CN111134842A - Robot-assisted fracture reduction path planning method - Google Patents
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Abstract
本发明涉及一种机器人辅助骨折复位手术的路径规划方法，采用骨折远端姿态调整及基于A*算法的双平面避碰复位路径规划方法。在mimics和Geomagic studio软件中进行基于健侧镜像匹配方法确定骨折偏差参数，在两个不同坐标平面内分别进行基于A*算法的骨折复位路径规划。本发明所述的骨折复位路径规划方法，能有效避免复位中远端的大幅度牵拉以及骨折远端与周围组织碰撞，实现短耗时、高精度、安全避碰的骨折复位操作。具有方法简单、安全有效等优点，适用于机器人辅助股骨、胫骨等长骨骨折复位手术，能够提高骨折复位操作的精度和安全性，提高复位效率，降低医生工作强度。
The invention relates to a path planning method for robot-assisted fracture reduction surgery, which adopts the attitude adjustment of the distal end of the fracture and a biplane collision avoidance reduction path planning method based on the A* algorithm. In mimics and Geomagic studio software, the fracture deviation parameters were determined based on the mirror matching method of the unaffected side, and the fracture reduction path planning based on the A* algorithm was carried out in two different coordinate planes respectively. The fracture reduction path planning method of the invention can effectively avoid the large pulling of the middle and distal end of the reduction and the collision of the distal end of the fracture with the surrounding tissue, and realize the fracture reduction operation with short time consumption, high precision and safe collision avoidance. It has the advantages of simple, safe and effective method, and is suitable for robot-assisted reduction of long bone fractures such as femur and tibia, which can improve the accuracy and safety of fracture reduction operation, improve reduction efficiency, and reduce the work intensity of doctors.
Description
Technical Field
The invention belongs to the technical field of robots, and relates to a path planning method for a robot-assisted fracture reduction operation.
Background
The operation reduction is a means of fracture surgical treatment, and the traditional fracture reduction operation is performed under the guidance of an X-ray machine by a doctor and is difficult to achieve high precision. The minimally invasive internal fixation for reduction of closed fracture treats femoral shaft fracture, and has the advantages of small operative wound, quick fracture healing, high healing rate, low infection incidence and the like. However, reduction of fractured ends, particularly rotational reduction, has been a surgical challenge because the fractured ends are not directly exposed.
With the development of the robot technology, the robot-assisted fracture reduction research is developed at home and abroad. The supplementary fracture operation that resets of robot, doctor operation robot observe the condition of resetting of patient's fracture position through the X ray machine, and the accurate reasonable route planning that resets before the art guarantees the prerequisite of operation safety, has the significance to improving the operation precision, reducing patient's operation damage.
In the process of robot-assisted fracture reduction, the following points need to be considered:
(1) during reduction, the distal end of the fracture cannot collide with the tissue surrounding the fracture. After the fracture, traction forces caused by the impingement of the musculoskeletal tissues and surrounding soft tissues impede the desired reduction motion. If no rational path planning is performed before surgery, the nervous system, soft tissues and muscle tissues are easily stretched and distorted, causing secondary injuries to the patient, wherein the damage to the nervous system is the most serious and the damage is likely to have irreversible consequences. In order to avoid secondary damage possibly caused by the robot reset operation, improve the safety and the precision of the robot auxiliary reset operation and shorten the operation time, a reasonable and safe collision-preventing reset path is necessary to be planned before the operation.
(2) For closed fractures, there is usually a deviation in displacement as well as a deviation in angular rotation. Under the condition that the internal part around the fracture is difficult to observe, preoperative path planning is needed, and accurate and safe reduction operation on the fracture is realized.
(3) In robotic-assisted surgery, the limited working space and the possibility of collisions between the end of the robotic manipulator arm and the surrounding environment present challenges in robotic-assisted surgery where the end effector of the surgical robot must reach the anatomical target of the patient and not collide with the patient or surrounding instruments.
The path planning refers to searching and finding a collision-free path from a starting point to a target point in an environment with obstacles according to certain evaluation criteria (such as distance, time, cost and the like), and the core of the path planning is a path planning algorithm. The traditional path planning algorithm comprises an artificial potential field method, a fuzzy logic algorithm, a grid method, a free space method and the like. With the development of artificial intelligence technology, some intelligent algorithms for path planning appear, such as ant colony algorithm, genetic algorithm, neural network algorithm, and the like.
The preoperative collision avoidance reduction path planning is to determine a moving path when a robot assists the fracture reduction operation. On the basis, an operation navigation system is utilized to carry out accurate resetting operation, the broken and dislocated bones after the fracture are restored to the normal anatomical positions, and dislocation does not occur in the bone healing process.
For long bone fracture types of femur and tibia, after fracture, axial offset, longitudinal offset, radial (or transverse) offset and rotational offset of a far end relative to a near end occur, and 6 fracture deviation parameters exist. Aiming at the closed reduction of the long bone fracture, a robot is adopted to assist the operation of the fracture reduction operation, the near end of the fracture is fixed on an operating bed, and the robot assists the reduction operation of aligning the far end of the fracture to the near end of the fracture. In the prior art, when the robot-assisted operation is used for resetting, medical accidents are easy to happen due to the large-amplitude traction of the far end and the collision of the fracture far end and surrounding tissues, and the precision and the safety are insufficient.
Disclosure of Invention
The invention relates to a collision-prevention path planning method for a robot-assisted fracture reduction operation, which is characterized in that a fracture near end is fixed, the tail end of a robot is firmly connected with a fracture far end, and the robot drives the fracture far end to move in a collision-prevention manner relative to the fracture near end to perform reduction operation until fracture sections of the far end and the near end are butted to a correct anatomical position, so that robot-assisted fracture reduction is completed. The invention relates to a path planning method for robot-assisted fracture reduction operation, in particular to a fracture distal attitude adjustment and biplane collision prevention reduction path planning method based on an A-algorithm. The method for planning the fracture reduction path can effectively avoid the large-amplitude traction of the far end in the reduction and the collision of the fracture far end and surrounding tissues, and realize the fracture reduction operation with short time consumption, high precision and safe collision avoidance. The preoperative path planning method for robot-assisted fracture reduction has the advantages of simplicity, safety, reliability and the like, and is suitable for not only robot-assisted femoral fracture reduction operations, but also tibial and long-bone fracture reduction operations. The fracture reduction robot can effectively improve the precision and the safety of the robot for assisting fracture reduction operation, improve the reduction efficiency and reduce the damage of ray radiation to doctors and patients.
In order to achieve the above purpose, the technical scheme of the path planning method of the invention comprises the following steps:
a path planning method for a robot-assisted fracture reduction operation comprises the following steps:
1) aiming at the closed reduction of the long bone fracture, when a robot is adopted to assist the operation of the fracture reduction operation, the fracture near end is fixed, and the robot assists to align the fracture far end to the near end for the reduction operation;
2) before an operation, according to CT scanning data of a fracture side and a healthy side bone of a patient before the operation provided by a doctor, a reverse modeling method is adopted to reconstruct and obtain a three-dimensional digital model of the fracture side and the healthy side bone;
3) based on the principle of reduction of healthy side mirror image registration, determining axial, longitudinal, radial or transverse displacement deviation and rotation deviation of the fracture in mimics and Geomagic studio software by an image registration method, and analyzing the displacement and rotation deviation values of the fracture; determining a fracture deviation value as a basis for planning a reduction path;
4) adjusting the fracture far-end space posture:
the posture of the far end of the fracture relative to the near end is adjusted by a robot, so that the far end of the fracture achieves a reasonable anatomical posture relative to the near end of the fracture, and meanwhile, 3 posture angles of the far end of the fracture are tested in real time by an NDI optical tracking array fixed on the far end of the fracture, so that the posture adjustment of the far end of the fracture and the requirement on the reduction precision after the reduction is finished are met;
5) reset path planning preparation:
first, a grid map of the fracture model is given, the number and spacing of the grids obeying two conditions:
(1) the grid spacing is smaller than the reset precision;
(2) accurately representing the shape of the obstacle on the premise of meeting the precision;
then, the lower half parts of the fracture far end and the fracture near end are similar to cylinders, and the parts of the near end and the far end which do not influence the reset path are abandoned;
6) planning collision avoidance paths:
determining an optimal collision avoidance reduction path by using a fracture reduction path planning algorithm based on an A-x algorithm;
7) planning a reset path:
respectively projecting the three-dimensional digital model of the long bone fracture into two rectangular coordinate planes, and respectively planning a reduction path in the two planes by adopting an A-x algorithm;
8) coordinates of data points obtained by planning the reset path based on the A-x algorithm are stored as data files and transmitted to a reset robot controller, and the robot controls the fracture distal end to perform reset operation according to the planned reset path;
9) fixing NDI optical tracking system navigation frames at the far end and the near end of the fracture respectively, and testing the spatial poses of the near end and the far end of the fracture; and the near end and the far end of the fracture are respectively fixed with an optical tracking array of an NDI positioning system, and the relative spatial postures of the near end and the far end of the fracture are tested.
As a preferred technical scheme of the invention, in the step 6), a biplane collision avoidance reduction path planning method based on an a-x algorithm is adopted to determine a fracture reduction path; and projecting the proximal end and the distal end of the fracture into two rectangular coordinate planes, and planning a reduction path in the two coordinate planes by respectively adopting an A-x algorithm.
As a preferred technical solution of the present invention, in the step 6), the a-algorithm determines the search direction through an estimation function, expands from the starting point to the periphery, obtains the cost value of each peripheral node through calculation of a valuation function, selects the minimum cost node as the next expansion node, repeats this process until reaching the target point, and generates the final reset path.
As a preferable technical solution of the present invention, in the step 1), when performing the closed reduction operation with the robot assistance for the long bone fracture of femur or tibia, the proximal end of the fracture is fixed to the operating bed, and the robot assistance is performed for the reduction operation in which the distal end of the fracture is aligned with the proximal end of the fracture.
As a preferable technical scheme of the present invention, in the step 4), the navigation frame is fixed to the fracture distal end, the robot adjusts the posture of the fracture distal end according to the fracture rotation deviation value, and observes the posture angle between the navigation frame and the NDI reference coordinate system in real time until the posture of the fracture distal end is adjusted in place.
As a preferred technical solution of the present invention, in the step 5), in the fracture model projection diagram projected into the rectangular coordinate plane, a series of feature points including a start point and a stop point for planning a fracture reduction path and a plurality of obstacle points on the path are determined, where the obstacle points are used as obstacle avoidance constraint points for planning the reduction path, so as to ensure that collision between the distal end and the proximal end of the femur during reduction operation should be avoided.
Before the path planning is carried out by adopting the A-star algorithm, a grid graph of a fracture model needs to be given. The number and spacing of the grids follows two conditions: the grid spacing is smaller than the reset precision; the shape of the obstacle is accurately represented on the premise of meeting the precision. The lower halves of the fracture distal and proximal ends are approximated to be cylindrical, leaving away portions of the proximal and distal ends that do not affect the reduction path. Determining the starting point and the ending point of the fracture reduction path planning and the characteristic points of a plurality of obstacle points on the path. The soft tissue balance and the collision avoidance of the tissues around the fractured bone during the reduction operation are considered. Because the tissues around the fracture are complex, in order to avoid secondary injury in the reduction operation, the collision between the far end and the near end of the femur is avoided during the reduction operation, and a series of obstacle points are set in the projection drawing of the fracture model and are used as obstacle avoidance constraint points for planning the reduction path.
As a preferred embodiment of the present invention, in the step 6), a fracture reduction path planning algorithm based on the a-algorithm is used. The A-star algorithm based on the grid method can determine the optimal collision avoidance reset path more quickly and effectively. When the path planning is performed on the grid graph by the algorithm A, the center of each grid is assumed to be a node, so that the number of adjacent nodes of each node is limited to 8, and the moving direction angle of each node is also limited to integral multiple.
As a preferred technical scheme of the invention, the A-algorithm determines the search direction through an estimation function, expands from a starting point to the periphery, obtains the cost value of each node around through calculation of the evaluation function, selects the minimum cost node as the next expansion node, repeats the process until reaching the target point, and generates the final reset path.
As a preferred technical solution of the present invention, in the search process, each node on the path is a node with the minimum cost, and therefore the obtained path cost is the minimum. The valuation function of the a-algorithm is: . Wherein, the evaluation function which represents the arrival of the target point from the starting point through any node represents the actual cost from the starting point to the node and represents the nodenEstimated cost to target point.
Manhattan distance: the sum of the distances of the projections generated by the line segment formed by two points on the fixed rectangular coordinate system of the Euclidean space to the axis is the result of summing the distances in multiple dimensions. For example, the manhattan distance between nodes on a plane is as follows. Euclidean distance: the euclidean distance in two-dimensional space is the distance between two points. Such as euclidean distance between nodes on a plane.
As a further preferable technical solution of the present invention, in the step 6), when calculating the valuation function, a calculation formula of manhattan distance and euclidean distance is used; when the nodes are searched along the side length direction of the grid graph, a Manhattan distance formula is adopted for calculation; when the nodes are searched along the diagonal direction of the grid graph, the Euclidean distance formula is adopted for calculation.
Through repeated tests, the fracture reduction collision avoidance path planning method successfully solves the problem of a robot-assisted fracture reduction operation path.
In summary, the path planning method for the robot-assisted fracture reduction surgery operation, namely the method for adjusting the posture of the far end of the fracture and planning the biplane collision prevention reduction path based on the a-algorithm, determines the fracture deviation parameters based on the healthy side mirror image matching method in the mimics and the Geomagic studio software, and plans the fracture reduction path based on the a-algorithm in two different coordinate planes respectively. The method for planning the fracture reduction path can effectively avoid the large-amplitude traction of the far end in the reduction and the collision of the fracture far end and surrounding tissues, and realize the fracture reduction operation with short time consumption, high precision and safe collision avoidance. The method has the advantages of simplicity, safety, effectiveness and the like, is suitable for the robot-assisted femoral fracture reduction operation, can improve the precision and safety of the fracture reduction operation, improves the reduction efficiency, and reduces the damage of ray radiation to doctors and patients.
Compared with the prior art, the invention has the following obvious prominent substantive characteristics and obvious advantages:
1. the invention relates to a path planning method for robot-assisted fracture reduction operation, in particular to a method for adjusting the posture of a fracture far end and planning a biplane collision prevention reduction path based on an A-x algorithm.
2. The invention is based on the principle of reduction of healthy side mirror images, and adopts a fracture deviation determination method based on image matching. And performing healthy side mirror image matching in mimics and Geomagic studio software to determine fracture deviation parameters.
3. According to the biplane reset path planning method, the reset path planning is carried out in two rectangular coordinate planes by adopting an A-algorithm respectively, and the optimal collision avoidance reset path can be determined more quickly and effectively by the A-algorithm based on the grid method.
4. The invention comprehensively considers the collision avoidance of the fracture far end and the surrounding tissues in the fracture reduction operation, and effectively improves the safety and the accuracy of the robot-assisted reduction operation.
5. The method has certain universality, and is suitable for femoral fractures and other long bone fracture types such as tibia and the like.
6. The fracture reduction path planning method has the advantages of being simple, safe, effective and the like, can effectively improve the precision and safety of fracture reduction operation, improve the reduction efficiency and reduce the damage of ray radiation to doctors and patients.
Drawings
FIG. 1 is a diagram of a bone model of a fractured side and a healthy side reconstructed based on a reverse modeling technique according to the present invention.
FIG. 2 is a schematic diagram of fracture deviation determination based on healthy side mirror image registration according to the present invention.
Fig. 3 is a projection schematic view of the fracture model of the invention in the yoz plane.
FIG. 4 is a schematic representation of the collision threshold of the proximal and distal fractures of the present invention.
Fig. 5 is a schematic diagram of a grid of the fracture model of the present invention in the yoz plane.
Fig. 6 is a schematic diagram of the planning result of the reset path of the yoz plane according to the present invention.
FIG. 7 is a schematic diagram of the biplane reduction path planning result of the fracture model of the present invention.
Detailed Description
The invention is further described with reference to specific embodiments and the accompanying drawings.
The embodiment is a patient femoral fracture. Reasonably arranging an operating bed, a reset robot, a fracture model, an NDI optical tracking system and the like. Two optical tracking arrays of the NDI optical tracking system are respectively fixed at the near end and the far end of the fracture and used for testing the spatial position and the posture of the near end and the far end of the fracture. And adjusting a reference coordinate system of the NDI positioning system, and adjusting the initial pose of the resetting robot to prepare for resetting operation.
In this embodiment, a path planning method for a robot-assisted fracture reduction operation includes the following steps:
1) aiming at the closed reduction of the long bone fracture, when a robot is adopted to assist the operation of the fracture reduction operation, the fracture near end is fixed, and the robot assists to align the fracture far end to the near end for the reduction operation; when the robot assists in fracture reduction operation, the near end of the fracture is fixed on an operating bed, the far end of the fracture is fixedly connected with the tail end of the robot, and the robot moves along with the robot, namely the robot moves the far end of the fracture relative to the near end of the fracture in a collision-preventing manner to perform reduction operation until the fracture sections of the far end and the near end are butted to a correct anatomical position;
2) before an operation, according to CT scanning data of a fracture side and a healthy side bone of a patient before the operation provided by a doctor, a reverse modeling method is adopted to reconstruct and obtain a three-dimensional digital model of the fracture side and the healthy side bone; as shown in fig. 1;
3) and (3) determining fracture deviation by software registration:
according to the bone registration principle of the fracture side and the healthy side based on the healthy side mirror image, in the mimics and the Geomagic student software, the axial, longitudinal, radial or transverse displacement deviation and rotation deviation of the fracture are determined by an image registration method, the displacement and rotation deviation values of the fracture are analyzed, and the registration is carried out to determine the fracture deviation, as shown in fig. 2;
4) the robot assists in finishing the posture adjustment of the far end of the fracture relative to the near end of the fracture, so that an ideal anatomical posture can be achieved after the fracture is reset; the posture of the far end of the fracture relative to the near end is adjusted by a robot, so that the far end of the fracture achieves a reasonable anatomical posture relative to the near end of the fracture, and meanwhile, 3 posture angles of the far end of the fracture are tested in real time by an NDI optical tracking array fixed on the far end of the fracture, so that the posture adjustment of the far end of the fracture and the requirement on the reduction precision after the reduction is finished are met;
5) reset path planning preparation:
and (4) planning a biplane collision avoidance reset path based on an A-star algorithm. The algorithm determines the searching direction through an evaluation function, expands from the starting point to the periphery, calculates the cost value of each node around through the evaluation function, selects the minimum cost node as the next expansion node, repeats the process until the end point is reached, and generates the final reset path;
planning a reset path based on an A-x algorithm in a rectangular coordinate plane; the lower half parts of the distal femur and the proximal femur are similar to cylinders, and the parts of the proximal femur and the distal femur, which do not influence the reduction path, are abandoned and projected to a certain plane; the proximal and distal fracture ends are projected in a rectangular coordinate plane as shown in FIG. 3;
6) planning collision avoidance paths:
soft tissue balance and collision avoidance of tissues around broken bones during reduction operation need to be considered; because the tissues around the fracture are complex, in order to avoid secondary damage in the reduction operation, the collision between the far end and the near end of the femur is avoided during the reduction operation, and then obstacle points are required to be set in the actual situation in the fracture model projection drawing; determining characteristic points such as a reset starting point, a reset ending point, a plurality of obstacle points and the like, wherein the obstacle points are used as obstacle avoidance constraint points for reset path planning; the fracture distal end slowly approaches the proximal end and is in a critical state when collision is about to occur, as shown in fig. 4, the left side is the fracture proximal end, and the right side is the fracture distal end; setting the obstacle range to the left part of the dotted line shown in fig. 4, and the obstacle cannot cross the green dotted line to the left during resetting; fracture reduction in the plane, i.e. moving from the starting point to the end point;
before planning the fracture reduction path by adopting an A-x algorithm, providing a grid diagram of a fracture model, as shown in figure 5; the number and spacing of the grids should follow two conditions: the distance is smaller than the reset precision; the shape of the obstacle can be accurately represented as much as possible under the condition of meeting the precision; in the figure, the symbol "x" represents an obstacle point. The fracture proximal characteristic point is the farthest boundary point; the far-end feature point is, the inner boundary point thereof. The initial reset point is, and the end point is; the symbol @ denotes the planned reset path point, as shown in fig. 6;
7) and during planning of the reduction path, the fracture far ends are respectively projected into two rectangular coordinate planes, and the reduction path planning is respectively carried out by adopting an A-x algorithm in the two coordinate planes. Determining a fracture reduction path by adopting a biplane collision avoidance reduction path planning method based on an A-x algorithm, wherein the plane coordinate value of a reduction path point is a coordinate relative to a characteristic point of the proximal end of the fracture, as shown in FIG. 7; respectively projecting the three-dimensional digital model of the long bone fracture into two rectangular coordinate planes, and respectively planning a reduction path in the two planes by adopting an A-x algorithm;
8) storing coordinate values of a series of path points generated by planning a reset path into a data file, transmitting the data file to a controller of the reset robot, starting the robot to move according to the planned reset path, and testing the reset path in real time by an NDI optical tracking system;
9) fixing NDI optical tracking system navigation frames at the far end and the near end of the fracture respectively, and testing the spatial poses of the near end and the far end of the fracture; and the near end and the far end of the fracture are respectively fixed with an optical tracking array of an NDI positioning system, and the relative spatial postures of the near end and the far end of the fracture are tested.
The embodiment relates to a path planning method for a robot-assisted fracture reduction operation. For long bone fracture types of femur, tibia, etc., after fracture, the distal end is axially, longitudinally, radially or laterally, and rotationally offset relative to the proximal end. Aiming at the closed reduction of the long bone fracture, a robot is adopted to assist the operation of the fracture reduction operation, the near end of the fracture is fixed on an operating bed, and the robot assists the reduction operation of aligning the far end of the fracture to the near end of the fracture. The invention relates to a path planning method for robot-assisted fracture reduction operation, which is used for planning a reduction path based on a C-arm perspective two-dimensional image, namely a fracture distal end posture adjustment and biplane collision prevention reduction path planning method based on an A-x algorithm. The square fracture reduction path planning method of the embodiment of the invention can effectively avoid the large-amplitude traction of the far end in the reduction and the collision of the fracture far end and surrounding tissues, and realize the fracture reduction operation with short time consumption, high precision and safe collision avoidance. The method has the advantages of simplicity, safety, effectiveness and the like, is suitable for robot-assisted fracture reduction operations of long bones such as thighbones and shinbones, can improve the precision and safety of fracture reduction operations, improves reduction efficiency, and reduces the damage of ray radiation to doctors and patients.
In conclusion, the invention provides a path planning method for a robot-assisted fracture reduction operation. Aiming at the fracture types of long bones such as thighbone and shinbone, the fracture near end is fixed on an operating bed, and the robot assists the reduction operation of aligning the fracture far end to the fracture near end. After fracture, longitudinal, transverse and rotational displacement of the distal end relative to the proximal end occurred, with 6 fracture deviation parameters. The invention relates to a path planning method for robot-assisted fracture reduction operation, in particular to a method for adjusting the posture of a fracture far end and planning a biplane collision prevention reduction path based on an A-x algorithm. Determining fracture deviation parameters based on a healthy side mirror image matching method in mimics and Geomagic studio software, and respectively planning fracture reduction paths based on an A-star algorithm in two different coordinate planes. The method for planning the fracture reduction path can effectively avoid the large-amplitude traction of the far end in the reduction and the collision of the fracture far end and surrounding tissues, and realize the fracture reduction operation with short time consumption, high precision and safe collision avoidance. The method has the advantages of simplicity, safety, effectiveness and the like, is suitable for robot-assisted fracture reduction operations of long bones such as thighbones and shinbones, and can improve the precision and safety of fracture reduction operations, improve the reduction efficiency and reduce the working strength of doctors.
The embodiments of the present invention have been described with reference to the accompanying drawings, but the present invention is not limited to the embodiments, and various changes and modifications can be made according to the purpose of the invention, and any changes, modifications, substitutions, combinations or simplifications made according to the spirit and principle of the technical solution of the present invention shall be equivalent replacement means, so long as the technical principle and the inventive concept of the path planning method for robot-assisted fracture reduction surgery of the present invention are met, and the present invention shall fall within the protection scope of the present invention.
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Cited By (11)
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| CN111590584A (en) * | 2020-05-27 | 2020-08-28 | 京东方科技集团股份有限公司 | Determination method and device for safety limit area, reset method and medical robot |
| CN112043384A (en) * | 2020-07-29 | 2020-12-08 | 上海大学 | An external force prediction method for fracture reduction robot |
| CN112370154A (en) * | 2020-11-13 | 2021-02-19 | 山东中医药大学附属医院 | Fracture distal end reduction trajectory planning method and reduction system based on mirror image method |
| CN112741688A (en) * | 2020-12-11 | 2021-05-04 | 北京信息科技大学 | Path planning method for minimally invasive surgery software manipulator |
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