CN107953340B - Universal six-degree-of-freedom manipulator inverse solution engineering algorithm - Google Patents
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- CN107953340B CN107953340B CN201810037293.9A CN201810037293A CN107953340B CN 107953340 B CN107953340 B CN 107953340B CN 201810037293 A CN201810037293 A CN 201810037293A CN 107953340 B CN107953340 B CN 107953340B
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Abstract
The invention relates to the technical field of robot control, and provides an inverse solution algorithm for solving by using space geometric knowledge, which is provided for a robot inverse solution method. Compared with the conventional inverse matrix inversion calculation method, the calculation efficiency of the inverse solution is greatly improved, and the complexity of the inverse matrix algorithm is reduced. In the specific solving process, the rotation angle of the waist of the robot is firstly solved, a plane coordinate system is added on the arm of the robot, and then the space geometric problem is converted into a plane geometric problem to be solved, so that the calculation complexity is reduced, and the calculation efficiency is improved.
Description
Technical Field
The invention relates to the technical field of robot control, in particular to a universal six-degree-of-freedom manipulator inverse solution engineering algorithm.
Background
With the continuous development of scientific technology, the technology in the related field of robots is becoming a subject of common attention in all countries. When the robot performs a series of work such as grabbing, the position of a target object needs to be positioned, and then calculation is performed according to the position of the tail end to obtain the angle value of each axis of the robot. Therefore, the accuracy and reliability of the inversion process and the result are the basis of the robot control technology, and are also an important factor for realizing the robot control.
At present, many methods adopting inverse matrix solving are adopted, which causes complex calculation and has the defects of non-intuitive solving, multi-solution occurrence and the like.
For the complex situation of the robot working environment, if the control technology of the robot is unreliable, unsafe factors are introduced. Welding robots, polishing robots and the like on the market adopt six-degree-of-freedom robots in many cases. The calculation is complex by using an inverse matrix solving method; there is also a useful space geometric algorithm to solve the inverse, but there is a requirement for the robot structure, and no general effect is achieved.
Disclosure of Invention
The invention aims at improving a space resolution geometric inverse solution method of a mechanical arm with a special structure in the prior art, so that the method is applicable to a six-degree-of-freedom mechanical arm geometric inverse solution algorithm with a general structure, and further provides an inverse motion solution engineering algorithm for realizing multi-joint linkage of the mechanical arm.
The invention realizes the purpose by the following technical scheme:
the six-degree-of-freedom inverse solution method provided by the invention does not adopt an inverse matrix method for solution, and aims at a universal six-degree-of-freedom manipulator, a space problem is firstly converted into a plane problem, and the inverse solution step is simplified
(1) And determining an actual target point P (X, Y, Z) for grabbing, and not considering the target posture problem.
(2) The rotation of the 4 th and 6 th joints of the manipulator is fixed without considering the problem of the target posture, and the angle between the small arm and the horizontal plane is always defined as beta, and then theta is obtained1、θ2、θ3、θ5。
(3) When the inverse solution is obtained, the waist is firstly rotated to obtain theta1The latter solution simplifies the solution for the planar problem.
(4) Calculating theta2、θ3、θ5
Further, in the step (1), the target point P (X, Y, Z) is found by performing teleoperation manually or is provided visually by a robot.
Further, in the above steps (2) and (3), regardless of the posture problem, the rotation of the 4 th and 6 th joints of the robot is fixed, the angle between the arm and the horizontal plane is always defined as β, the target point P (X, Y, Z) is positioned at the center of the gripper, a plane coordinate system { X, Y } is fixed to the robot arm, and θ is obtained by turning the waist first1And then, the problem of the space coordinate system is simplified into the problem of the plane coordinate system, so that the calculation is simplified. The origin of the plane coordinate system { X, Y } on the mechanical arm is coincident with the origin of the coordinate system { X, Y, Z } of the mechanical arm, and the Y-axis of the plane coordinate system { X, Y } is also coincident with the Z-axis of the space coordinate system { X, Y, Z }, and the two coordinate systemsThe relationship of the coordinate system and the related parameters are shown in fig. 1.
After waist turning, the problem is known easily according to space geometric knowledge, and then the problem solving is carried out in a plane coordinate system { x, y } according to points P ', P ' and P ' in the space coordinate system; combining the plane coordinate system, the expression of each point in the plane coordinate system { x, y } can be obtained:
P(x0,y0):
y0＝Pz
P′(x0′,y0′):x0′＝x0-d6*cosβ；y0′＝y0+d6*sinβ
P″(x0″,y0″):x0″＝a2*cosθ2+a1；y0″＝a2*sinθ2
P″′(x0″′,y0″′)：x0″′＝x0″+a3*cos(θ2+θ3)；,y0 ③＝y0″+a3*sin(θ2+θ3)
further, in the step (4), after the space coordinate system is converted into the plane coordinate system, as shown in fig. 2, the following is obtained according to the plane geometry knowledge:
is simple and easy to obtain
Discussion of θ required according to FIG. 23Several cases of (1), schematic ofAs shown in fig. 3.
Due to a3、d4For the manipulator parameters, it is determined and Δ P 'P "P'" is Rt Δ, so the corresponding angle is also determined.
Can obtain
By analysis, theta3There are several situations:
when 0< alpha + gamma < pi
θ3＝-(π-α-γ)＝α+γ-π
② when Pi < alpha + gamma and gamma < Pi
θ3＝α-(π-γ)＝α+γ-π
③ when pi < alpha + gamma and gamma > pi
θ3＝γ-π+α＝α+γ-π
In view of the above, it is desirable to provide,
according to the geometric relationship of the two groups,
can ask for
Wherein, the theta is obtained1、θ2、θ3、θ5Then, according to the factIf the posture of the target is required to be adjusted, the posture of the hand can be manually adjusted, and reasonable work is realized. Compared with the prior art, the engineering algorithm can avoid the complexity of an inverse matrix solving algorithm, and provides a space geometry algorithm for a universal six-degree-of-freedom manipulator, so that the solving efficiency is improved to a great extent.
Drawings
Fig. 1 is a schematic diagram of a six-degree-of-freedom manipulator spatial coordinate system of the present invention.
Fig. 2 is a schematic structural diagram of the present invention simplified into a planar coordinate system.
FIG. 3 is a discussion of the present invention θ3Schematic representation of several cases.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The six-degree-of-freedom inverse solution method provided by the invention does not adopt an inverse matrix method for solution, and aims at a universal six-degree-of-freedom manipulator, a space problem is firstly converted into a plane problem, and the inverse solution step is simplified
(1) And determining an actual target point P (X, Y, Z) for grabbing, and not considering the target posture problem.
(2) The rotation of the 4 th and 6 th joints of the manipulator is fixed without considering the problem of the target posture, and the angle between the small arm and the horizontal plane is always defined as beta, and then theta is obtained1、θ2、θ3、θ5。
(3) When the inverse solution is obtained, the waist is firstly rotated to obtain theta1The latter solution simplifies the solution for the planar problem.
(4) Calculating theta2、θ3、θ5
Further, in the step (1), the target point P (X, Y, Z) is found manually by teleoperation or visually provided by a robot.
Further, in the steps (2) and (3), the rotation of the 4 th and 6 th joints of the manipulator is fixed, the angle between the forearm and the horizontal plane is defined as beta, and the target point is set regardless of the postureP (X, Y, Z) is positioned at the center of the gripper, and a planar coordinate system { X, Y } is fixed to the robot arm to determine θ for waist-first rotation1And then, the problem of the space coordinate system is simplified into the problem of the plane coordinate system, so that the calculation is simplified. The origin of the plane coordinate system { X, Y } on the robot arm coincides with the origin of the robot's own coordinate system { X, Y, Z }, and the Y-axis of the plane coordinate system { X, Y } also coincides with the Z-axis of the spatial coordinate system { X, Y, Z }, and the relationship and related parameters of the two coordinate systems are shown in fig. 1.
After the waist is turned, theta is easily known according to the space geometric knowledge1＝atan2(PY,PX) The subsequent problem solving is the solving in a plane coordinate system { x, y }, and is carried out according to points P ', P' in a space coordinate system; combining the plane coordinate system, the expression of each point in the plane coordinate system { x, y } can be obtained:
P(x0,y0):
y0＝Pz
P(x0′,y0′):x0′＝x0-d6*cosβ；y0′＝y0+d6*sinβ
P(x0″,y0″):x0″＝a2*cosθ2+a1；y0″＝a2*sinθ2
P(x0″′,y0″′)：x0″′＝x0″+a3*cos(θ2+θ3)；,y0 ③＝y0″+a3*sin(θ2+θ3)
further, in the step (4), after the space coordinate system is converted into the plane coordinate system, as shown in fig. 2, the following is obtained according to the plane geometry knowledge:
is simple and easy to obtain
Discussion of θ required according to FIG. 23The schematic diagram of the above-mentioned cases is shown in FIG. 3.
Due to a3、d4For the manipulator parameters, it is determined and Δ P 'P "P'" is Rt Δ, so the corresponding angle is also determined.
Can obtain
By analysis, theta3There are several situations:
when 0< alpha + gamma < pi
θ3＝-(π-α-γ)＝α+γ-π
② when Pi < alpha + gamma and gamma < Pi
θ3＝α-(π-γ)＝α+γ-π
③ when pi < alpha + gamma and gamma > pi
θ3＝γ-π+α＝α+γ-π
In view of the above, it is desirable to provide,
according to the geometric relationship of the two groups of the,
can ask for
Wherein, the theta is obtained1、θ2、θ3、θ5And then, according to the posture of the actual target, if the actual target needs to be adjusted, the hand-grasping posture can be manually adjusted, so that reasonable work is realized.
Claims (6)
1. A universal six-degree-of-freedom manipulator inverse solution engineering algorithm is characterized by comprising the following steps:
(1) determining an actual target point P (X, Y, Z) for grabbing, and not considering the target posture problem;
(2) because the problem of target posture is not considered, the rotation of the 4 th joint and the 6 th joint of the manipulator is fixed; and the included angle between the small arm and the horizontal plane is specified to be beta all the time, and then theta is obtained1、θ2、θ3、θ5；
(3) When the inverse solution is obtained, the waist is firstly rotated to obtain theta1The subsequent solution is simplified to the solution of the plane problem;
(4) calculating theta2、θ3、θ5；
In the step (4), the following can be obtained according to the plane geometry knowledge:
is simple and easy to obtain
The following can be obtained:
due to a3、d4For the manipulator parameters, it is determined and Δ P 'P "P'" is Rt Δ, so the corresponding angle is also determined,
can obtain
According to the geometric relationship of the two groups,
can ask for
2. The universal six-DOF manipulator inverse solution engineering algorithm according to claim 1, wherein the target point P (X, Y, Z) in step (1) is provided by finding points through teleoperation manually or by finding characteristic points visually by a robot.
3. The universal six-degree-of-freedom manipulator inverse solution engineering algorithm according to claim 1, wherein in the step (2), the rotation of the 4 th and 6 th joints of the manipulator is fixed, the angle between the forearm and the horizontal plane is defined as β, the target point P (X, Y, Z) is positioned at the center of the manipulator jaw, a plane coordinate system { X, Y } is fixed on the manipulator arm, and θ is obtained by waist-turning first, regardless of the posture problem1Then, the problem of the space coordinate system is simplified into the problem of the plane coordinate system, so that the calculation is simplified; plane coordinate system { x, y } original point on mechanical arm and mechanical arm bookThe origin of the body coordinate system { X, Y, Z } coincides, and the Y-axis of the plane coordinate system { X, Y } also coincides with the Z-axis of the spatial coordinate system { X, Y, Z }.
4. The universal six-degree-of-freedom manipulator inverse solution engineering algorithm according to claim 1, wherein in the step (3), θ is easily known according to the spatial geometry knowledge1＝atan2(PY,PX) The subsequent problem solving is the solving in the plane coordinate system { x, y }, according to the points P ', P'; combining the plane coordinate system, the expression of each point in the plane coordinate system { x, y } can be obtained:
P(x0,y0):
y0＝Pz
P′(x0′,y0′):x0′＝x0-d6*cosβ；y0′＝y0+d6*sinβ
P″(x0″,y0″):x0″＝a2*cosθ2+a1；y0″＝a2*sinθ2
P″′(x0″′,y0″′)：x0″′＝x0″+a3*cos(θ2+θ3)；y0 ③＝y0″+a3*sin(θ2+θ3)。
5. the universal six-degree-of-freedom manipulator inverse solution engineering algorithm of claim 1, wherein θ is found1、θ2、θ3、θ5Then, the posture of the robot hand is manually adjusted to meet the task of the robot on the target object in accordance with the actual requirements.
6. The universal six-degree-of-freedom manipulator inverse solution engineering algorithm of claim 4, wherein θ is calculated2、θ3、θ5Is made byThe method for converting space geometry into plane geometry firstly calculates the angle of waist rotation and then calculates other joint angles.
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