Planning safe cyclic motions under repetitive task constraints
Summary (2 min read)
1 Introduction
- The use of robots for surgical interventions is a an approach that is now proven to increase the quality of operations and to establish new types of surgical procedures (see [1] for an up-to-date overview of this research field).
- Here, robots help the surgeon to regain virtually direct access to the operation field he is seperated from: actuated instruments provide him with full dexterity inside the patient as in open surgery.
- Offering a new possibility of force measurement in MIRS.
- Force control and experimental results are given in Sect.
- A discussion of the results and further directions for research are given in Sect.
2 Robot and Kinematics
- A robot used in the operating room (OR) has to be lightweight and compact, as only a small amount of space for additional equippment is available.
- As shown in Fig. 2 the robot is comprised of two parts: the lower part moves the trocar and is a compact spherical 2 DoFs mechanism (Θ1 and Θ2) providing an invariant center at the fulcrum point.
- The upper part is mounted on the trocar and provides 2 DoFs: rotation about the instrument axis (Θ3) and translation along the instrument axis (d4).
- For the second singularity, Θ2 = π cannot be reached due to joint limits.
3 Force Measurement
- In manual MIS manipulation forces cannot be sensed by the surgeon anymore, due to the friction in the trocar.
- Furthermore, measurement of forces is a prerequisite for force control.
- This, again, helps to avoid damage of tissue and suturing material and might also lead to new operation techniques as manipulation with predefined forces become possible [4,2,3].
- Force measurement can be realized by placing miniaturized force/torque sensors near the instrument tip inside the patient [5].
- Here, questions of sterilizability and electromagnetic compatibility still need to be answered.
3.1 Measurement Principle
- The solution proposed here is a new trocar in which the sensor is integrated, but placed outside the patient, avoiding the before mentioned problems.
- The trocar is depicted in Fig. 3: the instrument is placed inside a passive guidance, which increases the rigidity of the system.
- (10) Remarkably, neither the friction between the instrument and the passive guidance, w1→3, nor the wrench between the trocar and the patient’s skin, w 5→6, influence the measurement.
- Usually, wd ≈ 0 holds, as velocities and accelerations in MIS are rather small.
3.2 Gravity Compensation
- The influence of gravity is calculated using a model of the robot whith several unknown parameters, which need to be identified.
- These parameters can be divided into two groups: fixed parameters which do not change between experiments and variable parameters which vary between experiments.
- One of the variable parameters is the unknown weight 0p = m 0g expressed in the robot base frame F0.
- The high accuracy of this approach can be seen in Fig. 4 where the measured data and the model based values are given.
4 Force Control
- This section describes the chosen force control structure in detail and gives first experimental results.
- Additionally, the measured forces (two planar components 4fy and 4fz) and torque at the fulcrum point (one component 4tx) corresponding to the externally applied force are represented in green.
- Finally, note that in comanipulation, when there is an equilibrium between the surgeon force and the organ force, the system stays still (see Fig. 6 a3 and Fig. 6 b3).
5 Conclusions and Outlook
- In this paper a compact and lightweight robot for force control in MIS is presented.
- This robot posesses an invariant point due to its kinematics and is mounted on the patient.
- A new trocar with an integrated force sensor allowing for the measurement of contact forces is described.
- Although this sensor is placed outside the patient friction inside the trocar does not deteriorate the measurements.
- Experimental force control results are given, validating the chosen concepts.
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"Planning safe cyclic motions under ..." refers methods in this paper
...In summary, a bidirectional search of the task-constrained configuration space Ctask is performed by growing two Rapidly-exploring Random Trees (RRTs, see [21])....
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"Planning safe cyclic motions under ..." refers background in this paper
...Traditionally, task-constrained motion in configuration space for redundant robots is generated through kinematic control techniques [1], [2], [3], [4]....
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Frequently Asked Questions (18)
Q2. What future works have the authors mentioned in the paper "Planning safe cyclic motions under repetitive task constraints" ?
For redundant robotic systems subject to repetitive task constraints, the authors have presented a control-based approach for planning cyclic, collision-free configuration space paths. Future work will be aimed at several objectives, such as: • the use of specific metrics for Ctask ; • a formal proof of probabilistic completeness for the planner ; • the extension of the proposed approach to robotic systems subject to nonholonomic constraints ( e. g., wheeled mobile manipulators ). The authors believe that their contribution fills a void in the literature.
Q3. How many steps did the authors use to generate the motions?
The authors used4 N + 1 = 11 equispaced samples of the desired task path and generated motions using Euler’s method with integration step ∆s = 0.002.
Q4. What is the degree of redundancy in the drawing task?
Since the drawing task is 3-dimensional, the degree of redundancy is 6 − 3 = 3 (the wrist roll is frozen because it is irrelevant for the task).
Q5. How many vertices are there in the KUKA LWR-IV?
At the end, the forward and backward trees contain 29 and 34 vertices, respectively, while the mean and the maximum task errors are 0.0275 mm and 0.0418 mm.
Q6. What is the purpose of the loop closure procedure?
As customary in bidirectional search, extension steps are occasionally replaced (a parameter controls this event) by connection steps aimed at reducing the gap between the two trees.
Q7. What is the solution to the C-TCMP problem?
When closure is obtained, a solution to the C-TCMP problem is reconstructed by patching together the subpath from qstart to qfw on Tfw, the loop closure subpath from qfw to qbw, and the subpath from qbw to qstart on Tbw (in the reverse direction).
Q8. What is the basic idea of the algorithm?
The basic idea here is to identify a suitable subset of nq − nt ‘redundant’ configuration variables, and to perform the desired reconfiguration on these variables.
Q9. What is the cyclic task in the KUKA LWR-IV?
For redundant robotic systems subject to repetitive task constraints, the authors have presented a control-based approach for planning cyclic, collision-free configuration space paths.
Q10. What is the purpose of this paper?
Since the problem addressed in this paper is a special case of Task-Constrained Motion Planning (TCMP), the authors will adopt the terminology and framework introduced in [17].
Q11. What is the inverse kinematic solution for qrand?
At each iteration, a random configuration qrand is first generated3 in Ctask; this is done by picking a value for s ∈ {s1, . . . , sN−1}, and then choosing one of the inverse kinematic solutions for the corresponding sample of td(s).
Q12. What is the kinematic form of a tcp?
For path or motion planning purposes, it is appropriate to use the geometric form of such model, which specifies the admissible tangent vectors to a configuration space path q(s), where s is a path parameter, asq′ = ṽ, (1)with the notation ( )′ = d( )/ds.
Q13. How is the qrand generated in Ctask?
For each value of w̃, the motion generation scheme (3–4) is then integrated numerically starting from qnear at s = si and ending at s = si+1.
Q14. What is the mean and maximum value of the task error norm?
The mean and the maximum value of the task error norm over the whole path are, respectively, 0.0729 mm and 0.1354 mm, confirming that the proposed method guarantees continued satisfaction of the task constraint.
Q15. What is the difference between the two types of motion planners?
The authors emphasize that, unlike sampling-based constrained motion planners, the use of the motion generation scheme (3– 4) guarantees that the task variables move along the desired path throughout the motion.
Q16. What is the cyclicity of the configuration space?
Cyclicity in configuration space is confirmed by Fig. 5, which shows that the displacement with respect to the initial configuration returns to zero at the end of the motion.
Q17. How long did it take to compute the tree?
The solution shown in Fig. 3 took 83 s to compute, with a final size of the forward and backward trees of 116 and 33 vertices, respectively.
Q18. What are the main objectives of the proposed approach?
Future work will be aimed at several objectives, such as: • the use of specific metrics for Ctask; • a formal proof of probabilistic completeness for theplanner;• the extension of the proposed approach to robotic systems subject to nonholonomic constraints (e.g., wheeled mobile manipulators).