Design of an anthropomorphic robotic finger system with biomimetic artificial joints

Abstract

We describe a new robotic finger that is composed of three biomimetic joints whose biomechanics and dynamic properties are close to their human counterparts. By using five pneumatic cylinders, the robotic finger is actuated through a series of simplified antagonistic tendons whose insertion points and moment arms at each finger joint are determined by the anatomy of the human hand. Air dynamic model is empirically solved for controlling the pneumatic system. In order to optimize our future controller for the robotic finger, we use Multi-Joint dynamics with Contact(MuJoCo) - a physics engine custom-developed - to construct a kinematic model for simulating the interaction between the fingers joints and tendons. Experimental data of the tendon excursions are used to validate the efficacy of the robotic finger model. Good fits are observed both in the DIP and PIP flexors (R2 = 0.93 and R2 = 0.83) and central extensor (R2 = 0.96).

Full text

Design of an Anthropomorphic Robotic Finger
System with Biomimetic Artificial Joints
Zhe Xu, Vikash Kumar, Yoky Matsuoka and Emanuel Todorov
Abstract—We describe a new robotic finger that is composed
of three biomimetic joints whose biomechanics and dynamic
properties are close to their human counterparts. By using five
pneumatic cylinders, the finger is actuated through a series
of simplified antagonistic tendons whose insertion points and
moment arms mimic the anatomy of the human hand. We
develop simulation models of the kinematics and air dynamics,
and validate them using experimental data. Preliminary results
on controlling the finger are also described.
I. INTRODUCTION
The human hand has been used as an irreplaceable model
for the development of different robotic hands due to its
impressive compliance and dexterity that can accommodate
a variety of gasping and manipulation conditions. Towards
this end, anthropomorphic robotic hands have been widely
investigated because of their inherent similarity to the human
hand and can potentially bring many benefits to the fields
ranging from hand prosthetics to healthcare robots to space
exploration. Current prosthetic hands are often made with few
degrees of freedom as an approach to preferably providing
human hand appearance with comfortable weight and size.
For personal assistance, rather than duplicating a dexterous
human hand, industrial style gripper is commonly adopted to
focus on executing tasks with precision and robustness. As
for space exploration, space walking is still a routine task
for astronauts to perform the repair of orbiting or spacecraft.
Prosthetic/Robotic hands from each of these categories are
often designed with restrictions resulting from not only the
technological limitations, but also from our understanding
about the human hand. In order to design an anthropomorphic
robotic hand with appearance and functionality closely resem-
bling our own, there are many significant challenges need
to be overcome, here we focus on investigating the intrinsic
biomechanic features required to replicate the compliance and
kinematics of a human finger.
The fingers of the human hand possess several biological
features that are hard to mimic simultaneously. These include:
(1) the unique shape of the bones at the joints, which deter-
mines the degrees of freedom at the joint; (2) a joint capsule
formed by fine ligaments, which set the range of motion for the
joint; and (3) cartilage and synovial fluid, enabling low-friction
contact between two articulated surfaces [1]; (4) non-linear
interactions between the tendons and bone topology, which
Authors are with the Department of Computer Science & Engineering,
University of Washington, WA 98195, USA
e-mail: zhexu@cs.washington.edu, vikash@cs.washington.edu,
yoky@cs.washington.edu, todorov@cs.washington.edu
Fig. 1. Anthropomorphic robotic finger with biomimetic finger joints.
dynamically determine the motion of the finger. Typically
researchers have not designed anthropomorphic robotic hands
to incorporate these biological features or to be anatomically
correct.
Over the last decades, many robotic hands have been devel-
oped for serving different purposes. Among the most relevant
anthropomorphic hands, several important features have been
achieved, including high degree of modularity [2], [3], light
weight [4]–[6], cable driven [4], [7]–[13], gear transmission
with linkage mechanism [14]–[16]. These robotic hands often
need complicated joint mechanism such as hinges, gimbals,
linkages, or gears and belts in order to achieve the right num-
ber of DOFs and mimic kinematic characteristics of the human
hand. However, few of them incorporate built-in compliance
which is necessary for a human hand to explore uncertainties
in the unstructured real world. On the contrary, under-actuated
gripper/hand [17]–[19] can comply with different shapes of
objects during grasping, but keeps only the basic DOFs. Due
to different design constraints, it seems that a compromise
has to be made between build-in compliance and high DOFs.
Although tremendous progresses have been made, the ability
of most of the existing robotic hands to perform human-level
manipulation tasks remains limited.
Although standard design methodology, such as above, can
mimic the kinematic behavior of a finger joint it does little to
illuminate the salient features that make the human hand irre-
placeable for many dexterous tasks. It is therefore necessary to
develop artificial finger joints, based on accurate physiology,
in order to quantitatively identify these characteristics thus
providing insight into anthropomorphic robotic hand design.

A challenging alternative to conventional robotic hand de-
sign is to develop mechanisms which directly utilize the unique
articulated shapes of human joints, as well as a tendon hood
structure to actuate individual fingers. Following a biologically
inspired design may also reduce the total number of individual
components, resulting in an elegant design.
The anthropomorphic robotic finger addressed in this paper
(as shown in Figure 1) is based on a previously described
artificial finger joint [20] whose degrees of freedom, range of
motion, and dynamic properties are close to that of a human
finger, In this paper, we are interested in designing a close
replica of the human index finger along with its pneumatic
actuation, and preparing it for high speed actuation through
kinematic model based simulation. In the following sections
the innovative mechanical design of the anthropomorphic
robotic finger is detailed, air dynamic model of the pneumatic
system is derived, then the modeling and simulation results
are validated through the experimental data.
II. DE VE LO PM EN T OF A N AN THROP OM OR PH IC RO BOTIC
FIN GE R
Although the anatomy of the human hand provides detailed
sources of static models, such as joint structure, tendons
routing, and layered skin, how to organically incorporate
state-of-the-art engineering advances into a fully functional
robotic hand system is what we want to achieve in this paper.
This section describes the mechanical design and prototyping
process of our robotic finger.
A. Biomimetic design of bones and joints
In the human hand, the bones at the finger joints possess
several biological features (As shown in Figure 2), including
the unique shape of the bones at the MCP, PIP and DIP
joints, which determines the degrees of freedom at the joint;
the shapes of the finger bones along the tendon routing path
create moment arms for the tendons that vary with joint
angle, a behavior critical for accurate hand function [21]. The
variable moment arms are necessary for achieving human-
like joint-muscle movement relationships [22]. Developing an
anatomically correct robotic hand can help researchers to find
more critical human hand features that can only be revealed
through dynamic interactions with objects.
In order to accurately match the size and shape of the
human finger bones. We used the index finger from a Stratasys
Corporation’s laser-scan model of human left hand bones
supplied in STL format, imported the tessellate facets into
Pro/Engineer, and created solid models for each bone by fitting
new surfaces to the scan geometry. Detailed parameters of the
robotic finger are listed in Table I and II.
At each joint of the human finger, joint capsule is formed
by fine ligaments that seals the joint space and provides
passive stability by limiting movements through its ligaments,
therefore sets the range of motion for the joint. As shown in
Figure 3, we have developed an artificial joint makes use of
three main components: a 3D printed joint with true to life
bone topology, crocheted ligaments used to realize the right
Fig. 2. 3D model of the laser-scanned human index finger.
TABLE I
PHY SIC AL PAR AM ETE RS OF T HE RO BOT IC FI NGE R SKE LE TON
Phalange Length (mm) Weight (g)
MCP to PIP 53.4 5.5
PIP to DIP 32.0 2.0
Distal phalange 23.7 1.2
TABLE II
APP ROXI MATE JO IN T MOT ION L IM ITS O F TH E ROBO TIC FI NG ER
Joint Minimum Maximum
MCP 30◦extension 90◦flexion
35◦abduction 35◦adduction
PIP 0◦extension 110◦flexion
DIP 0◦extension 70◦flexion
Fig. 3. Biomimetic artificial joint design from [20].
range of motion, and a silicon rubber sleeve providing the
passive compliance for the artificial joint. The artificial finger
joint designed in this way possesses the similar stiffness and
damping properties to those of the human finger [20].
Between the two articulated joint surfaces of the human
finger, cartilage and synovial fluid can realize low-friction
contact. In our design, thermoplastic coating is adopted to
provide low-friction surface at the finger joint. Although, when
encountered with the long term tear and wear, commonly

engineered materials cannot regenerate like biological tissues,
we believe that through low-cost, rapid prototyping technology
the modular design can make maintenance of our proposed
robotic finger/hand economically regenerable.
B. Tendon hood design and its simplification for the extensor
system
Underneath the skin of the human finger over the dorsal side
of the finger bone, extension motion of the finger is realized
via a complex web structure as shown in the leftmost picture
of Figure 4(a). On the palmar side of the finger, antagonistic
tendons called flexors are connected from the bone insertion
points to the extrinsic muscles located in the forearm to enable
the flexion motion.
(a)
(b)
Fig. 4. Comparison of the extensor mechanism between the human hand
[23], the ACT Hand and the robotic finger (a) Design evolution of the tendon
hood. (b) Schematic drawing of the pulley system used for the robotic finger.
Previously, we designed a tendon hood for the ACT Hand
to mimic the extensor web of the human finger(as shown in
the middle picture of 4(a)). The artificial extensor is fabricated
by crocheting nylon composite to emulate the geometry and
functionality of the human counterpart as closely as possible.
Instead of adopting the same extensor design, in this paper we
apply what we learn from the ACT Hand and keep only the
tendons essential for the index finger flexion/extension and
abduction/adduction in order to concentrate on investigating
the performance of our robotic finger.
As shown in the rightmost picture of Figure 4(a), the
locations of insertions points and string guides of the robotic
finger are all inherited from the ACT Hand. The tendons are
made of 0.46 mm Spectra R
fiber (AlliedSignal, Morristown,
NJ). The fiber was chosen because of its strength (200N
breaking strength), high stiffness, flexibility, and its ability
to slide smoothly through the string guides. In the case of
the human hand, tendons from the three extensor insertion
(a) 3D model of the actuation system
(b) Experiemntal setup
Fig. 5. The actuation system of the anthropomorphic robotic finger.
points are all merged with the extensor hood at the MCP joint,
therefore a pulley system is used to make sure each individual
tendon is constantly in tension (see Figure 4(b)).
III. ACTUATION SYSTEM
Our robotic finger system is actuated using a ”Pulling-
only pneumatic actuation system” (see Figure 5a). Because
of its robustness, smooth dynamics and inherent damping
properties, pneumatic actuation seems promising for modeling
muscle behaviors. The robotic finger system consists of five
double-acting cylinders (Airpel-anti stiction cylinders, model
M9D37.5NT2) evenly mounted along the perimeter of a cylin-
drical beam through five sliding brackets. Cylinders being used
are modules specially designed for low friction-anti stiction
operations. Stiction and friction values are so small that the
piston falls under its own weight if cylinder is not horizontal.
The sliding brackets are designed to eliminate any potential
slack between the tendons and actuators. The pistons of the
five cylinders are connected to the central extensor, abduction
and adduction tendons, DIP and PIP flexors, respectively.
The front chamber of each cylinder is connected to a
proportional 5/3 pressure valve (Festo, model MPYE-5-M5-
010-B). When pressurized the front chamber resembles the
muscle contraction and the back chamber is left open to
the atmospheric pressure as tendons cannot push the finger
(Pulling-only actuation). The valve receives a command volt-

age from a National Instruments D/A board. This voltage (0-
10V) specifies the position of a linear actuator inside the valve,
which in turn sets the aperture connecting the front chamber
to the compressor (90 PSI above atmospheric pressure). The
control command (in Volts) 5 - 10 pressurizes the systems
and 5 - 0 exhausts. The pressure inside the front chamber
is measured with a solid-state pressure sensor (SMC, model
PSE540-IM5H). The sensor data are sampled at 50 KHz, and
averaged in batches of 500 to yield a very clean signal at 100
Hz. The difference between the pressures in the two chambers
of each cylinder (denoted D) is proportional to the linear
force exerted on the piston. For protection of the finger, each
cylinder’s piston contraction is limited by excursion of the
tendon it acts upon.
IV. MODEL OF AIR DYNAMICS
Ideally we would be able to control the piston force
with minimal delay. This is difficult to achieve in pneumatic
systems because the air dynamics have non-negligible time
constants that depend on multiple factors such as compressor
pressure, valve throughput and response time, length of the
air tubes between the valve and the cylinder, volume of the
chamber, and air temperature. These effects are hard to model
accurately, yet for control purposes it is important to have a
model that enables the controller to anticipate the resulting
delays and compensate for them. We did rigorous system
identification to find the model for air dynamics.
Ideally we would be able to control the piston force
with minimal delay. This is difficult to achieve in pneumatic
systems because the air dynamics have non-negligible time
constants that depend on multiple factors such as compressor
pressure, valve throughput and response time, length of the
air tubes between the valve and the cylinder, volume of the
chamber, and air temperature. These effects are hard to model
accurately, yet for control purposes it is important to have a
model that enables the controller to anticipate the resulting
delays and compensate for them.
We performed rigorous system identification to find the
model for air dynamics, evaluating all models up to fourth
order in pressure (P), flowrate (dP/dt), valve voltage (V),
valve voltage rate (dV/dt), chamber volume (v) and chamber
volume velocity (dv/dt). Models were evaluated in parallel
over 24 cores of 3.33 GHz Intel Xeon with 24 Gb RAM
running Matlab2010bfor about 25 hours.
Unlike models used in [24], [25] which are for big cylinders
with significant chamber volume (the length of the cylinder is
of 50 cm), our system consists of compact cylinders(3.75 cm)
fed using high flow valves. Benefits from accounting for the
chamber volume for our cylinders were so low that we choose
to ignore it for a simpler model.
dP/dt =a0+a1V2+a2V3+a3P+a4P V +a5P V 2+a6P V 3
Above model was validated with five cylinders. Model
parameters aiwere independently determined for individual
cylinders using linear regression. For all the cylinders, our
model outperformed other models with R2>0.9 over wide
Fig. 6. Original flow rate vs model predicted flow rate comparison
Fig. 7. Pressurization/Depressurization flow rate for different voltage step
change starting from extreme pressure values
range of unseen datasets collected at different frequencies.
Figure 6 shows model predictions for one randomly selected
cylinder.
Pneumatic systems incur non zero-latency due to response
time of the valves and tube length connecting valve with cylin-
der. To investigate the latency of the air dynamics incurred by
our system, we performed a sequence of instantaneous pressur-
ization and depressurization experiments. During a pressuriza-
tion/ depressurization experiment, we started with a depressur-
ized (V= 2 volts)/ pressurized (V= 8 volts) chamber. At the
beginning of each experiment, valve’s command voltage was
instantaneously changed to an intermediate voltage. Figure 7
shows flow rate response due to instantaneous voltage change
during pressurization and depressurization experiments. We
observe that air dynamics incurs a latency of about 6 ms,
irrespective of the intermediate voltage level, before it reaches
its maximum effect.

Fig. 8. 3D Visualization of the kinematic model of the robotic finger in
OpenGL.
Third order air dynamics and latencies from pneumatic
actuation on top of the non-linearities from the tendon routings
and wrapping along bone segments make our control problem
quite challenging. At the same time, pneumatic actuation is de-
sirable from the perspective of bio-robotics as they have many
essential properties (detailed in [25]) of biological muscles at
mechanism level; which we believe are very different from
trying to recreate them using properties of feedback controller.
V. KI NE MATI C MO DE L OF T HE S KE LE TON AND TENDONS
We constructed a kinematic model of the finger skeleton
and the tendon paths. This was done by taking the numeric
data from the CAD file used to 3D-print the finger, and
importing it in an XML file that is then read by our modeling
software. Our software – called MuJoCo which stands for
Multi-Joint dynamics with Contact – is a full-featured new
physics engine, with a number of unique capabilities including
simulation of tendon actuation. In this paper we only use the
kinematic modeling features of the engine, as well as the built-
in OpenGL visualization.
The skeletal modeling approach is standard: the system con-
figuration is expressed in joint space, and forward kinematics
are used at each time step to compute the global positions
and orientations of the body segments along with any objects
attached to them. Tendon modeling is less common and so we
describe our approach in more detail. The path of the tendon
is determined by a sequence of routing points (or sites) as
well as geometric wrapping objects which can be spheres or
cylinders. The software computes the shortest path that passes
through all sites defined for a given, and does not penetrate
any of the wrapping objects (i.e. the path wraps smoothly over
the curved surfaces). The latter computation is based on the
Obstacle Set method previously developed in biomechanics.
Let qdenote the vector of joint angles, and
s1(q),· · · ,sN(q)denote the 3D positions (in global
coordinates) of the routing points for a given tendon. These
positions are computed using forward kinematics at each time
step. Then the tendon length is
L(q) =
N−1
X
n=1 (sn+1 (q)−sn(q))T(sn+1 (q)−sn(q))1/2
The terms being summed are just the Euclidean vector norms
ksn+1 −snk, however we have written them explicitly to
clarify the derivation of moment arms below. When the
tendon path encounters a wrapping object, additional sites are
dynamically created at points where the tendon path is tangent
to the wrapping surface. These sites are also taken into account
in the computation of lengths and moment arms.
Moment arms are often defined using geometric intuitions
– which work in simple cases but are difficult to implement
in general-purpose software that must handle arbitrary spatial
arrangements. Instead we use the more general mathematical
definition of moment arm, which is the gradient of the tendon
length with respect to the joint angles. Using the chain rule,
the vector of moment arms for our tendon is
∂L (q)
∂q=
N−1
X
n=1 ∂sn+1 (q)
∂q−∂sn(q)
∂qTsn+1 (q)−sn(q)
ksn+1 (q)−sn(q)k
This expression can be evaluated once the site Jacobians
∂s/∂qare known. Our software automatically computes all
Jacobians, and so the computation of moment arms involves
very little overhead.
The extensor tendon of our finger uses a pulley mechanism,
which is modeled as follows. The overall tendon length L
is equal to the sum of the individual branches, weighted by
coefficients which in this case are 1/2for the long path and
1/4for the two short paths. Once Lis defined, the moment
arm vector is computed as above via differentiation.
TABLE III
MOM ENT A RM S THAT TH E SI MUL ATOR C OMP UTE D IN T HE DE FAULT
POSTURE (IN M M)
Finger
joint
Central
extensor
DIP
flexor
PIP
flexor
Abduction
tendon
Adduction
tendon
MCP
(ab/ad.)
0.00 -0.00 0.00 -8.44 8.86
MCP
(fl/ex.)
10.93 -13.47 -13.47 -6.17 -6.06
PIP
(fl/ex.)
1.81 -7.99 -7.99 0.00 0.00
DIP
(fl/ex.)
1.13 -6.14 0.00 0.00 0.00
Numerical values for the moment arms computed by the
model in the resting finger configuration are shown in Table
III. These values change with finger configuration in a complex
way, and are automatically recomputed at each time step.
Moment arms are useful for computing the tendon velocities
given the joint velocities:
˙
L=∂L (q)
∂q˙q

and also for computing the vector of joint torques τcaused by
scalar tension fapplied to the tendon by the corresponding
linear actuator:
τ=∂L (q)
∂qT
f
Note that these are the same mappings as the familiar map-
pings between joint space and end-effector space, except that
the Jacobian ∂L/∂qhere is computed differently. Another
difference of course is that tendons can only pull, so f≤0.
Following our initial control experiments, we realized that
the tendons cannot move the finger in all directions for
all postures. To analyze this phenomenon, we extended our
software to compute the 3D acceleration of the fingertip
resulting from the activation of each tendon. The results are
shown in Figure 8 with red lines. Note that these lines lie
close to a 2D plane, meaning that moving the finger outside
that plane is very difficult – it requires strong co-activation of
actuators that are near-antagonists. This prompted us to add
another actuator (a second extensor) and rearrange the tendon
attachment points, aiming to decorrelate the tendon lines of
action to the extent possible. The model in Figure 8 is after
the rearrangement; the problem is alleviated to some extent but
still remains. The underlying difficulty is that the flexors and
extensors acting on the distlal joints also have large moment
arms on the proximal joint. The only way to avoid this would
be to route the tendons for the distal flexors/extensors closer
to the center of the proximal joint – which we will investigate
in future work.
VI. EX PE RI ME NTAL VAL IDATION OF THE KINEMATIC
MODEL
To validate our model (before the addition of the 6th
actuator), we performed the following experiment. Infrared
markers (PhaseSpace, 120 Hz sampling rate) were glued
to the fingertip, proximal finger segment, and the moving
part of each cylinder. Another 3 markers were glued to the
immobile base so as to align the reference frames of the motion
capture system and the model. All markers were glued at
(approximately) known positions which we entered into our
kinematic model as sites, similar to the sites used to route
tendons. The cylinders were pressurized slightly above the
stiction point (using empirically determined pressure values),
so that they always pulled on the tendons and prevented tendon
slack. We moved the finger manually to different poses in
its workspace, attempting to span the entire workspace. After
each repositioning we waited for a couple of seconds, so as
to let everything ”settle” and obtain clean position data.
The data analysis began with frame alignment, by sub-
tracting the translational bias between the centers of mass
of the modeled and measured base marker positions, and
then performing orthogonal procrustes analysis to compute
the optimal rotation between the motion capture and model
frames. The data for the moving markers were then trans-
formed into the model coordinate frame, and were further
processes as follows. We implemented a MATLAB script
that automatically identified non-overlapping time intervals in
(a) (b)
(c) (d)
(e) (f)
Fig. 9. Comparison of measured and estimated tendon excursion data (a)-(e)
and illustration of tendon structures at the MCP joint of our proposed robotic
finger (f).
which every marker position remained within a ball of radius
2 mm (i.e. all markers were stationary), and averaged the
position data for each marker within each time interval. This
yielded 460 data points, each consisting of the 3D positions
of the seven module markers (five on the cylinders, two on
the finger).
The next step was to infer the joint angles of the finger given
the positions of the two finger markers. This was done by an
automated procedure (which is part of the MuJoCo engine),
whereby the residual difference between the observed and
predicted marker positions is minimized with respect to the set
of joint angles (note that the predicted positions are functions
of the joint angles). The minimization is done using a Gauss-
Newton method with cubic line-search. Even at the optimal
joint angles, there was some residual in the marker positions
(around 5 mm on average) which we believe is mostly due to
the fact that the finger is somewhat flexible and has additional
degrees of freedom (even though their range of motion is very

limited). Data points where the residual was larger than 7 mm
were excluded from further analysis, leaving us with 400 data
points.
Once the joint angles in each pose were inferred, we applied
our tendon model to compute the predicted tendon lengths,
and compared them to the measured positions of the cylinder
markers. The comparison is shown in Figure 9 for all five
tendons. Overall the fit is very good, especially for the flexors
and extensor that have larger excursions. The adduction tendon
shows saturation, which we realized is caused by the position
limiter on the cylinder (we attempted to place those limiters
just outside the finger motion range, but this one ended up
inside the range) causing the tendon to go slack in some
extreme poses. The abduction tendon is the most noisy, which
we believe is due to the fact that it presses on the joint capsule
and curves over it. This can be corrected by adjusting the
routing points.
VII. SUMMARY AND FUTURE WORK
We have described the design of an anthropomorphic robotic
finger system that has the potential to become a close replica
of the human finger. The system has three main components:
a modular design of three highly biomimetic finger joints, a
series of simplified pulley-based tendon mechanisms, and a
pneumatic actuation system with low friction and inertia and
high force output. We also presented models of the joint and
tendon kinematics and air dynamics, as well as preliminary
work on control strategies that utilize our models to achieve
accurate control of the new robot.
Our results to date show that the new robotic finger is
very capable, but also requires advanced control techniques
and accurate modeling. In future work we will refine our
models, and apply optimal control techniques to overcome the
complexity and nonlinearity of the system.
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