Task-Dependent Impedance Improves User Performance with a Virtual Prosthetic Arm Amy Blank, Allison M. Okamura, and Louis L. Whitcomb Abstract— Recent studies of neuromotor control have shown that humans modulate the impedance of their arms for different tasks, motivating the development of a prosthetic arm with user-selectable impedance characteristics. While impedance control has been extensively studied in robotics, prosthetic arms present a unique combination of human and robotic control, in which human capabilities and preferences play an important role. To understand the desirable impedance characteristics of prosthetic arms, we studied human control of a one-degreeof-freedom virtual prosthetic limb with variable stiffness and damping in tasks involving (1) force minimization and (2) trajectory tracking. Subjects performed best with different patterns of impedance modulation depending on task goals and available feedback, suggesting that the ability to modulate the impedance of a prosthetic limb may be beneficial to the wearer. The results of this study inform the future design of prosthetic limbs in which the wearer can vary limb impedance to improve performance in a variety of manipulation tasks.
I. I NTRODUCTION Studies of neuromotor control over the past decade have shown that humans modulate the impedance (multidirectional stiffness and damping) of their arms for different tasks (e.g., [4], [5], [6], [17], [18]). The relaxed limb has low impedance, which is desirable for exploratory tasks in unknown environments [10]. Cocontraction of antagonist muscles can increase the limb’s impedance, and this ability is often used to stabilize the arm in unstable environments or to resist perturbations [21]. We hypothesize that an upper-limb prosthesis with user-selectable impedance may provide users with better functionality and performance than present-day fixed-impedance prosthetic limbs. In commercially available prosthetic arms, the impedance is typically determined by the mechanical design in a bodypowered prosthesis, or the gains of a proportional velocity controller in a conventional myoelectric prosthesis [16]. Neither provides the wearer with variable impedance. Some state-of-the-art prostheses are able to vary their impedance, but methods for users to vary the impedance are a nascent topic of research [12], [19]. While impedance control has been well studied in robotics [9], [11], prosthetic arms present a unique combination of human and robotic control in which human capabilities and preferences play a major role. For example, energy costs are a consideration in determining human arm impedance [6]. While a robot might have a single goal of minimizing This work was supported by a National Science Foundation Graduate Research Fellowship and the Johns Hopkins University. The authors are with the Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA ablank2,
aokamura,
[email protected]
tracking errors, a human might have a primary goal of bounding tracking error and a secondary goal of minimizing energy consumption. Moreover, humans can often predict the results of an interaction, combining impedance control and feedforward behaviors to compensate for expected forces. In light of these considerations, studies of impedance control in the specific case of prosthesis use are needed to understand the desirable impedance characteristics of next-generation prosthetic arms. In order to create a simple and intuitive variable-impedance prosthesis, we need to determine which impedance parameters are most important for a user to control directly. To address this issue, we examine the performance of different tasks while allowing the user to select the stiffness and damping properties of a virtual prosthesis. Studies of human arm impedance modulation motivate and inform this work; however, human arm studies are not sufficient to resolve this issue for prosthesis design. Previous studies have explored changes in human arm impedance for tasks including isometric force generation and point-to-point motions [17], [18]. Franklin et al. observed increased multijoint arm impedance during reaching motions subject to external disturbances or unstable force fields [4], [6]. These studies showed that the relaxed human arm has low impedance, and humans tend to increase this impedance by only the amount necessary to achieve a desired level of performance, while minimizing the energy cost due to cocontraction to the extent possible [6]. This relationship between impedance level and physical effort has two notable implications. First, people make a tradeoff between performance and effort when choosing impedance levels. Second, human arm studies cannot distinguish between a task in which people prefer low impedance and a task in which the impedance level does not matter, because low impedance minimizes physical effort. In a prosthesis, the controller design can alter or eliminate the relationship between impedance level and physical effort, allowing the wearer to choose impedance levels based solely on task performance. Previously reported experiments with variable-impedance prosthetic arms used electromyographic (EMG) measurements of cocontraction of an antagonist muscle pair as the control signal to determine the variable impedance parameter [1], [2], [19]. These studies suggest the utility of variableimpedance prostheses, but the results were partially confounded by the control method and tasks chosen. AbulHaj and Hogan’s study [1] gives some qualitative indication that variable impedance improved performance in a crank-turning task, but they do not report a quantitative assessment. Sensinger and Weir [19] reported that subjects
Fig. 1. (a) Schematic of a one-degree-of-freedom prosthetic arm. (b) The prosthesis is modeled as a mass (m) with position xa connected to the desired position xd by a spring (k) and damper (b) representing prosthesis impedance. Fe represents environment forces applied on the prosthesis. (c) For this experiment, we represent the virtual prosthesis in Cartesian space.
did not modulate impedance if the impedance was near a preferred value, but they suggest that the use of noisy EMG signals made precise impedance modulation difficult and, moreover, that the chosen task did not encourage a variety of impedance levels. The use of muscular cocontraction as a control input in [1] and [19] requires subjects to make a tradeoff between task performance and physical effort, thus partially confounding the results. In this work, we seek to quantify the relationship between impedance modulation and task performance and to determine whether users will modulate impedance differently for different tasks when impedance modulation is not coupled to physical effort. We developed a virtual environment in which an able-bodied person controls the motion of a one-degreeof-freedom virtual prosthetic limb in which selecting and maintaining an impedance level requires minimal physical effort. One benefit of employing a virtual prosthesis is that it enables complete control over the simulated prosthesis physical parameters, control inputs, sensory outputs, and control parameters that would be difficult to achieve in a physical prosthetic arm. Here, we describe two human subject studies in which users interacted with virtual environments in force minimization and trajectory tracking tasks. We show that subjects perform best with different impedance levels and show different impedance modulation behavior in different types of tasks, depending on task goals and available feedback, and we discuss the implications for the usefulness of user-selectable impedance in prosthetic limbs. II. E XPERIMENT D ESIGN We conducted two consecutive human subject studies using the virtual prosthesis system. The system and experiment design for both studies are discussed here. A. Modeling and Control of the Virtual Limb Users control the motion of a one-degree-of-freedom virtual prosthetic limb modeled as a point mass (m). The impedance of the virtual prosthesis is modeled as a spring (k) and damper (b) connecting the actual position xa of the prosthesis to a desired position xd commanded by the user, as shown in Figure 1. This model is not intended to mimic the complex impedance characteristics of a real arm, because this complexity need not exist in a prosthesis. Instead, we attempt to create a simple relationship between actual and desired motion that users can understand and control. Summing the
Fig. 2. Experimental setup (left). The subject controls the virtual prosthesis motion by pushing and pulling on the handle attached to the force sensor (bottom right). At certain times, the subject also controls the prosthesis impedance by turning the dial(s) (top right). One dial is used in Experiment 1, and both are used in Experiment 2. Both the force sensor and the dial(s) are controlled with the subject’s dominant hand. The non-dominant hand holds a push button (not shown) that is used to start or end trials.
forces on the mass gives m¨ xa = −b(x˙ a − x˙ d ) − k(xa − xd ) + Fe ,
(1)
where Fe is the sum of forces applied on the virtual prosthesis by the environment. This equation defines the motion of the virtual prosthesis under the influence of external forces. The user specifies the desired virtual prosthesis motion with a force input, as shown in Figure 2. The desired velocity of the virtual prosthesis endpoint, x˙ d , is specified by an admittance relationship, with a deadband C, as α(Fu + C) if Fu < −C α(Fu − C) if Fu > C x˙ d = (2) 0 otherwise, where Fu is the force input applied by the user and α is a constant. C = 0.05 N for both studies. α = 0.5 m/N-s for the first study. It was later noted that user fatigue may depend on arm strength, so for the second study α was scaled based on the maximum voluntary torque (MVT) about the elbow joint. The resulting admittance range was 0.26 to 0.86 m/Ns. C and the relationship between α and MVT were chosen based on preliminary testing to be comfortable for users. The impedance parameters k and b are changed within the program, and at certain times they can be changed by the user via input from two dials, seen in Figure 2. The use of dials to specify impedance levels allows users to maintain an impedance level without exerting physical effort (which would be required in a system using EMG measurements of cocontraction). From Equation 2, the desired position xd of the virtual prosthesis endpoint can be determined by integrating x˙ d over time. This control method was chosen to be analogous to the control of a conventional myoelectric prosthesis, as depicted in Figure 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 [16]. Since EMG readings indicate muscle activation levels, they provide a measure of muscle force. Thus force control provides a simple analog to EMG control, requiring less training and complex hardware. This type of force control has
Fig. 3. (a) Control diagram for the virtual prosthesis. The user’s applied force, Fu , specifies a proportional desired velocity, x˙ d , which is integrated to specify a desired position, xd . The actual motion of the virtual prosthesis is determined by its interaction with the virtual environment and the values of stiffness k and damping b, which are specified by the user or by the experiment program. The user receives feedback about the state of the virtual prosthesis 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, x˙ d , 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.
been used successfully in other work [3], [7], [15]. Subjects reported that the force control was intuitive and the training was sufficient. Equation 1 shows the roles of high and low impedance. If an external force is applied to the limb, increasing the impedance tends to reduce the tracking error. If the actual trajectory is constrained by the environment, then decreasing the impedance will tend to reduce contact forces. B. System The subject’s force on the handle is measured by a force sensor, and two potentiometers act as sensors for dials that allow the user to tune the impedance parameters. A push button begins and ends trials. These devices are connected to the computer through a data acquisition card. The computer monitor is laid flat such that pushing and pulling on the handle corresponds to virtual prosthesis motion away from and toward the user, respectively. Inputs were sampled at a nominal frequency of 83.33 Hz for Experiment 1 and 200 Hz for Experiment 2, an order of magnitude faster than voluntary human force control, which is commonly understood to be limited to frequencies below about 10 Hz [8]. C. Tasks Subjects completed two simple tasks in the virtual environment: a force minimization task and a trajectory tracking task. These tasks represent two common goals in people’s interactions with their environment, and we expect them to encourage the use of different impedance levels. 1) Force Minimization: The first task is a one-dimensional analog of holding a moving object, as in the example of holding another person’s hand while walking. The moving object is modeled as a mass rigidly coupled to the virtual prosthesis,
Fig. 4. (a) Model of the force minimization task. M represents the combined mass of the virtual prosthesis and the moving object, which are rigidly coupled. Here, xa represents the position of their combined center of mass. The moving object has its own impedance (k2 , b2 ) and desired trajectory (xd2 ), and the environment forces (Fe ) applied on the virtual prosthesis result from the impedance of the moving object when its desired trajectory is not equal to the actual trajectory. (b) Graphical display for the force minimization task. The green ball (top) represents the user’s virtual prosthetic limb. The red ball (bottom) represents the desired trajectory of the moving object, which travels up and down in a sinusoidal pattern. The red ball is shown in Experiment 1, but not in Experiment 2. The arrow represents the environment force resulting from the impedance of the virtual object. The user’s task is to minimize this environment force.
with desired trajectory xd2 and impedance represented by a spring (k2 ) and damper (b2 ), as shown in Figure 4a. In this case, the environment forces on the virtual prosthesis result from the impedance of the moving object. Summing forces on the coupled mass yields Mx ¨a = −b(x˙ a − x˙ d ) − k(xa − xd ) + Fe ,
(3)
Fe = −b2 (x˙ a − x˙ d2 ) − k2 (xa − xd2 ),
(4)
where and M is the combined mass of the virtual prosthesis and the moving object. In this task, the user is asked to minimize the magnitude of the applied environment force, Fe , which is displayed as a vector connected to the virtual prosthesis, with a length of 1 cm representing about 15 N of force. As seen in Equation 3, the goal can be achieved by either (1) commanding low impedance or (2) trying to control the actual trajectory of the virtual prosthesis to match the desired trajectory of the moving object. The visual representation of the task for Experiment 1 is shown in Figure 4b. The user is able to see the motion of the virtual prosthesis, the desired motion of the moving object, and a vector whose length is proportional to the resulting environment force. For Experiment 2, the desired motion of the moving object was not displayed, because subjects in Experiment 1 appeard to be tracking the moving object rather than trying to minimize the force vector. The situation in Experiment 2 is also more realistic, in that the desired trajectory of an object would be unknown, and must be inferred from force feedback. The desired trajectory of the moving object for Experiment 1 is π xd2 = 0.75 sin (t + φ) + 0.75 sin (2t + + φ), (5) 2 where φ is chosen randomly from [0, 2π) for each trial. For Experiment 2, the desired trajectory of the moving object is xd2 = c(0.8 sin (1.2t) − 0.6 sin (1.9t)),
(6)
the potentiometer inputs. In Experiment 1, subjects could vary one parameter, while the other was fixed. In Experiment 2, subjects could vary both parameters at the same time. In the user-selected impedance trials, subjects were asked to choose the parameter value(s) that made the task easiest. They were instructed that the task performance was no longer being recorded, but they should try to perform as instructed in the fixed impedance condition. Thus, subjects were free to vary the impedance parameter(s) without penalty. E. Subjects Fig. 5. Top: Graphical display for the trajectory tracking task (Experiment 1). The green ball (top) represents the user’s virtual prosthesis. The target 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.
where c = ±1 chosen at random. The new trajectory was chosen because some subjects were able to anticipate the trajectory in Experiment 1. 2) Trajectory Tracking: The second task (Experiment 1 only) is a trajectory tracking task in one dimension. The target trajectory scrolls across the screen from right to left at a constant speed, as shown in Figure 5. The user’s task is to move the virtual prosthesis to follow the target trajectory, which is the same trajectory from the previous task, given in Equation 5. 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 such that the resulting momentum would produce a perturbation large enough that subjects would not ignore it, with a speed slow enough that subjects had time to notice the projectile before impact. 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 time between perturbations. 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 direction is chosen at random. D. Conditions 1) Fixed Impedance: Subjects completed each task several times with fixed impedance selected by the program. In these fixed impedance trials, the performance metric is environment force or tracking error, depending on the task, as described above. 2) User-Selected Impedance: Subjects were sometimes able to vary one or both of the impedance parameters using
Nine subjects between the ages of 24 and 39 were enrolled in Experiment 1, and eleven subjects between the ages of 23 and 34 were enrolled in Experiment 2. The subjects were a mix of right- and left-handed. The dominant hand was always used for the force sensor and potentiometer inputs in both experiments. Experimental procedures were approved by the Johns Hopkins University Institutional Review Board, and all subjects gave informed consent. F. Procedures 1) Experiment 1: For each task, subjects completed four sets: a practice set of fixed impedance trials, an experiment set of fixed impedance trials, a practice set of user-selected impedance trials, and an experiment set of user-selected impedance trials. 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. For the force minimization task, the moving object was given mass m2 = 1.5 kg, stiffness k2 = 20 N/m and viscosity b2 = 2.5 N-s/m. Fixed impedance sets consisted of nine trials, one under each combination of fixed k ∈ {2, 20, 200} N/m and b ∈ {0.25, 2.5, 25} N-s/m. These values were chosen to cover the range of values (orders of magnitude) of elbow impedance reported by Popescu et al. [18]. The mass of the virtual prosthetic limb, m, was set to 1.5 kg, which is the approximate mass of the human forearm [20]. Fixed impedance practice trials lasted twenty seconds each, and experiment trials lasted sixty seconds each. Each trial began when the subject pressed the push button and ended after the specified time. User-selected impedance experiment sets consisted of six trials: three trials with k fixed (one for each level of k) and three with b fixed (one for each level of b). Practice sets consisted of two pre-selected example trials. In these trials, users could vary k within [2, 500] N/m or b within [0.1, 80] N-s/m. The length of these trials was not fixed. Each trial began when the subject pressed the push button and ended when the subject pressed the button again, indicating that the parameter value at that time was the one the subject felt made it easiest to complete the task. After the experiment, subjects were asked for any comments about the tasks, the impedance conditions, and the experiment in general. 2) Experiment 2: Experiment 2 was conducted in two sessions. Only the force minimization task was used in this experiment, but the environment impedance was varied. In
the first session, all subjects completed the same two practice sets: one set of six fixed impedance trials, and one set of two user-selected impedance trials. The remainder of the first session consisted of four fixed impedance sets and one user-selected impedance set. Each fixed impedance set consisted of twelve trials, one under each combination of fixed k ∈ {2, 20, 200} N/m and b ∈ {0.25, 2.5, 25, 250} N-s/m, for a single combination of environment impedance levels k2 ∈ {20, 200, 2000} N/m and b2 ∈ {2.5, 25, 250} N-s/m. The highest user damping value, 250 N-s/m, was added for the Experiment 2 after observing that subjects preferred higher damping values in the Experiment 1. The environment impedance values were chosen to cover the higher end of the range of environment impedance levels tested by Jones and Hunter in human subject studies on stiffness and viscosity discrimination [13], [14] in order to explore whether environment impedance would affect optimal user impedance. Combinations of these impedance levels covered a variety of environment types, both overdamped and underdamped. Each user-selected impedance set consisted of nine trials, one for each combination of environment impedance levels. In these trials, users were allowed to vary k within [2, 500] N/m and b within [0.1, 250] N-s/m. The second session consisted of the remaining five fixed impedance sets and another user-selected impedance set. Before the experiment trials, subjects were given the option of completing the practice set again; two subjects chose to do so. The order of the sets and trials was randomized for each subject. Trials for both sessions were conducted as in Experiment 1. After each session, subjects were asked for any comments about the tasks, the impedance conditions, and the experiment in general. G. Analysis We consider three performance metrics: (1) root mean square (RMS) environment force for fixed impedance force minimization, (2) RMS position error for fixed impedance trajectory tracking, and (3) chosen impedance values for user-selected impedance tasks. For fixed impedance sets, a two-factor 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 conduct 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. When applicable, we also test for linear trends using the Roy-Bose critical value, an extension of Scheff´e’s method. All tests use a family-wise α level of 0.05. These tests are intended to identify which impedance levels result in the best performance for each task and environment. For user-selected impedance sets, a two-factor withinsubjects ANOVA was run on the chosen impedance value using factors of the fixed parameter level and the task type
Fig. 6. RMS environment force as a function of stiffness and viscosity for Experiment 1 force minimization task averaged over subjects (n = 9). Error bars indicate standard deviation. Significant differences are marked with brackets and a ?. In this task, users generally performed better with higher viscosity and lower stiffness.
Fig. 7. RMS tracking error as a function of stiffness and viscosity for Experiment 1 trajectory tracking task averaged over subjects (n = 9). Error bars indicate standard deviation. Significant differences are marked with brackets and a ?. In this task, users generally performed better with higher viscosity and higher stiffness.
(Experiment 1) or k2 and b2 (Experiment 2). Follow-up tests were the same as for the fixed impedance sets. These tests are intended to determine whether the users’ preferred impedance levels change for different tasks or environments. III. R ESULTS Due to space constraints, numerical results of statistical tests are not provided here. The raw data and statistical results are available at https://dscl.lcsr.jhu.edu/ People/Amy_Blank/data. A. Experiment 1 1) Fixed Impedance Trials: For the force minimization task, there were significant main effects of stiffness and viscosity and a significant interaction. Figure 6 shows the RMS environment force averaged over subjects. Follow-up tests found significant pairwise differences as indicated in Figure 6. Subjects tended to perform better with higher viscosity levels and one of the lower stiffness levels. For the trajectory tracking task, there were significant main effects of stiffness and viscosity and a significant interaction. Figure 7 shows the RMS tracking error as a function of stiffness and viscosity. Follow-up tests found significant
Fig. 8. Stiffness (left) and viscosity (right) values chosen by subjects for trajectory tracking (red squares) and force minimization (blue circles). Means and standard deviations also shown (filled circles and squares) to the left (trajectory tracking) and right (force minimization) of the individual values. The x-axis gives the value of the fixed parameter.
Fig. 10. Color map of RMS environment force in each environment (k2 , b2 ) for force minimization task in Experiment 2, averaged over subjects (n = 11). Each plot represents one environment. Within a plot, the color of each square represents the magnitude of the average RMS environment force for a particular user impedance combination, normalized within that environment. Maximum and minimum forces for each environment are given in Table I. In each plot, b is along the x-axis and k is along the y-axis. For each environment, best performance generally results from low k and b.
Fig. 9. Differences in chosen impedance values between the trajectory tracking and force minimization tasks. ∆k = ktracking − kf orcemin and ∆b = btracking − bf orcemin . Users usually preferred higher stiffness values for trajectory tracking than for force minimization. Many users also preferred higher viscosity for the trajectory tracking task than for the force minimization task, but this trend was not statistically significant.
pairwise differences as indicated in Figure 7. Subjects tended to perform better with higher stiffness and viscosity levels. 2) User-selected Impedance Trials: Figure 8 shows the impedance values chosen by subjects in the user-selected impedance trajectory tracking and force minimization tasks. For both tasks, subjects usually chose high values for both stiffness and viscosity. We note that for the force minimization task, the chosen stiffness values tend to be much greater than the values corresponding to the best performance in the fixed impedance trials. Figure 9 shows the difference in chosen impedance values between the trajectory tracking task and the force minimization task. In both cases, we see that subjects tended to choose higher impedance values for the trajectory tracking task. For trials where users varied the stiffness, two-factor ANOVA found a significant main effect of task type, and no significant effect of viscosity level, indicating that subjects chose higher stiffness for trajectory tracking than for force minimization. For trials where users varied the viscosity, the trends were not statistically significant. B. Experiment 2 1) Fixed Impedance Trials: Main effects of stiffness and viscosity were significant in all environments, and the interaction was significant in all environments except k2 = 2000, b2 = 2.5 and k2 = 2000, b2 = 25. Figure 10 shows RMS environment force data for all environments. Figure 11 shows detailed RMS force data and significant pairwise
Fig. 11. RMS environment force as a function of stiffness and viscosity for Experiment 2 force minimization task averaged over subjects (n = 11) for environment impedance k2 = 20, b2 = 25. Error bars indicate standard deviation. Significant differences are marked with brackets and a ?. In this task, users generally performed better with lower viscosity and lower stiffness. Similar trends regarding best impedance values were observed in all tested environments.
comparisons for one example environment, k2 = 20, b2 = 25. Though the results of follow-up tests varied across environments, subjects generally performed best with low stiffness and damping for all environments. In most cases, there is no significant difference between k = 2 and k = 20. Also in most cases, b = 0.25 gives best performance, except in the case of k2 = 20, b2 = 2.5, where best performance is for b = 2.5. 2) User-selected Impedance Trials: Figure 12 shows the impedance values chosen by subjects in the user-selected impedance force minimization task of Experiment 2 for each environment. Though the values varied widely in all environments, within-subjects ANOVA results do indicate some trends. For low environment damping (b2 = 2.5), users tend to increase both stiffness and damping when environment stiffness also gets low. For low environment stiffness (k2 = 2), users tend to increase stiffness when environment damping also gets low.
TABLE I M AXIMUM AND MINIMUM RMS ENVIRONMENT FORCES
The results of the two experiments indicate different preferred impedance levels for different tasks, depending on both task goals and feedback, suggesting potential benefits of user-modulated impedance in a prosthetic limb. However, users’ selected impedance values often differ from the values that yield best performance. Here, we discuss users’ impedance modulation behavior in comparison to their performance and the implications for the design of variableimpedance prosthetic limbs.
based on the theory of impedance control in robotics, and this behavior was indeed observed in Experiment 2. However, in Experiment 1, subjects performed best with low stiffness and high damping. We attribute this difference to the difference in feedback given to the user. In both experiments, force feedback was provided visually via a force vector displayed on the screen. In Experiment 1, the desired motion of the moving object was also displayed, and users may have been treating this as a position goal because following this trajectory tended to reduce environment forces. Subject comments from Experiment 1 indicated that higher damping made the prosthesis motion easier to control. Thus, it would seem that higher damping could help subjects follow the desired trajectory of the moving object, reducing environment forces when this feedback was available. To test this conjecture, we removed the visual display of the moving object position for Experiment 2, forcing subjects to rely entirely on the force information. As expected, subjects then performed best with low stiffness and damping. Previous studies of human arm impedance have not demonstrated a need for low limb impedance beyond physical energy concerns, because they were unable to separate control of impedance levels from muscular cocontraction. The current study shows that even when the energy concerns associated with cocontraction are lifted, people still tend to perform better with lower impedance for some tasks, indicating that reducing physical energy cost is not the only reason for having low impedance in the relaxed arm. Observations of better performance for low impedance in force minimization in Experiment 2 and for high impedance in trajectory tracking in Experiment 1 suggest that usermodulated impedance could be beneficial in prosthetic arms. Further, the observation of best performance for mixed impedance levels (low stiffness and high damping) for force minimization in Experiment 1 suggests that for certain tasks with certain types of feedback, added benefit may be realized with independent control over both stiffness and damping. 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.
A. Optimal impedance depends on task goals and feedback
B. Users select different impedance levels for different tasks
Three different optimal impedance patterns were observed in the fixed impedance trials. For trajectory tracking in Experiment 1, subjects achieved their best performance for high stiffness and high damping. For force minimization in Experiment 1, they achieved their best performance for low stiffness and high damping. For force minimization in Experiment 2, their best performance was for low stiffness and low damping. The observation of better performance for high impedance in trajectory tracking was expected; many previous studies have shown the importance of humans’ ability to increase limb impedance, especially in response to disturbances or destabilizing forces [4], [5], [6], [17], [18]. The observation of two different optimal impedance patterns for force minimization is surprising. Subjects were expected to perform best with low impedance in force minimization,
Users’ impedance preferences varied depending on the task. In the Experiment 1 user-selected impedance trials, users tended to choose high damping for both tasks, consistent with their performance in the fixed impedance trials, which was best with higher damping. Users also tended to choose higher stiffness for trajectory tracking than for force minimization, consistent with the observations in the fixed impedance trials that performance improved with higher stiffness for trajectory tracking and lower stiffness for force minimization. In Experiment 2, chosen impedance values depended on the environment impedance. Results indicate some preference for higher prosthesis impedance in lower impedance environments. Although the user-selected impedance values varied by task, they were not necessarily the values associated with best
k2 (N/m) b2 20 20 20 200 200 200 2000 2000 2000
(N-s/m) Fmax (N) 2.5 16.3 25 21.3 250 135.3 2.5 61.6 25 68.3 250 147.8 2.5 283.7 25 321.7 250 205.3
Fmin (N) 5.8 4.7 4.9 5.6 4.8 4.7 4.7 4.7 4.8
Fig. 12. Selected impedance values for Experiment 2. Dashed lines mark the edges of the allowed parameter space. For low environment damping (b2 = 2.5), users tend to increase both stiffness and damping when environment stiffness also gets low. For low environment stiffness (k2 = 2), users tend to increase stiffness when environment damping also gets low.
IV. D ISCUSSION
task performance in the fixed impedance trials. However, for some subjects and environments the performance was very similar for a few different impedance levels, for example, as in Figure 11 with k = 2, b = 0.25 and k = 2, b = 2.5. We hypothesize that subjects chose values that yielded performance “close” to the best performance case in some sense. A likely scenario is that the feedback provided was insufficient for subjects to distinguish between the effects of impedance levels that resulted in similar performance. Further analysis of how much the performance differs between the selected impedance values and the best fixed impedance values is being done to evaluate this possibility. Subjects may also have difficulty exploring a continuous two-dimensional parameter space thoroughly, so we are repeating the userselected impedance trials with a discrete parameter space. Different impedance preferences for different tasks and environments indicate that users are willing to modulate impedance to improve performance and are aware that different situations may require different impedance levels to improve performance. However, high variability in the selected values for the force minimization task suggests that users have difficulty in accurately judging their performance in force minimization. Users’ inability to identify optimal impedance levels in the force minimization tasks presented here may indicate a need for better feedback or a simpler parameter space, but further study is needed to determine whether this is the case. V. C ONCLUSION In this study, we explored the potential importance of usermodulated impedance in a prosthetic limb. By working in a virtual environment, we were able to design a simple system that decoupled the selection and maintenance of impedance levels from physical effort. The results indicate that the ability to modulate prosthesis impedance could benefit an upper-limb prosthesis wearer by allowing the arm to be adapted to different goals such as trajectory tracking and force minimization. Further, different optimal impedance patterns suggest value in modulating both stiffness and damping independently, if users can learn to control both parameters. The question of how well users can learn to control impedance parameters is still under study. Our initial results suggest some difficulty in selecting optimal impedance parameters from a continuous two-dimensional parameter space. Further analysis of subject performance in these experiments and continued study of feedback types and simpler parameter spaces will provide some insight into how to design a variable-impedance prosthesis so users can effectively select impedance parameters. In future work, we will continue to study the impedance properties that could be most beneficial for users to control in prosthetic arms. Studies planned for the immediate future will investigate the degree of precision needed in control of impedance parameters (i.e., continuous- or discrete-valued parameters) and the ability to change impedance levels quickly during a task. Extensions of this work to multiple degrees of freedom, exploration of the usefulness of force
feedback for impedance modulation, and implementation on a real robot arm or prosthesis are also planned. Building on these results, the end goal of this work is to develop prosthetic limbs that will enable improved manipulation performance in a variety of tasks. ACKNOWLEDGMENTS The authors are grateful to N. Gurari, R. Hearty, J. P. Swensen, and S. Charles for their assistance. R EFERENCES [1] C. Abul-Haj and N. Hogan. Functional assessment of control systems for cybernetic elbow prostheses. I. Description of the technique. IEEE Trans. Biomed. Eng., 37(11):1025–1036, 1990. [2] C. Abul-Haj and N. Hogan. Functional assessment of control systems for cybernetic elbow prostheses. II. Application of the technique. IEEE Trans. Biomed. Eng., 37(11):1037–1047, 1990. [3] A. Blank, A. M. Okamura, and K. J. Kuchenbecker. Identifying the role of proprioception in upper-limb prosthesis control: Studies on targeted motion. ACM Trans. on Applied Perception, 7(3):15, 2010. [4] D. W. Franklin, E. Burdet, R. Osu, M. Kawato, and T. E. Milner. Functional significance of stiffness in adaptation of multijoint arm movements to stable and unstable dynamics. Exp. Brain Res., 151:145–157, 2003. [5] D. W. Franklin and T. E. Milner. Adaptive control of stiffness to stabilize hand position with large loads. Exp. Brain Res., 152:211– 220, 2003. [6] D. W. Franklin, U. So, M. Kawato, and T. E. Milner. Impedance control balances stability with metabolically costly muscle activation. J. Neurophysiol., 92:3097–3105, 2004. [7] N. Gurari, K. J. Kuchenbecker, and A. M. Okamura. Stiffness discrimination with visual and proprioceptive cues. In Proc. World Haptics, pages 121–126, 2009. [8] A. Z. Hajian, D. S. Sanchez, and R. D. Howe. Drum roll: increasing bandwidth through passive impedance modulation. In Proc. ICRA, pages 2294–2299, 1997. [9] N. Hogan. Impedance control - an approach to manipulation. I Theory. II - Implementation. III - Applications. J. Dynamic Systems, Measurement, and Control, 107:1–24, 1985. [10] N. Hogan. Skeletal muscle impedance in the control of motor actions. J. Mech. Med. Biol., 2(3-4):359–373, 2002. [11] N. Hogan and S. P. Buerger. Impedance and interaction control. In T. R. Kurfess, editor, Robotics and Automation Handbook, chapter 19. CRC Press, LLC, Boca Raton, 2005. [12] Johns Hopkins University Applied Physics Laboratory. Revolutionizing Prosthetics 2009 team delivers first DARPA limb prototype, 2007. http://www.jhuapl.edu/newscenter/pressreleases/2007/070426.asp, Accessed January 8, 2010. [13] L. A. Jones and I. W. Hunter. A perceptual analysis of stiffness. Exp. Brain Res., 79(1):150–156, Jan. 1990. [14] L. A. Jones and I. W. Hunter. A perceptual analysis of viscosity. Exp. Brain Res., 94(2):343–351, June 1993. [15] K. J. Kuchenbecker, N. Gurari, and A. M. Okamura. Effects of visual and proprioceptive motion feedback on human control of targeted movement. In Proc. ICORR, pages 513–524, June 2007. [16] P. A. Parker, K. B. Englehart, and B. Hudgins. Myoelectric signal processing for control of powered limb prostheses. J. Electromyography and Kinesiology, 16(6):541–548, 2006. [17] E. J. Perreault, R. F. Kirsch, and P. E. Crago. Multijoint dynamimcs and postural stability of the human arm. Exp. Brain Res., 157:507– 517, 2004. [18] F. Popescu, J. M. Hidler, and W. Z. Rymer. Elbow impedance during goal-directed movements. Exp. Brain Res., 152:17–28, 2003. [19] J. W. Sensinger and R. F. Weir. User-modulated impedance control of a prosthetic elbow in unconstrained perturbed motion. IEEE Trans. Biomed. Eng., 55(3):1043–1055, 2008. [20] R. Shadmehr and F. A. Mussa-Ivaldi. Adaptive representation of dynamics during learning of a motor task. J. Neurosci., 14(5):3208– 3224, 1994. [21] R. Shadmehr and S. P. Wise. The Computational Neurobiology of Reaching and Pointing. MIT Press, Cambridge, MA, 2005.
