Virtual fixture control of a hybrid parallel-serial robot for assisting ophthalmic surgery: An experimental study
Summary (3 min read)
Introduction
- Since the 1970s when the first pars plana vitrectomy was performed [1], there has been an important change in trends in ophthalmic operations, particularly in VitreoRetinal surgery.
- For instance Remote Center of Motion (RCM) guarantees that during the Vitreo-Retinal surgery there won’t be a damage to sclera.
- In this method the kinematics of the robot is designed in a way that physically limits the motions.
- 2- Semi Mechanically constrained virtual fixtures (see e.g. [4]): Flexibility of the virtual fixtures plays an important role for Vitreo-Retinal surgery.
B. Model of the Eye
- The cannula for inserting the tool into the eye is placed about 3.5mm away from the cornea [9] and defines the location of the RCM.
- Additionally, another constraint is taken into account: because the surgeon uses the microscope during intra-ocular operations, it is essential that the areas which are accessible overlap with the field of view of the microscope.
- The radius of the circular hole is set to the average radius of the cornea.
- Fig. 3 shows the relevant parameters of the model.
- By tilting the eye about its center the RCM is relocated and the line of sight transforms accordingly as displayed in Fig.
III. METHODOLOGY
- The restriction of motions through the entry point of the patient’s body is one of the most important characteristics of minimally invasive surgery assisted by robots.
- More specifically, the link penetrating the tissue is only allowed to translate along its axis and rotate about the entry point.
- As the surgeon uses the microscope to look at the retina through the widened pupil the position of the eye should be maintained while moving the tooltip.
- The first is based on the concept of taskpriority [10] as implemented in [8] and the second on the alternative kinematics [11] (also referred to as extended Jacobian footnote distinguishing [12]) approach as shown in [7] [14].
- With the augmented kinematics applied in the control design further singularities can be introduced due to rank deficiency or linear dependencies in the sub matrix JRCM [12].
IV. DISCUSSION
- Considering only translational movement, that is parallel movement of the first four piezo positioners with travel ranges of ±15mm, the workspace is limited by a cube of dimensions 30× 30× 30 mm, also known as Reachability analysis.
- It is desirable that most of the points within the workspace are also accessible when enforcing an RCM constraint.
- In their analysis the authors assume that by rotating the eye about its center the RCM location can be automatically determined.
- For determining the best location of the eye with respect to the robot base as well as the necessary tilt of the robot the authors apply the following method: First, the location is determined experimentally until it yields satisfactory results within a certain predefined range of rotations of the eye.
- Green dots would indicate areas that are visible and reachable.
V. RESULTS
- The candidates obtained for each tilt with the best overlap of visible and reachable areas, which the authors will refer to as coverage or performance, are chosen as the center of a sphere with diameter of 10mm.
- Candidates within this neighbourhood are considered by their analysis and are illustrated in Fig. 7 within the workspace.
- The exact locations of the candidates with the best performance are listed in Table I. Fig. 8 illustrates the average coverage and the standard deviation for each configuration within the region of interest.
- The deviation is also very high and at worst only a coverage of around 45% is obtained.
- Thus the regions of interest obtained in the analysis should be considered as where to roughly place the eye.
VI. EXPERIMENTAL EVALUATION
- The elaborated model and its results are evaluated experimentally using the simulation environment and the area that can be reached experimentally is examined.
- The RCM is set manually, which inhibits to place it exactly at the position where the maximum coverage could be obtained.
- Fig. 10 shows the top view on the determined areas on the retina for the best position of the eye with no tilt of the robot for each considered rotation.
- Looking at the percentage of reachable areas within the visible area vM and vE , the model yields better results than those obtained during the evaluation run.
- By pushing the button on the 3D mouse, the coordinates of the marker are recorded and after the fourth registration procedure the parameters of a sphere can be determined as explained in the following.
A. Clinical Experiments
- Ex-vivo clinical experiments was performed at ophthalmic operation theater of klinikum rechts der isar, Munich (See Fig. 11).
- Using the standard 23G trocar system the cannula was docked into the porcine eye.
- The RCM point (incision point) was detected at the beginning of insertion phase and it was chosen by pressing a bottom on input device.
- There is also the ability of changing the RCM point by pressing the bottom, moving it to the new position (e.g. for eye rotation) and selecting of the new point by pressing the bottom once more.
- Fig. 12 shows the error from the raw position data in x, y and zdirection, which was captured during clinical experiments.
VII. CONCLUSION
- The virtual fixture control of the hybrid parallel-serial micromanipulator has been investigated in this paper.
- The feasibility of this feature, the method of implementation, modeling and experimental validation are the elements of this investigation.
- It has also been shown that the distribution of visible-accessible intraocular points is highly dependent on the location of the incision point and the robot.
- This dependency and the optimum locations of the robot, with respect to the eye, have been also discussed in this work.
- The virtualfixture control methods was simulated and experimentally evaluated.
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Frequently Asked Questions (9)
Q2. What is the main characteristic of minimally invasive surgery assisted by robots?
The restriction of motions through the entry point of the patient’s body is one of the most important characteristics of minimally invasive surgery assisted by robots.
Q3. How do the authors get rid of configurations that yield much worse results than their reference?
To get rid of configurations that yield much worse results than their reference the authors first filter the workspace by analysing the reachability of the robot without rotating the eye but by tilting the robot about the z-axis within the range of 0− 30 degrees with 10 degree steps.
Q4. What is the effect of the RCM constraint?
By fulfilling the RCM constraint the degrees of freedom of the robot are reduced by two, i.e. for fulfilling a task in an nt -dimensional space the robot must have at least n≥ nt +2 degrees of freedom [7].
Q5. What is the simplest way to control the robot?
Five sub micron precision piezo actuators are used to drive the robot and it is controlled using a middle-ware based architecture [6].
Q6. How many degrees of rotation is the maximum for the eye ball?
5. In their analysis the authors assume a maximum rotation of the eye → 30 degrees about the z-axis, maximum rotation in the direction of the cannula (around the x-axis) → −15 degrees and the maximum rotation around the y-axis→ ±10 degrees.
Q7. What is the kinematics of the extended task?
Taking the RCM constraint into account the extended task can be defined as:xext = ( xTt pTrcm )T = ( x φ ψ xrcm yrcm zrcm)T ∈ R×S2×R3 (8) And the kinematics of the extended task are then given by:ẋext = (Jt 03×1 Jrcm )( q̇ λ̇ ) = Jext ( q̇ λ̇ ) (9)Assuming a desired robot task xd and the position of the RCM, which is defined by the location of the trocar ptrocar the extended task error is given by:eext = (xext −xd ptrocar−prcm) (10)Similar to the unrestricted movement the kinematic control is written as: (q̇ λ̇) = J†ext ( Kt 03×303×3 Krcm) eext (11)where Kt and Krcm are both postive definite diagonal matrices in R3×3.
Q8. What is the general way of describing the geometry of a sphere?
The most general way of describing the geometry of a sphere is implicitly in the projective space P3 with the equationxT Qx = 0with x representing a point in P3 and Q the quadric surface, which is given by the diagonal matrix Q = diag(1,1,1,−1) (see e.g.[15]).
Q9. What is the main advantage of this approach?
In this work the second approach was followed; using thealternative kinematics where the RCM constraint can be directly incorporated into the robot task.