CN116587289A - Seven-degree-of-freedom wrist joint bias mechanical arm inverse solution method, system and medium - Google Patents
Seven-degree-of-freedom wrist joint bias mechanical arm inverse solution method, system and medium Download PDFInfo
- Publication number
- CN116587289A CN116587289A CN202310870918.0A CN202310870918A CN116587289A CN 116587289 A CN116587289 A CN 116587289A CN 202310870918 A CN202310870918 A CN 202310870918A CN 116587289 A CN116587289 A CN 116587289A
- Authority
- CN
- China
- Prior art keywords
- mechanical arm
- joint
- degree
- coordinate system
- rotation angle
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 44
- 210000003857 wrist joint Anatomy 0.000 title claims abstract description 33
- 210000000323 shoulder joint Anatomy 0.000 claims abstract description 14
- 230000014509 gene expression Effects 0.000 claims description 30
- 239000011159 matrix material Substances 0.000 claims description 13
- 230000009466 transformation Effects 0.000 claims description 12
- 210000000707 wrist Anatomy 0.000 claims description 12
- 230000000593 degrading effect Effects 0.000 claims description 4
- 238000004590 computer program Methods 0.000 claims description 3
- 230000008859 change Effects 0.000 claims description 2
- 238000003860 storage Methods 0.000 claims description 2
- 238000004458 analytical method Methods 0.000 abstract description 7
- 210000001503 joint Anatomy 0.000 description 8
- 238000004364 calculation method Methods 0.000 description 6
- 238000004804 winding Methods 0.000 description 4
- 230000008901 benefit Effects 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- GIYXAJPCNFJEHY-UHFFFAOYSA-N N-methyl-3-phenyl-3-[4-(trifluoromethyl)phenoxy]-1-propanamine hydrochloride (1:1) Chemical compound Cl.C=1C=CC=CC=1C(CCNC)OC1=CC=C(C(F)(F)F)C=C1 GIYXAJPCNFJEHY-UHFFFAOYSA-N 0.000 description 2
- 239000004973 liquid crystal related substance Substances 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 238000000844 transformation Methods 0.000 description 2
- 238000004378 air conditioning Methods 0.000 description 1
- 230000004888 barrier function Effects 0.000 description 1
- 238000004422 calculation algorithm Methods 0.000 description 1
- 239000003054 catalyst Substances 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 239000012636 effector Substances 0.000 description 1
- 210000002310 elbow joint Anatomy 0.000 description 1
- 238000003825 pressing Methods 0.000 description 1
- 230000001131 transforming effect Effects 0.000 description 1
Classifications
-
- 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
-
- 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
- B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
-
- 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
- B25J9/1612—Programme controls characterised by the hand, wrist, grip control
Landscapes
- Engineering & Computer Science (AREA)
- Automation & Control Theory (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Health & Medical Sciences (AREA)
- General Health & Medical Sciences (AREA)
- Orthopedic Medicine & Surgery (AREA)
- Artificial Intelligence (AREA)
- Evolutionary Computation (AREA)
- Fuzzy Systems (AREA)
- Software Systems (AREA)
- Manipulator (AREA)
Abstract
The application relates to the technical field of robot kinematics control methods, in particular to a seven-degree-of-freedom wrist joint offset mechanical arm inverse solution method, a system and a medium. The application provides a novel thought for solving the inverse kinematics of a mechanical arm in a narrow space in a cabin, which aims at solving the problem that the on-orbit operation wrist joint offset mechanical arm facing space constraint is realized by inverting a shoulder joint and a wrist joint, wherein the three axes of the shoulder joint of the mechanical arm with the configuration are orthogonal to one point, but the wrist joint is provided with offset, the conventional inverse kinematics analysis method cannot realize, and the position and the gesture are decoupled by inverting the shoulder joint to solve the joint angle.
Description
Technical Field
The application relates to the technical field of robot kinematics control methods, in particular to a seven-degree-of-freedom wrist joint offset mechanical arm inverse solution method, a system and a medium.
Background
The mechanical arm for ground application generally does not need to consider space constraint, but space station cabin operation is performed by adopting a seven-degree-of-freedom wrist offset mechanical arm, particularly an elbow and wrist offset mechanical arm due to space constraint problem. The robot with three joints at the tail end not intersecting at one point or three axes not parallel is commonly called a wrist joint offset mechanical arm, and the mechanical arm has the characteristics of high structural strength and flexible movement.
The existing mechanical arm inverse kinematics solution has two methods of analysis and numerical method, and can solve the joint angle of the mechanical arm under the condition of given terminal position and posture. However, the numerical method requires Jie Yake to be larger than a matrix, particularly for mechanical arms with more than 7 joints and redundant degrees of freedom, the calculation amount of the solution of the Jacobian pseudo-inverse matrix is large, the main frequency of an on-orbit chip is low, the calculation capability of the on-orbit chip cannot solve the Jacobian pseudo-inverse matrix in real time, namely the seven-degree-of-freedom wrist joint bias mechanical arm cannot be solved by adopting a numerical method, and only can be solved by adopting an analytic method with a clear expression.
However, the reverse kinematics solution is difficult due to the generation of the wrist bias of the mechanical arm, and the solution is difficult to be carried out by adopting an analytic method, so that the technical bias that the 7-degree-of-freedom wrist bias mechanical arm is difficult to be applied to the aerospace field is generated.
Disclosure of Invention
The technical problems solved by the application are as follows: the defects of the prior art are overcome, and the inverse solution method of the seven-degree-of-freedom wrist joint offset mechanical arm is provided, and the joint angle is solved by decoupling the position and the posture through the inversion of the shoulder joint and the wrist joint, so that the problem of inverse kinematics analytic solution of the seven-degree-of-freedom wrist joint offset mechanical arm, in particular the elbow and wrist offset mechanical arm, which is subjected to on-orbit operation and faces space constraint is solved. The technical scheme provides a new idea for solving inverse kinematics of the mechanical arm in a narrow space in the cabin.
The technical scheme of the application is as follows: the inverse solution method of the seven-degree-of-freedom wrist joint offset mechanical arm is based on the seven-degree-of-freedom mechanical arm, wherein the wrist joint of the mechanical arm is offset, and the three axes of the shoulder joint of the mechanical arm are orthogonal to one point;
a seven-degree-of-freedom wrist joint bias mechanical arm inverse solution method is characterized in that: based on a seven-degree-of-freedom mechanical arm, the wrist joint of the mechanical arm is offset, and the three axes of the shoulder joint of the mechanical arm are orthogonal to one point;
the inverse solution method of the mechanical arm comprises the following steps S1-S4:
s1, establishing an inverted D-H coordinate system of the mechanical arm, wherein a base coordinate system O x y z0-000 Is fixed at the center of the tail end joint of the wrist joint of the mechanical arm, and the tail end coordinate system O x y z7-777 The shoulder joint base center of the mechanical arm is fixed;
calibrating an inversion D-H parameter of the mechanical arm according to the inversion D-H coordinate system of the mechanical arm, wherein the inversion D-H parameter is a rod torsion angle alpha corresponding to the connecting rod i i Length of rod a i Distance d of joint i And joint rotation angle theta i Wherein i=1, …,7; at this time, θ 5 、θ 6 、θ 7 To affect only the joint rotation angle of the posture, theta 1 、θ 2 、θ 3 、θ 4 Joint rotation angle for influencing position;
s2, degrading the degree of freedom, and presetting the joint rotation angle of any affected position as a constant with a value interval of [ -pi, pi ];
s3, carrying out positive kinematics solving after the mechanical arm is inverted according to the inverted D-H parameters set in the step S1;
according to the general formula of the change of the connecting rod
，
Wherein c represents cos, s represents sin;
obtaining an inverted positive kinematic transformation matrix:
，（1）；
wherein px, py and pz represent positional expressions in three directions of x, y and z; wherein nx, sx, ax represent x-direction posture expressions; ny, sy, ay represent y-direction pose expressions; nz, sz, az represent z-direction pose expressions;
s4, according to the positive kinematic transformation matrix in the step S3, decoupling the position and the gesture of the mechanical arm to obtain a resolving result:
θ=[θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ 7 ]；
step S4 includes the following steps S41-S42:
s41, substituting constant joint rotation angle values affecting the position according to the position expression, and solving three variable joint rotation angles affecting the position;
s42, according to the gesture expression, solving three joint rotation angle expressions theta affecting the gesture 5 、θ 6 、θ 7 。
The mechanical arm system is based on the inverse solution method of the seven-degree-of-freedom wrist joint offset mechanical arm, and comprises a mechanical arm, wherein the mechanical arm is a seven-degree-of-freedom mechanical arm, the mechanical arm wrist joint is offset, and the three axes of the mechanical arm shoulder joint are orthogonal to one point.
A computer readable storage medium storing a computer program which when executed by a processor performs the steps of the method of the seven degree of freedom wrist offset robotic arm inverse solution method.
Compared with the prior art, the application has the advantages that:
(1) The application provides a seven-degree-of-freedom wrist joint offset mechanical arm inverse solution method, which is applicable to a low-calculation chip by using a mechanical arm with offset wrist joints and non-offset shoulder joints, changing a conventional mechanical arm D-H coordinate system establishing method, establishing a mechanical arm inverted D-H coordinate system, adopting an analytic method, and solving expressions of other 6 joint angles after degrading joint angles at one position. Therefore, the inverse solution method of the seven-degree-of-freedom wrist joint offset mechanical arm provided by the application enables the seven-degree-of-freedom wrist joint offset mechanical arm to be suitable for application scenes such as aerospace and the like which adopt low-computation chips. The technical prejudice that the seven-degree-of-freedom wrist joint bias mechanical arm cannot be solved by using an analytic method and is difficult to apply to the application scene of aerospace and the like adopting a low-calculation-force chip is broken.
(2) The application provides a seven-degree-of-freedom wrist joint offset mechanical arm inverse solution method, which is based on a seven-degree-of-freedom wrist joint offset configuration mechanical arm, in particular to an elbow wrist offset configuration mechanical arm, can solve the problem that an inverse kinematics conventional analytic solution method cannot solve, and avoids adopting a method for carrying out numerical solution with large calculation amount, so that the method has the technical advantage of being convenient for on-orbit application.
(3) The application provides a mechanical arm system which can be used in the scenes of space stations, surface detection of an extraterrestrial celestial body, on-orbit construction of a large spacecraft and the like, and the technical advantage of fine operation of an on-orbit mechanical arm in a narrow space is realized in the scenes.
Drawings
FIG. 1 is a schematic illustration of a robotic arm having an elbow and wrist offset configuration to be solved according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a conventional D-H coordinate system setting rule of a mechanical arm to be solved according to an embodiment of the application;
FIG. 3 is a table of parameters obtained by calibration of a conventional D-H coordinate system of a mechanical arm to be solved according to an embodiment of the present application;
FIG. 4 is a schematic diagram of a setting rule of an inverted D-H coordinate system of a mechanical arm to be solved according to an embodiment of the application;
FIG. 5 is a table of parameters obtained by calibration under an inverted D-H coordinate system of a mechanical arm to be solved according to an embodiment of the application;
fig. 6 is a schematic diagram of position and posture decoupling after the mechanical arm to be solved is inverted according to the embodiment of the application.
Detailed Description
The application is described in further detail below with reference to the drawings and the specific embodiments.
As shown in fig. 1, the mechanical arm to be solved in the embodiment is an elbow-wrist offset mechanical arm, the three axes of the three joints corresponding to the shoulder joint are orthogonal to one point, the elbow joint and the wrist joint have offset, and the conventional inverse kinematics analysis method cannot solve the inverse kinematics solving problem of the elbow-wrist offset mechanical arm. The mechanical arm of this embodiment has 7 joints, and the lower part is the base, and the mechanical arm has 6 joints and can realize the omnidirectional operation, has the mechanical arm of 7 joints more than as redundant mechanical arm, and unnecessary one joint can be realized avoiding the barrier or as the backup use under the trouble.
Corresponding to the mechanical arm, the seven-degree-of-freedom wrist joint bias mechanical arm inverse solution method of the embodiment comprises the following steps:
s1, establishing a mechanical arm inversion D-H coordinate system, and calibrating mechanical arm inversion D-H parameters.
As shown in fig. 2, for the robot arm to be solved in the present embodiment, the conventional D-H coordinate system setting rule is as follows,
1) Establishing a base coordinate system: the intersection point of the ground on the base and the axis of the joint 1 is taken as an origin O 0 The positive direction of the motion axis of the joint 1 isz 0 Shaft, establishing right-hand orthogonal coordinate system O x y z0-000 Wherein x is 0 The direction of the axis being z 0 ×z 1 Wherein z is 1 Is the positive direction of the motion axis of the joint 2, y 0 Axis and x 0 ，z 0 In the right-hand system, i.e. y 0 The direction of the axis being z 0 ×x 0 ；
2) For each connecting rodi(i＝1、…，7) Completing 3 to 6 steps;
3) Each connecting rodi, establishing a coordinate system;establishing a connecting rodi, iOf a coordinate systemzShaft (i.ez i The axis) is the joint axis (the joint can only rotate around one axis): by jointsiThe positive direction of the motion (rotation) axis of +1 isz i A shaft; (joint number from proximal to distal is sequentially increased by 1);
4) Establishing a connecting rodiOrigin of coordinate systemO i : if it isz i Andz i-1 the axes intersect, then take intersection point of two axes as origin; if it isz i Andz i-1 the axes are different or parallel, and the common perpendicular lines of the two axes are used for connecting withz i Intersection of axesThe point is the origin;
5) Establishing a connecting rodiOf a coordinate systemxShaft (i.ex i Shaft): pressing the buttonx i ＝Establishment ofx i Shafts, i.e.x i Shaft and method for producing the samez i-1 A kind of electronic device with high-pressure air-conditioning systemz i The axes are vertical at the same time; if it isz i-1 And (3) withz i Axes being parallel, the common perpendicular line thereof beingx i A shaft;
6) Establishing a connecting rodiOf a coordinate systemyShaft (i.ey i Shaft): according to the establishment ofx i Shaft and method for producing the samez i Shaft, set up according to right hand ruley i Shaft, i.e. ordery i 。
Definition: torsion angle of rod pieceα i : winding machinex i The shaft rotates, fromz i-1 Rotate toz i Is a corner of (2);
length of roda i : edge of the framex i Shaft, slavez i-1 The shaft moves toz i The distance of the axis;
joint distanced i : edge of the framez i-1 Shaft, slavex i-1 Move tox i Is a distance of (2);
joint cornerθ i : winding machinez i-1 The shaft rotates, fromx i-1 Rotate tox i Is a function of the angle of (a).
The conventional D-H coordinate system setting rule is adopted, and in this embodiment, the calibration D-H parameters of the mechanical arm to be solved are obtained as a table shown in fig. 3.
In the embodiment, in step S1, an inverted D-H coordinate system of the mechanical arm is established. Specific: handle baseStandard series O x y z0-000 The center of the wrist joint tail end joint of the mechanical arm, namely the center of the forward tail end joint; coordinates of the end of the shaft x y z7-777 Is positioned at the center of the shoulder joint base of the mechanical arm, namely the center of the forward base. In the present embodiment, the intersection point of the axes of the joint 1 and the joint 2 is taken as the origin O 0 The positive direction of the motion axis of the joint 1 isz 0 Shaft, establishing right-hand orthogonal coordinate system O x y z0-000 Wherein, the method comprises the steps of, wherein,x 0 is z in the direction of 0 ×z 1 ，z 1 Is the positive direction of the axis of motion of the joint 2,y 0 axis and x 0 ，z 0 In the right-hand system, i.e. y 0 The direction of the axis being z 0 ×x 0 . With respect to the end coordinate system O in the rule of setting the conventional D-H coordinate system x y z7-777 The position (shown in fig. 2) is directly replaced by a base coordinate system of an inverted D-H coordinate system, so that the offset can be reduced, and the algorithm can be simplified. In the embodiment, the intersection point of the ground on the base and the axis of the joint 7 is taken as the origin O 7 The positive direction of the motion axis of the terminal coordinate system isz 7 Shaft, establishing right-hand orthogonal coordinate system O x y z7-777 Wherein, the method comprises the steps of, wherein,x 7 the axial direction is z 5 ×z 6 ，z 5 And z 6 The positive direction of the axis of motion of the joint 6 and the joint 7 respectively,y 7 axis and x 7 ，z 7 In the right-hand system, i.e. y 7 The direction of the axis being z 7 ×x 7 . As shown in fig. 4, the robot arm inversion D-H coordinate system is re-established. As shown in fig. 5, the calibration robot arm inverts the D-H parameters.
At this time, θ 5 、θ 6 、θ 7 To affect only the joint rotation angle of the posture, theta 1 、θ 2 、θ 3 、θ 4 To affect the joint rotation angle of the position.
And S2, degrading the degree of freedom, and presetting the joint rotation angle of any affected position as constant con, wherein the value interval of con is [ -pi, pi ].
In order to realize the analytic solution, the 7 degrees of freedom are firstly degraded to 6 degrees of freedom, namely, a certain joint is fixed, so that the corresponding joint angle of the connecting rod is a fixed value, and then the joint angle is changed and then solved if the degraded joint movement is needed.
In the present embodiment, the joint rotation angle θ of the fixed link 1 1 To ensure that the variables in the positive kinematic matrix are as few as possible for a fixed value, this joint angle is set to 0.
And S3, carrying out positive kinematics solving of the mechanical arm to be solved according to the inverted D-H parameters set in the step S1.
Knowing the angular displacement of each joint and the geometric parameters of the connecting rod, solving the posture and the position of the end effector of the mechanical arm relative to the base, namely, the positive kinematics of the mechanical arm.
According to the inverted D-H parameters of the mechanical arm, the transformation matrix of each joint can be obtained, the transformation matrix of each joint is multiplied in sequence, and a positive kinematic formula is obtained, and the detailed process is as follows;
transforming matrices by means of rods i-1 T i Description of the first embodimentiThe coordinate system of the joints is ati-pose in 1 joint coordinate system. i- 1 T i Representing a connecting rodiThe coordinate system being relative to the connecting rodi-1 transformation of the coordinate system by the connecting rodiThe coordinate system is obtained through the following four sub-transformations in sequence:
1) Winding machinex i-1 Rotation alpha i-1 A corner;
2) Edge of the framex i-1 Shaft movementa i-1 ；
3) Winding machinez i Rotation theta of axis i A corner;
4) Edge of the framez i Shaft movementd i ；
The above transformations are described in terms of a dynamic coordinate system, and the general formula of the link transformation is obtained according to the principle of 'left to right':
，
c represents cos, s represents sin;
the connecting rods are transformed i-1 T i (i=1, 2,) n,a robot arm transformation matrix can be obtained:
0 T n = 0 T 1 1 T 2 ... n-1 T n ，
in the method, in the process of the application,nrepresenting the total number of joints;
from the above, it can be seen that 0 T n Is thatnThe function of the individual joint variables represents the description of the end coordinate system relative to the base coordinate system, so far the positive kinematic calculation formula of the mechanical arm can be obtained:。
according to the above calculation formula, the inverse positive kinematic transformation matrix is obtained as (n=7).
（1）
Wherein P is x 、P y 、P z A positional expression representing three directions of x, y, z; wherein n is x 、s x 、a x Representing an x-direction pose expression; n is n y 、s y 、a y Representing a y-direction pose expression; n is n z 、s z 、a z Representing a z-direction pose expression.
And S4, performing decoupling treatment on the position and the posture of the elbow and wrist offset configuration mechanical arm according to the positive kinematic transformation matrix in the step S3.
Referring to FIG. 6, in the present embodiment, the flow rate of the catalyst is shown as O 1 Corresponding origin of coordinate system to O 5 The corresponding coordinate system origin is at a distance from the joint rotation angle theta 2 、θ 3 、θ 4 Related to the joint rotation angle theta 1 、θ 5 、θ 6 、θ 7 Independent of position and attitude decoupling, θ 5 、θ 6 、θ 7 Only the pose is affected and the position is not affected. Then, px, py, pz in formula (1) contain only θ 2 、θ 3 、θ 4 Three equations, three unknowns, can solve for θ 2 、θ 3 、θ 4 . Thus, the position andthe poses can be solved separately.
Step S41, according to the decoupled position expressions px, py and pz in step S3, the joint rotation angle theta affecting the position is obtained 2 、θ 3 、θ 4 。
Step S411, solving for θ 4 。
The following formula is listed according to formula (1):
1 T 5 =( 0 T 1 ) -1 0 T 7 ( 5 T 7 ) -1 ，（2）；
the position quantity on the right of the equal sign of (2) is obtained and substituted into theta 1 Is a value of (2).
，
O in FIG. 6 0 -O 5 The distance expression is: r=p x ^2+P y ^2+P z ^2，
The position quantity on the left of the equal sign of formula (2) is according to the distance list from the base coordinate system to the end coordinate system:
simplifying and eliminating theta 2 、θ 3 Obtaining theta 4 An expression.
Step S412, solving θ 3 。
According to pz = 0 T 7 (3, 4) equations containing θ together 3 Is simplified into a unitary quadratic equation system to obtain theta 3 An expression.
Step S413, solving θ 2 。
According to px = 0 T 7 (1, 4) and py = 0 T 7 The (2, 4) equations can be used to determine θ 2 Each formula can solve at most two solutions, only the solutions meeting the two equations simultaneously are true solutions, the other solutions are false solutions, the true solutions are reserved, and the false solutions are omitted.
Step S42, according to the decoupled gesture expressions nx, sx, ax, ny, sy, ay, nz, sz and az in the step S3, solving gesture related angles;
posture-related angle is theta 5 、θ 6 、θ 7 Will be 4 T 7 = 4 T 5 5 T 6 6 T 7 Expanded, the right side of the left middle sign only contains 4 T 7 = 4 T 5 5 T 6 6 T 7 And the three angles respectively correspond to Euler angles alpha, beta and gamma for describing the tail end gesture of the mechanical arm, and the sequence conversion method of the Euler angles in the embodiment is ZYZ. Alpha, beta, gamma can pass 4 T 7 And (5) obtaining.
4 T 7 =( 0 T 4 ) -1 0 T 7
Wherein, the liquid crystal display device comprises a liquid crystal display device, 4 T 7 containing theta as previously determined 1 、θ 2 、θ 3 、θ 4 While 0 T 7 Is a known quantity.
Then θ can be obtained by the following three equations 5 、θ 6 、θ 7 ：
θ 5 =α，θ 6 =β，θ 7 =γ。
Step S43, integrating the results to complete the inverse kinematics solution of the mechanical arm to be solved,
solving 7 joint angles of the mechanical arm to be solved as follows:
θ=[θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ 7 ]
wherein, each angle expression is simplified as follows:
thus, the solution of the inverse kinematics of the elbow-wrist offset configuration mechanical arm in the embodiment is completed.
Claims (8)
1. A seven-degree-of-freedom wrist joint bias mechanical arm inverse solution method is characterized in that: based on a seven-degree-of-freedom mechanical arm, the wrist joint of the mechanical arm is offset, and the three axes of the shoulder joint of the mechanical arm are orthogonal to one point;
the inverse solution method of the mechanical arm comprises the following steps S1-S4:
s1, establishing an inverted D-H coordinate system of the mechanical arm, wherein a base coordinate system O x y z0-000 Is fixed at the center of the tail end joint of the wrist joint of the mechanical arm, and the tail end coordinate system O x y z7-777 The shoulder joint base center of the mechanical arm is fixed;
calibrating an inversion D-H parameter of the mechanical arm according to the inversion D-H coordinate system of the mechanical arm, wherein the inversion D-H parameter is a rod torsion angle alpha corresponding to the connecting rod i i Length of rod a i Distance d of joint i And joint rotation angle theta i Wherein i=1, …,7; at this time, θ 5 、θ 6 、θ 7 To affect only the joint rotation angle of the posture, theta 1 、θ 2 、θ 3 、θ 4 Joint rotation angle for influencing position;
s2, degrading the degree of freedom, and presetting the joint rotation angle of any affected position as a constant with a value interval of [ -pi, pi ];
s3, carrying out positive kinematics solving after the mechanical arm is inverted according to the inverted D-H parameters set in the step S1;
according to the general formula of the change of the connecting rod，
Wherein c represents cos, s represents sin;
obtaining an inverted positive kinematic transformation matrix:
（1）
wherein px, py and pz represent positional expressions in three directions of x, y and z; wherein nx, sx, ax represent x-direction posture expressions; ny, sy, ay represent y-direction pose expressions; nz, sz, az represent z-direction pose expressions;
s4, according to the positive kinematic transformation matrix in the step S3, decoupling the position and the gesture of the mechanical arm to obtain a resolving result:
θ=[θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ 7 ]；
step S4 includes the following steps S41-S42:
s41, substituting constant joint rotation angle values affecting the position according to the position expression, and solving three variable joint rotation angles affecting the position;
s42, according to the gesture expression, solving three joint rotation angle expressions theta affecting the gesture 5 、θ 6 、θ 7 。
2. The seven-degree-of-freedom wrist offset manipulator inverse solution method according to claim 1, wherein the method comprises the following steps: if the joint corresponding to the joint rotation angle set as the constant in the step S2 needs to move, after changing the constant of the joint rotation angle, the steps S3 to S4 are executed to solve for other joint rotation angles.
3. The seven-degree-of-freedom wrist-biased mechanical arm inverse solution method according to claim 2, wherein the method comprises the following steps: in step S1, the base coordinate system O x y z0-000 And taking the intersection point of the axes of the first joint at the tail end and the second joint at the tail end of the mechanical arm as an origin.
4. The seven-degree-of-freedom wrist-biased mechanical arm inverse solution method according to claim 2, wherein the method comprises the following steps: in step 2, the joint rotation angle is set to be a constant value θ 1 。
5. The seven-degree-of-freedom wrist offset manipulator inverse solution method according to claim 4, wherein the method comprises the following steps: step S41 includes the following steps S411-S413:
step S411, solving first, according to formula (1), listing the following formula:
1 T 5 =( 0 T 1 ) -1 0 T 7 ( 5 T 7 ) -1 ，（2）；
the position quantity on the right of the equal sign of the formula (2) is obtained and substituted to obtain the value
；
O 0 -O 5 The distance expression is: r=p x ^2+P y ^2+P z ^2，
The position quantity on the left of the equal sign of formula (2) is listed according to the distance from the base coordinate system to the end coordinate system
Simplifying and eliminating theta 2 、θ 3 Obtaining theta 4 An expression;
step S412, solving θ 3 According to pz= 0 T 7 (3, 4) equations containing θ together 3 Is simplified into a unitary quadratic equation system to obtain theta 3 An expression;
step S413, solving θ 2 According to px = 0 T 7 (1, 4) and py = 0 T 7 The (2, 4) equations can be used to determine θ 2 ，θ 2 The solutions satisfying both equations are taken.
6. The seven-degree-of-freedom wrist offset manipulator inverse solution method according to claim 5, wherein the method comprises the following steps: in step S42, three joint rotation angle expressions θ affecting the posture are obtained 5 、θ 6 、θ 7 When it will 4 T 7 = 4 T 5 5 T 6 6 T 7 Expanded, the right side of the left middle sign only contains theta 5 、θ 6 、θ 7 The three angles respectively correspond to Euler angles alpha, beta and gamma for describing the tail end gesture of the mechanical arm, and pass through 4 T 7 =( 0 T 4 ) -1 0 T 7 The euler angles alpha, beta, gamma are determined, wherein, 4 T 7 containing theta as previously determined 1 、θ 2 、θ 3 、θ 4 ， 0 T 7 Alpha, beta, gamma are obtained by the method and correspond to theta respectively 5 、θ 6 、θ 7 。
7. A robotic arm system, characterized by: a seven-degree-of-freedom wrist-joint-biased robotic inverse solution as claimed in any one of claims 1 to 6, comprising a robotic arm, said robotic arm being a seven-degree-of-freedom robotic arm, said robotic arm wrist-joint being biased, said robotic arm shoulder joint being tri-axial orthogonal to a point.
8. A computer readable storage medium storing a computer program, characterized in that the computer program when executed by a processor implements the steps of the method of any one of claims 1 to 6.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310870918.0A CN116587289B (en) | 2023-07-17 | 2023-07-17 | Seven-degree-of-freedom wrist joint bias mechanical arm inverse solution method, system and medium |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310870918.0A CN116587289B (en) | 2023-07-17 | 2023-07-17 | Seven-degree-of-freedom wrist joint bias mechanical arm inverse solution method, system and medium |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN116587289A true CN116587289A (en) | 2023-08-15 |
| CN116587289B CN116587289B (en) | 2024-03-29 |
Family
ID=87612028
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310870918.0A Active CN116587289B (en) | 2023-07-17 | 2023-07-17 | Seven-degree-of-freedom wrist joint bias mechanical arm inverse solution method, system and medium |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116587289B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117817668A (en) * | 2024-01-30 | 2024-04-05 | 哈尔滨工业大学 | Kinematic reconstruction method for single joint fault of SSRMS (single-arm-single-joint) configuration mechanical arm |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103252779A (en) * | 2012-02-16 | 2013-08-21 | 精工爱普生株式会社 | Robot control device, robot control method, robot control program, and robot system |
| JP2014018912A (en) * | 2012-07-18 | 2014-02-03 | Seiko Epson Corp | Robot control device, robot control method, robot control program and robot system |
| CN104866722A (en) * | 2015-05-26 | 2015-08-26 | 宁波韦尔德斯凯勒智能科技有限公司 | Inverse kinematics solution method for seven-shaft industrial robot arm |
| CN106202713A (en) * | 2016-07-11 | 2016-12-07 | 尔智机器人（上海）有限公司 | A kind of biasing mechanism arm inverse kinematics method |
| CN108789406A (en) * | 2018-06-05 | 2018-11-13 | 上海大学 | A kind of inverse solution method for solving for redundant mechanical arm approachability analysis |
| CN112091979A (en) * | 2020-10-10 | 2020-12-18 | 哈尔滨工业大学 | Seven-degree-of-freedom mechanical arm limiting optimization method based on position-level inverse kinematics |
| CN114952868A (en) * | 2022-07-26 | 2022-08-30 | 之江实验室 | 7-degree-of-freedom SRS (sounding reference Signal) type mechanical arm control method and device and piano playing robot |
-
2023
- 2023-07-17 CN CN202310870918.0A patent/CN116587289B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103252779A (en) * | 2012-02-16 | 2013-08-21 | 精工爱普生株式会社 | Robot control device, robot control method, robot control program, and robot system |
| JP2014018912A (en) * | 2012-07-18 | 2014-02-03 | Seiko Epson Corp | Robot control device, robot control method, robot control program and robot system |
| CN104866722A (en) * | 2015-05-26 | 2015-08-26 | 宁波韦尔德斯凯勒智能科技有限公司 | Inverse kinematics solution method for seven-shaft industrial robot arm |
| CN106202713A (en) * | 2016-07-11 | 2016-12-07 | 尔智机器人（上海）有限公司 | A kind of biasing mechanism arm inverse kinematics method |
| CN108789406A (en) * | 2018-06-05 | 2018-11-13 | 上海大学 | A kind of inverse solution method for solving for redundant mechanical arm approachability analysis |
| CN112091979A (en) * | 2020-10-10 | 2020-12-18 | 哈尔滨工业大学 | Seven-degree-of-freedom mechanical arm limiting optimization method based on position-level inverse kinematics |
| CN114952868A (en) * | 2022-07-26 | 2022-08-30 | 之江实验室 | 7-degree-of-freedom SRS (sounding reference Signal) type mechanical arm control method and device and piano playing robot |
Non-Patent Citations (1)
| Title |
|---|
| 闫文彬 等: "一种七自由度冗余机械臂的逆运动学优化算法", 《系统科学与数学》, vol. 35, no. 7, pages 823 - 837 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117817668A (en) * | 2024-01-30 | 2024-04-05 | 哈尔滨工业大学 | Kinematic reconstruction method for single joint fault of SSRMS (single-arm-single-joint) configuration mechanical arm |
Also Published As
| Publication number | Publication date |
|---|---|
| CN116587289B (en) | 2024-03-29 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107738254B (en) | Conversion calibration method and system for mechanical arm coordinate system | |
| CN116587289B (en) | Seven-degree-of-freedom wrist joint bias mechanical arm inverse solution method, system and medium | |
| CN108656116B (en) | Series robot kinematic parameter calibration method based on dimension reduction MCPC model | |
| CN113386136B (en) | Robot posture correction method and system based on standard spherical array target estimation | |
| CN111801198A (en) | Hand-eye calibration method, system and computer storage medium | |
| CN113442169A (en) | Method and device for calibrating hands and eyes of robot, computer equipment and readable storage medium | |
| CN107817682A (en) | A kind of space manipulator on-orbit calibration method and system based on trick camera | |
| CN111590567B (en) | Space manipulator teleoperation planning method based on Omega handle | |
| CN104866722A (en) | Inverse kinematics solution method for seven-shaft industrial robot arm | |
| CN112454366A (en) | Hand-eye calibration method | |
| WO2022141138A1 (en) | Hybrid master-slave mapping method, robotic arm system, and computer device | |
| CN110871434A (en) | Kinematics calibration method of parallel processing equipment | |
| CN114407013A (en) | Motion trajectory planning method for mechanical arm servo rolling satellite docking ring | |
| CN109129469B (en) | Mechanical arm kinematics inverse solution method and device and mechanical arm | |
| CN109366486B (en) | Flexible robot inverse kinematics solving method, system, equipment and storage medium | |
| CN112476435B (en) | Calibration method and calibration device for gravity acceleration direction and storage medium | |
| CN112536792B (en) | Robot arm inverse solution method based on spherical geometric analysis method | |
| JP2652880B2 (en) | Vertical articulated robot | |
| CN112828862A (en) | Master-slave mapping method for parallel platform, mechanical arm system and storage medium | |
| CN112643656B (en) | Attitude control method and system for serial six-joint manipulator | |
| CN115771146A (en) | Robot posture interpolation method and device and storage medium | |
| Chen et al. | An analytical solution of inverse kinematics for a 7-DOF redundant manipulator | |
| JP3331674B2 (en) | Elbow rotation method for 7-axis articulated robot manipulator | |
| CN117325143A (en) | Redundant mechanical arm singular position type lower kinematics optimization method | |
| CN115670660A (en) | Calibration method, calibration device, surgical robot, electronic device and storage medium |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |