Article
Task-dependent impedance and
implications for upper-limb prosthesis
control
The International Journal of
Robotics Research
1–20
© The Author(s) 2014
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DOI: 10.1177/0278364913517728
ijr.sagepub.com
Amy A Blank1 , Allison M Okamura2 and Louis L Whitcomb1
Abstract
Modern-day prosthetic limbs are currently unable to imitate the versatile interaction behaviors of real human arms.
Although humans can vary the impedance of their arms, commercially available prosthetic limbs have impedance properties that cannot be directly controlled by users. We investigate the hypothesis that user-selectable prosthesis impedance
properties could improve the user’s ability to interact effectively with a variety of environments. We report the results of a
series of human subject studies exploring this hypothesis using either a virtual prosthesis or a robot arm as a prosthesis
proxy. We observed human performance with different stiffness and damping levels in the prosthesis proxy in two onedegree-of-freedom tasks: (1) a force minimization task and (2) a trajectory tracking task. The virtual prosthesis studies
focus on human performance in an ideal simulated system to avoid limitations of a physical implementation, whereas the
robot arm study focuses on performance changes that result from limitations of physical robotic hardware. The virtual
prosthesis results showed that task-dependent impedance can improve user performance and that users can evaluate the
effects of changing impedance. The robot arm results showed similar performance benefits of task-dependent impedance
in a physical robotic system. These studies identified areas in which non-ideal characteristics of the physical system limited users’ performance; most notably, the physical system could not achieve the low damping levels that helped subjects
reduce contact forces in the virtual prosthesis studies. Thus, we identify some design considerations for prostheses with
user-selectable impedance that can achieve useful impedance ranges for improving user performance.
Keywords
User-selectable impedance, prosthetic arms, variable impedance control
1. Introduction
Studies of neuromotor control have shown that humans
have the ability to change the mechanical impedance (multidirectional stiffness and damping) of their arms as needed
for different tasks (e.g. Franklin and Milner, 2003; Popescu
et al., 2003; Franklin et al., 2003a,b, 2004; Perreault et al.,
2004). The relaxed arm has low impedance, which has been
shown to be desirable for exploratory tasks in unknown
environments (Hogan, 2002). The limb’s impedance can
be increased through co-contraction of antagonist muscles,
which is often used to stabilize the arm in unstable environments or to resist perturbations (Franklin et al., 2003a).
Reflex actions to resist perturbations also contribute to
the apparent impedance of the limb (Shadmehr and Wise,
2005). These behaviors are crucial for natural and efficient interaction with the environment (Burdet et al., 2001;
Franklin et al., 2008); they allow humans to accommodate
changing environments and perform tasks with different
goals. For example, controllable arm impedance enables a
variety of behaviors, ranging from simple tasks like holding
a cup of coffee without spilling to more complex behaviors like smooth leading and following in partner dancing.
This ability to control limb impedance properties makes the
human arm a highly versatile tool, capable of specializing
its dynamics for many disparate physical interaction tasks.
In contrast, modern-day prosthetic limbs have impedance
properties that cannot be directly controlled by the user
during normal operation. In a body-powered prosthesis,
the impedance of a prosthesis joint is determined by the
impedance of the intact human joint driving it and mechanical design of the prosthesis. In a conventional myoelectric
prosthesis, the joint impedance is typically determined by
the gains of a proportional velocity controller (Parker et al.,
1 Mechanical
Engineering, Johns Hopkins University, Baltimore, MD,
USA
2 Mechanical Engineering, Stanford University, Stanford, CA, USA
Corresponding author:
Amy A Blank, Johns Hopkins University, 112 Hackerman Hall, 3400
North Charles Street, Baltimore, MD 21218, USA.
Email: [email protected]
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The International Journal of Robotics Research
2006). In both prosthesis types, the functional impedance at
the endpoint of the device is also affected by the mechanical properties of the interface between the prosthesis and
the residual limb (Silver-Thorn, 1999; Zheng et al., 2001;
Sensinger and Weir, 2008b). This lack of user-selectable
impedance properties results in prostheses that are specialized for a limited subset of the tasks a user might like to
accomplish. We conjecture that user-selectable prosthesis
impedance properties could improve users’ ability to interact effectively with a variety of environments. Therefore,
in this work we aim to identify (1) the most important
characteristics of human impedance modulation that should
be implemented in prosthetic arms with user-selectable
impedance and (2) design considerations for implementing
user-selectable impedance control in a way that users can
understand.
1.1. Background
Several methods have been developed to vary the mechanical impedance of robot and prosthesis joints, using series
elastic actuators (Pratt and Williamson, 1995; Sensinger
and Weir, 2008a), pneumatic actuators (Hajian et al., 1997;
Shen and Goldfarb, 2005, 2007), magnetorheological fluids (Herr and Wilkenfeld, 2003), and electric motors under
impedance control (Hogan, 1985; Koeppe et al., 2003).
These methods have addressed the problem of how to physically vary the joint impedance. However, comparatively few
studies have addressed methods for human users to actually
command robot impedance levels online, although promising work is starting to be done in this area (Rao et al., 2010;
Ajoudani et al., 2011, 2012; Hocaoglu and Patoglu, 2012).
Although impedance control has been well studied in
robotics (e.g. Hogan, 1985; Hogan and Buerger, 2005; Yang
et al., 2011; Ganesh et al., 2012), prosthetic arms present a
unique combination of human and robotic control in which
human capabilities and preferences may play an important
role in choosing impedance values. For example, physical effort (often termed ‘metabolic effort’ or ‘metabolic
cost’ in the literature) has been argued to be a major factor in determining human arm impedance (Franklin et al.,
2003b, 2004). A robot might have a single goal of minimizing tracking errors, whereas a human might have dual
goals of bounding tracking error and minimizing physical
effort (Shadmehr and Krakauer, 2008). Moreover, humans
can often predict the results of an interaction with the environment, allowing them to combine impedance control with
feedforward behaviors to compensate for expected forces.
In light of these considerations, we argue that studies of
impedance control in the specific case of prosthesis use
are needed to understand the utility of variable impedance
characteristics for next-generation prosthetic arms.
Preliminary experiments suggesting the utility of
variable-impedance prosthetic arms have been reported
using impedance control (Abul-Haj and Hogan, 1987,
1990a,b) and series elastic actuators (Sensinger and Weir,
2008a). These devices used electromyographic (EMG)
measurements of muscular co-contraction to specify
the variable impedance parameter. Abul-Haj and Hogan
(1990a,b) reported more natural patterns of muscle coordination and more realistic prosthesis motions when users
were able to control prosthesis impedance in a crankturning task than when they used fixed impedance; however,
no quantitative analysis of task performance was conducted.
Sensinger and Weir (2008a) reported a quantitative assessment of performance in perturbed point-to-point motions.
This study found that subjects did not modulate impedance
if the impedance was near a preferred value, but the use
of noisy EMG signals to measure co-contraction levels (for
user command of arm impedance) made precise impedance
modulation difficult for subjects. Moreover, the task chosen
was not one that encouraged a variety of impedance levels.
To our knowledge, no systematic study of user-controlled
impedance modulation for prostheses has been reported
previously.
1.2. Overview
This paper reports the results of a series of human subject studies addressing the relationship between impedance
modulation and task performance. Our primary concern in
this work is human performance with variable impedance;
we aim to characterize patterns of human performance
to inform later designs of prostheses with user-selectable
impedance. In the studies reported herein, we focus on
(1) the performance of different tasks with changing
impedance properties in a virtual prosthesis and a physical robotic arm and (2) users’ understanding of the effects
of changing impedance levels. Other facets of the prosthesis control problem include the availability and quality of control signals (e.g. Kuiken et al., 2005; Castellini
and van der Smagt, 2009; Rao et al., 2010; Hocaoglu and
Patoglu, 2012) and the effects of the mechanical properties
of the human–prosthesis interface (e.g. Silver-Thorn, 1999;
Zheng et al., 2001; Sensinger and Weir, 2008b); these issues
are not addressed herein, as they can be separated from the
issues of human performance and questions of ideal desired
impedance characteristics.
In our studies, users controlled a virtual or physical prosthesis proxy in real and simulated environments. The first
set of studies used a virtual prosthesis system in which ablebodied users controlled a simulated one-degree-of-freedom
variable-impedance prosthesis as a proxy for a one-degreeof-freedom prosthetic limb, and the final study used a physical robotic arm as a proxy for a prosthetic limb. Using
these systems, users complete two one-degree-of-freedom
tasks: (1) a force minimization task in which the goal was
to minimize contact forces between the prosthesis proxy
and a moving object in the environment and (2) a trajectory tracking task in which the goal was to track a specified
trajectory with the prosthesis proxy while experiencing random perturbations. These tasks were chosen to represent
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Blank et al.
3
two common interaction goals, and we expected them to
encourage the use of different impedance levels.
Our previous work (Blank et al., 2011, 2012) showed that
humans controlling a virtual prosthesis can achieve better
interaction performance with task-dependent impedance.
These results were observed in a perfect virtual prosthesis
system, which had no noise or modeling errors and which
could achieve any desired impedance level; thus, questions
arose as to how user performance would be affected by the
physical limitations of a robotic system. The present paper
expands upon the previous work by presenting new data
from the human subject study with a physical robotic system and by presenting a comparative analysis of the virtual
prosthesis results in the context of the new study in a physical robotic system. The combined results of these studies
show that task-dependent impedance can improve user performance in interaction tasks with both systems and identify
some design considerations for developing physical robotic
systems with which users can take full advantage of userselectable impedance capabilities. We anticipate that these
results will inform future designs of prosthetic limbs and
other teleoperated systems with user-selectable impedance.
2. Virtual prosthesis experiments
The virtual prosthesis system was used in three human subject studies. The same basic system was used for all three
virtual prosthesis studies, although the details of the task
and the feedback varied. Because our current focus is on
comparison of the virtual prosthesis studies with the physical robot study, only the version that most closely matches
the physical robotic system and the corresponding experimental results will be discussed in detail here. Further
information about the different versions of the system is
available in Blank et al. (2011, 2012).
2.1. System
The virtual prosthesis system hardware is shown in Figure
1(b). The subject’s force on the handle was measured by
a force sensor (Omega, LCCA-50). Visual feedback was
provided via a computer monitor, which was laid flat such
that pushing and pulling on the handle corresponded to
virtual prosthesis motion away from and toward the user,
respectively. For one of the virtual prosthesis studies, a
key pad (not shown) was provided for subjects to rate the
difficulty of trials. These devices were connected to the
computer through a data acquisition card (Measurement
Computing PCI-DAS6014). Inputs were sampled at a nominal frequency of 83 Hz or higher for all experiments, at least
an order of magnitude faster than voluntary human force
control, which is commonly understood to be limited to frequencies below about 10 Hz (Hajian et al., 1997). The code
for the final virtual prosthesis experiment was programmed
using Robot Operating System (ROS); this code is available
online in a ROS package.1
2.2. Modeling and control
Users controlled the motion of a one-degree-of-freedom
virtual prosthetic limb. As shown in Figure 2, the virtual
prosthesis is represented as a point mass m at position xa .
The prosthesis impedance is modeled as a spring with stiffness k and a damper with damping b connecting the actual
position xa of the virtual prosthesis to the desired position xd
commanded by the user. This model is not intended to realistically capture the complex impedance characteristics of a
real arm, because this complexity need not exist in a prosthesis. Instead, this model creates a relationship between
actual and commanded motion that is simple enough for
users to control easily. The equation of motion for the
virtual prosthesis is given by
mẍa = −b( ẋa − ẋd ) −k( xa − xd ) +Fe
(1)
where Fe represents the environment force acting on the
virtual prosthesis. This equation defines the motion of the
virtual prosthesis under the influence of external forces.
The virtual prosthesis system was designed to be analogous to a conventional amplitude-modulated myoelectric
prosthesis under proportional velocity control, as shown in
Figures 1 and 3. In an amplitude-modulated myoelectric
prosthesis, joint velocity is controlled to be proportional to
the level of EMG readings in the residual limb, with a deadband to prevent unwanted movement due to noise (Parker
et al., 2006). In our system, an isometric force input from
the dominant hand is used as a simple analog to EMG control, as shown in Figure 1; input force is used as a proxy
for muscle activation levels to simplify the hardware and
reduce the required training time as has been done successfully in previous studies (Kuchenbecker et al., 2007; Gurari
et al., 2009; Blank et al., 2010). The desired velocity of
the virtual prosthesis endpoint, ẋd , is then specified by an
admittance relationship, with a deadband C, as
⎧
⎨ α( Fu + C) if Fu < −C
α( Fu − C) if Fu > C
(2)
ẋd =
⎩
0 otherwise
where Fu is the force input applied by the user and α is a
constant. Here C = 0.05 N for all of the virtual prosthesis studies. Values for α ranged from 0.26 to 0.86 m/N·s.
Values for C and α were chosen during preliminary testing to be comfortable for users based on the amount of
noise present in input force readings (for C) and the scale
of the motion feedback (for α) (Blank et al., 2011, 2012).
From (2), the desired position xd of the virtual prosthesis
endpoint can be determined by integrating ẋd over time.
Subjects reported that this control method was intuitive and
the training was sufficient.
The utility of variable prosthesis impedance is suggested
by (1). If an external force is applied to the virtual prosthesis, increasing the impedance tends to reduce the tracking
error. If the virtual prosthesis trajectory is constrained by
the environment, then decreasing the impedance tends to
reduce contact forces from the environment.
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The International Journal of Robotics Research
Fig. 1. Analog between the virtual prosthesis system used in this experiment and a conventional myoelectric prosthesis. (a) Schematic
of a conventional myoelectric prosthesis. Muscle activation levels are measured using EMG signals and used to command prosthesis
motion. The user can watch the movement of the prosthesis to obtain visual feedback. (b) Virtual prosthesis system setup. The subject
controls the virtual prosthesis motion by pushing and pulling on a handle attached to a force sensor with his or her dominant hand; this
force input provides a proxy for EMG signals. Visual feedback about the virtual prosthesis motion is provided via a computer monitor.
Fig. 2. Virtual prosthesis model. (a) Schematic of an idealized one-degree-of-freedom prosthetic arm. We represent the virtual prosthesis as a point mass m at position xa . The prosthesis impedance is modeled as a spring with stiffness k and a damper with damping
b connecting the actual position to the desired position xd . Fe represents environment force applied on the prosthesis. (b) For these
studies, the virtual prosthesis is represented in Cartesian space.
2.3. Tasks
Subjects completed two simple tasks: (1) minimizing contact forces between the virtual prosthesis and a moving
object in the virtual environment and (2) tracking a specified trajectory while experiencing random perturbations.
These tasks represent two common goals in people’s interactions with their environment, and they were chosen to
encourage the use of different impedance levels. We conjectured that minimizing contact forces between the limb
and the environment should be easier with low impedance,
whereas minimizing tracking errors under the influence of
external disturbances should be easier with high impedance.
Such preferences would be expected based on the theory
of impedance control in robotics (Hogan, 1985; Hogan and
Buerger, 2005), but in regard to impedance modulation in
prosthetic arms, they have not been quantified previously.
2.3.1. Force minimization task. The first task is a onedimensional analog of holding a moving object, similar to
the scenario of holding someone’s hand while walking. In
the virtual prosthesis version of the task, the moving object
is modeled as a mass rigidly coupled to the virtual prosthesis, with desired trajectory xd2 and impedance represented
by a spring with stiffness k2 and a damper with damping
b2 , as shown in Figures 4(a) and (b). Here, xa represents the
position of their combined center of mass. In this task, the
environment forces on the virtual prosthesis result from the
impedance of the moving object. Summing forces on the
coupled mass yields
M ẍa = −b( ẋa − ẋd ) −k( xa − xd ) +Fe
(3)
Fe = −b2 ( ẋa − ẋd2 ) −k2 ( xa − xd2 )
(4)
where
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Blank et al.
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Fig. 3. (a) Control diagram for the virtual prosthesis system. The user’s applied force, Fu , specifies a proportional desired velocity, ẋd ,
which is integrated to specify a desired position, xd . The motion of the virtual prosthesis is determined by its interaction with the virtual
environment and the values of stiffness k and damping b. The user receives feedback about the state of the virtual prosthesis and the
applied environment forces via a visual display. (b) General control diagram for a conventional myoelectric prosthesis. EMG readings
from the user’s residual limb command a desired joint velocity, ẋd , and electric motors are controlled to produce actual motion, xa , close
to the desired motion. Environment forces, Fe , cause differences between the desired motion and the actual motion. The user receives
feedback via vision and socket forces and torques.
Fig. 4. (a) Model of the force minimization task in the virtual prosthesis system. M represents the combined mass of the virtual
prosthesis and the moving object (in this example, another person holding hands with the prosthesis), which are rigidly coupled. Here,
xa represents the position of their combined center of mass. The moving object has its own impedance, k2 and b2 , and desired trajectory
xd2 . The environment force Fe acting on the virtual prosthesis results from the impedance of the moving object when its desired
trajectory is not equal to its actual trajectory. (b) The representation of the task model in Cartesian space. (c) Graphical display for
the force minimization task in the virtual prosthesis system. The green ball represents the user’s virtual prosthetic limb. The arrow
represents the environment force resulting from the impedance of the virtual object. The user’s task is to minimize this environment
force. Annotation labels are added here for clarity; these are not displayed during the experiment.
and M is the combined mass of the virtual prosthesis and
the moving object.
The visual representation of the task is shown in Figure 4(c). The user sees the motion of the virtual prosthesis
and a vector whose length is proportional to the resulting
environment force, Fe . Previous work in sensory substitution has shown that visually displayed force information
can be understood and used by humans during robotic
interaction tasks (Kitagawa et al., 2005), and our subjects
reported that they understood the feedback provided during the experiment. One unit of virtual prosthesis motion
according to (3) corresponds to about 6.7 cm of motion on
the computer screen. The force vector is scaled such that
a length of 1 cm represents about 15 N of environment
force on the monitor used with the virtual prosthesis system, and about 1.5 N of environment force on the larger
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Fig. 5. Top: Graphical display for the trajectory tracking task in
the virtual prosthesis experiments. The green ball (top) represents
the user’s virtual prosthesis. The goal trajectory, shown in black,
scrolls across the screen from left to right at a constant speed. New
portions of the trajectory continue to appear at the right edge of
the screen until the end of the programmed trajectory. The user
moves the virtual prosthesis vertically to keep it on the desired
trajectory, while random perturbations are applied. The perturbations are modeled as impacts with objects represented by smaller
yellow balls (bottom two balls). These balls appear at the top or
bottom of the screen and move toward the green ball at a constant
velocity, disappearing upon impact. Bottom: The progression of
the graphical display over time. Balls are enlarged for visibility.
Adapted from Blank et al. (2011).
monitor used with the physical robotic system. In this task,
the user is asked to minimize the magnitude of the applied
environment force.
As seen in (3), it is possible to reduce the environment
force by commanding the actual trajectory of the virtual
prosthesis to match the desired trajectory of the moving
object. However, because the desired trajectory of the moving object is unknown to the user, we expect that this task
will be easier with low impedance values (k and b), which
will reduce the effect of differences in the two trajectories.
The desired trajectory of the moving object is either
π
(5)
xd2 = 0.75 sin ( t + φ) + 0.75 sin 2t + + φ
2
where φ is chosen randomly from [0, 2π) for each trial, or
xd2 = c( 0.8 sin ( 1.2t) − 0.6 sin ( 1.9t))
(6)
where c = ±1 is chosen at random for each trial. These
equations were chosen based on preliminary testing to cover
a significant portion of the system’s range of motion and to
be reasonable for users to follow.
2.3.2. Trajectory tracking task. The second task is a trajectory tracking task in one dimension. In this task, the goal
trajectory scrolls across the screen from right to left at a
constant speed, as depicted in Figure 5. The user’s task is to
control the virtual prosthesis to follow the goal trajectory,
which is the same trajectory as in the previous task, given
in (5) or (6). During this task, perturbations are applied to
the virtual prosthesis at random times. These perturbations
are modeled as elastic collisions with objects of mass 1 kg
and velocity 3 m/s before impact, represented on the computer screen by smaller yellow balls. The speed and mass
of the balls were chosen during preliminary testing to produce a perturbation large enough that subjects would not
ignore it, with a speed slow enough for subjects to notice
the projectile before impact. During practice trials, subjects
responded to these perturbations without prompting. After
impact, the projectiles disappear from the screen. Up to five
projectiles may be on the screen at a time. This limit was
chosen to provide the user with enough time between perturbations to notice new projectiles. If fewer than five are
present, at each timestep there is a probability of 0.01 that
a new projectile will be added. This probability was chosen
to create enough projectiles to be challenging but not overly
frustrating for subjects. The projectile direction is chosen at
random.
2.4. Procedures
At the start of each experiment, subjects were informed that
the purpose of the study was to explore the effects of variable stiffness and damping on prosthesis use. Next, subjects
were shown the different tasks and given task instructions.
They were instructed to push and pull on the force sensor to control the motion of the virtual prosthesis, and they
were informed that environment forces would also affect the
motion. They were also told that the effect of the force input
would change from trial to trial (this would be the result of
changing impedance, which was not explained to the subjects). For the force minimization task, subjects were asked
to control the motion of the virtual prosthesis to minimize
the length of the force vector displayed on the screen. For
the trajectory tracking task, subjects were asked to control
the motion of the virtual prosthesis to keep the position as
close to the displayed trajectory as possible.
For each task, subjects completed a set of practice trials before beginning the experiment trials. Sets of practice
trials consisted of one trial under each impedance combination. Each trial lasted either 60 s (in the first virtual
prosthesis experiment) or 15 s (all other experiments). The
order of the tasks and experiment trials was randomized
for each subject, but the same sets of practice trials were
given to all subjects. Each task was completed one or more
times with each impedance combination used in that experiment. The repetitions were added in later experiments to
provide more robust performance measurements and trial
length was reduced to help subjects more easily remember
their performance across the whole trial.
The virtual prosthesis impedance was chosen from
fixed stiffness k ∈ {2, 20, 200} N/m and damping b ∈
{0.25, 2.5, 25, 250} N·s/m. These values were chosen to
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Blank et al.
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cover the range of values (orders of magnitude) of elbow
impedance reported by Popescu et al. (2003), plus an extra
high damping level that subjects found to be useful in the
first virtual prosthesis experiment. The mass of the virtual
prosthetic limb, m, was set to 1.5 kg, which is the approximate mass of the human forearm (Shadmehr and MussaIvaldi, 1994). For the force minimization task, multiple sets
of impedance values for the moving object were tested.
Here, only the set corresponding to the values used in the
robot experiment will be discussed. For this set, the moving
object was given mass m2 = 1.5 kg, stiffness k2 = 20 N/m,
and damping b2 = 2.5 N·s/m so that users would experience
using stiffness and damping values both larger and smaller
than the environment values. The user impedance levels
covered a range of underdamped and overdamped conditions, whereas the environment was always underdamped.
The resulting range of damping ratios is wider than the
range achieved in real human limbs because we decoupled
the stiffness and damping, whereas in the human limb the
stiffness and damping vary together such that the damping
ratio remains fairly constant (Perreault et al., 2004).
In the final virtual prosthesis experiment, subjects were
asked to rate the difficulty of that trial on a scale of 1 (easiest) to 5 (most difficult). The difficulty ratings were added
to provide a way to quantify how well subjects can evaluate
their own task performance.
Following the experiment, subjects were asked to complete a post-experiment survey in which they provided comments on the tasks, impedance conditions, and strategies
they used under different conditions. For further details
regarding the differences in procedures across experiments,
see Blank et al. (2011, 2012) and Blank (2012).
2.5. Subjects
The three virtual prosthesis experiments enrolled 9, 11,
and 10 subjects, respectively. All subject groups included
both males and females who were both right-hand dominant and left-hand dominant. Experimental procedures were
approved by the Johns Hopkins University Institutional
Review Board, and all subjects gave informed consent.
3. Physical robot experiment
The physical robotic system was used in one human subject study in which users controlled the motion of a sevendegree-of-freedom robot arm in one degree of freedom
in Cartesian space. In order to allow comparison between
the results obtained with the virtual prosthesis system, the
physical robotic system was controlled to match the virtual
prosthesis system as closely as possible.
3.1. System
The robot arm used in this experiment is the Whole Arm
Manipulator (WAM) (Barrett Technology, Inc.). This arm
has seven degrees of freedom, including a three-degree-offreedom wrist. Each joint contains an encoder for position
sensing. The WAM is controlled through a computer running real-time Linux (Ubuntu with Xenomai). Graphics are
displayed via a large computer monitor placed behind the
robot, as shown in Figures 6 and 7. These figures show two
different configurations of the experimental setup for the
two different tasks. User input is measured through a force
sensor (Omega LCCA-50), which is read through a data
acquisition card (Measurement Computing PCI-DAS6014).
When interaction with a physical environment was needed,
the end of the user-controlled WAM was rigidly attached to
the end of another WAM (controlled autonomously by the
computer) with an aluminum connecting rod, as shown in
Figure 6. The autonomous WAM has a second force sensor
attached to its end to measure the interaction forces between
the two robots. Finally, a keyboard is provided for user input
between trials, as shown in Figures 6 and 7.
The experiment software was written using C++ and
ROS (Quigley et al., 2009), with the Computer Integrated
Surgical Systems and Technology (CISST) libraries (Jung
et al., 2010) for robot control. The software system is implemented as six ROS nodes: (1) a node to receive data input
from the data acquisition card, nominally running at 1 kHz;
(2) a node to control the graphical display, nominally updating at 100 Hz; (3) a node to interface with the CISST code,
which handles WAM control, nominally running at 500 Hz;
(4) an experiment manager node to handle the progression of experiment trials, nominally running at 10 Hz; (5)
a logger node to store data and save to file between trials,
nominally running at 1 kHz; and (6) a node to simulate projectiles in the virtual environment, nominally running at 1
kHz. Communication between nodes is handled via ROS
topics. The CISST code handles WAM feedback, controller
calculations, desired trajectory calculations, and sending
joint torque commands to the WAMs. All of this code is
available online in a ROS package.2
3.2. Modeling and control
The user controls the robot arm to move in one degree
of freedom corresponding to horizontal motion along a
specified line. Although the arm has seven degrees of freedom, we reduce the experiment to one degree of freedom to match the virtual prosthesis system by using a
stiff proportional-derivative (PD) controller to keep the
arm endpoint on the specified line with a constant orientation. As in the virtual prosthesis system, the chosen degree of freedom is along a straight line in Cartesian space. It is not known whether variable prosthesis
impedance should, in general, be controlled in joint space,
Cartesian space, or some other parameterization of the
workspace, but this question is beyond the scope of the
current study.
In the direction of motion under the user’s control, the
desired equation of motion is the same as in the virtual
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Fig. 6. WAM setup for the force minimization task. The user controls the right arm by pushing and pulling to the left and right on a
force sensor. In the force minimization task, the user-controlled right arm is rigidly connected to the autonomous left arm, as shown. A
second force sensor measures the interaction forces between the two arms, and the visual display shows a force vector whose length is
proportional to the size of this force.
Fig. 7. WAM setup for the trajectory tracking task. The user controls the arm by pushing and pulling on the force sensor. The visual
display shows a trajectory that the user is asked to track. The display also shows the positions of projectiles in the virtual environment
that affect the motion of the arm. In the trajectory tracking task, only one arm is used.
prosthesis studies (1). In this case, Fe is the measured environment force and k, b, and m are the stiffness, damping,
and effective inertia of the arm in the direction of motion.
The effective inertia is defined as the element of the operational space inertia matrix corresponding to the desired
direction of motion.
As in the virtual prosthesis studies, the user specifies the
desired arm motion with an isometric force input, as shown
in Figures 6 and 7. The desired velocity of the arm endpoint, ẋd , is again specified by an admittance relationship
with a deadband C, as in (2). For this study, C = 0.4 N and
α = 0.075 m/N·s. These values were chosen based on preliminary testing to maintain the users’ required force input
in a comfortable range and to limit the speed so that the
controller kept the robot on the desired path (with an accuracy of 2.5 cm measured perpendicular to the commanded
line of motion). As in the virtual prosthesis experiments,
users reported no difficulty in controlling the robot arm
movement after minimal training.
The impedance controller for the arm was implemented
in Cartesian space for both position and orientation (Khatib,
1987). Ideally, this controller would result in motion along
a line as in (1). However, gravity forces, Coriolis forces,
modeling errors (e.g. friction and errors in link lengths
and masses), and noise in the position and velocity sensing
result in positioning errors. Furthermore, workspace limits
and motion in the redundant degree of freedom affect how
well the arm tracks the line. To compensate for these nonidealities, we added feedforward terms to the controller and
included a nullspace PD controller to reduce motion in the
redundant degree of freedom (Khatib, 1987; Albu-Schäffer
et al., 2003); for more details, see Blank (2012).
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Blank et al.
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Fig. 8. Graphical display for the force minimization task in the physical robotic system. The vertical line marks the position of the usercontrolled robot arm’s endpoint. The horizontal vector indicates the magnitude and direction of the environment force Fenv resulting
from the connection between the two arms. The user’s task is to control the user-controlled arm to minimize this environment force.
Gray blocks at the left and right edges of the screen indicate workspace limits implemented in the controller. The gray block at the
bottom of the screen turns yellow to indicate that the maximum command input has been reached. Annotation labels are added here for
clarity; these are not displayed during the experiment.
3.3. Tasks
For the physical robot experiment, the tasks from the virtual prosthesis experiments were adapted for the physical
robotic system, as described here.
3.3.1. Force minimization task. The physical version of
the force minimization task is shown in Figure 6. In this
system, one unit of motion corresponds to about 9 cm of
robot movement. The user-controlled robot arm is rigidly
connected to another robot arm, which acts as the moving
object in the environment and is controlled autonomously
by the computer. The autonomous arm tracks its own
desired trajectory (unknown to the user) and uses the
same type of impedance controller as the user-controlled
arm but with different stiffness and damping levels. The
user’s goal is to minimize the contact forces between the
two arms by commanding appropriate motion of the usercontrolled arm.
As in the virtual prosthesis experiments, we provide the
contact force information to the user visually, and users are
instructed to minimize the environment force by moving
the user-controlled arm in the direction of the force vector. A force sensor mounted at the end of the autonomous
arm measures the interaction force between the two arms,
and a force vector is displayed on the screen, as shown in
Figure 8. Before beginning the experiment, the graphics on
the monitor are scaled and shifted to align the robot visually with the graphics shown on the screen. The calibration
is user-specific because the user’s height and sitting posture affect the vertical and horizontal distances between the
user’s eyes and the robot, which change how the graphics
appear to line up with the robot arm.
Also shown in Figure 8 are three gray blocks that are displayed on the screen. The two blocks at the left and right
edges of the screen indicate the workspace limits implemented in the controller; when the user reaches these limits,
the blocks darken to indicate the controller change. The
block at the bottom of the screen indicates a maximum
command input; when the user is commanding the maximum speed, this block turns yellow. The purpose of these
blocks is explained to the user before the experiment
begins.
3.3.2. Trajectory tracking task. In the physical version of
this task, shown in Figure 7, the trajectory scrolls across
the screen from top to bottom while the user controls the
arm to move left and right along a horizontal line. Because
of the difficulty in producing random perturbations in the
physical robotic system, the perturbations are simulated in
the controller. The perturbations are modeled as elastic collisions in a virtual environment between the user-controlled
arm and virtual objects with mass 3 kg and velocity 0.5 m/s
before impact. The objects are represented in the visual
display by small orange balls, as shown in Figure 9. The
speed and mass of the balls were chosen based on preliminary testing such that the resulting momentum change
would produce a noticeable perturbation, but not so much
that it would destabilize the arm. These values are different
from those in the virtual prosthesis experiments due to differences in mass and speed between the robotic arm and
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Fig. 9. Graphical display for the trajectory tracking task in the physical robotic system. The goal trajectory moves from the top to
the bottom of the screen. The user’s task is to control the arm such that the endpoint follows this trajectory. Projectiles in the virtual
environment are displayed as small solid orange circles moving from the sides of the screen toward the center; projectiles disappear
upon contact with the arm. Gray blocks at the bottom and sides of the screen indicate workspace limits and maximum command input,
as in the force minimization task. Annotation labels are added here for clarity; these are not displayed during the experiment.
the virtual prosthesis. As in the virtual prosthesis experiments, subjects responded to these perturbations during
practice trials without prompting from the experimenter.
The forces resulting from collisions in the virtual environment are converted to joint torques and added to the controller. Because the graphics are scaled to match the robot
motion, the projectiles appear to impact the endpoint of the
arm at the moment the perturbation is applied. The projectiles disappear upon collision. The goal trajectory displayed on the screen is the same as the desired trajectory of
the autonomous arm in the force minimization task, given
by (6).
As in the force minimization task, the graphics are scaled
and shifted to match the actual position of the robot based
on the user’s height and sitting position to ensure that the
graphical feedback on the monitor appears properly aligned
with the actual visual feedback of the robot position. Again,
the three gray blocks displayed on the screen indicate the
workspace limits and the maximum command input.
of magnitude in stiffness and damping. However, stability
concerns prevented the use of the full range of orders of
magnitude used in the virtual prosthesis experiments. As
mentioned previously, the effective inertia varies depending
on the configuration of the arm links, so the natural frequency and damping ratio also vary for fixed stiffness and
damping; over the whole workspace and all subjects, the
effective inertia varied from 1.5 kg to about 4.37 kg. For the
force minimization task, the impedance of the computercontrolled arm was chosen as in the virtual prosthesis studies to be in the middle of the user impedance range. In
this case, k2 = 200 N/m and b2 = 1 N·s/m. This choice
allowed users to experience impedance levels both higher
and lower than the impedance levels of the autonomous
arm. As in the final virtual prosthesis experiment, subjects
were asked to rate their performance in each trial; however,
in this experiment the scale was reversed, so subjects rated
their performance on a scale of 1 (worst) to 5 (best).
3.5. Subjects
3.4. Procedures
The procedures for the physical robot experiment closely
followed the procedures from the virtual prosthesis experiments, except for a few differences described here. In
the robotic arm experiments, the impedance was chosen
from fixed stiffness k ∈ {20, 200, 1000} N/m and damping
b ∈ {0.1, 1.0, 10, 40} N·s/m. Since the mass of the robotic
arm differed from the mass of the virtual prosthesis, the
stiffness and damping values were chosen to provide similar natural frequencies and damping ratios to those used in
the virtual prosthesis studies, with a similar range of orders
The robot arm experiment enrolled 9 subjects, including
both males and females who were both right-hand dominant and left-hand dominant. Experimental procedures were
approved by the Johns Hopkins University Institutional
Review Board, and all subjects gave informed consent.
4. Analysis
The analysis of subjects’ task performance considered (1)
root mean square (RMS) environment force for the force
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Table 1. RMS environment force Fenv (N) averaged over repetitions and subjects with the virtual prosthesis.
b = 0.25 N·s/m
b = 2.5 N·s/m
b = 25 N·s/m
b = 250 N·s/m
k = 2 N/m
k = 20 N/m
k = 200 N/m
0.21 ± 0.01
0.18 ± 0.02
0.25 ± 0.05
0.32 ± 0.11
0.31 ± 0.13
0.22 ± 0.05
0.24 ± 0.05
0.32 ± 0.08
0.43 ± 0.06
0.40 ± 0.07
0.32 ± 0.07
0.32 ± 0.09
Table 2. RMS environment force Fenv (N) averaged over repetitions and subjects with the robot arm.
b = 0.1 N·s/m
b = 1 N·s/m
b = 10 N·s/m
b = 40 N·s/m
k = 20 N/m
k = 200 N/m
k = 1000 N/m
3.13 ± 0.16
3.24 ± 0.25
3.25 ± 0.38
4.77 ± 1.10
8.31 ± 0.94
7.91 ± 1.67
7.87 ± 1.48
6.86 ± 1.53
10.45 ± 1.86
10.25 ± 2.41
10.29 ± 1.77
9.90 ± 2.03
minimization task and (2) RMS position error for the trajectory tracking task. When multiple repetitions of impedance
conditions were used, subject performance was averaged
over repetitions of the same impedance condition. A twofactor within-subjects analysis of variance (ANOVA) was
run on the metric of interest using factors of k and b
within each task or environment. The Geisser–Greenhouse
ˆ adjustment was used to correct for violations of the
sphericity assumption. Where follow-up tests are appropriate, we conducted a one-factor ANOVA or pairwise comparisons, using the Bonferroni adjustment for the α level.
Pairwise comparisons tested the null hypothesis that the
mean difference of the metric between the two conditions
is zero. All tests used a family-wise α level of 0.05.3 These
tests were intended to identify which impedance levels
result in the best performance for each task.
To measure subjects’ ability to evaluate their performance, correlation coefficients between difficulty rating
and task performance were calculated for each subject for
those experiments in which difficulty ratings were available. Because difficulty rating is an ordinal variable, the
Spearman rank correlation coefficient was used as a nonparametric alternative to the more common Pearson correlation coefficient. For each subject, a t-test was performed
on the correlation coefficient against the null hypothesis
of zero correlation. In the virtual prosthesis experiments,
subjects rated the difficulty of each trial on a scale of 1 (easiest) to 5 (most difficult), so a positive correlation indicates
an ability to evaluate task performance. In the robot arm
experiment, subjects rated their performance on a scale of
1 (worst) to 5 (best), so a negative correlation indicates an
ability to evaluate task performance.
5. Results
The following sections present the significant trends found
in our analysis, along with data tables and tabulated results
of statistical tests.
5.1. Force minimization
5.1.1. Force minimization performance. Figure 10(a)
shows performance results for all subjects in one of
the virtual prosthesis experiments with visual feedback
(see Tables 1 and 3).4 The two-factor within-subjects
ANOVA found a significant interaction between stiffness
and damping. Follow-up tests resulted in the significant
pairwise comparisons shown in Figure 10(a). Under both
feedback conditions, subjects performed best with lower
stiffness and medium damping. The general trends shown
in this plot are typical also of the previous virtual prosthesis
experiment when the same visual feedback was used.
Performance results for all subjects with the physical
robotic system are shown in Figure 10(b) (see Tables 2
and 4). The two-factor within-subjects ANOVA showed
a significant interaction between stiffness and damping.
Follow-up tests indicated significant pairwise comparisons
as shown in Figure 10(b). Subjects tended to perform better
with low stiffness, whereas damping had little or no effect.
5.1.2. User evaluation of performance. Subjects’ ability
to evaluate their own performance was measured using
the correlation between their subjective performance ratings and their actual measured performance. In the force
minimization task, lower RMS environment force indicates
better performance.
Figure 11(a) plots difficulty ratings versus performance
for a typical subject with the virtual prosthesis. This subject shows a positive correlation, indicating that the subject tended to rate trials with worse performance as more
difficult. A positive correlation indicates that the subject
was able to correctly identify trials that were more difficult
than others; in other words, the subject was able to correctly evaluate his or her performance to some extent. For
this task, eight of the ten subjects showed significant positive correlations, whereas the other two showed no significant correlation. For tabulated results for all subjects, see
Table 5.
Figure 11(b) shows ratings versus RMS environment
force for a typical subject with the physical robotic system. This subject shows a negative correlation, indicating that the subject correctly rated performance as worse
(lower rating) for larger RMS environment force. For this
task, all subjects showed a significant negative correlation, indicating that they were all able to correctly evaluate
their performance. For tabulated results for all subjects, see
Table 6.
5.2. Trajectory tracking
5.2.1. Tracking performance. For the trajectory tracking
task with the virtual prosthesis, there were significant main
effects of stiffness and damping and a significant interaction. Figure 12(a) shows the RMS tracking error as a
function of stiffness and damping (see Tables 7 and 9).
Follow-up tests found significant pairwise differences as
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The International Journal of Robotics Research
Table 3. Statistical significance results for performance (RMS environment force) in the force minimization task with the virtual
prosthesis; * indicates statistical significance.
Statistical Test
α
F
ˆ
p
* Main effect of k
Main effect of b
* Interaction k × b
* Main effect of b within k = 2
* b = 0.25 versus b = 2.5
b = 0.25 versus b = 25
b = 0.25 versus b = 250
* b = 2.5 versus b = 25
* b = 2.5 versus b = 250
b = 25 versus b = 250
Main effect of b within k = 20
* Main effect of b within k = 200
b = 0.25 versus b = 2.5
* b = 0.25 versus b = 25
* b = 0.25 versus b = 250
* b = 2.5 versus b = 25
* b = 2.5 versus b = 250
b = 25 versus b = 250
* Main effect of k within b = 0.25
k = 2 versus k = 20
* k = 2 versus k = 200
k = 20 versus k = 200
* Main effect of k within b = 2.5
k = 2 versus k = 20
* k = 2 versus k = 200
* k = 20 versus k = 200
* Main effect of k within b = 25
k = 2 versus k = 20
* k = 2 versus k = 200
* k = 20 versus k = 200
Main effect of k within b = 250
0.025
0.025
0.025
0.0083
0.0014
0.0014
0.0014
0.0014
0.0014
0.0014
0.0083
0.0083
0.0014
0.0014
0.0014
0.0014
0.0014
0.0014
0.0063
0.0021
0.0021
0.0021
0.0063
0.0021
0.0021
0.0021
0.0063
0.0021
0.0021
0.0021
0.0063
F( 2, 18) = 41.5
F( 3, 27) = 4.6
F( 6, 54) = 17.9
F( 3, 27) = 17.0
F( 1, 9) = 71.9
F( 1, 9) = 3.6
F( 1, 9) = 11.4
F( 1, 9) = 23.3
F( 1, 9) = 23.7
F( 1, 9) = 20.3
F( 3, 27) = 3.7
F( 3, 27) = 28.4
F( 1, 9) = 9.8
F( 1, 9) = 68.5
F( 1, 9) = 29.2
F( 1, 9) = 31.8
F( 1, 9) = 23.8
F( 1, 9) = 0.0
F( 2, 18) = 16.8
F( 1, 9) = 5.4
F( 1, 9) = 183.8
F( 1, 9) = 6.5
F( 2, 18) = 70.4
F( 1, 9) = 9.8
F( 1, 9) = 137.7
F( 1, 9) = 52.7
F( 2, 18) = 58.5
F( 1, 9) = 2.7
F( 1, 9) = 58.4
F( 1, 9) = 72.1
F( 2, 18) = 0.1
0.69
0.39
0.28
0.35
1
1
1
1
1
1
0.35
0.59
1
1
1
1
1
1
0.52
1
1
1
0.67
1
1
1
0.71
1
1
1
0.89
< 0.0001
0.0522
0.0002
0.0022
< 0.0001
0.0902
0.0083
0.0009
0.0009
0.0015
0.0849
< 0.0001
0.0121
< 0.0001
0.0004
0.0003
0.0009
0.8346
0.0023
0.0458
< 0.0001
0.0312
< 0.0001
0.0122
< 0.0001
< 0.0001
< 0.0001
0.1322
< 0.0001
< 0.0001
0.8564
Fig. 10. Force minimization performance results averaged over subjects for (a) the virtual prosthesis (one experiment with typical results
shown here, n = 10) and (b) the robot arm (n = 9). Lower RMS environment force indicates better performance. Error bars indicate the
standard deviation across all subjects. Significant differences are marked with brackets. In this task, users generally performed best with
low/medium stiffness and damping with the virtual prosthesis. With the robot arm, they generally performed best with low stiffness,
whereas damping had little significant effect.
indicated in Figure 12(a). Subjects tended to perform better
with higher stiffness and damping levels.
Performance results for all subjects with the physical
robotic system are shown in Figure 12(b) (see Tables 8
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Fig. 11. User ratings versus RMS environment force for typical subjects in the force minimization task. Lower RMS environment force
indicates better performance. (a) With the virtual prosthesis, correct evaluation of performance is indicated by significant (p < 0.05)
positive correlation (r = 0.65) between rating and performance, as explained in Section 4. (b) With the robot arm, correct evaluation of
performance is indicated by a significant (p < 0.05) negative correlation (r = −0.82) between rating and performance, as explained in
Section 4. The y-axis of this plot is inverted for easier visual comparison between the two plots.
Table 4. Statistical significance results for performance (RMS environment force) in the force minimization task with the robot arm; *
indicates statistical significance.
Statistical Test
α
F
ˆ
p
* Main effect of k
Main effect of b
* Interaction k × b
* Main effect of b within k = 20
b = 0.1 versus b = 1
b = 0.1 versus b = 10
* b = 0.1 versus b = 40
b = 1 versus b = 10
* b = 1 versus b = 40
* b = 10 versus b = 40
* Main effect of b within k = 200
b = 0.1 versus b = 1
b = 0.1 versus b = 10
* b = 0.1 versus b = 40
b = 1 versus b = 10
* b = 1 versus b = 40
b = 10 versus b = 40
Main effect of b within k = 1000
* Main effect of k within b = 0.1
* k = 20 versus k = 200
* k = 20 versus k = 1000
* k = 200 versus k = 1000
* Main effect of k within b = 1
* k = 20 versus k = 200
* k = 20 versus k = 1000
* k = 200 versus k = 1000
* Main effect of k within b = 10
* k = 20 versus k = 200
* k = 20 versus k = 1000
* k = 200 versus k = 1000
* Main effect of k within b = 40
* k = 20 versus k = 200
* k = 20 versus k = 1000
* k = 200 versus k = 1000
0.05
0.05
0.05
0.0167
0.0028
0.0028
0.0028
0.0028
0.0028
0.0028
0.0167
0.0028
0.0028
0.0028
0.0028
0.0028
0.0028
0.0167
0.0125
0.0042
0.0042
0.0042
0.0125
0.0042
0.0042
0.0042
0.0125
0.0042
0.0042
0.0042
0.0125
0.0042
0.0042
0.0042
F( 2, 16) = 150.1
F( 3, 24) = 0.4
F( 6, 48) = 13.2
F( 3, 24) = 21.0
F( 1, 8) = 4.3
F( 1, 8) = 1.1
F( 1, 8) = 22.5
F( 1, 8) = 0.0
F( 1, 8) = 21.0
F( 1, 8) = 26.8
F( 3, 24) = 7.5
F( 1, 8) = 1.0
F( 1, 8) = 1.1
F( 1, 8) = 26.9
F( 1, 8) = 0.0
F( 1, 8) = 19.1
F( 1, 8) = 11.6
F( 3, 24) = 1.2
F( 2, 16) = 121.7
F( 1, 8) = 295.5
F( 1, 8) = 147.7
F( 1, 8) = 18.7
F( 2, 16) = 76.1
F( 1, 8) = 79.5
F( 1, 8) = 83.9
F( 1, 8) = 38.0
F( 2, 16) = 150.4
F( 1, 8) = 139.2
F( 1, 8) = 187.7
F( 1, 8) = 63.0
F( 2, 16) = 142.1
F( 1, 8) = 113.7
F( 1, 8) = 178.3
F( 1, 8) = 97.2
0.56
0.66
0.47
0.41
1
1
1
1
1
1
0.75
1
1
1
1
1
1
0.76
0.82
1
1
1
0.80
1
1
1
0.94
1
1
1
0.84
1
1
1
< 0.0001
0.6865
< 0.0001
0.0007
0.0710
0.3298
0.0015
0.9750
0.0018
0.0008
0.0033
0.3452
0.3149
0.0008
0.8674
0.0024
0.0093
0.3221
< 0.0001
< 0.0001
< 0.0001
0.0025
< 0.0001
< 0.0001
< 0.0001
0.0003
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
and 10). The two-factor within-subjects ANOVA showed
a significant interaction between stiffness and damping.
Follow-up tests indicated significant pairwise comparisons
as shown in Figure 12(b). Similar to the virtual prosthesis
results, subjects tended to perform better with high stiffness
and/or high damping in the physical robotic system.
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Fig. 12. Trajectory tracking performance results averaged over subjects for (a) the virtual prosthesis (n = 9) and (b) the robot arm
(n = 9). Error bars indicate the standard deviation across all subjects. Significant differences are marked with brackets. In this task,
users generally performed better with higher stiffness and/or higher damping with both the virtual prosthesis and the robot arm.
Table 5. Statistical significance results for Spearman correlation
coefficients between difficulty ratings and performance for force
minimization with the virtual prosthesis; * indicates statistical
significance at α = 0.05.
Fig. 13. User ratings versus trajectory tracking performance for
a typical subject in the robot impedance experiment. Lower RMS
position error indicates better performance. This subject showed
a significant (p < 0.05) negative correlation between rating and
performance (r = −0.78), indicating that the subject had some
ability to evaluate performance correctly.
5.2.2. User evaluation of performance Figure 13 shows
ratings versus performance for a typical subject in the trajectory tracking task in the robot arm experiment. This
subject shows a negative correlation, indicating that the
subject correctly rated performance as worse (lower rating)
for larger RMS tracking error. As in the force minimization task, all subjects showed a significant negative correlation, indicating that they were all able to correctly evaluate
their performance. For tabulated results for all subjects, see
Table 11.
User ratings are not available for the trajectory tracking
task in the virtual prosthesis experiments.
Subject
r
t
p
1
2
3
4
5
6
7
8
9
10
0.773*
0.676*
0.653*
0.865*
0.453*
0.146
0.779*
0.132
0.638*
0.668*
t( 58) = 9.3
t( 58) = 7.0
t( 58) = 6.6
t( 58) = 13.1
t( 58) = 3.9
t( 58) = 1.1
t( 58) = 9.5
t( 58) = 1.0
t( 58) = 6.3
t( 58) = 6.8
< 0.0001
< 0.0001
< 0.0001
< 0.0001
0.0003
0.2655
< 0.0001
0.3162
< 0.0001
< 0.0001
Table 6. Statistical significance results for Spearman correlation coefficients between difficulty ratings and performance for
force minimization with the robot arm; * indicates statistical
significance at α = 0.05.
Subject
r
t
p
1
2
3
4
5
6
7
8
9
−0.511*
−0.860*
−0.564*
−0.757*
−0.824*
−0.815*
−0.861*
−0.704*
−0.901*
t( 46) = −4.0
t( 46) = −11.4
t( 46) = −4.6
t( 46) = −7.9
t( 46) = −9.9
t( 46) = −9.6
t( 46) = −11.5
t( 46) = −6.7
t( 46) = −14.1
0.0002
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
6. Discussion
The results of these experiments indicate different preferred
impedance levels for different tasks, suggesting potential
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Table 7. RMS tracking error (xa − xgoal ) (m) averaged over
subjects with the virtual prosthesis.
b = 0.25 N·s/m
b = 2.5 N·s/m
b = 25 N·s/m
k = 2 N/m
k = 20 N/m
k = 200 N/m
4.16 ± 1.56
1.44 ± 0.94
0.40 ± 0.08
0.72 ± 0.14
0.75 ± 0.19
0.33 ± 0.05
0.24 ± 0.06
0.24 ± 0.06
0.22 ± 0.06
Table 8. RMS tracking error (xa − xgoal ) (cm) averaged over
repetitions and subjects with the robot arm.
b = 0.1 N·s/m
b = 1 N·s/m
b = 10 N·s/m
b = 40 N·s/m
k = 20 N/m
k = 200 N/m
k = 1000 N/m
7.60 ± 1.07
7.24 ± 1.01
4.03 ± 0.89
2.82 ± 0.55
3.79 ± 0.64
3.97 ± 0.61
3.37 ± 0.76
2.86 ± 0.61
2.89 ± 0.71
2.78 ± 0.46
2.78 ± 0.72
2.61 ± 0.43
benefits to user-modulated impedance in a prosthetic limb.
This section discusses users’ performance and understanding of their performance. Where results differ between
the simulated system and the physical robotic system, this
section aims to identify reasons for those differences and
consider implications for variable-impedance prosthesis
design.
6.1. Task-dependent impedance improves user
performance
Both the virtual prosthesis studies and the robot arm study
showed the same general performance trends: subjects
showed better performance in force minimization for low
or medium impedance and better performance in trajectory tracking for high impedance. Specifically, the virtual
prosthesis studies showed that subjects performed better in
force minimization with low or medium stiffness and low
damping and better in trajectory tracking with high stiffness
and damping. In the robot study, subjects performed better
in force minimization with low stiffness and in trajectory
tracking with high stiffness and high damping. These results
suggest that user-modulated impedance could be beneficial
in prosthetic arms. If a prosthesis wearer could control these
parameters effectively, he or she could select appropriate
impedance levels to improve performance in a variety of
common tasks. In future studies, a larger subject pool and
testing of more intermediate impedance levels may allow us
to model the human input and predict more specific patterns
of how human performance varies with impedance levels
in order to explain the nuances of the interaction effects
observed in the current studies.
The general results presented here suggest that stiffness
and damping can be coupled, since best performance was
observed with both values low in force minimization and
both values high in trajectory tracking. We note, however,
that in a virtual prosthesis study not discussed in detail in
this paper, users showed best performance with low stiffness and high damping in a version of the force minimization task with different feedback information (Blank et al.,
2011). Thus, we conclude that there may be value in modulating stiffness and damping independently, though the
potential benefits may be negated by the added difficulty of
such non-intuitive control over impedance levels. Further
study will be required to determine whether stiffness and
damping should be coupled in practical use.
The strong similarities between the results in the physical robotic system and the virtual prosthesis system also
suggest that virtual prostheses will be generally useful to
identify desirable characteristics of prosthetic arms with
user-selectable impedance and to test different control
methods for such systems. Differences between the virtual
prosthesis results and the robot arm results lie in the details
of the performance trends. With the virtual prosthesis, both
stiffness and damping had significant effects in both tasks,
whereas with the robot arm users showed reduced effects
of damping in both tasks (although damping was still significant for the trajectory tracking task). To investigate these
differences, we measured the effective damping of the robot
in the direction of motion by commanding a sinusoidal
motion with increasing frequency and comparing force (calculated from the applied joint torques) to measured velocity
in that direction. The effective damping varies with position, so values were calculated for different areas of the
workspace. In most of the workspace, the measured effective damping was on the order of 10 N·s/m. Thus, when
low damping values of 0.1 and 1 N·s/m were commanded,
the actual damping was much higher due to the damping in
the physical robotic system. This effect would produce the
results seen here, where little difference is observed in subject performance across damping values. Since this effect
was not present in the virtual prosthesis studies, the results
of changing damping in those experiments were preserved.
This comparison suggests that prostheses with userselectable impedance should be carefully designed to provide the full range of useful impedance levels for tasks of
interest. From the virtual prosthesis results, we observe that
the ability to command low damping can improve performance in force minimization, and such an effect would
likely be present in a real robot if such damping values
could be achieved. However, the robot joint actuators and
the controller used in this experiment were not capable of
achieving such values. One possible solution for prosthesis design is to have torque-sensing at the joints to enable
low-level force control, which can be used with a highlevel impedance controller to ensure that the commanded
impedance is actually displayed at the robot end effector.
This has been done in other implementations of variableimpedance robot control (e.g. Albu-Schäffer et al., 2007). If
joint torque sensors are prohibitively expensive, care should
be taken to reduce the damping of the physical robotic system in order to allow the user to achieve low impedance
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16
The International Journal of Robotics Research
Table 9. Statistical significance results for performance (RMS tracking error) in the trajectory tracking task with the virtual prosthesis.
Statistical Test
α ( F∗)
F
ˆ
p
* Main effect of k
* Main effect of b
* Interaction k × b
* Main effect of b within k = 2
* b = 0.25 versus b = 2.5 N·s/m
* b = 0.25 versus b = 25 N·s/m
* b = 2.5 versus b = 25 N·s/m
* Main effect of b within k = 20
b = 0.25 versus b = 2.5 N·s/m
b = 0.25 versus b = 25 N·s/m
* b = 2.5 versus b = 25 N·s/m
* Main effect of b within k = 200
b = 0.25 versus b = 2.5 N·s/m
* b = 0.25 versus b = 25 N·s/m
* b = 2.5 versus b = 25 N·s/m
* Main effect of k within b = 0.25
k = 2 versus k = 20 N/m
* k = 2 versus k = 200 N/m
* k = 20 versus k = 200 N/m
* Main effect of k within b = 2.5
k = 2 versus k = 20 N/m
* k = 2 versus k = 200 N/m
* k = 20 versus k = 200 N/m
* Main effect of k within b = 25
0.05
0.05
0.05
0.0167
0.0019
0.0019
0.0019
0.0167
0.0019
0.0019
0.0019
0.0167
0.0019
0.0019
0.0019
0.0167
0.0019
0.0019
0.0019
0.0167
0.0019
0.0019
0.0019
0.0167
F( 2, 16) = 46.8
F( 2, 16) = 47.6
F( 4, 32) = 38.7
F( 2, 16) = 51.3
F( 1, 8) = 44.2
F( 1, 8) = 57.8
F( 1, 8) = 121.73
F( 2, 16) = 14.0
F( 1, 8) = 7.2
F( 1, 8) = 16.5
F( 1, 8) = 103.8
F( 2, 16) = 34.6
F( 1, 8) = 7.7
F( 1, 8) = 50.3
F( 1, 8) = 60.2
F( 2, 16) = 41.7
F( 1, 8) = 37.2
F( 1, 8) = 55.8
F( 1, 8) = 12.0
F( 2, 16) = 30.6
F( 1, 8) = 0.2
F( 1, 8) = 61.5
F( 1, 8) = 63.9
F( 2, 16) = 2.3
0.86
0.50
0.38
0.51
1
1
1
0.52
1
1
1
0.80
1
1
1
0.86
1
1
1
0.62
1
1
1
0.59
< 0.0001
0.0001
< 0.0001
< 0.0001
0.0002
0.0001
< 0.0001
0.0052
0.0278
0.0037
< 0.0001
< 0.0001
0.0238
0.0001
0.0001
< 0.0001
0.0003
0.0001
0.0086
0.0002
0.7128
0.0001
< 0.0001
0.17
Table 10. Statistical significance results for performance (RMS tracking error) in the trajectory tracking task with the robot arm.
Statistical Test
α ( F∗)
F
ˆ
p
* Main effect of k
* Main effect of b
* Interaction k × b
* Main effect of b within k = 20
b = 0.1 versus b = 1
* b = 0.1 versus b = 10
* b = 0.1 versus b = 40
* b = 1 versus b = 10
* b = 1 versus b = 40
* b = 10 versus b = 40
* Main effect of b within k = 200
b = 0.1 versus b = 1
b = 0.1 versus b = 10
* b = 0.1 versus b = 40
b = 1 versus b = 10
* b = 1 versus b = 40
b = 10 versus b = 40
Main effect of b within k = 1000
* Main effect of k within b = 0.1
* k = 20 versus k = 200
* k = 20 versus k = 1000
* k = 200 versus k = 1000
* Main effect of k within b = 1
* k = 20 versus k = 200
* k = 20 versus k = 1000
* k = 200 versus k = 1000
* Main effect of k within b = 10
k = 20 versus k = 200
* k = 20 versus k = 1000
k = 200 versus k = 1000
Main effect of k within b = 40
0.05
0.05
0.05
0.0167
0.0028
0.0028
0.0028
0.0028
0.0028
0.0028
0.0167
0.0028
0.0028
0.0028
0.0028
0.0028
0.0028
0.0167
0.0125
0.0042
0.0042
0.0042
0.0125
0.0042
0.0042
0.0042
0.0125
0.0042
0.0042
0.0042
0.0125
F( 2, 16) = 106.7
F( 3, 24) = 98.0
F( 6, 48) = 57.8
F( 3, 24) = 110.5
F( 1, 8) = 0.7
F( 1, 8) = 142.8
F( 1, 8) = 204.9
F( 1, 8) = 139.5
F( 1, 8) = 172.1
F( 1, 8) = 28.4
F( 3, 24) = 15.1
F( 1, 8) = 1.8
F( 1, 8) = 5.3
F( 1, 8) = 26.9
F( 1, 8) = 7.9
F( 1, 8) = 30.7
F( 1, 8) = 10.3
F( 3, 24) = 0.9
F( 2, 16) = 122.9
F( 1, 8) = 82.9
F( 1, 8) = 254.8
F( 1, 8) = 18.8
F( 2, 16) = 115.9
F( 1, 8) = 98.7
F( 1, 8) = 185.9
F( 1, 8) = 23.2
F( 2, 16) = 9.6
F( 1, 8) = 4.5
F( 1, 8) = 21.5
F( 1, 8) = 4.7
F( 2, 16) = 1.7
0.93
0.79
0.57
0.73
1
1
1
1
1
1
0.61
1
1
1
1
1
1
0.72
0.58
1
1
1
0.82
1
1
1
0.74
1
1
1
0.71
< 0.0001
< 0.0001
< 0.0001
< 0.0001
0.4145
< 0.0001
< 0.0001
< 0.0001
< 0.0001
0.0007
0.0003
0.2126
0.0510
0.0008
0.0227
0.0005
0.0125
0.4142
< 0.0001
< 0.0001
< 0.0001
0.0025
< 0.0001
< 0.0001
< 0.0001
0.0013
0.0053
0.0677
0.0017
0.0625
0.2205
values. In some systems, it may also be important to control
the effective stiffness and inertia of the prosthesis similarly.
In a real prosthesis, the physical interface between the
prosthesis and the residual limb may affect the actual
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Blank et al.
17
Table 11. Statistical significance results for Spearman correlation
coefficients between difficulty ratings and performance for trajectory tracking with the robot arm; * indicates statistical significance
at α = 0.05.
Subject
r
t
p
1
2
3
4
5
6
7
8
9
−0.509*
−0.688*
−0.704*
−0.576*
−0.777*
−0.761*
−0.800*
−0.615*
−0.780*
t( 46) = −4.0
t( 46) = −6.4
t( 46) = −6.7
t( 46) = −4.8
t( 46) = −8.4
t( 46) = −8.0
t( 46) = −9.0
t( 46) = −5.3
t( 46) = −8.4
0.0002
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
< 0.0001
achievable impedance range (Silver-Thorn, 1999; Zheng
et al., 2001; Sensinger and Weir, 2008b), though some of
this effect can be mitigated through careful socket design
(Sensinger and Weir, 2008b). Furthermore, prosthesis wearers can often modulate the impedance of the residual limb
to some extent, so commanding precise impedance levels would require compensating for this effect (Sensinger
and Weir, 2008b). Depending on the task, users might also
experience additional feedback through socket forces and
torques on the residual limb. Such concerns were beyond
the scope of the current work, which sought only to identify
desirable impedance characteristics and identify limitations
in robotic systems that might affect the ability to achieve
desirable impedance levels in a prosthesis. However, for
practical implementation in prosthetic arms, careful socket
design and analysis of the limitations will be crucial, as will
analysis of the effects of additional feedback through the
physical interface.
A further consideration for application to real prostheses
is control over multiple degrees of freedom. In this work, we
considered a one-degree-of-freedom system because it is
the simplest possible system that would allow us to explore
the potential benefits of variable impedance for prostheses.
The results here could be applied to limbs with multiple
degrees of freedom to some extent; for example, prostheses with multiple degrees of freedom could be controlled
to have the same endpoint impedance in all directions, and
we might expect to see some benefit even from such simple impedance modulation. However, real human behavior
includes modulating endpoint impedance differently in different directions (Franklin et al., 2003b, 2004), so there
may be the possibility for more nuanced control in multiple
degrees of freedom in a prosthesis. Given the encouraging
results that we found with the one-degree-of-freedom system, we plan to address the complexities of multiple degrees
of freedom in future work.
6.2. User understanding of task performance
In these experiments, subjects were able to successfully
evaluate their performance in both tasks, as shown by
the significant correlations between ratings and performance. Thus, we conclude that subjects can identify taskappropriate impedance levels, given sufficient feedback and
proper training. This ability is an important precursor to
actually commanding appropriate impedance levels, which
will also depend on factors such as the set of available
impedance levels and the control input used for selection.
For the force minimization task, subjects were better at
evaluating their performance with the robot than they were
with the virtual prosthesis. There are several possible reasons for this discrepancy. First, as noted in the virtual prosthesis study in Blank et al. (2012), feedback scaling plays
a critical role in subjects’ ability to evaluate their performance. With the larger monitor in the robot experiment,
the visually displayed force vector was larger, so subjects
may have had an easier time distinguishing between different levels of environment force. Second, user training
was improved for the robot experiment. In the virtual prosthesis studies, the force minimization task was explained
with words only, and subjects may not have understood the
underlying task model. In the robot experiment, the experimenter showed the user what was physically happening in
the task by first taking the subject’s hand and moving it
while asking the subject to follow, and then pointing out the
parallel behavior in the two robots. Finally, seeing the physical robot present may have improved subjects’ understanding of what was happening in the physical robotic system,
making it easier for them to complete the task correctly.
The improvement in subjects’ understanding of performance in the physical robotic system suggest that an actual
variable-impedance prosthesis may be easier for subjects
to understand than a virtual prosthesis because the interactions with the environment are more familiar and intuitive.
Furthermore, the improved effectiveness of training and
feedback in this study as compared to the simulation study
supports the earlier claim that proper feedback and training
can improve subjects’ ability to understand the effects of
changing impedance.
7. Conclusions and future work
The results of these studies suggest potential benefits of
user-selectable impedance in prosthetic arms. Specifically,
these results:
1. Show that task-dependent impedance improves user
performance with both a virtual prosthesis and a robot
arm, suggesting that user-selectable impedance may
benefit prosthesis users.
2. Show that users can evaluate the effects of impedance
changes in a virtual prosthesis and a robot arm, indicating that prosthesis users may be able to select taskappropriate impedance levels.
3. Validate the use of a virtual prosthesis system to identify desirable characteristics of variable-impedance systems by showing similar results with a physical robotic
system.
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18
The International Journal of Robotics Research
4. Identify some design considerations for developing
physical robotic systems that provide a wider range of
useful impedance levels.
The performance benefits of task-dependent impedance
that were observed with the virtual prosthesis system were
replicated in a physical robotic system with real-world limitations, suggesting that similar benefits would be observed
with a real prosthetic arm if these impedance variations
could be achieved. Lower impedance improves user performance when the goal is to minimize contact forces with
the environment, whereas higher impedance improves user
performance when the goal is to minimize position error
in trajectory tracking. Subjects were able to both perform
these tasks effectively and evaluate their levels of performance correctly, indicating that they would be able to
understand the effects of changing impedance for different
tasks. These results suggest a strong possibility that prosthesis users would be able to select and use task-appropriate
impedance levels to improve their performance of simple
tasks in prosthesis use.
Differences observed in the effects of damping point to
the importance of accounting for the characteristics of the
physical robotic system. The physical impedance of the
mechanical system limits the impedance range that can be
reliably commanded under a particular control strategy. To
achieve a wider range of impedance values, joint torque
sensing may be useful because it would allow a controller
that can sense the impedance level actually being displayed
at the endpoint of the arm.
Finally, we note that because user performance trends
were largely consistent between the virtual prosthesis studies and the robot arm study, it is reasonable and potentially
useful to continue exploring the effects of user-selectable
impedance with a virtual prosthesis system. Use of the virtual prosthesis system allows us to focus on user performance and preferences to identify useful impedance characteristics without the limitations of a particular physical
implementation. Then, testing on a physical robotic system shows how well the desired impedance characteristics
can be implemented and identifies characteristics of the
physical robotic system that should be improved to provide
users with a wider range of useful impedance levels. In the
future, we hope to add another stage of testing with different types of actual prosthesis systems to gather information about how well the robot impedance transfers to actual
prosthetic devices and how the physical interface between
the prosthesis and the user affects task performance. This
multi-stage research process will allow easier testing of different control methods. Testing with a virtual prosthesis
identifies some design considerations and provides baseline
performance results to guide the development of physical
systems.
The next stage in this line of research will be to give
users control over stiffness and damping in both the virtual
prosthesis system and the physical robotic system in one
degree of freedom. It is expected that with proper feedback
and training users will be able to choose task-appropriate
impedance levels in both systems; further testing will quantify a relationship between feedback scaling and impedance
modulation ability and will allow development of effective training strategies. Another future direction would be
to control robot movement in multiple degrees of freedom
and explore user performance with variable impedance in
multiple directions, both in the virtual prosthesis system
and in the physical robotic system. These studies will be
the next step towards understanding the potential effects of
variable impedance for multi-degree-of-freedom prostheses
and other teleoperated systems (e.g. for surgery or satellite
repair), and they will identify further design considerations
for implementation of user-selectable impedance in such
systems.
Acknowledgements
The authors are grateful to J Bohren for ROS technical support, setting up the real-time Linux system, and programming
the CISST/ROS interface; S Leonard for CISST support; and
N Gurari for thought-provoking discussions. Preliminary results
were reported previously at the 2011 IEEE International Conference on Robotics and Automation (Blank et al., 2011) and the
2012 IEEE International Conference on Biomedical Robotics and
Biomechatronics (Blank et al., 2012).
Funding
This work was supported by a National Science Foundation
Graduate Research Fellowship, a Link Foundation Fellowship in
Advanced Simulation and Training, an ARCS Scholarship, and
the Johns Hopkins University.
Notes
1. http://code.google.com/p/jhu-lcsr-ros-pkg/wiki/simulation_
impedance_experiment (as of 10 February 2013).
2. http://code.google.com/p/jhu-lcsr-ros-pkg/wiki/wam_impeda
nce_experiment (as of 16 August 2013).
3. For one of the virtual prosthesis experiments, the original
experiment included a third factor of feedback condition with
two levels for the force minimization task (Blank et al., 2012).
Here, we address only the visual feedback case, so the analysis
for this experiment uses an α level of 0.025.
4. The results shown here are from the final virtual prosthesis
study, which had experimental procedures most similar to the
procedures used in the robot arm study. Force minimization
performance results from the other virtual prosthesis studies
showed similar trends (Blank et al., 2011, 2012).
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