CN111958602B - Real-time inverse solution method for wrist offset type 6-axis robot - Google Patents

Real-time inverse solution method for wrist offset type 6-axis robot Download PDF

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CN111958602B
CN111958602B CN202010842411.0A CN202010842411A CN111958602B CN 111958602 B CN111958602 B CN 111958602B CN 202010842411 A CN202010842411 A CN 202010842411A CN 111958602 B CN111958602 B CN 111958602B
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CN111958602A (en
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宋宝
唐小琦
王国栋
周向东
熊烁
刘永兴
钟靖龙
肖千红
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Huazhong University of Science and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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Abstract

The invention discloses a real-time inverse solution algorithm of a wrist offset type 6-axis robot, which is used for completing calculation by using an improved Gauss-Newton algorithm on the basis of rapid convergence of an iterative method and aiming at the problems that the conventional Newton-Rafsen iterative method has a large number of iterations and a singular position cannot be solved in the solving process. And for the problem that the iterative algorithm depends on the starting point to be close to the accurate solution, a dynamic table is introduced to complete the dynamic supply of the iterative starting point. The method is tested in the actual industrial application occasions of the robot, and the algorithm is verified to have high real-time performance and accuracy.

Description

Real-time inverse solution method for wrist offset type 6-axis robot
Technical Field
The invention relates to the technical field of robots, in particular to a real-time inverse solution algorithm of a wrist offset 6-axis robot.
Background
Inverse kinematics is used as a foundation stone for trajectory planning and motion control of a robot, and the real-time performance and the accuracy of the inverse kinematics are important concerns during motion analysis. For most 6R robots, the mechanical structure meets the requirement that adjacent three joints are intersected or parallel, so that decoupling processing can be performed by using a Pieper criterion to complete analytic solution. However, with the development of robot research and the change of requirements of application industries such as spraying and welding, some robots which do not meet the Pieper criterion, such as wrist offset type 6R robots, come into force.
At present, the research of the inverse solution method of a common 6R robot at home and abroad can be roughly divided into an elimination method, an iteration method and an intelligent algorithm. The Raghavan and Roth construct 14 basic equations through vector operation, and a conclusion of 16 groups of inverse solution upper limits of a general 6R robot is obtained by adopting a null method. On the basis, Monocha introduces 24-order matrix decomposition, and improves the precision and stability of the elimination method. The Liu Loose nations rebuild the basic equation based on the elimination method, reduces the 24-order matrix to 16 orders, eliminates 8 root additions and compresses the average calculation time to the level of 1-2ms for the first time. However, the method is extremely sensitive to the DH parameters of the robot, and when the structural parameters (such as a1, α 1, etc.) are 0, the method is often disabled. And when the key matrixes R1 and R2 are irreversible or the eigenvalues are virtual roots, the solution cannot be continued. Although the Liu method of Leinnesen et al introduces the concept of matrix condition number and uses the Jocabe numerical method to solve in case of key matrix failure, such a strategy results in increased computation time, which can be up to 8 ms.
In the aspect of iterative solution, the traditional Newton-Raphson iterative method carries out iterative solution by calculating the inverse of the Jacobian. However, the method often has the problem that matrix singularity and initial iteration points need to be close to an accurate solution, otherwise, effective convergence cannot be achieved. The real estate and the like avoid the singular problem in the description of the Euler angle based on the improved Newton method and the introduction of quaternion interpolation. Cuong et al constructed a pose equation based on the geometric relationship of the non-spherical wrist 6R robot and then used an iterative process equation to solve the root. Party Lei et al adopt homotopy continuous method to search in large scale, can accomplish all root solutions, but this method needs to transform initial value and real-time nature is poor, can't satisfy the online requirement. For the research of an intelligent algorithm, the Yanghui and the like are based on a niche genetic algorithm, the Euclidean distance between individuals is introduced, self-adaptive improvement is carried out, and the global optimization capability and the convergence speed are improved. The forest yang adopts a multi-population genetic algorithm for coevolution, population information exchange is realized by using a migration operator, the convergence capability and the local optimal 'precocity' problem of the traditional single-population genetic algorithm are improved, and the calculation stability and the real-time performance cannot meet the industrial application requirements.
Disclosure of Invention
The invention aims to solve the problems and provide a real-time inverse solution algorithm of a wrist offset type 6-axis robot.
The invention realizes the purpose through the following technical scheme:
the invention comprises the following steps:
s1: establishing a coordinate system for each joint of the robot, and obtaining connecting rod parameters; link transformation matrix for improved DH coordinate system
Figure GDA0003557266370000021
The expression general formula is:
Figure GDA0003557266370000022
substituting DH parameters into the transformation matrix right-multiplication rule to obtain the transformation matrix from the terminal link coordinate system {6} to the base coordinate system {0}, and
Figure GDA0003557266370000023
the following were used:
Figure GDA0003557266370000024
s2: repeating for many times, correcting regression coefficient until the residual square sum of original model | | | rn| is less than error epsilon (epsilon)>0) (ii) a Using the product J of the Jacobian matrix JTJ approximately replaces a second-order Hansen matrix H in a Newton method, so that complex second-order matrix operation is omitted; the basic iterative formula is as follows:
xn+1＝xn-(JTJ)-1JTrn (3)
for a 6R robot, defining the Jacobian matrix J (theta) of velocity of the manipulator arm refers to the velocity vector from the joint
Figure GDA0003557266370000031
To the operating velocity vector
Figure GDA0003557266370000032
The general transmission ratio of the transmission, i.e.
Figure GDA0003557266370000033
Since velocity can be considered as a differential motion per unit time, the above equation is equivalent to a mapping of a differential motion D from joint space D θ to Cartesian space, i.e.
D＝J(θ)dθ (5)
Wherein D ═ dx dy dz δ x δ y δ z; j (theta) is a velocity Jacobian matrix obtained by differential transformation; by substituting the above formula (3) for the formula (5), a compound having a structure represented by the formula
θn+1＝θn-(JTJ)-1JTD (6)
S3: in order to solve the defects caused by matrix singularity, J is subjected to damping coefficient lambda introductionTInversion of J is replaced by pair (J)TJ + Lambda I), the problem of singularity and ill-conditioned property of a Jacobian matrix is effectively avoided; wherein I is an identity matrix of 6 th order, and lambda belongs to (0, 1)]；
θn+1＝θn-(JTJ+λI)-1JTD (7)
In each iteration process, the coefficient lambda is adjusted according to the change of the iteration residual square sum e (the two norms of the residual vector D | | | D |); when e isi<ei-1When the iteration residual is converged, the lambda is reduced; otherwise, the residual error is still larger, and the lambda is increased to control the iteration step length to be rapidly converged;
s4: in order to reduce the amount of iterative operation, a damping coefficient lambda is set before calculation to accelerate convergence; and setting an upper limit imax of iteration times and residual error precision e, and establishing a termination condition to finish calculation or avoid overlong iteration time.
When the iteration starting point is far away from the precise point or unreliable;
firstly, a kinematic model needs to be corrected; the axial offset of the J5, J6 joints is set to 0, namely in Table 1D 'is updated on the basis of DH parameter of'5＝0、d′60, and constructing a kinematic model according to equation (2)
Figure GDA0003557266370000034
Secondly, for the target point pose T provided by the offset 6R robotendCarrying out correction; correcting the J6 axial offset in the target point position, and improving the corrected motion model
Figure GDA0003557266370000041
And correction target point location T'endThe workspace overlap ratio of (a); the correction formula is as follows
Figure GDA0003557266370000042
For meeting Pieper criterion after correction
Figure GDA0003557266370000043
And target point T'endResolution can be accomplished by analytical methods; an inverse transformation method is adopted to obtain 8 groups of preliminary joint space inverse solutions corresponding to the position and posture of the point;
at the moment, joint attributes are introduced, and the preliminary inverse solution is divided; dividing the bit patterns into 8 groups of states by respectively adopting front and back, upper and lower and pitching 3 boundary combinations by taking the singular bit patterns as dividing boundaries; when the center point of the wrist of the robot is positioned on the rotation axis of the J1 joint, a plane formed by the axes of J1 and J2 is taken as a front boundary and a rear boundary, and two sides of the plane are respectively defined as front attributes and rear attributes; when the mechanical arm connecting rod 2 and the connecting rod 3 are parallel, a plane determined by the axes of the connecting rod 2 and the J3 is taken as a boundary, and the upper attribute and the lower attribute are respectively defined on two sides; when the axes of the joints J4 and J6 are parallel, a plane determined by the intersecting axes of the joints J4 and J5 is taken as a boundary, and the two sides are respectively defined as pitch and yaw attributes;
when a2 × c2+ d4 × s23 is more than or equal to 0, m is set to 0 to be the front attribute, and on the contrary, 1 is set to be the rear attribute; when theta 3 is less than or equal to 90 degrees, n is set to be 0 to represent the lower attribute, otherwise, 1 is set to be the upper attribute; when theta 5 is less than or equal to 0 degree, j is placed in a position of 0 to bow, otherwise, 1 is placed in a position of facing upward;
where ci is cos (θ i), si is sin (θ i), s23 is sin (θ 2+ θ 3), c23 is cos (θ 2+ θ 3), and so on; defining variables
Figure GDA0003557266370000044
k31＝p′xc1+p′ys1,
Figure GDA0003557266370000045
Figure GDA0003557266370000046
Figure GDA0003557266370000047
c5＝(axc1+ays1)s23-azc23,c4c5＝axs1-ayc1,
c4s5＝(axc1+ays1)c23+azs23,s23＝a2c3p′z+k31(a2s3+d4),
c23＝(-d4+a2s3)p′z+k31·a2c3；
Establishing a relation between the pose form of the robot and the dynamic number by using mnj setting arrangement; when the analytic method is used for reverse solution, the corresponding preliminary reverse solution angle theta can be uniquely determined according to the provided dynamic table number1′～θ6'; then the joint angle theta is adjusted1′～θ6' used as iteration starting point, i.e. completed by inputting dynamic number->Transition to Joint Attribute->Uniquely determine shape and position>And outputting a dynamic table query step of an iteration starting point.
The invention has the beneficial effects that:
the invention relates to a real-time inverse solution method for a wrist offset type 6-axis robot, which is characterized in that on the basis of rapid convergence of an iteration method, an improved Gauss-Newton algorithm is used for completing calculation aiming at the problems that the iteration times of a common Newton-Raffson iteration method in the solution process are large and singular position type can not be solved. And for the problem that the iterative algorithm depends on the starting point to be close to the accurate solution, a dynamic table is introduced to complete the dynamic supply of the iterative starting point. The method is tested in the actual industrial application occasions of the robot, and the algorithm is verified to have high real-time performance and accuracy.
Drawings
FIG. 1 is an HSR-BR610 robot coordinate system;
FIG. 2 is a flow chart of a modified Gauss-Newton iteration method;
FIG. 3 is a 6-axis robot joint attribute partitioning;
FIG. 4 is a flow chart of an iterative algorithm based on a dynamic table.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
as shown in fig. 1: the wrist offset type 6R robot can be classified into 3 types of upper end offset, front end offset, and side end offset according to the geometry of the offset wrist. Taking the side-offset HSR-BR610 robot arm as an example, the robot tip J5 has a lateral offset that avoids J4, J6 joint interference and internal line kinking during pronation, increasing wrist flexibility and working range.
According to the Moddify-DH method, a coordinate system (figure 1) is established for each joint of the robot, and the parameters of the connecting rod are shown in a table 1.
TABLE 1 Link parameters of HSR-BR610 robot
Figure GDA0003557266370000061
Link transformation matrix for improved DH coordinate system
Figure GDA0003557266370000062
The expression general formula is:
Figure GDA0003557266370000063
substituting DH parameters into the transformation matrix right-multiplication rule to obtain the transformation matrix from the terminal link coordinate system {6} to the base coordinate system {0}, and
Figure GDA0003557266370000064
the following were used:
Figure GDA0003557266370000065
iterative algorithm based on dynamic tables:
modified gauss-newton method:
the Gauss-Newton method (Gauss-Newton) is simplified and modified on the basis of the Newton method, so that the method can be used for solving the nonlinear least square problem. The basic principle of the Gauss-Newton method is to use Taylor series expansion to approximately fit a nonlinear regression model, and then to correct the regression coefficient through multiple iterations until the sum of the residual squares of the original model | | rn| is less than error epsilon (epsilon)>0). Using the product J of the Jacobian matrix JTThe J approximation replaces a second-order Hansen matrix H in the Newton method, so that complex second-order matrix operation is omitted. The basic iterative formula is as follows:
xn+1＝xn-(JTJ)-1JTrn (3)
for a 6R robot, defining the Jacobian matrix J (theta) of velocity of the manipulator arm refers to the velocity vector from the joint
Figure GDA0003557266370000066
To the operating velocity vector
Figure GDA0003557266370000071
The general transmission ratio of the transmission, i.e.
Figure GDA0003557266370000072
Since velocity can be considered as a differential motion per unit time, the above equation is equivalent to a mapping of a differential motion D from joint space D θ to Cartesian space, i.e.
D＝J(θ)dθ (5)
Wherein D ═ dx dy dz δ x δ y δ z; j (theta) is a velocity Jacobian matrix obtained by differential transformation; by substituting the above formula (3) for the formula (5), a compound having a structure represented by the formula
θn+1＝θn-(JTJ)-1JTD (6)
When the iteration method is adopted to solve the target joint angle, the target joint angle can be converged to the target point simply and quickly. However, when the jacobian matrix xor is a pathologic matrix, a small differential motion D often causes a great change in joint angle, so that iteration cannot converge.
In order to solve the defects caused by matrix singularity, J is subjected to damping coefficient lambda introductionTInversion of J is replaced by pair (J)TJ + Lambda I), and the problems of singularity and ill-conditioned property of a Jacobian matrix are effectively avoided. Wherein I is an identity matrix of 6 th order, and lambda belongs to (0, 1)]。
θn+1＝θn-(JTJ+λI)-1JTD (7)
And in each iteration process, the coefficient lambda is adjusted according to the change of the iteration residual square sum e (the two-norm D of the residual vector D). When e isi<ei-1When the iteration residual is converged, the lambda is reduced; otherwise, the residual error is still larger, and the lambda is increased to control the iteration step size to converge quickly.
To reduce the amount of iterative computation, a damping coefficient λ is set prior to computation to accelerate convergence. And setting an upper limit imax of iteration times and residual error precision e, and establishing a termination condition to finish calculation or avoid overlong iteration time.
Dynamic table taking account of joint attributes
In the robot pose inverse solution calculation, the improved Gaussian-Newton normal target point is adopted for iterative convergence. When a computation based on the provided iteration starting point can successfully converge to the exact solution, we call this starting point close to the exact solution or the starting point is reliable. Conversely, when the starting point is far from the precise point or unreliable, it is often difficult to obtain the correct result quickly and effectively by relying on the iterative algorithm alone. Therefore, a dynamic table based on joint attributes and an analytic solution is introduced, an iteration starting point near a corresponding target point is provided by using the table, then the table is looked up according to the joint attributes to obtain a corresponding starting point for iterative computation, and finally, the accurate solution is obtained through rapid convergence. The basic idea of the dynamic table is as follows:
first, the kinematic model needs to be corrected. Setting the axial offset of the J5, J6 joints to 0, i.e., updating d 'on the basis of the DH parameters in Table 1'5＝0、d′60, and constructing a kinematic model according to equation (2)
Figure GDA0003557266370000081
Secondly, for the target point pose T provided by the offset 6R robotendAnd (6) correcting the deviation. Correcting the J6 axial offset in the target point position, and improving the corrected motion model
Figure GDA0003557266370000082
And correction target point location T'endThe workspace overlap ratio of (a). The correction formula is as follows
Figure GDA0003557266370000083
For meeting Pieper criterion after correction
Figure GDA0003557266370000084
And target point T'endResolution may be accomplished using analytical methods. The inverse transformation method is adopted to obtain 8 groups of preliminary joint space inverse solutions corresponding to the point poses.
At the moment, joint attributes are introduced, and the preliminary inverse solution is divided. According to the method, a singular bit pattern is used as a dividing boundary, and 3 boundary combinations of front and back, up and down and pitching are respectively adopted (as shown in figure 3), so that the bit pattern is divided into 8 groups of states. When the center point of the wrist of the robot is positioned on the rotation axis of the J1 joint, a plane formed by the axes of J1 and J2 is taken as a front boundary and a rear boundary, and two sides of the plane are respectively defined as front attributes and rear attributes; when the mechanical arm connecting rod 2 and the connecting rod 3 are parallel, a plane determined by the axes of the connecting rod 2 and the J3 is taken as a boundary, and the upper attribute and the lower attribute are respectively defined on two sides; when the axes of the joints J4 and J6 are parallel, the plane defined by the intersecting axes of the joints J4 and J5 is taken as a boundary, and the two sides are respectively defined as the pitch and the pitch attributes.
Taking the HSR-BR610 robot as an example, when a2 × c2+ d4 × s23 is more than or equal to 0, m is set to 0 to be the front attribute, and otherwise, 1 is set to be the rear attribute; when theta 3 is less than or equal to 90 degrees, n is set to be 0 to represent the lower attribute, otherwise, 1 is set to be the upper attribute; when theta 5 is less than or equal to 0 degree, j is placed at 0 degree to indicate depression, and conversely, 1 degree is placed at elevation.
Where ci is cos (θ i), si is sin (θ i), s23 is sin (θ 2+ θ 3), c23 is cos (θ 2+ θ 3), and so on; defining variables
Figure GDA0003557266370000091
k31＝p′xc1+p′ys1,
Figure GDA0003557266370000092
Figure GDA0003557266370000093
Figure GDA0003557266370000094
c4s5＝(axc1+ays1)c23+azs23,s23＝a2c3p′z+k31(a2s3+d4),
c23＝(-d4+a2s3)p′z+k31·a2c3；
TABLE 2 HSR-BR610 dynamic Table
Figure GDA0003557266370000095
As shown in table 2, the relationship between the pose shape of the robot and the dynamic number is established by using mnj setting arrangement. When the analytic method is used for reverse solution, the corresponding preliminary reverse solution angle theta can be uniquely determined according to the provided dynamic table number1′～θ6'. Then the joint angle theta is adjusted1′～θ6Used as iteration starting point, i.e.Completing the input of dynamic number->Transition to Joint Attribute->Uniquely determine shape and position>And outputting a dynamic table query step of an iteration starting point.
The algorithm flow comprises the following steps:
the solving steps of the algorithm are shown in figure 4 by combining the Gaussian-Newton iteration method and the dynamic table query.
Before the iterative algorithm starts, the target attribute Flg and the starting point attribute Flg0 are checked to judge whether the iteration starting point is reliable. And if the solution is unreliable, introducing a dynamic table to update the starting point, otherwise, directly using an improved Gauss-Newton algorithm to carry out iterative computation, and finally converging to obtain a unique solution matched with the Flg.
The foregoing shows and describes the general principles and features of the present invention, together with the advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present 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. A real-time inverse solution algorithm of a wrist offset type 6-axis robot is characterized by comprising the following steps:
s1: establishing a coordinate system for each joint of the robot, and obtaining connecting rod parameters; link transformation matrix for improved DH coordinate system
Figure FDA0003580950780000011
The expression general formula is:
Figure FDA0003580950780000012
substituting DH parameters into the transformation matrix right-multiplication rule to obtain the transformation matrix from the terminal link coordinate system {6} to the base coordinate system {0}, and
Figure FDA0003580950780000013
the following:
Figure FDA0003580950780000014
s2: repeating for many times, correcting regression coefficient until the residual square sum of original model | | | rn| is less than error epsilon (epsilon)>0) (ii) a Using the product J of the Jacobian matrix JTJ approximately replaces a second-order Hansen matrix H in a Newton method, so that complex second-order matrix operation is omitted; the basic iterative formula is as follows:
xn+1＝xn-(JTJ)-1JTrn (3)
for a 6R robot, defining the Jacobian matrix J (theta) of velocity of the manipulator arm refers to the velocity vector from the joint
Figure FDA0003580950780000017
To the operating velocity vector
Figure FDA0003580950780000015
The general transmission ratio of the transmission, i.e.
Figure FDA0003580950780000016
Since velocity can be considered as a differential motion per unit time, the above equation is equivalent to a mapping of a differential motion D from joint space D θ to Cartesian space, i.e.
D＝J(θ)dθ (5)
Wherein D ═ dx dy dz δ x δ y δ z; j (theta) is a velocity Jacobian matrix obtained by differential transformation; by substituting the above formula (3) for the formula (5), a compound having a structure represented by the formula
θn+1＝θn-(JTJ)-1JTD (6)
S3: in order to solve the defects caused by matrix singularity, J is subjected to damping coefficient lambda introductionTThe inversion of J is replaced by pair (J)TJ + Lambda I), the problem of singularity and ill-conditioned property of a Jacobian matrix is effectively avoided; wherein I is an identity matrix of 6 th order, and lambda belongs to (0, 1)]；
θn+1＝θn-(JTJ+λI)-1JTD (7)
In each iteration process, the coefficient lambda is adjusted according to the change of the iteration residual square sum e (the two norms of the residual vector D | | | D |); when e isi<ei-1When the iteration residual is converged, the lambda is reduced; otherwise, the residual error is still larger, and the lambda is increased to control the iteration step length to be rapidly converged;
s4: in order to reduce the amount of iterative operation, a damping coefficient lambda is set before calculation to accelerate convergence; setting an upper limit imax of iteration times and a residual error precision e, and establishing a termination condition to finish calculation or avoid overlong iteration time;
when the iteration starting point is far away from the precise point or unreliable;
firstly, a kinematic model needs to be corrected; setting the axial offset of J5 and J6 joints to 0, namely updating d 'on the basis of DH parameters'5＝0、d′60, and constructing a kinematic model according to equation (2)
Figure FDA0003580950780000021
Secondly, to avoid corrected unbiased models
Figure FDA0003580950780000022
The working space is reduced compared with that of the offset 6R robot; for a target point pose T provided by an offset 6R robotendCarrying out correction; correcting the J6 axial offset in the target point position, and improving the homomorphic unbiased model
Figure FDA0003580950780000023
And correction target point location T'endThe workspace overlap ratio of (a); the correction formula is as follows
Figure FDA0003580950780000024
For meeting Pieper criterion after correction
Figure FDA0003580950780000025
And target point T'endResolution can be accomplished by analytical methods; an inverse transformation method is adopted to obtain 8 groups of preliminary joint space inverse solutions corresponding to the position and posture of the point;
at the moment, introducing joint attributes, and dividing the preliminary inverse solution; dividing the bit patterns into 8 groups of states by respectively adopting front and back, upper and lower and pitching 3 boundary combinations by taking the singular bit patterns as dividing boundaries; when the center point of the wrist of the robot is positioned on the rotation axis of the J1 joint, a plane formed by the axes of J1 and J2 is taken as a front boundary and a rear boundary, and two sides of the plane are respectively defined as front attributes and rear attributes; when the connecting rods 2 and 3 of the mechanical arm are parallel, a plane determined by the axes of the connecting rods 2 and J3 is taken as a boundary, and two sides are respectively defined as upper attributes and lower attributes; when the axes of the joints J4 and J6 are parallel, a plane determined by the intersecting axes of the joints J4 and J5 is taken as a boundary, and the two sides are respectively defined as pitch and yaw attributes;
when a2 × c2+ d4 × s23 is more than or equal to 0, m is set to 0 to be the front attribute, and on the contrary, 1 is set to be the rear attribute; when theta 3 is less than or equal to 90 degrees, n is set to be 0 to represent the lower attribute, otherwise, 1 is set to be the upper attribute; when theta 5 is less than or equal to 0 degree, j is placed in a position of 0 to bow, otherwise, 1 is placed in a position of facing upward;
where ci is cos (θ i), si is sin (θ i), s23 is sin (θ 2+ θ 3), c23 is cos (θ 2+ θ 3), and so on; defining variables
Figure FDA0003580950780000031
k31＝p′xc1+p′ys1，
Figure FDA0003580950780000032
Figure FDA0003580950780000033
c5＝(axc1+ays1)s23-azc23，c4c5＝axs1-ayc1，c4s5＝(axc1+ays1)c23+azs23，s23＝a2c3p′z+k31(a2s3+d4)，c23＝(-d4+a2s3)p′z+k31·a2c3；
Establishing a relation between the pose form of the robot and the dynamic number by using mnj setting arrangement; when the analytic method is used for reverse solution, the corresponding preliminary reverse solution angle theta can be uniquely determined according to the provided dynamic table number1′～θ6'; then the joint angle theta is adjusted1′～θ6The method is used as an iteration starting point, namely, the dynamic table query step of inputting dynamic numbers- > converting into joint attributes- > uniquely determining form and position- > outputting the iteration starting point is completed;
on the basis of fast convergence of an iterative method, aiming at the problems that the common Newton-Lawson iterative method has more iteration times and the singular position type cannot be solved in the solving process, an improved Gauss-Newton algorithm is used for completing calculation; for the problem that the iterative algorithm depends on the starting point to be close to the accurate solution, a dynamic table is introduced to complete the dynamic supply of the iterative starting point; the method is tested in the actual industrial application occasions of the robot, and the algorithm is verified to have high real-time performance and accuracy.
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