CN108972550B - Inverse kinematics solving method of concentric tube robot - Google Patents
Inverse kinematics solving method of concentric tube robot Download PDFInfo
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Abstract
The invention provides a concentric tube robot inverse kinematics solving method, which comprises the following steps: s1, generating a DDA table; s2, use of DDA table; step S2 includes the following substeps; s21, determining according to the coordinate information of the target pointDetermining a corresponding column in a DDA table; s22, determining the length l of the outer tube1And length l of the inner tube2(ii) a S23, determining the rotation angle phi of the inner tube relative to the world coordinate system2(ii) a S24, applying the inverse kinematics solution result of the concentric tube robot to the motion control of the concentric tube robot consisting of a straight tube and a bent tube, wherein the straight tube is an outer tube, and the bent tube is an inner tube. The invention has the beneficial effects that: the precision of the motion control of the concentric tube robot can be improved.
Description
Technical Field
The invention relates to a concentric tube robot, in particular to an inverse kinematics solving method of the concentric tube robot.
Background
In recent years, a concentric tube robot has played an increasingly important role as a novel continuous robot in the medical field. Due to the characteristics of small size and flexible bending, the concentric tube robot can better show the advantages in the complex and multi-obstacle narrow space. However, it is difficult to solve the inverse kinematics of a concentric tube robot relative to a robot having a definite rigid joint. So far, when the concentric tube robot is composed of variable-curvature concentric tubes or the number of the concentric tubes exceeds 2, it is extremely difficult or even impossible to solve the inverse kinematics.
There are currently some generally accepted approaches to solving the forward and reverse kinematics of concentric tube robots. First, assuming that the concentric tubes are piecewise constant curvature, there is only a bending force on the tube-to-tube interaction. Based on the assumption, a kinematic model of the concentric tube robot is established, and positive kinematics is solved by utilizing the Euler-Bernoulli beam principle. The forward kinematics was analyzed step by step in the reverse direction to solve the inverse kinematics of the concentric tube robot. Another is the exponential-product of-exponential method, which uses the related knowledge of lie group algebra and rotation theory to solve the forward and inverse kinematics.
Although there are currently some feasible methods in both modeling of the kinematics of a concentric tube robot and solution of the kinematic equations, there are some problems with these methods. Both of these problems reduce the accuracy of the concentric tube robot motion control. The related problems are now expressed as follows:
1. when the kinematic model is built, the concentric tubes are idealized to be of a piecewise constant curvature, which is difficult to realize in real-world tube processing.
2. The most common concentric tube material today is a superelastic nitinol tube, but over time the tube undergoes irreversible plastic deformation, indirectly resulting in less and less accurate kinematic solutions.
3. Almost all models do not consider the problems of tube-to-tube shearing and axial deformation.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an inverse kinematics solving method of a concentric tube robot, which can improve the motion control precision of the concentric tube robot.
The invention provides a concentric tube robot inverse kinematics solving method, which comprises the following steps:
s1, generating a DDA table;
s2, use of DDA table;
step S2 includes the following substeps;
s21, determining a corresponding column in the DDA table according to the coordinate information of the target point;
s22, determining the length l of the outer tube1And length l of the inner tube2；
S23, determining the rotation angle phi of the inner tube relative to the world coordinate system2；
S24, applying the inverse kinematics solution result of the concentric tube robot to the motion control of the concentric tube robot consisting of a straight tube and a bent tube, wherein the straight tube is an outer tube, and the bent tube is an inner tube.
As a further improvement of the present invention, step S1 includes: first, the outer tube length of the concentric tube robot remains at a maximum, i.e./1＝l1maxAngle of rotation phi of the inner tube coordinate system relative to the world coordinate system2Remains at 0; the inner tube is then moved axially relative to the outer tube to a length l of the inner tube2From l1maxMovement changes to2maxObtaining a DDA table with 6 rows and n columns, wherein the first three rows of the DDA table are respectively the length l of the outer tube1Inner tubeLength l of2And angle of rotation phi of the inner tube2The last three rows of the table are the components of the concentric tube robot tip position in the x, y, z axes for the same column input.
As a further development of the invention, the inner tube length l2From l1maxChange to2maxThis course of movement represents the course of movement of the inner tube relative to the outer tube; in the initial state, the inner pipe and the outer pipe are completely overlapped, namely the inner pipe is completely nested in the outer pipe; in the movement process, the inner pipe moves axially relative to the outer pipe, namely the inner pipe gradually extends out of the outer pipe; assuming that the arc length of the inner tube extending out of the outer tube is denoted by s, the length l of the inner tube2From l1maxMovement changes to2maxIs the length l of the inner tube2Gradually increasing in certain increment, the inner pipe gradually extends out of the outer pipe from s-0 to s-l21In which l21Showing the arc length of the 1 st bend of the inner tube distal from the mounting end.
As a further improvement of the present invention, in step S2, the coordinates (x) of any point in the feasible space of the concentric tube robot are knowni，yi，zi) The data obtained from the DDA table are the length l of the outer tube1Length of the inner tube l2And the rotation angle phi of the inner tube relative to the world coordinate system2。
As a further improvement of the present invention, step S21 includes: when the inner tube of the concentric tube robot rotates for one circle relative to a world coordinate system, a locus circle is drawn in space by a point at any arc length s on the inner tube, and the size of the locus circle is determined by the extension arc length of the inner tube relative to the tail end of the outer tube; therefore, the radius r of the track circle is used to select the corresponding column in the DDA table, and the rotating radius r corresponding to the target point is matched with the rotating radius r corresponding to the end point in the DDA tableiAnd comparing one by one, and selecting the column with the minimum difference value to prepare for solving the input quantity of the following robot.
As a further improvement of the present invention, step S22 includes: in step S21, one of the columns in the DDA table has been locked, that is, the specific value (l) of the input amount when the robot reaches the target position1i，l2i) (ii) a In the generation of DDA tablesDDA Table is generated on the premise that the outer tube length reaches a maximum value l1＝l1max(ii) a Therefore, when the target point does not satisfy this condition,/1iAnd l2iThe value of (c) needs to be corrected; assuming that the inner tube rotates to obtain a first trajectory circle when the length of the outer tube is maximum and the end point of the concentric tube robot rotates to obtain a second trajectory circle when the target position is actually reached, the correct value is represented as (l)1，l2)，
l1＝l1i+e
l2＝l2i+e
Wherein e>0 is a correction value, i.e. the center O of the first locus circle1And a center O of a second locus circle2The distance of (c).
As a further improvement of the present invention, step S23 includes: assuming T is the target location, all that needs to be determined is the vector O1T and vector O1The angle of rotation between G; suppose the vector O1T and vector O1The angle of rotation between G is theta2iThen there is
θ2iThe angle being in the range of [0,180 °]；
Assuming that the target point is rotated within 0,180 deg. counterclockwise, the angle of rotation is positive, and vice versa, there is,
alpha represents the rotation angle theta capable of distinguishing the two side spaces2iThe coordinate value of the sign is determined.
The invention has the beneficial effects that: through the scheme, the motion control precision of the concentric tube robot can be improved.
Drawings
FIG. 1 is a flow chart of an inverse kinematics solution method for a concentric tube robot according to the present invention.
FIG. 2 is a schematic diagram of the rotation of the inner tube of the inverse kinematics solution method of the concentric tube robot according to the present invention.
FIG. 3 is a schematic diagram of length correction of an inverse kinematics solution method of a concentric tube robot according to the present invention.
Detailed Description
The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.
As shown in fig. 1 to 3, an inverse kinematics solution method for a concentric tube robot includes the following steps:
s1, generating a DDA table, wherein DDA is an abbreviation of English Date-drive Approach and indicates that the method is a method based on data acquisition and processing;
s2, use of DDA table;
step S2 includes the following substeps;
s21, determining a corresponding column in the DDA table according to the coordinate information of the target point;
s22, determining the length l of the outer tube 11And the length l of the inner tube 22；
S23, determining the rotation angle phi of the inner tube 2 relative to the world coordinate system2；
S24, applying the inverse kinematics solution result of the concentric tube robot to the motion control of the concentric tube robot consisting of a straight tube and a bent tube, wherein the straight tube is the outer tube 1, and the bent tube is the inner tube 2.
The invention provides an inverse kinematics solving method of a concentric tube robot, which is a method based on data acquisition and table lookup solving, and is applied to the concentric tube robot consisting of a straight tube and a bent tube, and in order to express the use of the inverse kinematics solving method clearly, the detailed description is as follows:
1. DDA Table Generation
The generation of the DDA table is obtained based on the manner of data acquisition. As shown in FIG. 2, first the length of the outer tube 1 of the concentric tube robot is kept at a maximum, i.e./1＝l1maxThe rotation angle Φ of the coordinate system of the inner tube 2 with respect to the world coordinate system is kept at 0. Then the length l of the inner tube 22From l1maxExercise of sportsTo l2maxAcquiring coordinate data of the tail end of the concentric tube robot and corresponding robot motion input quantity in the motion process, namely the length l of the inner tube 22Recording the coordinate data (x) of the tail end of the concentric tube robot in each extension incrementi，yi，zi) And the motion input l of the concentric tube robot1i，l2i，Φ2i. The size of the motion increment of the inner tube 2 finally determines the calculation precision of inverse kinematics by using the method. Finally, a DDA table of 6 rows and n columns is obtained, wherein the first three rows of the table are respectively the length l of the outer tube 11Length l of inner tube 22And the angle of rotation phi of the inner tube 22The last three rows of the table are the components of the concentric tube robot tip position in the x, y, z axes for the same column input.
Length l of inner tube 22From l1maxChange to2maxThis course of movement represents the course of movement of the inner tube 2 relative to the outer tube 1; in an initial state, the inner tube 2 and the outer tube 1 are completely overlapped, namely, the inner tube 2 is completely nested in the outer tube 1; in the movement process, the inner tube 2 moves axially relative to the outer tube 1, namely, the inner tube 2 gradually extends out of the outer tube 1; assuming that the arc length of the inner tube 2 protruding from the outer tube 1 is denoted by s, the length l of the inner tube 22From l1maxMovement changes to2maxIs the length l of the inner tube 22The inner tube 2 is gradually extended out of the outer tube 1 in increments from s to l21In which l21Showing the arc length of the curved portion of the inner pipe 2 at the 1 st segment away from the mounting end.
2. The use of DDA tables;
inverse kinematics solution is the process of finding the robot input quantity required by the robot end to reach the target position of the known robot. That is, the coordinate (x) of any point in the feasible space of the known concentric tubei，yi，zi) The data obtained from the DDA table are the length l of the outer tube 11Length l of inner tube 22And a rotation angle phi2(since the outer tube 1 is a straight tube, the angle of rotation phi here1No determination is required). The solving process can be divided into three steps, which are described separately below.
1) Determining corresponding columns in the DDA table according to the coordinate information of the target point
When the inner tube 2 of the concentric tube robot rotates one circle relative to the world coordinate system, a point at any arc length s on the inner tube 2 draws a circle in space, as shown in fig. 2. It will be readily apparent from the figures that the length of the arc of protrusion of the inner tube 2 relative to the end of the outer tube 1 determines the size of this circle. The radius r of the circle is used here to select the corresponding column in the DDA table. The rotating radius r corresponding to the target point is compared with the rotating radius r corresponding to the end point in the DDA tableiAnd comparing one by one, and selecting the column with the minimum difference value to prepare for solving the input quantity of the following robot.
2) Determining the length l of the outer and inner tubes1，l2
In the last step, one of the columns in the DDA table has been locked, that is, the specific value (l) of the input amount when the robot reaches the target position1i，l2i). But from the analysis of the feasible space of a dual-tube concentric tube robot, it can be seen that this set of values is not necessarily the final correct solution. In the generation of the front table, the DDA table is generated on the premise that the length of the outer tube 1 reaches the maximum value l1＝l1max. Therefore, when the target point does not satisfy this condition,/1iAnd l2iThe value of (c) needs to be corrected. As shown in fig. 3, it is assumed that the dotted circle is obtained by rotating the inner tube 2 when the length of the outer tube 1 is maximum, and the solid circle is obtained by rotating the end point of the concentric tube robot when the target position is actually reached. Then, the correct value should be expressed as (l)1，l2)，
l1＝l1i+e
l2＝l2i+e
Wherein e>0 is a correction number, i.e. two centers O in FIG. 31And O2The distance of (c).
3) Determining the rotation angle phi of the inner tube 2 relative to the world coordinate system2
Assuming that T is the target location, as shown in FIG. 3, all that needs to be determined is the vector O1T and vector O1G. Suppose that the rotation angle is θ2iThen there is
Where theta is2iThe angle being in the range of [0,180 °]It is clear that when the concentric tube robot rotates forward and backward, the results are not the same, and therefore the sign of the rotation angle needs to be determined. Assume a counterclockwise rotation of the target point of [0,180 °]Within the scope of which the angle of rotation is positive and vice versa, there are,
where α represents a rotation angle θ capable of distinguishing spaces on both sides2iThe coordinate value of the sign is determined. If the inner tube coordinate system F2(0) Is shown in fig. 3, then α is the y coordinate value of the target point, otherwise it is the projection value of the target point on the y axis.
The inverse kinematics problem of the double-tube concentric tube robot can be calculated by the method.
The invention provides an inverse kinematics solving method of a concentric tube robot, which is based on inverse kinematics solving of data acquisition, and the method does not need to consider the specific curvature value of a concentric tube, whether the concentric tube is a constant curvature tube or not, and the influence of the shearing, bending, friction and other acting forces between the tubes on the precision of a conventional inverse kinematics calculating method. Since these factors, which are practically difficult to control, are already included in the DDA table. At the same time, this method also solves the problem of irreversible plastic deformation of the concentric tubes over time, since the change in curvature of the tubes is also included in the DDA table. Therefore, the inverse kinematics solution method is simple to operate and high in precision, and can effectively improve the precision of the motion control of the concentric tube robot.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (7)
1. The inverse kinematics solving method of the concentric tube robot is characterized by comprising the following steps of:
s1, generating a DDA table;
s2, use of DDA table;
step S2 includes the following substeps;
s21, determining a corresponding column in the DDA table according to the coordinate information of the target point;
s22, determining the length l of the outer tube1And length l of the inner tube2；
S23, determining the rotation angle phi of the inner tube relative to the world coordinate system2；
S24, applying the inverse kinematics solution result of the concentric tube robot to the motion control of the concentric tube robot consisting of a straight tube and a bent tube, wherein the straight tube is an outer tube, and the bent tube is an inner tube.
2. The concentric tube robot inverse kinematics solution method according to claim 1, wherein step S1 comprises: first, the outer tube length of the concentric tube robot remains at a maximum, i.e./1＝l1maxAngle of rotation phi of the inner tube coordinate system relative to the world coordinate system2Remains at 0; the inner tube is then moved axially relative to the outer tube to a length l of the inner tube2From l1maxMovement changes to2maxObtaining a DDA table with 6 rows and n columns, wherein the first three rows of the DDA table are respectively the length l of the outer tube1Length of the inner tube l2And angle of rotation phi of the inner tube2The last three rows of the table are the components of the concentric tube robot tip position in the x, y, z axes for the same column input.
3. The concentric tube robot inverse kinematics solution method according to claim 2, wherein: length l of inner tube2From l1maxChange to2maxThe motion process represents the inner tube relativeThe movement process of the outer pipe; in the initial state, the inner pipe and the outer pipe are completely overlapped, namely the inner pipe is completely nested in the outer pipe; in the movement process, the inner pipe moves axially relative to the outer pipe, namely the inner pipe gradually extends out of the outer pipe; assuming that the arc length of the inner tube extending out of the outer tube is denoted by s, the length l of the inner tube2From l1maxMovement changes to2maxIs the length l of the inner tube2Gradually increasing in certain increment, the inner pipe gradually extends out of the outer pipe from s-0 to s-l21In which l21Showing the arc length of the 1 st bend of the inner tube distal from the mounting end.
4. The concentric tube robot inverse kinematics solution method according to claim 3, wherein: in step S2, the coordinates (x) of any point in the feasible space of the concentric tube robot are knowni，yi，zi) The data obtained from the DDA table are the length l of the outer tube1Length of the inner tube l2And the rotation angle phi of the inner tube relative to the world coordinate system2。
5. The concentric tube robot inverse kinematics solution according to claim 4, comprising, at step S21: when the inner tube of the concentric tube robot rotates for one circle relative to a world coordinate system, a locus circle is drawn in space by a point at any arc length s on the inner tube, and the size of the locus circle is determined by the extension arc length of the inner tube relative to the tail end of the outer tube; therefore, the radius r of the track circle is used to select the corresponding column in the DDA table, and the rotating radius r corresponding to the target point is matched with the rotating radius r corresponding to the end point in the DDA tableiAnd comparing one by one, and selecting the column with the minimum difference value to prepare for solving the input quantity of the following robot.
6. The concentric tube robot inverse kinematics solution method according to claim 5, wherein step S22 comprises: in step S21, one of the columns in the DDA table has been locked, that is, the specific value (l) of the input amount when the robot reaches the target position1i，l2i) (ii) a In the generation of DDA tables, the DDA tables are generatedThe premise is that the length of the outer tube reaches a maximum value l1＝l1max(ii) a Therefore, when the target point does not satisfy this condition,/1iAnd l2iThe value of (c) needs to be corrected; assuming that the inner tube rotates to obtain a first trajectory circle when the length of the outer tube is maximum and the end point of the concentric tube robot rotates to obtain a second trajectory circle when the target position is actually reached, the correct value is represented as (l)1，l2)，
l1＝l1i+e
l2＝l2i+e
Wherein e>0 is a correction value, i.e. the center O of the first locus circle1And a center O of a second locus circle2The distance of (c).
7. The concentric tube robot inverse kinematics solution method according to claim 6, wherein step S23 comprises: assuming T is the target location, all that needs to be determined is the vector O1T and vector O1The angle of rotation between G; suppose the vector O1T and vector O1The angle of rotation between G is theta2iThen there is
θ2iThe angle being in the range of [0,180 °]；
Assuming that the target point is rotated within 0,180 deg. counterclockwise, the angle of rotation is positive, and vice versa, there is,
alpha represents the rotation angle theta capable of distinguishing the two side spaces2iThe coordinate value of the sign is determined.
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