CN108527373A - The parameter measurement of mechanical arm and discrimination method and device, terminal, storage medium - Google Patents
The parameter measurement of mechanical arm and discrimination method and device, terminal, storage medium Download PDFInfo
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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
- B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis
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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
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1671—Programme controls characterised by programming, planning systems for manipulators characterised by simulation, either to verify existing program or to create and verify new program, CAD/CAM oriented, graphic oriented programming systems
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Abstract
The present invention provides a kind of parameter identification method of mechanical arm, defines M DH parameters, and write out the homogeneous transform matrix between joint coordinate system；Each theoretical joint angle angle value is obtained, Method of Calculation of Robotic Movements model solution is substituted into and obtains theoretical terminal position and error expression；Actual end position is measured, and solves the error amount between the theory terminal position and actual end position；The terminal position for measuring multigroup artis is established system of linear equations and is solved the error amount of M DH parameters using least-squares algorithm；M DH parameters are corrected, revised terminal position is obtained using modified M DH parameters；Judge whether revised terminal position and the error of actual end position restrain, if the determination result is YES, then terminates flow.The present invention also provides a kind of measurement method of parameters of mechanical arm and parameter identification device, terminal installation and the storage mediums of device, mechanical arm.Using the embodiment of the present invention, parameter identification precision can be promoted.
Description
Technical Field
The invention relates to the technical field of robots, in particular to a method and a device for measuring parameters of a mechanical arm, a method and a device for identifying parameters of the mechanical arm, a terminal and a storage medium.
Background
This section is intended to provide a background or context to the implementation of the embodiments of the invention that is recited in the claims and the detailed description. The description herein is not admitted to be prior art by inclusion in this section.
With the vigorous development of aerospace industry in China, the space robot is more and more widely applied, and in a complex environment, the space robot is applied to capture and fault maintenance of satellites, assembly of spacecrafts and assistance of spacemen to finish space experiments. However, after the space robot enters the space flight orbit, due to the influence of complex space environments such as extreme cold, extreme heat and radiation, and the influence of non-geometric parameters such as elasticity, transmission error and return difference of joints and connecting rods of the space robot, the transfer matrix relationship between various kinematic parameters of the space robot and the pose of an actual terminal manipulator will change, the terminal precision of the robot changes along with the change, and the operation of the space robot is further influenced.
The existing parameter identification method of the mechanical arm comprises an extended Kalman filtering method, a Levenberg-Marquardt algorithm, a recursive linear equation, an extended Kalman filtering method and a rotating radius method based on an S model. The extended Kalman filtering method is used for identifying kinematic parameters and can process the uncertain problem in parameter estimation, but the method does not consider the error distribution condition, sometimes the parameter identification precision is low and the divergence is easy. The Levenberg-Marquardt algorithm combines a gradient descent method and a Newton method, and the calculation occupies a large memory space. The method is based on the rotation center and the rotation plane of the S model, and introduces methods such as the rotation radius and the like, so that the algorithm is complex and the operation difficulty is high.
Disclosure of Invention
In view of this, the present invention provides a method and an apparatus for identifying parameters of a robot arm, a method and an apparatus for measuring parameters of a robot arm, a terminal and a storage medium, which can improve the accuracy of identifying parameters of a robot arm.
The first aspect of the embodiments of the present invention provides a method for identifying parameters of a robot arm, where the method for identifying parameters of a robot arm includes:
step 1: defining M-DH parameters, and writing a homogeneous transformation matrix between joint coordinate systems according to the M-DH parameters;
step 2: obtaining the angle value of each theoretical joint, substituting the angle value into a positive solution model of the kinematics of the robot to solve to obtain a theoretical terminal position and an error expression;
and step 3: establishing a world coordinate system, carrying out parameter measurement to obtain an actual tail end position, and solving an error value between the theoretical tail end position and the actual tail end position;
and 4, step 4: measuring the tail end positions of a plurality of groups of joint points, establishing a linear equation set and solving the error value of the M-DH parameter by using a least square algorithm;
and 5: correcting the M-DH parameters, substituting the corrected M-DH parameters into a robot kinematics positive solution model to obtain a corrected terminal position;
step 6: comparing the error of the corrected tip position with the actual tip position;
and 7: judging whether the error is converged;
and 8: and continuing to measure the optimization model and returning to the step 2.
Further, in the method for identifying parameters of a robot arm provided in the embodiment of the present invention, the homogeneous transformation matrix is:
wherein, thetanIs the joint angle of the joint n, anLink length of link n, αnIs the torsion angle of the connecting rod n, dnIs a normal distance to the axis of the connecting rod n, βnThe torsional angle parameter of the connecting rod n is c is cos, and s is sin.
Further, in the method for identifying parameters of a mechanical arm provided in the embodiment of the present invention, the linear equation set is:
wherein,Land Y is the position error of the tail end of the robot.
In another aspect, an embodiment of the present invention provides a device for identifying parameters of a robot arm, where the device for identifying parameters of the robot arm includes:
the homogeneous transformation matrix calculation module is used for defining M-DH parameters and writing a homogeneous transformation matrix between joint coordinate systems according to the M-DH parameters;
the theoretical terminal position acquisition module is used for acquiring each theoretical joint angle value, substituting the values into the positive solution model of the robot kinematics to solve to obtain a theoretical terminal position and an error expression;
the error value calculation module is used for establishing a world coordinate system, measuring the actual tail end position and solving the error value between the theoretical tail end position and the actual tail end position;
the error value calculation module of the M-DH parameters is used for measuring the tail end positions of a plurality of groups of joint points, establishing a linear equation set and solving the error value of the M-DH parameters by utilizing a least square algorithm;
the parameter correction module is used for correcting the M-DH parameters, substituting the corrected M-DH parameters into the robot kinematics positive solution model to obtain a corrected tail end position;
an error comparison module for comparing the error between the corrected terminal position and the actual terminal position;
the convergence judging module is used for judging whether the error converges;
and the model optimization module is used for continuously measuring the optimization model.
A second aspect of the embodiments of the present invention provides a method for measuring parameters of a robot arm, where the method for measuring parameters of the robot arm includes:
establishing a terminal tool coordinate system;
acquiring a relation between a world coordinate system and the terminal tool coordinate system;
and calculating to obtain the actual terminal position according to the relation.
Further, in the parameter measurement method of the robot arm according to an embodiment of the present invention, the method for acquiring the world coordinate system includes:
placing the mechanical arm on a horizontal working platform, adjusting a control panel of the mechanical arm, and returning the mechanical arm to a zero position;
the control panel is utilized to enable the mechanical arm to rotate a first joint, and the laser tracker is used for measuring the positions of a plurality of groups of first rotating points;
fitting a rotation axis through the measured multiple groups of first rotation points to obtain an axis of the first joint;
adjusting a control panel of the mechanical arm, and returning the mechanical arm to a zero position;
the control panel is utilized to enable the mechanical arm to rotate a second joint, and the laser tracker is used for measuring the positions of a plurality of groups of second rotating points;
fitting a rotation axis through the measured multiple groups of second rotation points to obtain the axis of the second joint;
acquiring the coordinates of the intersection point of the axis of the first joint and the axis of the second joint;
calculating the origin coordinates of the world coordinate system according to the intersection point coordinates;
and obtaining a world coordinate system according to the origin coordinates.
Further, in the method for measuring parameters of a robot arm provided by an embodiment of the present invention, the method for establishing a coordinate system of an end tool includes:
placing a target ball of the laser tracker at the tail end of the mechanical arm, and measuring a plurality of groups of points on a tail end plane so as to fit the tail end plane;
the control panel is utilized to enable the mechanical arm to rotate the sixth joint, and the axis of the sixth joint is obtained;
establishing an end tool coordinate system based on the axis of the sixth joint.
In another aspect, an embodiment of the present invention provides a parameter measuring device for a robot arm, where the parameter measuring device for the robot arm includes:
the establishing module is used for establishing a terminal tool coordinate system;
the relation acquisition module is used for acquiring the relation between a world coordinate system and the terminal tool coordinate system;
and the calculation module is used for calculating to obtain the actual tail end position according to the relation.
In another aspect, the present invention further provides a terminal device, where the terminal device includes a processor, and the processor is configured to implement any one of the above-mentioned method for identifying a parameter of a robot arm and a method for measuring a parameter of a robot arm when executing a computer program stored in a memory.
An embodiment of the present invention further provides a computer-readable storage medium, on which computer instructions are stored, and the computer instructions, when executed by a processor, implement any one of the above steps of the method for identifying parameters of a robot arm and the method for measuring parameters of a robot arm.
The embodiment of the invention provides a method and a device for identifying parameters of a mechanical arm, a method and a device for measuring parameters of the mechanical arm, a terminal device and a computer readable storage medium, wherein M-DH parameters are defined, and a homogeneous transformation matrix between joint coordinate systems is written out; obtaining the angle value of each theoretical joint, substituting the angle value into a positive solution model of the kinematics of the robot to solve to obtain a theoretical terminal position and an error expression; measuring an actual terminal position and solving an error value between the theoretical terminal position and the actual terminal position; measuring the tail end positions of a plurality of groups of joint points, establishing a linear equation set and solving the error value of the M-DH parameter by using a least square algorithm; correcting the M-DH parameters, and obtaining corrected terminal positions by using the corrected M-DH parameters; and judging whether the error between the corrected tail end position and the actual tail end position is converged, and if so, ending the process. By using the embodiment of the invention, the precision of parameter identification can be improved.
Drawings
Fig. 1 is a flowchart of a method for identifying parameters of a robot arm according to a first embodiment of the present invention.
Fig. 2 is a schematic diagram of a Craig reference coordinate system model provided by the present invention.
Fig. 3 is a schematic structural diagram of a terminal according to an embodiment of the present invention.
Fig. 4 is an exemplary functional block diagram of the terminal shown in fig. 3.
Fig. 5 is a flowchart of a method for measuring a parameter of a robot arm according to a second embodiment of the present invention.
Fig. 6 is a schematic structural diagram of a terminal according to another embodiment of the present invention.
Fig. 7 is an exemplary functional block diagram of the terminal shown in fig. 6.
Fig. 8A is a real model diagram of UR5 provided in the present invention.
FIG. 8B is another real model diagram of UR5 provided by the present invention.
Fig. 8C is a joint coordinate system diagram of UR5 provided by the present invention.
Description of the main elements
| Terminal device | 1 |
| Memory device | 10 |
| Display screen | 20 |
| Processor with a memory having a plurality of memory cells | 30 |
| Homogeneous transformation matrix calculation module | 11 |
| Theoretical end position acquisition module | 12 |
| Error value calculation module | 13 |
| Error value calculation module of M-DH parameter | 14 |
| Parameter correction module | 15 |
| Error comparison module | 16 |
| Convergence judging module | 17 |
| Model optimization module | 18 |
| Building module | 19 |
| Relationship acquisition module | 20 |
| Computing module | 21 |
Detailed Description
So that the manner in which the above recited objects, features and advantages of embodiments of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof which are illustrated in the appended drawings. In addition, the features of the embodiments of the present application may be combined with each other without conflict.
In the following description, numerous specific details are set forth to provide a thorough understanding of embodiments of the invention, some, but not all embodiments of the invention. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without any creative effort belong to the protection scope of the embodiments of the present invention.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which embodiments of the present invention belong. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the embodiments of the invention.
Fig. 1 is a flowchart of a method for identifying parameters of a robot arm according to a first embodiment of the present invention. The method for identifying the parameters of the mechanical arm can comprise the following steps:
s101: M-DH parameters are defined, and a homogeneous transformation matrix between joint coordinate systems is written according to the M-DH parameters.
In one embodiment, it is assumed that one robot can be constructed in any form from a plurality of any number of links and joints. Taking the Craig reference coordinate system model as an example, as shown in fig. 2, fig. 2 is a schematic diagram of the Craig reference coordinate system model provided by the present invention. Three sequential joints and two links are shown in figure 2.Each joint may be rotatable or translatable. The first joint is designated as joint n (arranged from left to right), the second joint is joint n +1, and the third joint is joint n + 2. There may be other joints in front of and behind these joints. The link is also represented such that link n is located between joint n and joint n +1 and link n +1 is located between joint n +1 and joint n + 2. The z-axis and the origin of each joint are fixed on the front axis of the joint, the head and the tail of the two connecting rods are removed, and the axes of the two ends of each connecting rod in the middle are respectively provided with a normal. d represents the distance between the two normals (e.g., d as shown in FIG. 2n+1I.e. the axis Z at both ends of the connecting rod nn-1、ZnA is the length of the link (e.g., a is shown in fig. 2)nAnd an+1Length of link n and link n +1, respectively), α is link torsion angle (e.g., α, as shown in fig. 2)nAnd αn+1Respectively, link torsion angles of the link n and the link n + 1), and θ is a joint angle (e.g., as shown in fig. 2, θn、θn+1And thetan+2Joint angles of the joint n, the joint n +1, and the joint n +2, respectively). It will be appreciated that while these joints and links are not necessarily similar to those of any actual robot, they are quite common and can readily represent any joint of an actual robot. These joints may be rotational, translational, or both.
Before defining the M-DH parameters, a robot joint coordinate system needs to be established, and the method for establishing the robot joint coordinate system can comprise the following steps: determining the direction of the joint (for example, in the case of rotation, the direction of the rotation axis of the joint is the direction of the joint; in the case of translation, the direction of translation of the joint is the direction of the joint); selecting the Z coordinate axes of the joint coordinate system, wherein ZnThe direction of the coordinate axis is the same as the joint direction of the (n + 1) th joint; identifying Z-axis common normal, origin of coordinates O, of adjacent joint coordinate systemsnAt ZnAnd Zn+1On the common normal line of (c); according to Xn＝Zn*Zn+1Determining an X-axis of the joint coordinate system; according to the rule of right-handed screw Yn＝Zn*XnDeterminingAnd Y-axis of the joint coordinate system, thereby establishing a robot joint coordinate system.
Thus, the transformation formula between two adjacent joint coordinate systems can be obtained as follows:
and (3) performing homogeneous transformation on the formula 1 to obtain a homogeneous transformation matrix between two adjacent joint coordinate systems, wherein the homogeneous transformation matrix comprises 4 rows and 4 columns as follows:
for an N-degree-of-freedom robot, the transfer matrix from the base coordinate system to the end effector is:
the end position p of the robot can thus be found to be:
[p,1]T＝T·[0,0,0,1]Tequation 4
It will be appreciated that the above-described homogeneous coordinate transformation method is applied to model robot kinematics when αn| d | 0 | dn| → ∞. That is, when the joint axes of two adjacent connecting rods are parallel or nearly parallel, a small change in the joint axes will cause the parameter dnLarger variations and therefore modified D-H parameters are needed to overcome the above disadvantages. The corrected D-H model is still four parameters, namely joint angle thetanLength of connecting rod anTorsion angle αn、dn. When the axes of two adjacent connecting rod joints are parallel, dnFrom the torsional angle parameter βnInstead. According to the two conditions (the two adjacent connecting rod joint axes are parallel or not parallel)A unified expression is obtained, as follows:
for a transfer matrix T from the base coordinate system to the end effector, its differential transformation on the base coordinate can be expressed as:
a + dA ═ Trans (dx, dy, dz) Rot (k, d θ) a equation 6
If the coordinate system is converted into a specific coordinate system, and the specific coordinate system is represented by L, the specific coordinate system is transformed into a reference coordinate system as follows:
LdA＝A(Trans(Ldx,Ldy,Ldz)Rot(k,Ld θ) -I) equation 7
Namely:
LdA＝A·Ldelta equation 8
Further, it is possible to obtain:
LΔ＝A-1·LdA equation 9
By expressing the transition matrix a by a differential method, one can obtain:
substituting the coordinate transformation relation:
where δ x, δ y, and δ z respectively denote differential operators rotated around the axis X, Y, Z.
It can be understood that in an actual working environment, due to the influence of the mechanical structure of the robot and various physical fields, the various parameters of the robot slightly deviate from the standard parameters. Therefore, the error is analyzed by establishing a differential bias model. At this time, the above 4 rows and 4 columns conversion matrix can be expressed as:
in equation 13, c represents cos and s represents sin. Formula 13 is a homogeneous transformation matrix between the joint coordinate systems written according to the M-DH parameters.
S102: and obtaining the angle value of each theoretical joint, substituting the angle value into a kinematics forward solution model of the robot to solve to obtain a theoretical terminal position and an error expression.
In one embodiment, for a transformation matrix in a specific specified coordinate system, to obtain a specific kinematic error model, the differential may be used instead to take into account the effect of small changes in the D-H parameters on the actual recognition result. Now useRepresenting the actual homogeneous transformation matrix after considering the errors,representing a theoretical homogeneous transformation matrix, only considering differential transformations of a single joint n are:
through specific calculation, the following can be obtained:
from the above analysis, the position error and the posture error of the adjacent joints can be expressed by M-DH parameters:
converting equation 17 into a matrix multiplication is of the form:
it is understood that the model containing M-DH parameters is an M-DH parameter model.
S103: and establishing a world coordinate system, carrying out parameter measurement to obtain an actual tail end position, and solving an error value between the theoretical tail end position and the actual tail end position.
In one embodiment, a UR5 six degree-of-freedom robotic arm and a FARO corporation API laser tracker may be used for the measurements. The six degrees of freedom may include degrees of freedom of movement in the directions of three orthogonal axes x, y, and z and degrees of freedom of rotation about the three axes. Any one unconstrained object has 6 independent motions in space. The API laser tracker is a high-precision and large-size measurement work, and has the advantages of high measurement precision, real-time measurement, convenience in carrying, capability of directly measuring on site, large measurement range and the like. Has been widely used in the fields of aerospace, automobile manufacturing and military. The API laser tracker mainly comprises a laser head and a target, when laser emitted by the laser head irradiates the center of a target reflector, the reflector can return incident light along the original path, and when the laser is not positioned at the center of the reflector, the laser automatically rotates until the laser irradiates the center of the target.
The method of measuring the actual tip position may include: placing the mechanical arm on a smooth and horizontal working platform, adjusting a control panel of the UR5 mechanical arm, and returning the mechanical arm to a zero position; fixing a target ball seat of the API laser tracker on an arm rod of the mechanical arm by using a glue gun, placing the target ball into a ball seat, and enabling the mechanical arm to rotate a first joint by using a control panel; measuring the positions of multiple groups of rotation points by using a laser tracker, fitting the rotation axes through the measurement points, and obtaining the axis of the first joint as O0Z0(ii) a Adjusting the mechanical arm to a zero position by using a control panel, enabling the mechanical arm to rotate a second joint by using the control panel, measuring the positions of a plurality of groups of rotating points by using a laser tracker, fitting a rotating axis through the measuring points, and obtaining an axis of the second joint and recording the axis as O1Z1(ii) a The intersection of the axis of the first joint and the axis of the second joint is denoted as O1The coordinates (x) of O1 in the measurement coordinate system can be obtained1,y1,z1) (ii) a Placing the target ball on the working platform, measuring the positions of multiple points on the platform, fitting to obtain a horizontal platform surface, wherein the Z coordinate values of the points on the platform surface are the same in the measuring coordinate system and are marked as (x, y, Z)k) Subtracting the offset of the target sphere radius from the Z coordinate value by 19.2mm, and adding O1Move z downward1-zk+19.2mm, and obtaining an origin O of a world coordinate system; with point O as origin, O0Z0Is Z-axis positive, O1Z1The reverse direction of the coordinate system is the Y-axis forward direction, a right-hand coordinate system is established, and the established coordinate system is a world coordinate system O0-X0Y0Z0(ii) a Placing the target ball at the tail end of the mechanical arm, measuring multiple groups of points on the tail end plane, and fitting a tail end plane X6O6Y6(ii) a Rotating the sixth joint of the mechanical arm to obtain a joint axis O of the sixth joint6Z6With O6Z6For the Z-axis, an end tool coordinate system O is established6-X6Y6Z6Then O is6The point is the actual position point of the tail end to be measured; due to O6Difficult to measure directly, in laser trackersIn the measurement software, a world coordinate system O-XYZ and an end tool coordinate system O are established6-X6Y6Z6The actual end position point can be obtained according to the relation between the two points.
It can be understood that to measure the actual end position point under different motion states, only the end tool coordinate system needs to be continuously established, and the relationship between the world coordinate system and the end tool coordinate system is determined, so that the actual end position can be obtained. An error value between the theoretical tip position and the actual tip position can thus be solved.
S104: measuring the terminal positions of a plurality of groups of joint points, establishing a linear equation set and solving the error value of the M-DH parameters by using a least square algorithm.
In one embodiment, equation 18 is a differential representation of the differential change caused by the parameter error of the connecting rod n. Based on the actual measurements to be made on the robot end-tool coordinate system, it is therefore necessary to transform the error to the tool coordinate system. The differential transformation from link n to the tool coordinate system converts the single coordinate system error term to the end tool coordinate system with an error of:
in equation 19, the vector is taken from:
wherein, TnAnd representing a posture conversion matrix from the connecting rod n to the tail end of the mechanical arm.
The error of the tool coordinate system is the sum of all the errors transformed to the tool coordinate system by the single error, namely:
rewrite equation 21 to the following matrix form:
after an error model for robot parameter identification is established, a linear equation set, namely the formula 22, about the error quantity of the M-DH parameters can be obtained. The linear equation system theoretically includes robot end position errors and attitude errors. In actual experimental manipulation, the accurate value of the terminal coordinate system direction of the robot cannot be accurately measured, so that the kinematic parameters of the robot are identified only by using the terminal position error of the robot.
For linear system of equations to be solvedLY＝J·ΔX，LY represents the robot tip position error, which can be obtained by measurement. It can be understood that the N sets of M-DH parameters have 5N unknown parameters, and the end position error (Δ x, Δ y, Δ z) of each point includes three linear equations, so that in order to obtain the solution of the unknown parameters, it is necessary to satisfy that the number of linear equations is equal to or greater than the number of unknown parameters. Therefore, the number of the points of the end positions of the robot must be measured to be not less than K,and (4) respectively.
In equation 22, when J ∈ R3r×5N，LY∈R3r×1Calculating DeltaX ∈ R5N×1If Δ X is present, such that:
||LY-JΔX||2and obtaining a minimum value, wherein the delta X is the least square solution of the equation set.
The matrix J ∈ R3r×5NThe number of rows and columns is different, and the solution of the linear equation set cannot be solved directly according to the matrix inversion operation method. Therefore, only a least squares solution of the system of linear equations can be solved. For theLY ═ J · Δ X, in the system of equationsThe left and right sides of (a) simultaneously left multiply the transpose of matrix J, then there are:
JT·LY＝JTJ.DELTA.X equation 23
ΔX＝(JT·J)-1·JT·LY equation 24
When Δ X ═ JT·J)-1·JT·LY is |LY-JΔX||2And obtaining a minimum value, wherein the delta X at the moment is the least square solution of the over-determined nonlinear equation system. The overdetermined equation set refers to an equation set in which the number of equations is greater than the number of unknowns.
S105: and correcting the M-DH parameters, and substituting the corrected M-DH parameters into the robot kinematics positive solution model to obtain the corrected terminal position.
In one embodiment, solving a linear equation system about the error amount of the M-DH parameter according to a least square solution can obtain an error value of the M-DH parameter, and correcting the M-DH parameter according to the error value of the M-DH parameter. And substituting the M-DH parameters subjected to correction into a kinematics positive solution model to obtain the corrected tail end position of the robot.
S106: the error of the corrected tip position is compared with the actual tip position.
In an embodiment, a difference between the corrected end position and the actual end position may be calculated from the corrected end position value and the actual end position value of the robot.
S107: and judging whether the error is converged, if so, ending the process, otherwise, entering the step S108.
In one embodiment, convergence is an important tool in studying functions, meaning convergence to a point, approaching a certain value. If the judgment result is yes, the M-DH value after correction is shown to meet the kinematics positive solution model of the robot, and the process is ended. If the determination result is negative, the process proceeds to step S108.
S108: the optimization model continues to be measured and returns to step S102.
In this embodiment, the measurement optimization model specifically refers to a solving process of a least square method in an optimized M-DH parameter model. The method of optimizing a model may include: and measuring a plurality of groups of points in the whole motion space of the robot through the API laser tracker, and continuously performing iterative solution to eliminate accidental errors possibly caused by single solution.
The embodiment of the invention provides a method and a device for identifying parameters of a mechanical arm, a method and a device for measuring parameters of the mechanical arm, a terminal device and a computer readable storage medium, wherein M-DH parameters are defined, and a homogeneous transformation matrix between joint coordinate systems is written out; obtaining the angle value of each theoretical joint, substituting the angle value into a positive solution model of the kinematics of the robot to solve to obtain a theoretical terminal position and an error expression; measuring an actual terminal position and solving an error value between the theoretical terminal position and the actual terminal position; measuring the tail end positions of a plurality of groups of joint points, establishing a linear equation set and solving the error value of the M-DH parameter by using a least square algorithm; correcting the M-DH parameters, and obtaining corrected terminal positions by using the corrected M-DH parameters; and judging whether the error between the corrected tail end position and the actual tail end position is converged, and if so, ending the process. By utilizing the embodiment of the invention, the precision of parameter identification can be improved; the actual terminal pose of the robot is indirectly obtained by establishing a matrix relation between a world coordinate system and a terminal tool coordinate system, so that the problem of low precision of directly measuring the terminal pose of the mechanical arm is solved; the measurement precision is improved by adding one-time numerical settlement; the embodiment of the invention can accurately calibrate the points of the robot in the whole motion space, thereby solving the problem that the points in the whole motion space can not be measured due to the constraint condition of the joints of the mechanical arm in the traditional measuring method; the condition that the axes of adjacent joints of the robot are parallel is considered, joint parameters are corrected, and joint torsion angles are added, so that the result after identification is more reliable; the robot is identified by parameters based on the least square method, so that the algorithm complexity is reduced.
The above is a detailed description of the method provided by the embodiments of the present invention. The order of execution of the blocks in the flowcharts shown may be changed, and some blocks may be omitted, according to various needs. The following describes a terminal provided in an embodiment of the present invention.
An embodiment of the present invention further provides a terminal device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor executes the computer program to implement the steps of the method for identifying parameters of a robot arm and the method for measuring parameters of a robot arm in any one of the above embodiments.
Fig. 3 is a schematic structural diagram of a terminal according to an embodiment of the present invention, and as shown in fig. 3, the terminal 1 includes a memory 10, and the memory 10 stores a parameter identification device 100 of a robot arm. The terminal 1 may be an intelligent terminal such as a tablet computer and a personal digital assistant. The parameter identification device 100 of the mechanical arm can define M-DH parameters and write a homogeneous transformation matrix between joint coordinate systems according to the M-DH parameters; obtaining the angle value of each theoretical joint, substituting the angle value into a positive solution model of the kinematics of the robot to solve to obtain a theoretical terminal position and an error expression; establishing a world coordinate system, carrying out parameter measurement to obtain an actual tail end position, and solving an error value between the theoretical tail end position and the actual tail end position; measuring the tail end positions of a plurality of groups of joint points, establishing a linear equation set and solving the error value of the M-DH parameter by using a least square algorithm; correcting the M-DH parameters, substituting the corrected M-DH parameters into the kinematics positive solution model to obtain corrected terminal positions; comparing the error of the corrected tip position with the actual tip position; and judging whether the error is converged, and if so, ending the process. Therefore, the accuracy of the mechanical arm parameter identification can be improved.
In this embodiment, the terminal 1 may further include a display 20 and a processor 30. The memory 10 and the display screen 20 can be electrically connected with the processor 30 respectively.
The memory 10 may be of different types of memory devices for storing various types of data. For example, the memory or internal memory of the terminal 1 may be used, or a memory Card that can be externally connected to the terminal 1, such as a flash memory, an SM Card (Smart Media Card), an SD Card (Secure Digital Card), and the like. In addition, the memory 10 may include high speed random access memory, and may also include non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), at least one magnetic disk storage device, a Flash memory device, or other volatile solid state storage device. The memory 10 is used for storing various types of data, for example, various types of Applications (Applications) installed in the terminal 1, data set and acquired by applying the parameter identification method of the robot arm, and the like.
A display 20 is mounted to the terminal 1 for displaying information.
The processor 30 is used for executing the parameter identification method of the mechanical arm and various types of software installed in the terminal 1. The processor 30 includes, but is not limited to, a Central Processing Unit (CPU), a MicroController Unit (MCU), and other devices for interpreting computer instructions and Processing data in computer software.
The parameter identification apparatus 100 of the robot arm may include one or more modules stored in the memory 10 of the terminal 1 and configured to be executed by one or more processors (in this embodiment, a processor 30) to implement the embodiment of the present invention. For example, referring to fig. 4, the terminal 1 may include a homogeneous transformation matrix calculation module 11, a theoretical end position obtaining module 12, an error value calculation module 13, an error value calculation module 14 of an M-DH parameter, a parameter modification module 15, an error comparison module 16, a convergence determination module 17, and a model optimization module 18. The modules referred to in the embodiments of the present invention may be program segments that perform a specific function, and are more suitable than programs for describing the execution process of software in a processor.
It is understood that, in correspondence with the embodiments of the method for identifying parameters of the robot arm, the terminal 1 may include some or all of the functional modules shown in fig. 4, and the functions of the modules will be described in detail below. It should be noted that the same terms and specific explanations as used in the above embodiments of the method for identifying parameters of a robot arm may also be applied to the following functional descriptions of the modules. For brevity and to avoid repetition, further description is omitted.
The homogeneous transformation matrix calculation module 11 may be configured to define M-DH parameters and write a homogeneous transformation matrix between joint coordinate systems according to the M-DH parameters.
The theoretical terminal position obtaining module 12 may be configured to obtain each theoretical joint angle value, and substitute the values into the forward solution model of robot kinematics to obtain a theoretical terminal position and an error expression.
The error value calculation module 13 may be configured to establish a world coordinate system, measure an actual tip position, and solve for an error value between the theoretical tip position and the actual tip position.
The error value calculation module 14 for M-DH parameters may be configured to measure the end positions of multiple sets of joint points, establish a linear equation set, and solve the error value for M-DH parameters using a least squares algorithm.
The parameter modification module 15 may be configured to modify an M-DH parameter, and substitute the modified M-DH parameter into the kinematics positive solution model to obtain a modified end position.
The error comparison module 16 may be used to compare the error of the corrected tip position with the actual tip position.
The convergence judging module 17 may be configured to judge whether the error converges.
Model optimization module 18 may be used to continue measuring the optimized model.
Fig. 5 is a flowchart of a method for measuring a parameter of a robot arm according to a second embodiment of the present invention. As shown in fig. 5, the method for measuring the parameters of the robot arm may include the steps of:
s201: an end tool coordinate system is established.
In this embodiment, the method for establishing the coordinate system of the end tool may include: placing a target ball of the laser tracker at the tail end of the mechanical arm, and measuring a plurality of groups of points on a tail end plane so as to fit the tail end plane; the control panel is utilized to enable the mechanical arm to rotate the sixth joint, and the axis of the sixth joint is obtained; establishing an end tool coordinate system based on the axis of the sixth joint.
S202: a relationship between a world coordinate system and the end tool coordinate system is obtained.
In this embodiment, the method for establishing the world coordinate system may include: placing the mechanical arm on a smooth and horizontal working platform, adjusting a control panel of the mechanical arm, and returning the mechanical arm to a zero position; the control panel is utilized to enable the mechanical arm to rotate a first joint, and the laser tracker is used for measuring the positions of a plurality of groups of first rotating points; fitting a rotation axis through the measured multiple groups of first rotation points to obtain an axis of the first joint; adjusting a control panel of the mechanical arm, and returning the mechanical arm to a zero position; the control panel is utilized to enable the mechanical arm to rotate a second joint, and the laser tracker is used for measuring the positions of a plurality of groups of second rotating points; fitting a rotation axis through the measured multiple groups of second rotation points to obtain the axis of the second joint; acquiring the coordinates of the intersection point of the axis of the first joint and the axis of the second joint; calculating the origin coordinates of the world coordinate system according to the intersection point coordinates; and obtaining a world coordinate system according to the origin coordinates.
S203: and calculating to obtain the actual terminal position according to the relation.
In this embodiment, to measure the actual end position point in different motion states, only the end tool coordinate system needs to be continuously established, and the relationship between the world coordinate system and the end tool coordinate system is determined, so that the actual end position can be obtained.
Fig. 6 is a schematic structural diagram of a terminal according to another embodiment of the present invention. As shown in fig. 6, the terminal 1 includes a memory 10, and the memory 10 stores a parameter measuring device 200 of the robot arm. In this embodiment, the terminal 1 may further include a display 20 and a processor 30. The memory 10 and the display screen 20 can be electrically connected with the processor 30 respectively. It should be noted that the same terms and specific explanations as used in the above embodiments of the method for identifying parameters of a robot arm may also be applied to the following description of the method for measuring parameters of a robot arm. For brevity and to avoid repetition, further description is omitted.
The robot arm parameter measuring device 200 may include one or more modules stored in the memory 10 of the terminal 1 and configured to be executed by one or more processors (in this embodiment, a processor 30) to implement the embodiments of the present invention. For example, referring to fig. 7, the terminal 1 may include an establishing module 19, a relationship obtaining module 20, and a calculating module 21. The modules referred to in the embodiments of the present invention may be program segments that perform a specific function, and are more suitable than programs for describing the execution process of software in a processor.
It is understood that, in correspondence with the embodiments of the method for identifying parameters of the robot arm, the terminal 1 may include some or all of the functional modules shown in fig. 7, and the functions of the modules will be described in detail below.
The setup module 19 may be used to set up the end tool coordinate system.
The relationship acquisition module 20 may be used to acquire the relationship between the world coordinate system and the end tool coordinate system.
The calculation module 21 may be configured to calculate the actual tip position based on the relationship.
Fig. 8A is an entity model diagram of UR5 provided by the present invention, fig. 8B is another entity model diagram of UR5 provided by the present invention, and fig. 8C is a joint coordinate system diagram of UR5 provided by the present invention. As shown in fig. 8A, 8B and 8C, the UR5 robot arm has an open-chain joint structure with 6 degrees of freedom, referring to the structure of a human arm, so thatThe arm end effector can achieve any pose in space. Establishing a corresponding coordinate system for a given mechanical arm at each joint point thereof, comprising: 0 coordinate system (e.g., 0 coordinate system O)0-X0Y0Z0) 1 coordinate system, 2 coordinate system, 3 coordinate system, 4 coordinate system, 5 coordinate system and 6 coordinate system (fig. 8A shows 0 coordinate system, 1 coordinate system and 2 coordinate system, and fig. 8B shows 2 coordinate system, 3 coordinate system, 4 coordinate system, 5 coordinate system and 6 coordinate system. The numbers 0-6 in fig. 8A and 8B correspond to the positions of the 0-6 coordinate system, respectively). Wherein the Z axis of each coordinate system is coincident with the straight line where the corresponding joint rotating shaft is located.
An embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the method for identifying parameters of a robot arm and the method for measuring parameters of a robot arm in any of the above embodiments.
The module/unit integrated with the parameter identification device of the robot arm/the parameter measurement device of the robot arm/the terminal/the computer device may be stored in a computer-readable storage medium if it is implemented in the form of a software functional unit and sold or used as a separate product. Based on such understanding, all or part of the flow in the method according to the above embodiments may be implemented by a computer program, which may be stored in a computer-readable storage medium and used by a processor to implement the steps of the above method embodiments. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable storage medium may include: any entity or device capable of carrying the computer program code, cache media, usb disks, removable hard disks, magnetic disks, optical disks, computer Memory, Read-Only Memory (ROM), Random Access Memory (RAM), electrical carrier signals, telecommunications signals, and software distribution media, to name a few.
The Processor may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic, discrete hardware components, etc. The general purpose processor may be a microprocessor or the processor may be any conventional processor or the like, the processor being the control center of the parameter identification device/parameter measurement device/terminal of the robot, the various parts of the parameter identification device/parameter measurement device/terminal of the entire robot being connected by various interfaces and lines.
The memory is used for storing the computer program and/or the module, and the processor realizes various functions of the parameter identification device of the mechanical arm/the parameter measuring device/terminal of the mechanical arm by running or executing the computer program and/or the module stored in the memory and calling data stored in the memory. The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required for at least one function (such as a sound playing function, an image playing function, etc.), and the like. In addition, the memory may include high speed random access memory, and may also include non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), at least one magnetic disk storage device, a Flash memory device, or other volatile solid state storage device.
In the several embodiments provided in the present invention, it should be understood that the disclosed terminal and method can be implemented in other manners. For example, the system embodiments described above are merely illustrative, and for example, the division of the modules is only one logical functional division, and other divisions may be realized in practice.
It will be evident to those skilled in the art that the embodiments of the present invention are not limited to the details of the foregoing illustrative embodiments, and that the embodiments of the present invention are capable of being embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the embodiments being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned. Several units, modules or means recited in the system, apparatus or terminal claims may also be implemented by one and the same unit, module or means in software or hardware.
Although the embodiments of the present invention have been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the embodiments of the present invention.
Claims (10)
1. A method for identifying parameters of a mechanical arm comprises the following steps:
step 1: defining M-DH parameters, and writing a homogeneous transformation matrix between joint coordinate systems according to the M-DH parameters;
step 2: obtaining the angle value of each theoretical joint, substituting the angle value into a positive solution model of the kinematics of the robot to solve to obtain a theoretical terminal position and an error expression;
and step 3: establishing a world coordinate system, carrying out parameter measurement to obtain an actual tail end position, and solving an error value between the theoretical tail end position and the actual tail end position;
and 4, step 4: measuring the tail end positions of a plurality of groups of joint points, establishing a linear equation set and solving the error value of the M-DH parameter by using a least square algorithm;
and 5: correcting the M-DH parameters, substituting the corrected M-DH parameters into a robot kinematics positive solution model to obtain a corrected terminal position;
step 6: comparing the error of the corrected tip position with the actual tip position;
and 7: judging whether the error is converged, if so, ending the flow, otherwise, entering the step 8;
and 8: and continuing to measure the optimization model and returning to the step 2.
2. The method of claim 1, wherein the homogeneous transformation matrix is:
wherein, thetanIs the joint angle of the joint n, anLink length of link n, αnIs the torsion angle of the connecting rod n, dnNormal distance to the axis of the connecting rod n, βnThe torsional angle parameter of the connecting rod n is c is cos, and s is sin.
3. The method for identifying parameters of a mechanical arm according to claim 1, wherein the system of linear equations is:
wherein,Land Y is the position error of the tail end of the robot.
4. A parameter identification device of a robot arm, comprising:
the homogeneous transformation matrix calculation module is used for defining M-DH parameters and writing a homogeneous transformation matrix between joint coordinate systems according to the M-DH parameters;
the theoretical terminal position acquisition module is used for acquiring each theoretical joint angle value, substituting the values into the positive solution model of the robot kinematics to solve to obtain a theoretical terminal position and an error expression;
the error value calculation module is used for establishing a world coordinate system, measuring the actual tail end position and solving the error value between the theoretical tail end position and the actual tail end position;
the error value calculation module of the M-DH parameters is used for measuring the tail end positions of a plurality of groups of joint points, establishing a linear equation set and solving the error value of the M-DH parameters by utilizing a least square algorithm;
the parameter correction module is used for correcting the M-DH parameters, substituting the corrected M-DH parameters into the robot kinematics positive solution model to obtain a corrected tail end position;
an error comparison module for comparing the error between the corrected terminal position and the actual terminal position;
the convergence judging module is used for judging whether the error converges;
and the model optimization module is used for continuously measuring the optimization model.
5. A parameter measuring method applied to the robot arm of claim 1, characterized in that the parameter measuring method of the robot arm comprises:
establishing a terminal tool coordinate system;
acquiring a relation between a world coordinate system and the terminal tool coordinate system;
and calculating to obtain the actual terminal position according to the relation.
6. The method for measuring the parameters of the mechanical arm according to claim 5, wherein the method for acquiring the world coordinate system comprises the following steps:
placing the mechanical arm on a horizontal working platform, adjusting a control panel of the mechanical arm, and returning the mechanical arm to a zero position;
the control panel is utilized to enable the mechanical arm to rotate a first joint, and the laser tracker is used for measuring the positions of a plurality of groups of first rotating points;
fitting a rotation axis through the measured multiple groups of first rotation points to obtain an axis of the first joint;
adjusting a control panel of the mechanical arm, and returning the mechanical arm to a zero position;
the control panel is utilized to enable the mechanical arm to rotate a second joint, and the laser tracker is used for measuring the positions of a plurality of groups of second rotating points;
fitting a rotation axis through the measured multiple groups of second rotation points to obtain the axis of the second joint;
acquiring the coordinates of the intersection point of the axis of the first joint and the axis of the second joint;
calculating the origin coordinates of the world coordinate system according to the intersection point coordinates;
and obtaining a world coordinate system according to the origin coordinates.
7. A method of measuring parameters of a robotic arm as claimed in claim 5, wherein the method of establishing an end tool coordinate system comprises:
placing a target ball of the laser tracker at the tail end of the mechanical arm, and measuring a plurality of groups of points on a tail end plane so as to fit the tail end plane;
the control panel is utilized to enable the mechanical arm to rotate the sixth joint, and the axis of the sixth joint is obtained;
establishing an end tool coordinate system based on the axis of the sixth joint.
8. A parameter measuring device of a robot arm, characterized by comprising:
the establishing module is used for establishing a terminal tool coordinate system;
the relation acquisition module is used for acquiring the relation between a world coordinate system and the terminal tool coordinate system;
and the calculation module is used for calculating to obtain the actual tail end position according to the relation.
9. A terminal device comprising a processor, wherein the processor is configured to implement the steps of the method for identifying parameters of a robot arm according to any one of claims 1 to 3 and the method for measuring parameters of a robot arm according to any one of claims 5 to 7 when executing a computer program stored in a memory.
10. A computer readable storage medium having stored thereon computer instructions, wherein the computer instructions, when executed by a processor, perform the steps of the method for parameter identification of a robot arm according to any of claims 1-3 and the method for parameter measurement of a robot arm according to any of claims 5-7.
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| WO2023216466A1 (en) * | 2022-05-07 | 2023-11-16 | 北京长木谷医疗科技有限公司 | End tool error detection method and device for orthopedic surgical robot |
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