CN113282077B - Concentric tube robot motion planning method based on normal distribution and Jacobian matrix - Google Patents
Concentric tube robot motion planning method based on normal distribution and Jacobian matrix Download PDFInfo
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- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
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Abstract
A concentric tube robot motion planning method based on normal distribution RRT and Jacobian matrix calculates and draws a working space of the concentric tube robot according to parameters of the concentric tube robot and a positive kinematics model; generating a surgical work environment point cloud according to the anatomical structure; generating an optimal working path of the concentric tube robot by using a normal distribution RRT algorithm; and calculating the driving space input quantity corresponding to each point on the path by using inverse kinematics based on Jacobian, and calculating the input quantity q corresponding to each path point more quickly by using the input quantity as an integral initial value of the current step. Compared with the prior art, the invention can generate an optimal path which meets the shape requirements of an operation and a concentric tube in a shorter time.
Description
Technical Field
The invention relates to the field of surgical robots, in particular to a motion planning method for a concentric tube robot based on normal distribution RRT and a Jacobian matrix.
Background
In recent years, with the steady development of the medical level, various robots capable of playing a key role in surgery have been produced. The ability of a continuous robot of the concentric tube type to flex flexibly and follow a preoperatively planned nonlinear path to a specified focal point begins to receive widespread attention as compared to typical rigid instruments. However, the joint freedom of such a robot tends to be infinite, and its shape in free space is very complicated, resulting in a significant increase in the complexity of its motion planning.
The modeling design of the concentric tube is mostly established on the assumption that the constant curvature and rigidity of the segment dominate, and the information such as shear strain and friction which is difficult to quantify is ignored. On the basis, a concentric tube positive kinematics model established by using a statics balance method and an energy minimum principle can achieve higher precision, and in the aspect of path planning, a sampling path planning algorithm which is generally suitable for a high-dimensional space is widely concerned by people, such as PRM and RRT.
There are still a number of problems that prevent further development of concentric tube robotic systems: the nickel-titanium alloy tube which is the raw material of the concentric tube is difficult to process, and can age and deform along with the lapse of time, so that the ideal assumption requirement of a kinematic model and the high-precision requirement of an operation cannot be met.
Disclosure of Invention
In order to overcome the defects of the prior art and improve the overall operation capacity of a concentric tube system to a certain extent, the invention provides a concentric tube robot motion planning method based on normal distribution RRT and Jacobian matrix, which can improve the working efficiency of a robot in a complex operation environment.
The technical scheme adopted by the invention is as follows:
a concentric tube robot motion planning method based on normal distribution RRT and Jacobian matrix comprises the following steps:
1) for a concentric tube robot with known geometric parameters and mechanical parameters, the positive kinematics solution of the concentric tube robot is pre-calculated, the working space of the robot is drawn, and a data table with one-to-one correspondence of drive input and terminal poses is established
2) Generating point cloud of surgical anatomical structure by endoscope system mounted at end of concentric tube robot, wrapping points whose distance is less than section diameter d of concentric tube with a minimum sphere, and setting radius of i-th barrier as Ri；
3) And (3) performing path planning of the concentric tube robot by using a normally distributed RRT algorithm: from data sheet
Selecting a location x that is near a focal point and not within an obstacletargetAccording to the corresponding input, drawing the overall Shape of the robot in the working space by using a positive kinematics model, wherein the point set corresponding to the Shape is S0, and because the modeling of the concentric tube meets the assumption that the rigidity is dominant, if any point in S0 is not in an obstacle, the optimal working path of the concentric tube in the surgical environment is S0; if there is a section of the path
If the section is cut off by the ith barrier, a new path planning needs to be carried out on the section;
4) according to the step 3), the optimal path planning of the obstacle segment is realized, a path S2 is obtained, and the optimal path S of the concentric tube robot in the working space is obtained, namely S0-S1+ S2.
5) In order to enable the robot to reach the focus point along the path S, the robot driving input quantity q corresponding to each point x on the path is calculated step by using inverse kinematics based on a Jacobian matrix J;
6) and (5) using the input quantity calculated in the step 5) as an initial integral value of the current step, and calculating the input quantity q corresponding to each path point more quickly.
Further, the process of step 3) is as follows:
3.1) first, the desired planned starting position x is set according to S1initTarget position xgoalIteration number n, step length p and collision risk assessment index: dis (x)i0,x1)≥Ri+λr0Wherein r is0Is the section radius of the concentric tube robot, lambda is a safety constant, the larger lambda represents the higher safety requirement, xi0Is the center position coordinate, x, of the ith obstacle1Position coordinates of any node in the working space;
3.2) based on normal random distribution in free spaceTo generate a point xrandAnd the mean μ of the normal distribution is close to the target position xgoalThe standard deviation σ is 10;
3.3) find x in search Tree TrandNearest node xnearestAnd along xnearestPoint of direction xrandIn the direction of (1), a new node x is generated in step size pnew；
3.4) by xnewIs a center riTo search for the radius, find all potential parent nodes x in the search tree TppTo update xnew. First, all potential parent nodes x foundppPerforming collision risk assessment, eliminating nodes which do not accord with risk indexes, and finally forming a potential father node set Epp；
3.5) first disregarding the collision detection, EppEach point in (1) is respectively used as a parent node and xnewConnected, calculate from xinitTo xnewIf the path length is smaller than the original path length, collision detection is performed. If the detection fails, considering the next potential father node; if the detection is passed, deleting redundant edges in the search tree T, and taking the node as a new father node;
3.6) traversing all potential father nodes to obtain the updated tree T;
3.7) the steps 3.2) to 3.6) are one iteration of searching the optimal path based on the normal distribution RRT, and when the maximum iteration number n is reached, an asymptotically optimal path is found.
The technical conception of the invention is as follows: the method comprises the steps of firstly pre-calculating a working space of a designed concentric tube robot according to the concentric tube robot, then generating a three-dimensional point cloud of a robot motion space according to an anatomical structure, determining an initial position and a target position of path planning, planning an optimal path according with risk assessment requirements by using a normal distribution-based RRT method, and finally calculating driving input corresponding to each point on the path by using Jacobian-based inverse kinematics.
The invention has the beneficial effects that: through the scheme, the concentric tube robot working path which accords with a specific anatomical structure can be designed.
Drawings
FIG. 1 is a flow chart of a concentric tube robot motion planning method based on normally distributed RRT and Jacobian matrix;
FIG. 2 is a schematic workspace of a concentric tube robot;
fig. 3 is a schematic diagram of a path result obtained by the obstacle avoidance algorithm of the present invention, which is used for the following analysis.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 and 2, a method for planning the movement of a concentric tube robot based on normally distributed RRT and jacobian matrices includes the following steps:
1) for a concentric tube robot with known geometric parameters and mechanical parameters, the positive kinematics solution of the concentric tube robot is pre-calculated, the working space of the robot is drawn (as shown in figure 2), and a data table with one-to-one correspondence of driving input and end pose is established
2) Generating a point cloud of an operative anatomical structure by an endoscope system arranged at the tail end of a concentric tube robot, wrapping points with a minimum sphere, wherein the distance between the points is less than the diameter d of the section of the concentric tube, and setting the radius of the ith obstacle to be Ri；
3) Path planning of the concentric tube robot was performed using normal distribution based RRT algorithm: from data sheet
Selecting a location x that is near a focal point and not within an obstacletargetAccording to the corresponding input, the overall Shape of the robot in the working space is drawn by using a positive kinematics model, the point set corresponding to the Shape is S0, and because the modeling of the concentric tube meets the assumption that the rigidity is dominant, if any point in S0 is not in the obstacle, the optimal working path of the concentric tube in the operation environment is S0; if present, isA section of path
If the ith obstacle is intercepted, a new path planning needs to be performed on the segment, and the process is as follows:
3.1) first, the desired planned starting position x is set according to S1initTarget position xgoalIteration number n, step length p and collision risk assessment index: dis (x)i0,x1)≥Ri+λr0Wherein r is0Is the section radius of the concentric tube robot, lambda is a safety constant, the larger lambda represents the higher safety requirement, xi0Is the center position coordinate, x, of the ith obstacle1Position coordinates of any node in the working space;
3.2) generating a point x in free space based on a normal random distributionrandAnd the mean μ of the normal distribution is close to the target position xgoalThe standard deviation σ is 10;
3.3) find x in search Tree TrandNearest node xnearestAnd along xnearestPoint of direction xrandIn the direction of (1), a new node x is generated in step size pnew；
3.4) by xnewIs a center riTo search for the radius, find all potential parent nodes x in the search tree TppTo update xnew. First, all potential parent nodes x foundppPerforming collision risk evaluation, removing nodes which do not accord with risk indexes, and finally forming a potential father node set;
3.5) first disregarding the collision detection, EppEach point in (1) is respectively used as a parent node and xnewConnected, calculate from xinitTo xnewIf the path length is smaller than the original path length, collision detection is performed. If the detection fails, considering the next potential father node; if the detection is passed, deleting redundant edges in the search tree T, and taking the node as a new father node;
3.6) traversing all potential father nodes to obtain the updated tree T;
3.7) the steps 3.2) to 3.6) are one iteration of searching the optimal path based on the normal distribution RRT, and when the maximum iteration number n is reached, an asymptotically optimal path is found.
4) According to the step 3), the optimal path planning of the obstacle segment is realized, a path S2 is obtained, and then the optimal path S of the concentric tube robot in the working space is obtained, which is S0-S1+ S2, as shown in fig. 3;
5) in order to enable the robot to reach the focus point along the path S, the robot driving input quantity q corresponding to each point x on the path is calculated step by using the inverse kinematics based on the Jacobian matrix J,
6) and (5) using the input quantity calculated in the step 5) as an initial integral value of the current step, and calculating the input quantity q corresponding to each path point more quickly.
In this embodiment, a real anatomical point cloud generated by an endoscope is used as a surgical working environment, and surgical environment reconstruction with the same proportion is performed in MATLAB to perform path planning simulation of a concentric tube robot, and a method for planning motion of a concentric tube robot based on normally distributed RRT and jacobian matrix includes the following steps:
1) for the concentric tube robot with known geometric parameters and mechanical parameters, calculating the positive kinematic solution of the concentric tube robot in MATLAB, drawing a working space, and establishing a data table with one-to-one correspondence of drive inputs and terminal poses
2) Performing three-dimensional reconstruction of the same surgical environment in MATLAB;
3) path planning of the concentric tube robot was performed using normal distribution based RRT algorithm: from data sheet
Selecting a site near the focal pointAnd not at position x within the obstacletargetAccording to the corresponding input, the overall Shape of the robot in the working space is drawn by using a positive kinematics model, the point set corresponding to the Shape is S0, and because the modeling of the concentric tube meets the assumption that the rigidity is dominant, if any point in S0 is not in the obstacle, the optimal working path of the concentric tube in the operation environment is S0; if there is a path
If the section is cut off by the ith barrier, a new path planning needs to be carried out on the section;
3.1) first, the desired planned starting position x is set according to S1initTarget position xgoalIteration number n, step length p and collision risk assessment index: dis (x)i0,x1)≥Ri+λr0Wherein r is0Is the section radius of the concentric tube robot, lambda is a safety constant, the larger lambda represents the higher safety requirement, xi0Is the center position coordinate, x, of the ith obstacle1Position coordinates of any node in the working space;
3.2) the invention generates a point x in free space based on normal random distributionrandAnd the mean value μ of the normal distribution is close to the target position xgoalThe standard deviation σ is 10;
3.3) find x in search Tree TrandNearest node xnearestAnd along xnearestPoint of direction xrandIn the direction of (c), a new node x is generated in step pnew；
3.4) by xnewIs a center, riTo search for the radius, find all potential parent nodes x in the search tree TppTo update xnew. First, all potential parent nodes x foundppPerforming collision risk assessment, eliminating nodes which do not accord with risk indexes, and finally forming a potential father node set Epp；
3.5) first disregarding the collision detection, EppEach point in (1) as a parent node and x respectivelynewConnect and calculateFrom xinitTo xnewIf the path length is smaller than the original path length, collision detection is performed. If the detection fails, considering the next potential father node; if the detection is passed, deleting redundant edges in the search tree T, and taking the node as a new father node;
3.6) traversing all potential father nodes to obtain the updated tree T;
3.7) the steps 3.2) to 3.6) are one iteration of searching the optimal path based on the normal distribution RRT, and when the maximum iteration number n is reached, an asymptotically optimal path is found;
4) according to the step 3, the optimal path planning of the obstacle segment is realized, a path S2 is obtained, and the optimal path S of the concentric tube robot in the working space is obtained, namely S0-S1+ S2;
5) in order to enable the robot to reach the focus point along the path S, the invention uses inverse kinematics based on the Jacobian matrix J to gradually calculate the robot driving input quantity q corresponding to each point x on the path,
6) and (5) using the input quantity calculated in the step 5) as an initial integral value of the current step, and calculating the input quantity q corresponding to each path point more quickly.
By taking MATLAB R2018b simulation software as an embodiment, the concentric tube robot working path based on the normal distribution RRT algorithm can be obtained in a short time by using the method, and the shape of the concentric tube in the working space can be kept to the maximum extent on the premise of avoiding obstacles.
While the foregoing has described the invention in terms of a preferred embodiment, it will be appreciated that the invention is not limited to the embodiment described, but is capable of modification without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (2)
1. A concentric tube robot motion planning method based on normal distribution and a Jacobian matrix is characterized by comprising the following steps:
1) for a concentric tube robot with known geometric parameters and mechanical parameters, the positive kinematics solution of the concentric tube robot is pre-calculated, the working space of the robot is drawn, and a data table with one-to-one correspondence of drive input and terminal poses is established
2) Generating point cloud of surgical anatomical structure by endoscope system mounted at end of concentric tube robot, wrapping points whose distance is less than section diameter d of concentric tube with a minimum sphere, and setting radius of i-th barrier as Ri；
3) Path planning of the concentric tube robot was performed using normal distribution based RRT algorithm: from data sheet
Selecting a location x that is near a focal point and not within an obstacletargetAccording to the corresponding input, the overall Shape of the robot in the working space is drawn by using a positive kinematics model, the point set corresponding to the Shape is S0, and because the modeling of the concentric tube meets the assumption that the rigidity is dominant, if any point in S0 is not in the obstacle, the optimal working path of the concentric tube in the surgical environment is S0; if there is a path
If the section is cut off by the ith barrier, a new path planning needs to be carried out on the section;
4) realizing the optimal path planning of the obstacle segment according to the step 3), obtaining a path S2, and further obtaining an optimal path S (S0-S1 + S2) of the concentric tube robot in the working space;
5) in order to enable the robot to reach the focus point along the path S, the robot driving input quantity q corresponding to each point x on the path is calculated step by using inverse kinematics based on a Jacobian matrix J;
6) and (5) using the input quantity calculated in the step 5) as an initial integral value of the current step, and calculating the input quantity q corresponding to each path point more quickly.
2. The method for concentric tube robot motion planning based on normal distribution and Jacobian matrix as claimed in claim 1, wherein the process of step 3) is as follows:
3.1) first, the desired planned starting position x is set according to S1initTarget position xgoalIteration number n, step length p and collision risk assessment index: dis (x)i0,x1)≥Ri+λr0Wherein r is0Is the section radius of the concentric tube robot, lambda is a safety constant, the larger lambda represents the higher safety requirement, xi0Is the center position coordinate, x, of the ith obstacle1Position coordinates of any node in the working space;
3.2) generating a point x in free space based on a normal random distributionrandAnd the mean μ of the normal distribution is close to the target position xgoalThe standard deviation σ is 10;
3.3) find x in search Tree TrandNearest node xnearestAnd along xnearestPoint of direction xrandIn the direction of (1), a new node x is generated in step size pnew；
3.4) by xnewIs a center, riTo search for the radius, find all potential parent nodes x in the search tree TppTo update xnewFirst, all potential parent nodes x found are searchedppPerforming collision risk assessment, eliminating nodes which do not accord with risk indexes, and finally forming a potential father node set Epp；
3.5) first disregarding the collision detection, EppEach point in (1) is respectively madeIs a parent node and xnewConnected, calculate from xinitTo xnewIf the path length is smaller than the original path length, performing collision detection; if the detection fails, considering the next potential father node; if the detection is passed, deleting redundant edges in the search tree T, and taking the node as a new father node;
3.6) traversing all potential father nodes to obtain the updated tree T;
3.7) the steps 3.2) to 3.6) are one iteration of searching the optimal path based on the normal distribution RRT, and when the maximum iteration number n is reached, an asymptotically optimal path is found.
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