To verify the performance of the prototype, four experiments are conducted. Two experiments are conducted to verify the closed-loop response of the robot’s motion, and two are conducted to compare the manipulation performance of the robotic assistant with of a human assistant.
Velocity tracking experiment (auto-feed)
The objective of this experiment is to verify the performance of the robot in responding to an assigned velocity profile. In particular, we would like to verify the robot’s performance when moving with non-constant speeds. In this experiment, the four degrees of freedom of the robot are tested separately. To each joint, a time-varying velocity profile (a sinusoidal function of time) is assigned, which the robot must follow as accurately as possible. We denote the i th velocity input to the robot by
where v
i
represents the joint velocity and k
i
is a positive user-definable velocity gain.
The results of this velocity tracking experiment are shown in Figure 7. In the figure, the desired velocity profiles fed to the robot are represented by the black lines while the measured velocities of the joints are represented by the red lines. These experiments are obtained with the following velocity gains: k1=13, k2=27, k3=1.7, and k4=50. From these results, it is shown that the robot can closely track the time-varying velocity inputs.
Velocity tracking experiment (manual input from joystick)
As the robot is designed to be controlled and operated by the primary surgeon, this experiment is conducted in a manual-control mode. The objective of this experiment is similar to the auto-feed one, i.e., to verify the performance of the robot in responding to the user’s input commands.
In this experiment, the robot is manually controlled by human through a joystick interface. For these experiments, we denote the i th velocity input to the robot by
where J
i
represents a discrete (i.e. −1,1,0) input provided by the joystick interface. The user is asked to control the robot by pressing the buttons on the control joystick which correspond to the robot joints and their moving directions.
Similar to the auto-feed experiment, the joints of the robot are tested separately in this experiment. Figures 8 and 9 show the results of this experiment; Figure 8 shows the steady state response of the system while Figure 9 shows the transient responses. In the figures, the black lines indicate the input velocity profiles converted from the input commands from the joystick while the red lines indicate the measured joint velocities. These experiments are obtained with the following velocity gains: k1=20, k2=50, k3=3.5, and k4=60. From the results, it is shown that the robot can accurately regulate a constant speed profile provided by the user.
Manipulation experiment (one-dimensional distance)
In traditional laparoscopic hysterectomy, visual feedback is obtained from the laparoscopic camera inserted into the patient’s body through a small incision opened on the patient’s abdomen. In general, 2D visual feedback can be obtained and the surgery is performed with the use of this 2D visual information. This scenario is emulated in this experiment, and the experimental setup is shown in Figure 10. The objective of this experiment is to compare the manipulation performance of the robot with that of human.
In this experiment, a medical manikin is used as the simulated environment. To emulate the laparoscopic camera, a webcam is used to obtain the visual feedback from the manikin. With the webcam, images with resolution of 640 × 480 pixel are obtained. An artificial marker is attached to the uterus as a visual feedback tracking point. In this experiment, a standard non-motorized uterus manipulator (produced by Apple Med [15]) is used as the surgical tool to position the uterus of the manikin.
On the robot side, the uterus manipulator is grasped by the robotic positioning arm. Human participants are asked to move the marker to a desired image configuration with the assistance of the robot and retain that position. The robot is controlled by the participants using a joystick.
To compare the performance of the robot with the performance of a human, the same experiment is conducted without the assistance of the robot. The human participants are asked to hold the uterus manipulator by themselves and keep a specified image position without the use of any supporting device. All participants involved in this experiment are without medical background. Short training for both manipulating with and without the robot is given to the participants before the experiment started.
In this experiment, the desired image position is represented by a one-dimensional line as shown in Figure 11. The participants are asked to align the marker attached to the uterus of the manikin to any point of the line specified on the screen both with and without the use of the robot. We choose this task as it is a common procedure to move the uterus aside during laparoscopic hysterectomy.
Pixel error between the marker and the line is measured. As the image position of the desired destination is known and the image position of the marker attached to the manikin can be obtained by feature tracking, the pixel error can be calculated by
where e is the pixel error, p
d
is the pixel position of the desired destination, and p
m
is the pixel position of the marker. In this one-dimensional experiment, p
d
and p
m
can be understood as the x-coordinates of the desired destination and the marker on the image plane, respectively.
In both assisted and unassisted experiments, ten trials are conducted. The results are shown in Figure 12.
In Figure 12, the plot on the left shows the measured pixel error obtained the during manipulation with the assistance of the robot; the plot on the right shows the measured pixel error obtained without the use of the robot assistant. From these results, it is shown that with the use of the robot, the participants are able to manipulate the uterus to a specified image position in a more stable way compared to the traditional hand manipulation.
Manipulation experiment (two-dimensional point control)
To further verify the performance of the robot, the manipulation experiment is extended to the two-dimensional image space. In this experiment, the desired position is specified by an image point instead of a line, as shown in Figure 11. The pixel errors in both x and y directions on the image plane are measured to evaluate the performances.
Figures 13 and 14 compare the positioning performance of the robot with that of solely human manipulation. These results show that while both human and robot are able to manipulate the uterus to a desired position, the robot can retain the desired configuration in a more stable manner, as expected.