Speed-accuracy characteristics of human-machine cooperative manipulation using virtual fixtures with variable admittance.
A goal of human-machine cooperative systems is to enhance user performance of tasks at the limits of human motor control. For example, microsurgical procedures such as retinal vein cannulation require operation at scales that exceed the capabilities of all but the most skilled surgeons (Weiss, 2001). Even macro-scale tasks, such as tracking a tool along a curve, can be mentally and physically demanding. Tremor and fatigue greatly affect accuracy and completion time during tracking tasks (Riviere, Rader, & Thakor, 1998). Robots can be more precise and untiring than humans, but the complexity of tasks they can perform in unstructured environments is restricted, given the limitations of artificial intelligence. Human-machine cooperative systems are designed to integrate the intelligence and experience of humans, as well as the precision and accuracy of robots, by allowing shared control between the human operator and the robot. Cooperative systems are especially useful in small-scale tasks such as microassembly and microsurgery, in which visual and haptic feedback to the user is limited. Our research extends the assistance provided by cooperative systems through the application of virtual fixtures.
Virtual fixtures are a means of providing assistance to a human operator in a cooperative or teleoperated manipulation system. Using an admittance-controlled robot, we have developed "guidance" virtual fixtures that assist human operators in the execution of tasks related to microsurgery (Bettini, Lang, Okamura, & Hager, 2001). In our admittance controller, the velocity output is proportional to the input force through an admittance gain. A human user operates the robot by pushing on a handle, as shown in Figure 1. Computer vision is used to detect a planar path to be followed, and an admittance control law with a configuration-dependent anisotropic gain matrix provides the user with physical assistance to stay on that path. The virtual fixtures can provide differing levels of guidance; complete guidance strictly prevents the user from deviating from the reference path, whereas no guidance allows the user to move with equal ease in any direction. The system was created as a human-centered design (Sheridan, 2000), even though it is possible for the robot to run autonomously The details of this system, as configured for our experiments, are provided in the Method section.
[FIGURE 1 OMITTED]
In this study, two experiments were performed to investigate the relationship between virtual fixture admittance and performance. Experiment 1 was designed to determine this relationship for a path-following task. Experiment 2 compared the effect of different levels of virtual fixture guidance on user performance in three general tasks: path following, off-path targeting, and avoidance. We hypothesize that the complete guidance virtual fixture will result in the lowest error and execution time for the path-following task and that a high level of guidance will increase error and execution time for the off-path targeting and the avoidance tasks. Based on the experimental results, we created models that can be used to select the appropriate level of guidance to maximize speed and accuracy, based on the nature of the task.
Virtual fixtures have been previously applied to telemanipulation systems. Rosenberg (1993) provided an implementation of virtual fixtures for a peg-in-hole task in a teleoperated environment. The virtual fixtures were implemented using auditory feedback and impedance planes (virtual walls with stiffness and damping properties) on a haptic device master. Experimental results showed that the virtual fixtures improve task performance by as much as 70% as compared with when no fixtures are present.
Park, Howe, and Torchiana (2001) applied a virtual wall to the slave robot of a teleoperated surgical system, defining the position of the virtual fixture as the location of the internal mammary artery obtained from a preoperative CT scan. The virtual fixture was implemented and tested during in vitro blunt dissection for robot-assisted coronary bypass surgery, reducing execution time by 27% and eliminating any penetration into the wall. Because the virtual fixture was implemented only on the slave robot, this system did not provide any haptic feedback to the user.
Payandeh and Stanisic (2001) used a teleoperation system with haptic feedback for the purposes of performance enhancement and training. They implemented both forbidden-region and guidance virtual fixtures (they called the latter "force clues") and found in preliminary experiments that virtual fixtures reduce the time to complete assembly tasks for both novice and expert telerobot operators.
Most previous work on virtual fixtures has used impedance control devices, such as traditional haptic interfaces. In contrast, our robot operates by admittance control. Admittance-controlled robots are typically stiff and nonbackdrivable, making them appropriate for precise tasks. Impedance-controlled devices are backdrivable and typically not as stiff as admittance-controlled robots. In addition, our virtual fixtures guide the user along a desired path, whereas most virtual fixture implementations for teleoperation systems define forbidden regions in the master or slave workspace.
"Cobots" (collaborative robots; Peshkin et al., 2001) generate virtual fixtures that are effectively quite similar to ours. Cobots are specially designed admittance-controlled robots that can provide virtual fixtures for cooperative manipulation. The direction of motion of a cobot is associated with a single degree of freedom, which is actively steered within a higher dimensional task space. Essentially, this results in a virtual fixture that is a path in the task space, and the cobot design provides high passive stiffness orthogonal to the desired path. In order to simulate "free mode" motion (frictionless, massless, isotropic motion) in a cobot, the control gives equal effect to the input force in the directions orthogonal and parallel to the instantaneous allowed direction of motion. This is similar to the free motion (no guidance mode) of our system. However, we introduced virtual fixture admittance to vary the relative effectiveness of these two force components, creating different levels of guidance.
In another study of a cooperative system, Steele and Gillespie (2001) applied virtual fixtures in the form of haptic feedback in the manual control of vehicle heading. The definition of a path, provided by the Global Positioning System, was applied to control the steering of an agricultural vehicle to avoid collisions with obstacles along a straight path. Haptic feedback simulated a virtual spring with its center at the desired steering angle. Similar to our virtual fixture, it is designed as a shared control system in which the driver is able to override the controller because of virtual fixture compliance. Steele and Gillespie showed that haptic feedback reduced the chance of deviation from the path by 50% and decreased visual demand on the driver by 42%.
All previous studies indicate an advantage in using virtual fixtures in robotic operation, whether teleoperated or cooperative. However, the effect of the level of guidance on performance has not yet been studied. The level of control that an operator should have over a system is a question often encountered in shared-control systems. When a virtual fixture provides guidance, both speed and accuracy are improved. If too much automation is supplied, however, the operator may become accustomed to and overly reliant on the assistance. As a result, the operator may lose situation awareness and react slower in unexpected conditions. More importantly, many virtual fixtures are computed using some sensor (e.g., computer vision or medical imaging), so the virtual fixture provided may be based on incomplete information about the task or computed incorrectly because of image noise or changing light levels. In such systems the user should maintain some control over the machine, in case the virtual fixture is not placed or shaped exactly right. The ideal human-machine system would be able to provide what Wickens (1992) called "flexible automation," which describes adaptive systems that allow the user or the machine to choose the appropriate level of automation.
This research is also related to work in human motor control. There have been many studies on the trade-off between speed and accuracy of human operators. Fitts (1954) provided a foundation in this area by investigating the relation ship between speed and accuracy for a targeting experiment. Fitts' law describes the logarithmic relation between users' average movement times and the ratio of the distance between targets divided by their widths, effectively stating a fundamental limitation in the control of a movement. Accot and Zhai (1997) extended Fitts' law to find regularities in human-computer interaction trajectory-based tasks using computer interfaces, in particular tasks involving steering through a tunnel. In our work, we analyze speed and accuracy separately because the definition of optimal performance, which may be a weighted combination of the two metrics, is dependent on the nature of the task. In the case of microsurgery, accuracy generally has a higher priority than does speed.
In this section we describe the implementation of virtual fixtures on an admittance-controlled robot and the design of two experiments to examine the effect of virtual fixture admittance on performance.
Virtual Fixture Implementation on the Steady-Hand Robot
The experiments were conducted in a planar environment using the Johns Hopkins University Steady-Hand Robot (Taylor et al., 1999), as shown in Figure 1. The Steady-Hand Robot is an admittance control system in which the velocity of the end effector is proportional to the amount of force or torque applied by the human operator. It is explicitly designed for a cooperative manipulation. The robot has seven degrees of freedom, but only the x-y translation stages were used in the experiments.
The translation stages use off-the-shelf motorized micrometer stages (New England Affiliated Technologies, Lawrence, MA) that provide a position resolution of approximately 2.5 [micro]m in both the x and y directions. The operator applies forces to the robot through a handle at the robot's end effector, which is equipped with a six-degree-of-freedom force/torque sensor. The sensor has a resolution of 12.5 mN in force and 12.5 mN*mm in torque. The high-level virtual fixture controller relates the velocity of the robot to the force applied to this sensor by the operator. This velocity is then controlled using a low-level proportional-derivative (PD) controller (Motion Engineering, Inc., Raleigh, NC). The same low-level control parameters ([k.sub.p] = 6.10 mV/[micro]m and [k.sub.d] = 0.2 V/[micro]m in both the x and y directions) were used in both experiments.
The virtual fixture control algorithm for admittance-controlled cooperative manipulation and the controller performance are described in detail in Bettini et al. (2001). We now provide a description of the implementation used in the current study. The reference path for the virtual fixture was captured by a charge-coupled device (CCD) camera with a lens of 8 mm focal length, mounted on the end effector of the robot. For Experiment 1 the camera was elevated 95 mm from the path, yielding an average area of 0.004 [mm.sup.2] per pixel. For Experiment 2 the camera was elevated 125 mm from the path, yielding an average area of 0.003 [mm.sup.2] per pixel. The user could see only a portion of the path on the computer monitor. The image displayed an area of 8 [cm.sup.2], magnified by 30x in real time at 30 Hz. The XVision tracking system (Hager & Toyama, 1998) was used to determine the tangent to the reference path at the point closest to the image center in real time. Because computer vision is used to detect the path, the virtual fixture is not predefined. (In general, the performance of the vision system may be compromised for very sharp curvatures, noisy paths, or intersections, but this study was not affected by those limitations.) The accuracy of tracking is described in Bettini et al. (2001) and Hager and Toyama (1998).
The reference path for Experiments 1 and 2 was a sine curve printed in black on white paper with a 35-ram amplitude, 70-ram wavelength, and 0.59-mm line thickness. Users rested the elbow of the dominant hand on the table supporting the Steady-Hand Robot, and the geometry of the task required multisegmental arm movement (finger, wrist, and a small amount of elbow motion). Two additional visual cues, which did not affect detection of the reference path, were added for Experiment 2. For the avoidance task, a circle of radius 10 mm (185 pixels) was drawn with its center located at the midpoint of the sine curve. For the targeting task, a target was drawn as a dot on the perimeter of the circle along a line perpendicular to the sine curve at its midpoint.
The reference direction, [[delta].sub.p], is the tangent to the path detected by computer vision. When the tool tip of the robot (in our experimental setup, this point corresponds to the center of the image) deviates from the path, the minimum distance between the tool tip and the path is used to define the desired point on the path. The new reference direction vector, [[delta].sub.c], is then computed with the addition of an error term that servos the user onto the path:
(1) [[delta].sub.c]([x.sub.a]) = signum [f*[[delta].sub.p]([x.sub.a])] [[delta].sub.p] ([x.sub.a]) + [k.sub.e]e ([x.sub.a])
in which f is a vector that gives the instantaneous motion direction along the path, [x.sub.a] is the actual position of the end effector, and e([x.sub.a]) describes the error between the actual position of the tool tip and the desired position on the reference path. The use of the signum function ensures the correct relationship between the tangent to the path and the current motion direction of the robot. The dimensionless scalar gain, [k.sub.e] = 0.08, is assigned to govern the weight of the error term in the reference direction calculation. This was constant for all experiments. The user controls the tool tip position by applying a force, f, to the robot handle. By defining the matrix D = [[delta].sub.c][[delta].sub.c.sup.T] , the admittance controller can be written in the form
(2) v = [k.sub.s][[k.sub.[delta]]D + [k.sub.[tau]](I - D)]f
in which ks is a global scaling coefficient, I is the 3 x 3 identity matrix, and [k.sub.[delta]] and [k.sub.[tau]] are the admittance gains parallel and orthogonal to the reference direction, respectively. The scaling coefficient, [k.sub.s], controls the magnitude of velocity corresponding to the amount of the applied force. The value of [k.sub.s] was determined experimentally to provide smooth robot motion and remained fixed at 0.001 m/(N*S) throughout the experiment.
The admittance gain can be interpreted as a coefficient that indicates the "allowance" of motion. The stability of the system (without a virtual fixture controller) depends on the selection of the low-level PD gains used to achieve the desired velocity, v. The admittance controller combined with the virtual fixture control law is nonlinear, and complete analysis of controller performance is part of our ongoing work. Currently, the gains are set experimentally for stability. In addition, we set a maximum velocity threshold of 10 mm/s, as is routine to ensure steady-hand operation of the robot. This threshold could potentially skew the speed data but is necessary to generate a steady-hand admittance control system (Taylor et al., 1999). In addition, the data revealed that the few users who reached this maximum speed did so only on the straight portion of the sine curve and mostly when the virtual fixtures provided higher levels of guidance.
Changing the ratio of the two admittance gains provides different levels of guidance. When [k.sub.[delta]] = [k.sub.[tau]], there is no constraint, and the user can move with equal freedom in any direction. When [k.sub.[tau]] > [k.sub.[delta]], moving away from the path is easier than staying on it. Guidance occurs when [k.sub.[tau]] < [k.sub.[delta]]. For the tool tip to strictly stay on the path, the admittance gain in the direction normal to the reference path is [k.sub.[tau]] = 0. We define the admittance ratio as [k.sub.r] = [k.sub.[tau]]/ [k.sub.[delta]]. The minimum admittance ratio is 0, which provides complete guidance and prevents any deviation from the path. At the scales used in these experiments, the effect of the mechanical compliance of the robot is negligible. The maximum admittance ratio is 1 (indicating [k.sub.[tau]] = [k.sub.[delta]]), which provides no guidance. However, the operator's motion is still damped according to the choice of the scaling coefficient [k.sub.s].
Two experiments were conducted: path following (Experiment 1) and off-path motion (Experiment 2). Both used identical hardware, control parameters, and reference paths. Experiment 1 was a preliminary experiment to determine the relationship between the admittance ratio of the virtual fixture and accuracy/execution time for a path-following task. Experiment 2 compared the path-following task with two off-path motion tasks: targeting and avoidance. The off-path motion tasks represent cases in which the user is purposely deviating from the virtual fixture. The purpose of choosing these three tasks is to simulate a broader class of motions that can occur in the application of this system to microsurgery. By comparing the path-following tasks to the off-path motion tasks, an appropriate admittance ratio can be selected for general tasks.
During the experiments, the users sat directly opposite the robot and the monitor, providing a clear view of the image of the path. As the tasks were performed, the position of the robot "tool" (the image center) with respect to the reference path was shown on the screen in real time with a cross-shaped marker. An elbow rest was provided for the users to position themselves comfortably in front of the robot and minimize arm fatigue. For both experiments, the users were provided with written instructions, including task descriptions and specific protocols to follow (Figure 2). They were instructed to move along the path as quickly as possible without sacrificing accuracy, considering accuracy and speed with equal emphasis. For each task at each guidance level, the users familiarized themselves with the system during a practice run. A practice run was repeated if the user remained uncomfortable with a specific task or guidance level. The task and guidance level were presented to the user randomly; however, the experimenter informed the user of the task and guidance selection immediately before each trial. The users performed each task at each guidance level three times.
[FIGURE 2 OMITTED]
Experiment 1: Path following. This experiment followed the setup just described but was limited to the path-following task. To characterize the relationship between admittance ratio and performance, users performed the path following task with 11 admittance ratios from 0 to 1 (0.0, 0.1,.... 0.9, 1.0) three times each. Five users (3 males and 2 females between the ages of 16 and 36 years) with varying degrees of experience with the Steady-Hand Robot and virtual fixtures performed the experiment. Each user performed a total of 33 trials.
Experiment 2: Off-path motion. This experiment included all three tasks shown in Figure 2: path following (Task 1), off-path targeting (Task 2), and avoidance (Task 3). Although any admittance ratio value between 0 and 1 can be used for guidance virtual fixtures, this experiment tested only four discrete admittance ratios (0.0, 0.3, 0.6, and 1.0), corresponding to four guidance levels (complete, medium, soft, and no guidance). These four admittance ratio levels were selected because they provide virtual fixtures with distinctly different levels of guidance. Complete guidance prevents any user motion away from the path; medium guidance provides a large amount of guidance, giving the user little control over the direction of motion; soft guidance provides a small amount of guidance, giving the user some control over the direction of motion; and no guidance gives the user complete control over the direction of motion. Complete guidance (admittance ratio = 0) is not applicable to Tasks 2 and 3 because it completely restricts the user from deviating from the path.
The users performed each task at each selected guidance level three times, resulting in 30 trials per user. Eight users, different from those in Experiment 1, were included in Experiment 2. The users were 3 women and 5 men between the ages of 21 and 35 years with varying experience with the Steady-Hand Robot. In addition to the instructions provided for path following (identical to those in Experiment 1), the users were also given special instructions for the off-path motion tasks (Tasks 2 and 3 in Figure 2). For the off-path targeting task, users were instructed to avoid passing Point D by leaving and returning to the path as close to Point C as possible. For the avoidance task, users were told to leave and return to the reference path as close as possible to the intersection between the reference path and the circle (Area C). They avoided entering the Area C by traveling on the upper right half of its perimeter.
For the path-following task (in both experiments), the control computer recorded time and error from the moment the user started moving along the path (Point A) until he or she passed through the end point (Point B). The error is in millimeters, converted from a pixel error measuring the deviation of the tool tip from the path in the image. Registering the path to the position of the robot is difficult; therefore the CCD images were used to determine the position/ error data. The path was projected to the middle of the image plane, and the camera moved parallel to the plane of the path. Therefore, inaccuracy attributable to lens distortion for determining the tool position with respect to the path was minimal. The error for a trial is the sum of the error measured at each sample, divided by the number of samples.
For the off-path targeting task, the execution time considered was the time between the user's exit from and return to the path while acquiring the target. The error was measured by undershoot or overshoot from the target. In the avoidance task, the execution time was taken between the user's exit from and return to the path in order to move around the circle. In this task, users were asked only to avoid the circle; therefore, no error was measured for this task.
The data are sometimes presented as "normalized," meaning the error and time for each trial are divided by the maximum error and time, respectively, for each user across all admittance values. The normalization is used to determine the percentage improvement of a user over his or her worst-case performance when provided with different levels of guidance.
Experiment 1: Path Following
Figure 3 shows plots of admittance ratio versus normalized error and execution time, averaged over all users. The distribution of the data points indicates that error and time have linear relationships with admittance ratio. A linear fit of the data results in the following equations:
[FIGURE 3 OMITTED]
(3) e = 0.7505 [k.sub.r] + 0.1718, and
(4) t = 0.267 [k.sub.r] + 0.6937,
in which [k.sub.r], e, and t are admittance ratio, error, and time, respectively. The linear fits described by Equations 3 and 4 are the fits of the admittance ratio versus error and admittance ratio versus time, respectively. The [r.sup.2] values of Equations 3 and 4 are .98 and .92, respectively.
Experiment 2: Off-Path Motion
Table 1 shows the average performance results of Experiment 2. We ran a full analysis of variance (ANOVA) with a mixed model and then performed pairwise comparisons using Tukey's method (Kleinbaum, Kupper, Muller, & Nizam, 1998). The pairwise comparisons were made at a 95% confidence interval to determine significance in difference between the means of time and error (except for the avoidance task) for each admittance ratio level (Table 2). Tukey's method gives a confidence interval with a lower and an upper bound. If zero is excluded from the interval, the null hypothesis of the contrast can be rejected. In this case, the null hypothesis is that the means of the pair are not significantly different.
Task 1: Path following. The plots of normalized error and execution time are shown in Figure 4a. The closer the data point is to the origin of the plot, the more efficiently the user completed the task. The average execution times and average errors for all 8 users were tested to determine the statistical significance of user improvement with different guidance levels. The raw position and time data are shown in Table 1, and the results of the pairwise comparisons between guidance levels are shown in Table 2. A decrease in admittance ratio reduces error, except between medium and complete guidance, as indicated by the result of multiple pairwise comparison using Tukey's method. However, the pairwise comparisons for execution time among soft, medium, and complete guidance indicate that a decrease in admittance ratio does not necessarily improve execution time. We note that none of the users performed worse, in either time or error, when admittance ratio decreased.
[FIGURE 4 OMITTED]
Task 2: Off-path targeting. We have already examined the path-following portion of the task (Task 1), so we focus our analysis here on the error resulting from overshooting or missing the target. The errors and times shown in Table 1 were averaged and normalized with respect to the averaged result of medium guidance for each user. In Figure 4b, the results for one user with soft and no guidance are outliers and are off the scale in the plot. Table 2 shows that a higher guidance level significantly slows task execution. However, the execution times for no guidance and soft guidance do not differ significantly. The analysis also shows no difference in error for all guidance levels. Although the errors are not significantly different, Figure 4b shows that in general, reducing guidance reduces the time and error during target acquisition. The figure also indicates that medium guidance and no guidance offer the worst and the best performance, respectively.
Task 3: Avoidance. For this task only execution time was considered, because the goal presented to the users was to avoid an area rather than to accurately follow a path. The resulting execution times were averaged and normalized with respect to the maximum time taken by each user (Table 1). Table 2 gives the pairwise comparison results using Tukey's method. The results indicate that lowering the guidance level significantly reduces execution time. Similar to Task 2, in this task medium guidance and no guidance offered the worst and the best execution times, respectively, as shown in Figure 4c.
ADMITTANCE RATIO SELECTION
The linear relationship between admittance ratio and performance, demonstrated in Experiment 1, can be used to design admittance ratio selection parameters. Based on the data acquired during Experiment 2 with three tasks and four discrete values of admittance ratio, we created a system for selecting the admittance ratio for any task. We first find a linear relationship between the four discrete admittance ratios and time/ error. Next we create two scaling parameters, [s.sub.e] and [s.sub.t], for selecting the importance of guidance versus freedom for error and time, respectively. In addition, a weighting parameter, w, is used to identify the relative importance of time and error. The best admittance ratio value is computed using the linear equations describing the relationships between admittance ratio and time and admittance ratio and error, and the parameters [s.sub.e], [s.sub.t], and w.
Figure 5a shows linear fits of admittance ratio level versus average normalized error for Task 1 (path following) and Task 2 (off-path targeting). Figure 5b shows linear fits of admittance ratio level versus average normalized execution time for Task 1 and a combination of Tasks 2 and 3 (off-path targeting and avoidance). The experimental results for Tasks 2 and 3 are combined because these tasks both describe situations in which the user must work against a virtual fixture. The best-fit lines were evaluated based on the data of all 8 users. It is important to note here that the linear best-fit equations of this experiment in the path-following task also comply with the linear equations obtained from the experiment with 5 users and 11 admittance ratio values. The equations of these best-fit lines are
[FIGURE 5 OMITTED]
(5) [k.sub.1e] = 1.319e - 0.2659,
(6) [k.sub.2e] = -1.1729e - 1.4501,
(7) [k.sub.1t] = 4.1287t - 5.0716, and
(8) [k.sub.23t] = -2.1272t - 2.3985,
in which e is the error, t is the time, [k.sub.1e] is the fit for Task 1 error, [k.sub.2e] is the fit for Task 2 error, [k.sub.1t] is the fit for Task 1 time, and [k.sub.23t] is the fit for Task 2&3 time. Equations 5, 6, 7, and 8 have [r.sup.2] values of .95, .98, .89, and .94, respectively.
The intersections of the two lines on the plots for time and error represent the best admittance ratio for error, [K.sub.e], and the best admittance ratio for time, [K.sub.t], respectively, as shown in Figure 5. In general, we can separate the nature of the task into two selection parameters.
We use two scaling factors, [s.sub.e] and [s.sub.t], to represent the relative importance of guidance to operator control for error and for time, respectively. Error and time are considered separately. Because the admittance ratio attainable by the system is between 0 and 1, we use these limits to design the scaling factors. We apply the scaling factors on the equation obtained from Task 1 while keeping the equations of the other tasks, represented by Equations 6 and 8, the same. The equation representing the bestfit line for Task 1, considering for the optimal error, is now expressed as
(9) [k.sub.1e] = (1.519[s.sub.e])e - 0.2659,
in which [s.sub.e] [member of] [0.16, 2.50]. When [s.sub.e] [member of] [0.16, 1), Task 1 is more important, and when [s.sub.e] [member of] (1, 2.50], Task 2 is more important. The tasks are considered to be equally important when [s.sub.e] is set to 1. Similarly, the equation representing the best-fit lines for Task 1 considering the optimal execution time is now expressed as
(10) [k.sub.1t] = (4.1287[s.sub.t])t - 3.0716,
in which [s.sub.t] [member of] [0.66, 1.50]. When [s.sub.t] [member of] [0.66, 1), Task 1 is more important, and when [s.sub.t] [member of] (1, 1.50], Tasks 2 and 3 are more important. The tasks are considered to be equally important when st is set to 1. The lower bound and the upper bound of the scaling factors are chosen corresponding to the values giving the admittance ratio calculated from Equations 9 and 10 equal to 0 and equal to 1, respectively.
The effect of this scaling factor is shown in Figure 5, in which the model of Task 1 was scaled while keeping Tasks 2 and 3 the same. Here, [s.sub.e] = [s.sub.t] = 1.2 results in higher admittance ratios [K.sub.e] and [K.sub.t]. In this case, path following (Task 1) is considered to be less important than off-path targeting (Task 2) or avoidance (Task 3). Conversely, [K.sub.e] and [K.sub.t] decrease with lower values of the scaling factors and result in increased guidance.
We now focus on execution time versus error and introduce a weighting factor, w [member of] [0,1]. The appropriate admittance ratio can be selected based on the formula
(11) K = w[K.sub.e] + (1 - w)[K.sub.t],
in which K is the final admittance ratio value.
When w = 1 only error is considered, and when w = 0 only time is considered. When w equals 0.5, both speed and accuracy are weighted equally. When freedom and guidance are considered to be equally important (taskoriented parameters are [s.sub.e] = [s.sub.t] = 1), [K.sub.e] = 0.6424 and K, = 0.5585. When both time and error are considered equally (w = 0.5), the appropriate admittance ratio value is 0.5904 [approximately equal to] 0.6. This value of admittance ratio corresponds to soft guidance and corresponds with observations of the significant pairwise comparisons shown in Table 2. For path following, soft guidance significantly improves performance over no guidance. For the avoidance and targeting tasks, soft guidance does not significantly worsen performance over no guidance. Therefore, soft guidance ([k.sub.r] = 0.6) would be an appropriate choice for a general task.
Experiment 1 demonstrated a linear relationship between admittance ratio and error as well as between admittance ratio and time. This result is logical, considering that humans can generate trajectories by modulating the impedance (stiffness and damping) of their limbs (Latash & Gottlieb, 1991). Hollerbach (1981) proposed that humans produce curved trajectories using two orthogonal mass-spring systems that control the lateral and horizontal dimensions. For example, a circular trajectory can be made from a driving force in the horizontal dimension and an identical driving force in the lateral dimension but 90[degrees] out of phase (Zelaznik, 1996). By imposing a virtual fixture, the motion along the orthogonal direction to the reference path becomes more restricted as the admittance ratio decreases. This is similar to adjusting arm impedance by adding an appropriate additional damper in each direction, causing the limb to follow a trajectory along the reference path. Because the output velocity is linearly proportional to admittance ratio ([k.sub.r]), the linear relationships between admittance ratio and error as well as between admittance ratio and time can be expected.
Experiment 2 examined the effects of admittance ratio for several different types of tasks. For path-following tasks, complete guidance offered the best performance improvement. Therefore, an admittance ratio of zero is ideal if the virtual fixture shape and position can be assumed to be perfect. In contrast, high levels of guidance are not suitable for the tasks that require off-path motion. In Figure 6, for the off-path targeting task, significant effort to fight the virtual fixture in order to reach the target is evident, especially when the guidance provided by the system is quite high (admittance ratio [k.sub.r] = 0.3). The force data plotted are the magnitude of the force exerted in the direction orthogonal to the reference curve from the center of the curve to the target. The force decreases to zero as the user reaches the target. We note that the user cannot reach the target as smoothly with high guidance (Figure 6, middle and bottom panels) as with no guidance (Figure 6, top panel). The path-following portion of the task, which was not included in the data analysis of this task, reflected the performance obtained earlier for path following alone. The user could track the path more smoothly with low admittance ratios; however, he or she could not easily reach the target.
[FIGURE 6 OMITTED]
Similarly, for the avoidance task, Figure 7 shows the magnitude of the force exerted in the direction orthogonal to the portion of the reference curve enclosed by the circle for the three admittance ratios. The figure shows the user's effort to remain close to the perimeter despite the low-admittance virtual fixtures. The force exerted by the user is relatively high in the middle and bottom panels of Figure 7 as compared with the no-guidance case in the top panel. In accordance with the statistical analysis, these example data show that the user took the longest time to avoid the circle with medium guidance. In both Figures 6 and 7 the error data are also plotted, showing the amount of deviation from the reference curve.
[FIGURE 7 OMITTED]
In the off-path motion tasks, in which the operator needed to move away from the virtual fixture, medium guidance (low admittance ratio) reduced the accuracy and increased execution time dramatically. Soft guidance did not improve or worsen performance significantly as compared with when there was no guidance. However, the execution time was reduced significantly in the avoidance task when the admittance ratio increased from 0.6 (soft guidance) to 1 (no guidance). Because the difference between soft and no guidance was significant for the avoidance task but not for the targeting task, we conclude that users reacted differently to each of these two tasks: during avoidance tasks users require more freedom. For tasks that require off-path motions, higher-admittance virtual fixtures are recommended in general.
There are several limitations to our approach. Rather than selecting a single admittance ratio for an entire task, as was done in the section titled Admittance Ratio Selection, a user might want to tune the admittance ratio based on the requirements of each phase of a task. Thus automatic task segmentation is necessary for optimal performance of virtual fixtures. Our technique for selecting an optimal admittance ratio may be used in tuning based on a priori information regarding the purposes of different task segments. In addition, the total level of guidance provided by the virtual fixtures depends not only on the admittance ratio but also on the scaling factor, [k.sub.s], error gain, [k.sub.e], and PD control gains, all of which were constant in our experiments. The relationship between the admittance ratio values and the level of guidance provided is specific to our cooperative robot and may not be appropriate for other systems.
Other methods for implementing virtual fixtures involve control of impedance rather than admittance. The advantage of admittance control is the inherent passivity of the system, given that no motion will be commanded unless the operator is applying a force to the handle. In contrast, impedance control systems are backdrivable and display a force proportional to a change in position, so energy can be "stored" in a virtual spring and released even when the user is not touching the system. Implementations of impedance-type (also called "forbidden region") virtual fixtures have revealed the same instabilities as those occurring in haptic virtual environments (Gillespie & Cutkosky, 1996). Admittance control, however, requires a potentially expensive, noisy, and delicate force sensor mounted at the human-robot interface. In ongoing work, Abbott and Okamura (2005) are developing steady-hand teleoperation systems that have the advantages of admittance control while eliminating the force sensor requirement. Unfortunately, these control methods cannot be implemented on cooperative systems.
We conducted experiments On the effect of virtual fixture admittance on performance with a human-machine cooperative manipulation system. We considered three tasks: path following, off-path targeting, and avoidance. The amount of guidance offered by the system varied depending on the admittance ratio level. Complete guidance restricts the operator to the path, whereas soft guidance applies little constraint on direction of motion.
Changes in virtual fixture admittance affected user performance. We found that complete guidance (admittance ratio = 0) offered the best improvement in both execution time and error for tasks that involve only path following. However, any increase in the amount of guidance resulted in shorter time, more accuracy, or both, when compared with no guidance. In tasks for which more control from the user was necessary, such as object avoidance and off-path targeting, a high level of guidance (low admittance) reduced accuracy and increased execution time dramatically. This satisfies our hypothesis that the complete guidance virtual fixture will result in the lowest error and execution time for the path-following task and that a high level of guidance will increase error and execution time for the off-path targeting and avoidance tasks.
Our investigation showed that admittance ratio and performance have a linear relationship. Applying this linear model, we developed admittance ratio selection parameters that can be used to determine an appropriate admittance ratio level. By applying an appropriate scaling factor, the best admittance ratio for error and the best admittance ratio for time can be determined. Then a weighting parameter for time and error is chosen to compute the overall best admittance ratio. As suggested by parameters that equalize guidance versus freedom and time versus error, an admittance ratio of approximately 0.6 is recommended for general operation. This allows a significant increase in accuracy and decrease in time for tasks that include desired motions that both follow and move away from the reference path.
The results obtained from this experiment will be integrated into a future generation of virtual fixtures in which admittance ratio tuning is provided. Because suitable admittance ratio levels may vary from one user to another, specific admittance ratio settings should be set based on the individual's preference prior to task execution or updated online during task execution.
TABLE 1: Averaged Experimental Results of 8 Users for Experiment 2, Off-Path Motion Admittance Ratio ([k.sub.[tau]],/ Time (s) Error (mm) [k.sub.[delta]]) Average SD Average SD Task 1: Path Following 0 (Complete guidance) 18.710 1.357 0.061 0.013 0.3 (Medium guidance) 19.647 1.879 0.078 0.020 0.6 (Soft guidance) 20.425 2.042 0.121 0.030 1 (No guidance) 24.745 5.405 0.229 0.087 Task 2: Off-Path Targeting 0.3 (Medium guidance) 9.754 3.664 1.256 0.456 0.6 (Soft guidance) 7.148 3.178 0.910 0.180 1 (No guidance) 6.256 2.353 0.702 0.437 Task 3: Avoidance 0.3 (Medium guidance) 14.681 5.629 -- -- 0.6 (Soft guidance) 11.871 4.959 -- -- 1 (No guidance) 9.317 2.954 -- -- TABLE 2: Results of Pairwise Comparison Tests Using Tukey's Method for Experiment 2, Off-Path Motion Time Pairwise Lower vs. Significant Comparison Upper Bound Difference Task 1: Path Following No vs. soft -6.570 vs. -2.0700 Yes No vs. medium -7.350 vs. -2.850 Yes No vs. complete -8.290 vs. -3.780 Yes Soft vs. medium -3.000 vs. 1.440 No Soft vs. complete -3.930 vs. 0.502 No Med. vs. complete -3.150 vs. 1.280 No Task 2: Off-Path Targeting No vs. soft -1.330 vs. 3.110 No No vs. medium 1.280 vs. 5.720 Yes Soft vs. medium 0.389 vs. 4.820 Yes Task 3: Avoidance No vs. soft 0.337 vs. 4.770 Yes No vs. medium 3.150 vs. 7.580 Yes Soft vs. medium 0.593 vs. 5.030 Yes Error Pairwise Lower vs. Significant Comparison Upper Bound Difference Task 1: Path Following No vs. soft -0.149 vs. -0.067 Yes No vs. medium -0.192 vs. -0.110 Yes No vs. complete -0.208 vs. -0.127 Yes Soft vs. medium -0.084 vs. -0.003 Yes Soft vs. complete -0.100 vs. -0.020 Yes Med. vs. complete -0.057 vs. 0.024 No Task 2: Off-Path Targeting No vs. soft -3.040 vs. 3.460 No No vs. medium -2.690 vs. 3.800 No Soft vs. medium -2.900 vs. 3.600 No Task 3: Avoidance No vs. soft -- -- No vs. medium -- -- Soft vs. medium -- -- Note. The bold guidance levels provide lower average time and error values.
The authors thank A. Bettini, S. Lang, G. D. Hager, and J. J. Abbott for their contributions to this work. This material is based on work supported in part by the National Science Foundation under Grants #EEC-9731478 and #IIS-0099770.
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Date received: September 10, 2002
Date accepted: January 7, 2004
Panadda Marayong received her M.S. in mechanical engineering in 2003 from the Johns Hopkins University, where she is a doctoral student of mechanical engineering in the Haptic Exploration Laboratory.
Allison M. Okamura is an assistant professor of mechanical engineering at the Johns Hopkins University. She received her Ph.D. in mechanical engineering in 2000 from Stanford University.
Address correspondence to Panadda Marayong, 200 Latrobe Hall, Haptic Exploration Laboratory, Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218; email@example.com.
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|Title Annotation:||Displays and Controls|
|Author:||Marayong, Panadda; Okamura, Allison M.|
|Date:||Sep 22, 2004|
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