA chips (Xilinx Spartan-6) [23]. It consisted
of models of motoneuron pool including 768 spiking neurons
[52], one Hill-type muscle model [51], one spindle model
with 128 randomly unsynchronized outputs [19] and
monosynaptic stretch reflex [32]. The input of the
biorealistic controller was α motor command (or sEMG
signal from a residual muscle), which activated motoneuron
pool following Henneman’s size-principle [71]. The
activated spiking signal was converted to a twitch signal via
a low-pass filter twitch model to drive the Hill’s muscle
model. Muscle forces from neuromorphic muscle models of
flexor and extensor pulled the corresponding tendon
individually to control the movement of the prosthetic finger.
The spindle model accepted inputs of fascicle length, gamma
static (γs) and gamma dynamic (γd) commands to send a
volley of Ia afferents back to motoneuron pool to close the
reflex loop. The neuromorphic hardware chips were linked
to the virtual environment and transferred data
bidirectionally by a universal serial bus (USB) interface.
The sensory feedback system received contact force
information at fingertips in MuJoCo by user datagram
protocol (UDP) network communication and transferred it to
electrical pulses to amputees via a non-invasive neural
interface exploiting ETS in amputees with transcutaneous
electrical nerve stimulation (TENS) [27], [72].
C. Estimation of fascicle length of muscle
Fascicle length (Lce) plays a vital role in the biorealistic
reflex model. It can modulate the proprioception afferents
Fig. 5. (a) Virtual hand in MuJoCo. The virtual hand has five contact sensors, fourteen joints, ten tendons and ten actuators. (b) The block diagram of
the integrated virtual hand system. It consists of a tendon-driven virtual hand, a pair of neuromorphic muscles and a sensory feedback system. Force
perturbations can be applied at fingertip, or the tendon of flexor/extensor in the perturbation experiments.
This article has been accepted for publication in IEEE Open Journal of Engineering in Medicine and Biology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/OJEMB.2022.3215726
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/
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from spindle model and exert muscle force depend on length-
tension property in Hill-type muscle model. However, the
exact value of Lce at different finger configurations is unclear
from the literature. We need to estimate it according to the
available realistic parameters of target muscles in situ.
In our virtual prosthetic system, the anatomically length
information was derived from a pair of antagonistic muscles:
flexor digitorum profundus (FDP) and extensor digitorum
(ED), which is commonly used to control prosthetic hand by
forearm amputees. The real physiological length information
of these two muscles was listed in bold in Table S1 [73]. Due
to the lack of real musculoskeletal structure in the virtual
environment, we set the initial virtual tendon length of flexor
and extensor as the real musculotendinous unit length (Lmtu)
on the resting position. During the movement of the hand
grasp, the change of the virtual tendon length was equivalent
to the change of Lmtu (ΔLmtu). In the Hill’s muscle model of
biorealistic reflex (Fig. 1(b)), the change of fascicle length
(ΔLce) could be estimated by ΔLmtu based on Luo’s
calculation algorithm [23], [33].
In the integrated virtual hand, the calculated maximum
ΔLmtu of flexor and extensor was 1.11 and 1.52 cm, and the
corresponding ΔLce of flexor and extensor was 0.72 and 0.99
cm. We selected the normalized range of Lce of flexor and
extensor was 0.80 ~ 0.95 Lo (optimal length to peak force)
and 0.75 ~ 0.90 Lo respectively (Fig. 1(c)). Hence the actual
Lo in flexor and extensor on the initial position we set was
4.8 and 6.6 cm, as shown in Table S1. The selected operating
range is in the ascending limb of length-tension curve due to
the reason of stability.
D. Control capacity evaluation
We designed three sets of tests to evaluate the control
capacity of the virtual prosthetic hand. The first test was to
evaluate the capacity of force generation in flexion and
extension. The index finger was stabilized at a fixed
configuration by an activation pair of flexor and extensor
(αf=0.20 and αe=0.14). Two wooden blocks were placed at
the vertical direction of 0.5 cm from the fingertip and the
dorsal fingertip (left panel in Fig .1(d)). Continuously
increasing the αf command or αe command individually to
make the fingertip or dorsal fingertip press the wooden block
to generate the touching force, and the flexion and extension
force were shown in Fig .1(d).
The second test was to evaluate the effect of intrinsic
motor noise of control signals on fingertip force variability.
Fingertip force variability was characterized by the standard
deviation (SD) of the fingertip contact force. A source of
neuromuscular signal-dependent noise (SDN) was
introduced to the motor commands of each muscle. The
SDN was a Gaussian distributed noise with a standard
deviation (SD) proportional to the magnitude of the motor
command (α) with a constant coefficient of variation (CV =
SD/α = 0.2) [22], [34]. A pair of antagonistic α commands
with SDN noise was activated to control the virtual hand to
press the right wooden block. Each experiment lasted 12
seconds and the last 2 seconds of the fingertip force were
calculated for the subsequent analysis. Each pair of α
commands was repeated 5 times at each of seven different
target force levels ranging from approximately 20 to 80 %
maximum fingertip force.
The third test is to investigate the different control phases
when interaction with different external environments. An
eight-second ramp input with α commands was co-activated
to drive the index finger pressing a spring plate as in Fig. 1(a).
The stiffness of the spring plate was 30 N/m and the
maximum contraction distance of the spring was 2 cm.
E. Evaluation of compliant properties at equilibrium
positions
To measure the endpoint stiffness of fingertip and muscle
stiffness, a small vector of perturbation force was applied on
the tip of index finger when the finger stabilized at the
equilibrium position (EP), which enforced the finger
deviated to the new EP. For each EP, four different pairs of
α commands of antagonistic muscles drive the index finger
to the stable position.
Eight various orientations of perturbation force were
added to calculate the matrix of endpoint stiffness, the
deviation of the fingertip moving distance was about 0.5 cm.
Endpoint stiffness matrix K at fingertip was estimated using
the least square method:
For the stiffness matrix K of the endpoint, it could be
expressed by a stiffness ellipse:
In eq. (1) and (2), the four coefficients , ,
and are the four elements of the stiffness matrix K.
and represent the reaction forces in x and y directions,
and are the unit distances in the x and y coordinate axis.
Muscle stiffness was defined as the derivative of the
change in muscle force with respect to the change in muscle
fascicle length.
F. Quantification of reflex contribution
Reflex pathway delivers Ia afferent to the spinal cord to
regulate the movement of the limb and also enhances muscle
stiffness [39]. Ia afferent pathway was artificially cut off to
eliminate the role of reflex in biorealistic controller and the
contribution of reflex was evaluated in enhancing muscle and
endpoint stiffness. Lack of reflex feedback, a pair of
biorealistic controllers was in an open-loop state, and the
same paradigm of the perturbation experiments as in closed-
loop was applied on the index finger to calculate endpoint
stiffness ellipse and muscle stiffness at different
configurations under four increasing antagonistic co-
contraction (AC) levels.
The change of endpoint stiffness ellipse and muscle
stiffness was quantified using the following equation:
G. Compliant grasping of a soft spring
A simulation experiment was used to explore how the
compliant properties of biorealistic reflex were functioning
when grasping soft objects. A set of spring plates of different
This article has been accepted for publication in IEEE Open Journal of Engineering in Medicine and Biology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/OJEMB.2022.3215726
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/
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10
stiffness was fixed at the same position in MuJoCo (Fig.
4(b)). Four pairs of α motor commands that stabilized the
index finger at EP_C in closed-loop perturbation
experiments were used as driving signals to control the index
finger grasping a spring plate of different stiffness. The
spring plate kept contracting until the finger force was equal
to the spring resistance force, in which the finger-spring
combination was maintained at a steady state. A perturbation
force was added on the flexor or extensor tendon to change
the fingertip pressing force to move the spring plate until a
balance again appeared at the finger-spring interface. For
each experimental session, a perturbation force was added on
the flexor tendon and extensor tendon three times
respectively and it was adjusted as the increasing background
activation of flexor and extensor to move the spring plate
about 1 cm.
Muscle stiffness varied with the external object stiffness
under the same background activation. The range of muscle
stiffness was characterized as the standard deviation (SD) of
muscle stiffness produced by grasping objects of different
stiffness and the relation between SD of muscle stiffness
variability and α command was shown in Fig. 4(e).
SUPPLEMENTARY MATERIALS
Table S1. Parameters of the muscle model at the resting
position.
Video S1. Virtual hand interaction with a spring showing
adaptive stiffness regulation.
ACKNOWLEDGMENT
Authors appreciate lab engineer, Mr. R. Yue, who set up
the neuromorphic computing hardware for this study.
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This article has been accepted for publication in IEEE Open Journal of Engineering in Medicine and Biology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/OJEMB.2022.3215726
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