CN108663989B - Inverse solution engineering and trajectory planning algorithm of five-axis treatment bed - Google Patents
Inverse solution engineering and trajectory planning algorithm of five-axis treatment bed Download PDFInfo
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Abstract
The invention discloses an inverse solution engineering and a trajectory planning algorithm of a five-axis treatment couch, which comprises three parts of lesion space coordinate positioning, treatment couch kinematics inverse solution and efficient trajectory planning. The focus space coordinate positioning method determines the three-dimensional coordinate of the tumor position relative to the head top of a patient through an imaging device, and determines the position of the tumor relative to a treatment bed by combining the relative positioning of the treatment bed and the limbs of the patient. The tumor needs to be arranged at the target area of the therapeutic instrument, and the position of each joint in the target state is obtained through the inverse solution of the kinematics of the therapeutic bed. In order to relieve the tension of a patient, the five-axis treatment bed needs to keep stable operation in the movement process, complex movement is avoided, and the high-efficiency track planning can realize interpolation track planning of a straight line blind area and straight line track planning outside the blind area. According to the invention, the tumor is accurately arranged at the target area by a focus space coordinate positioning method and a treatment table kinematics inverse solution algorithm, so that the emotion control work before treatment is ensured, and the treatment effect is improved.
Description
Technical Field
The invention belongs to the field of mechanical arm kinematics, and particularly relates to an inverse solution engineering and trajectory planning algorithm of a five-axis treatment couch.
Background
Before the large-scale radiotherapy equipment carries out radiotherapy, a five-axis treatment couch is required to move the tumor to the center of a target area of the radiotherapy equipment, and accurate positioning is realized. The positioning process needs to meet the real-time requirement, and in view of the situation that the solution of inverse kinematics is relatively complex and multiple solutions or no solutions may occur, an efficient treatment table kinematics inverse solution algorithm needs to be developed urgently to accurately position the tumor to the target area, and the movement process is optimized by relying on an efficient trajectory planning algorithm, so that more comfortable treatment experience is provided for the patient.
The solution process provided by the invention can rapidly calculate the kinematic inverse solution of the mechanical arm, meets the real-time control requirement of the mechanical arm, and adopts a quintic polynomial interpolation algorithm to plan the track in a working space (reachable space defect) which does not meet the stable motion of a straight line. In a working space (peripheral space) meeting the requirement of straight-line stable motion, a straight-line track planning algorithm is adopted, and the adopted drive transformation function can realize stable movement (the speed and the acceleration of the drive transformation function are limited to start from a static state and end from the static state), so that the comfortable experience requirement of a patient on the treatment process is met.
Disclosure of Invention
The invention aims to provide an inverse solution engineering and trajectory planning algorithm, and particularly relates to an inverse solution engineering and trajectory planning algorithm of a five-axis treatment couch.
The technical problem of the invention is solved by the following scheme:
the method comprises the following three steps: a lesion space coordinate positioning method, a treatment table kinematics inverse solution algorithm and an efficient track planning algorithm.
(1) The focus space coordinate positioning method accurately positions the tumor to the center of the target area to realize the optimal treatment effect, and comprises the following steps:
a) imaging device determining tumor coordinates OCAnd the head vertex coordinate O of the patientHRelative position of
b) A laser ranging sensor is arranged at one end of the head on the lying plate of the treatment bed to determine the head top coordinate O of the patientHFixed coordinate O with lying plate of treatment bedBRelative position of
c) The tumor reaches the target area and the tumor is located at the position OCWith the central coordinate O of the target areaGCoinciding to obtain the fixed coordinate O of the lying plate of the treatment bedBWith the central coordinate O of the target areaGThe relative position of the two or more of the three or more of the,
d) target area OGFive-axis treatment bed base O0Relative position of
For fixed parameters, we obtain:
(2) the treatment couch kinematics inverse solution method realizes the rapid solution of the mechanical arm inverse kinematics, is an important basis of subsequent efficient trajectory planning, and comprises the following steps:
a) according to the Denavit-Hartenberg method, a coordinate system is established on each joint axis to obtain a No. 1-5 coordinate system, based on configuration and target motion process limitation, the fixed coordinate system of a treatment bed lying plate needs to be ensured to be consistent with the Z-axis direction of a five-axis treatment bed base coordinate system, and at the moment, the fourth joint corner needs to meet the requirement of theta4＝π-θ3；
b) Solving to obtain the fixed coordinate O of the lying plate of the treatment bedBRelative five-axis treatment bed base O0Position transformation matrix of (2):
wherein:
o＝-cos(θ1+θ2+θ5)；r＝-sin(θ1+θ2+θ5)；u＝0
p＝sin(θ1+θ2+θ5)；s＝-cos(θ1+θ2+θ5)；v＝0
q＝0；b＝0；w＝1
px＝a1*cos(θ1)-a2*cos(θ1+θ2)+a3*cos(θ1+θ2)*cos(θ3)
py＝a1*sin(θ1)-a2*sin(θ1+θ2)+a3*sin(θ1+θ2)*cos(θ3)
pz＝d0+d1+d4+d5+a3*sin(θ3)
wherein: o, r, u, p, s, v, q, b, w, px、py、pzThe position posture and the space position parameter value of the fixed coordinate system of the lying plate of the treatment bed relative to the global coordinate system of the base of the five-axis treatment bed are obtained.
c) And obtaining an analytic solution of each joint according to the position transformation matrix:
from the matrix (3,4) find:
from (1,4) and (2,4) in the matrix, the following are obtained:
cos(θ1)＝(px+a2*cos(θ1+θ2)-a3*cos(θ1+θ2)*cos(θ3))/a1
sin(θ1)＝(py+a2*sin(θ1+θ2)-a3*sin(θ1+θ2)*cos(θ3))a1
wherein: cos (theta)1)2+sin(θ1)2When the two equations are combined to obtain theta 11+θ2；
From the matrix (1,1) find:
θ1+θ2+θ5＝arccos(-o)
wherein: theta obtained by combining the above steps1+θ2To obtain theta5；
According to the matrix (1,4), the following steps are obtained: theta3、θ5、θ1+θ2Substituting:
θ1＝arcos[(px+a2*cos(θ1+θ2)-a3*cos(θ1+θ2)*cos(θ3))/a1]；
(3) the efficient track planning algorithm overcomes the defect of mechanical configuration, realizes stable linear operation of the body of the patient and achieves the effect of stabilizing the emotion of the patient. The method comprises the following steps:
a) determining a target motion path, namely linear motion;
b) according to the central defect of the reachable space, path segmentation is carried out, and the path segmentation is divided into: the linear motion of the space curve motion and the peripheral space at the position of the space defect can be achieved. And determines a state transfer point PTAnd switching the motion modes:
the middle point of the track process:
Pmid(t)＝L(t)*(PB-PI)+PI，t＝0.01*i，i∈[0,100]
c) due to configuration limitations, a section of the five-axis treatment couch behind the starting point may not be able to perform straight-line trajectory planning. Judging the existence of inverse solution by traversing from i to 0, and finding out the point P where the first inverse solution existsmid(tT)，i＝iT。
d) The spatial curvilinear motion at the spatial defect can be reached: and (3) carrying out interpolation by using a fifth-order polynomial, limiting the speed and the acceleration of the linear motor to start from a static state and end in the static state:
θ(t)＝a0+a1*t+a2*t2+a3*t3+a4*t4+a5*t5
e) linear motion of the peripheral space: and limiting the driving transformation function of the linear motion equation, the speed and the acceleration of which start from a static state and end from the static state, and the conditions are satisfied:
L(t)＝(-sin(2*π*t-π)/(4*π2)-(1/(2*π))*t)*(-2*π)
dL(t)＝(-cos(2*π*t-π)/(2*π)-(1/(2*π)))*(-2*π)
ddL(t)＝sin(2*π*t-π)*(-2*π)
the middle point of the linear path planning process is as follows:
Pmol(t)＝L(t)*(PB-PT)+PT，t＝0.01*i，i∈[0,100]。
the invention realizes the accurate positioning of the tumor and the target area through the inverse solution engineering and the trajectory planning algorithm of the five-axis treatment couch, and lays a good foundation for the subsequent ray treatment. Meanwhile, the movement speed of the limbs of the patient is limited within a comfortable range through an efficient trajectory planning algorithm, and the effect of stabilizing the emotion before treatment is achieved.
Drawings
Fig. 1 is a flow of solving a trajectory plan for a five-axis treatment couch according to the present invention;
FIG. 2 is a schematic diagram of coordinate systems established on the various joint axes of such a five-axis treatment couch;
FIG. 3 is a schematic axial view of the coordinate system established on each joint axis of the five-axis treatment couch of the present invention;
FIG. 4 is a schematic top view of the coordinate system established on each joint axis of the present invention;
FIG. 5 is a schematic front view of the coordinate system established on each joint axis according to the present invention;
FIG. 6 is a schematic left-side view of the coordinate system established on each joint axis according to the present invention;
FIG. 7 is a schematic diagram of a five-axis treatment couch for a subject of the present invention;
FIG. 8 is a front elevation view of a five axis treatment couch for a subject of the present invention;
FIG. 9 is a partial schematic view of FIG. 8;
FIG. 10 is a schematic view of a central defect region of a working space of a five-axis treatment couch;
FIG. 11 is a schematic view of a linear path segmentation of a five-axis treatment couch;
reference numbers in the figures: 1. a laser ranging sensor; 2. a therapeutic bed lying plate; 3. a radiation device; 4. a body rotating device; 5. five-axis treatment bed.
Detailed Description
For a better understanding and appreciation of the structural features and advantages achieved by the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings, in which:
as shown in fig. 1, an object of the present invention is to provide an inverse solution engineering and trajectory planning algorithm, and in particular, to an inverse solution engineering and trajectory planning algorithm for a five-axis treatment couch.
The method comprises the following three steps: a lesion space coordinate positioning method (see figure 1, algorithm block 1), a treatment table kinematics inverse solution algorithm (see figure 1, algorithm block 2) and an efficient trajectory planning algorithm (see figure 1, algorithm block 3).
As shown in fig. 1, the logic sequence of the execution of the three methods is shown.
(1) The focus space coordinate positioning method accurately positions the tumor to the center of the target area to realize the optimal treatment effect, and comprises the following steps:
a) imaging device determining tumor coordinates OCAnd the head vertex coordinate O of the patientHRelative position of
As shown in fig. 2, a tumor coordinate system C and a patient vertex coordinate system H are established;
b) a laser ranging sensor is arranged at one end of the head on the lying plate of the treatment bed to determine the head top coordinate O of the patientHFixed coordinate O with lying plate of treatment bedBRelative position of
c) As shown in FIGS. 8 and 9, the tumor reaches the target region and is located at the position OCWith the central coordinate O of the target areaGCoinciding to obtain the fixed coordinate O of the lying plate of the treatment bedBSit centrally in the target areaMark OGThe relative position of the two or more of the three or more of the,
d) target area OGFive-axis treatment bed base O0Relative position of
For fixed parameters, we obtain:
(2) the treatment couch kinematics inverse solution method realizes the rapid solution of the mechanical arm inverse kinematics, is an important basis of subsequent efficient trajectory planning, and comprises the following steps:
a) according to the Denavit-Hartenberg method, a coordinate system is established on each joint axis to obtain a No. 1-5 coordinate system, based on configuration and target motion process limitation, the fixed coordinate system of a treatment bed lying plate needs to be ensured to be consistent with the Z-axis direction of a five-axis treatment bed base coordinate system, and at the moment, the fourth joint corner needs to meet the requirement of theta4＝π-θ3；
b) Solving to obtain the fixed coordinate O of the lying plate of the treatment bedBRelative five-axis treatment bed base O0Position transformation matrix of (2):
wherein:
o＝-cos(θ1+θ2+θ5)；r＝-sin(θ1+θ2+θ5)；u＝0
p＝sin(θ1+θ2+θ5)；s＝-cos(θ1+θ2+θ5)；v＝0
q＝0；b＝0；w＝1
px＝a1*cos(θ1)-a2*cos(θ1+θ2)+a3*cos(θ1+θ2)*cos(θ3)
py＝a1*sin(θ1)-a2*sin(θ1+θ2)+a3*sin(θ1+θ2)*cos(θ3)
pz＝d0+d1+d4+d5+a3*sin(θ3)
wherein: o, r, u, p, s, v, q, b, w, px、py、pzThe position posture and the space position parameter value of the fixed coordinate system of the lying plate of the treatment bed relative to the global coordinate system of the base of the five-axis treatment bed are obtained.
c) And obtaining an analytic solution of each joint according to the position transformation matrix:
from the matrix (3,4) find:
from (1,4) and (2,4) in the matrix, the following are obtained:
cos(θ1)＝(px+a2*cos(θ1+θ2)-a3*cos(θ1+θ2)*cos(θ3))/a1
sin(θ1)＝(py+a2*sin(θ1+θ2)-a3*sin(θ1+θ2)*cos(θ3))/a1
wherein: cos (theta)1)2+sin(θ1)2When the two equations are combined to obtain theta 11+θ2；
From the matrix (1,1) find:
θ1+θ2+θ5＝arccos(-o)
wherein: theta obtained by combining the above steps1+θ2To obtain theta5；
According to the matrix (1,4), the following steps are obtained: theta3、θ5、θ1+θ2Substituting:
θ1＝arcos[(px+a2*cos(θ1+θ2)-a3*cos(θ1+θ2)*cos(θ3))/a1]；
(3) the efficient track planning algorithm overcomes the defect of mechanical configuration, realizes stable linear operation of the body of the patient and achieves the effect of stabilizing the emotion of the patient. The method comprises the following steps:
a) determining a target motion path, namely linear motion;
b) as shown in FIG. 10, the shaded area is the central defect in the reachable space (i.e., the origin O of the B coordinate systemBInaccessible area of). As shown in fig. 11, taking a straight path 1 as an example, the path is divided according to the central defect of the reachable space into: the linear motion of the peripheral space (the linear path 1-the peripheral space section) and the linear motion of the spatial defect (the linear path 1-the peripheral space section) can be achieved. And determines a state transfer point PTAnd switching the motion modes:
the middle point of the track process:
Pmid(t)＝L(t)*(PB-PI)+PI，t＝0.01*i，i∈[0,100]
c) due to configuration limitations, a section of the five-axis treatment couch behind the starting point may not be able to perform straight-line trajectory planning. Judging the existence of inverse solution by traversing from i to 0, and finding out the point P where the first inverse solution existsmid(tT)，i＝iT。
d) The spatial curvilinear motion at the spatial defect can be reached: and (3) carrying out interpolation by using a fifth-order polynomial, limiting the speed and the acceleration of the linear motor to start from a static state and end in the static state:
θ(t)＝a0+a1*t+a2*t2+a3*t3+a4*t4+a5*t5
e) linear motion of the peripheral space: and limiting the driving transformation function of the linear motion equation, the speed and the acceleration of which start from a static state and end from the static state, and the conditions are satisfied:
L(t)＝(-sin(2*π*t-π)/(4*π2)-(1/(2*π))*t)*(-2*π)
dL(t)＝(-cos(2*π*t-π)/(2*π)-(1/(2*π)))*(-2*π)
ddL(t)＝sin(2*π*t-π)*(-2*π)
the middle point of the linear path planning process is as follows:
Pmol(t)＝L(t)*(PB-PT)+PT，t＝0.01*i，i∈[0,100]。
the foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (1)
1. An inverse solution engineering and trajectory planning algorithm of a five-axis treatment couch is characterized by comprising the following steps:
(1) and positioning the space coordinates of the focus, wherein the process is as follows:
(1.1) determining tumor coordinates O by medical imaging equipmentCAnd the head vertex coordinate O of the patientHRelative position of
(1.2) a laser ranging sensor is arranged at one end of the head of the five-axis treatment bed lying plate, and the laser ranging sensor is used for determining the head top coordinate O of the patientHFixed coordinate O with lying plate of treatment bedBRelative position of
(1.3) tumor arrival target area, tumor coordinate OCWith the central coordinate O of the target areaGCoinciding to obtain the fixed coordinate O of the lying plate of the treatment bedBWith the central coordinate O of the target areaGRelative position of
(1.4) Central coordinate of target area OGFive-axis treatment bed base O0Relative position of
For fixed parameters, we obtain:
wherein
Is a five-axis treatment bed base O0Fixing coordinate O relative to the lying plate of the treatment bedBA three-dimensional space vector of (a);
(2) the five-axis treatment bed kinematics inverse solution operation comprises the following steps:
(2.1) establishing a coordinate system on each joint axis according to a Denavit-Hartenberg method to obtain a No. 1-5 coordinate system, and ensuring that the fixed coordinate system of the therapeutic bed lying plate is consistent with the Z-axis direction of a five-axis therapeutic bed base coordinate system based on configuration and target motion process limitation, wherein at the moment, the fourth joint corner needs to meet the requirement of theta4＝π-θ3(ii) a Wherein theta is3Refers to the angle of rotation, θ, of the third revolute joint4Refers to the rotation angle of the fourth rotational joint;
(2.2) solving to obtain the fixed coordinate O of the lying plate of the treatment bedBRelative five-axis treatment bed base O0Position transformation matrix of (2):
in the transformation matrix:
o＝-cos(θ1+θ2+θ5)；r＝-sin(θ1+θ2+θ5)；u＝0
p＝sin(θ1+θ2+θ5)；s＝-cos(θ1+θ2+θ5)；v＝0
q＝0；b＝0；w＝1
px＝a1*cos(θ1)-a2*cos(θ1+θ2)+a3*cos(θ1+θ2)*cos(θ3)
py＝a1*sin(θ1)-a2*sin(θ1+θ2)+a3*sin(θ1+θ2)*cos(θ3)
pz＝d0+d1+d4+d5+a3*sin(θ3)
wherein: o, r, u, p, s, v, q, b, w, px、py、pzIs the position attitude and space position parameter value theta of the fixed coordinate system of the lying plate of the treatment bed relative to the global coordinate system of the base of the five-axis treatment bed1、θ2、θ5The rotation angles of the first, second and fifth rotation joints are respectively referred;
(2.3) obtaining an analytic solution of each joint according to the position transformation matrix in the step (2.2):
2.3.1) from the elements (3,4) in the third row and the fourth column of the matrix:
2.3.2) from the elements (1,4) of the first row and the fourth column in the matrix and the elements (2,4) of the second row and the fourth column in the matrix:
cos(θ1)＝(px+a2*cos(θ1+θ2)-a3*cos(θ1+θ2)*cos(θ3))/a1
sin(θ1)＝(py+a2*sin(θ1+θ2)-a3*sin(θ1+θ2)*cos(θ3))/a1
wherein: cos (theta)1)2+sin(θ1)2When the two equations are combined to obtain theta 11+θ2；
2.3.3) from the elements (1,1) of the first row and the first column in the matrix:
θ1+θ2+θ5＝arc cos(-o)
wherein: theta obtained by combining the above steps1+θ2To obtain theta5；
2.3.4) Theta obtained in the above step is determined according to the elements (1,4) in the first row and the fourth column of the matrix3、θ5、θ1+θ2Substituting: theta1＝arcos[(px+a2*cos(θ1+θ2)-a3*cos(θ1+θ2)*cos(θ3))/a1]；
Can solve to obtain theta after substituting into the equation1Since theta is known1+θ2So can solve for θ2；
(3) The efficient track planning operation comprises the following processes:
(3.1) determining a target motion path I-linear motion;
(3.2) according to the central defect of the reachable space, dividing the path into space curvilinear motion at the position of the reachable space defect and linear motion of the peripheral space, and determining the state transfer point PTAnd switching the motion modes:
3.2.1) track process intermediate points:
Pmid(t)＝L(t)*(PB-PI)+PI，t＝0.01*i，i∈[0，100]
wherein the content of the first and second substances,
which represents a parameter of time that is,
PIrefers to the initial position vector of the lying plate of the treatment bed,
PBrefers to the target position vector of the therapeutic bed lying plate;
3.2.2) due to configuration limitation, a section of the five-axis treatment couch behind the starting point may not be subjected to straight-line trajectory planning, and the existence of the inverse solution is judged by traversing from i to 0, so as to find out the point P where the first inverse solution existsmid(tT)，i＝iT；
(3.3) for a spatial curvilinear motion at the accessible spatial defect: and (3) carrying out interpolation by using a fifth-order polynomial, limiting the speed and the acceleration of the linear motor to start from a static state and end in the static state:
θ(t)＝a0+a1*t+a2*t2+a3*t3+a4*t4+a5*t5
in the formula a0To a5Interpolation parameters of a fifth-order polynomial are automatically obtained by an MATLAB spherical stoolbox, a group of new polynomial interpolation parameters are regenerated for each joint corner, and t refers to time;
(3.4), linear motion for peripheral space: and limiting the driving transformation function of the linear motion equation, the speed and the acceleration of which start from a static state and end from the static state, and the conditions are satisfied:
L(t)＝(-sin(2*π*t-π)/(4*π2)-(1/(2*π))*t)*(-2*π)
dL(t)＝(-cos(2*π*t-π)/(2*π)-(1/(2*π)))*(-2*π)
ddL(t)＝sin(2*π*t-π)*(-2*π)
the middle point of the linear path planning process is as follows:
Pmol(t)＝L(t)*(PB-PT)+PT，t＝0.01*i，i∈[0，100]。
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