CN116277039A - Method, system, equipment and medium for planning track of robot arm passing wrist singular point - Google Patents
Method, system, equipment and medium for planning track of robot arm passing wrist singular point 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
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- B—PERFORMING OPERATIONS; TRANSPORTING
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- B25J9/00—Programme-controlled manipulators
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Abstract
The invention discloses a track planning method, a system, equipment and a medium for a robot arm to pass through a wrist singular point, which relate to the technical field of robot arm control and comprise the following steps: obtaining a position corresponding to each moment in a Cartesian space according to an initial path planned by the mechanical arm, and obtaining four-axis, five-axis and six-axis shaft angles corresponding to each moment in a four-axis, five-axis and six-axis constant speed state according to the total time of the initial path, the shaft angle of a starting point position and the shaft angle of an end point position; and obtaining the shaft angles of the first shaft, the second shaft and the third shaft according to the shaft angles of the four shafts, the fifth shaft and the sixth shaft corresponding to each moment and the positions corresponding to each moment, so that the motion track of the mechanical arm passing through the wrist singular point is obtained according to the shaft angles of the first shaft to the sixth shaft. The problem that four-six axes overspeed and large end precision errors cannot occur when the tail end of the mechanical arm passes through a singular position while the end position precision is ensured.
Description
Technical Field
The invention relates to the technical field of mechanical arm control, in particular to a method, a system, equipment and a medium for planning a track of a mechanical arm passing through a wrist singular point.
Background
When the mechanical arm moves straight in the Cartesian space, the condition that five axes are zero degrees easily occurs in a path, and the mechanical arm enters a wrist singular state at the moment, so that the speeds of four axes and six axes are infinitely large, and overspeed shutdown is caused.
At present, when most mechanical arms encounter singular problems, the positions are reselected or the postures are changed in error in the path to plan, and the path is easy to lose due to the fact that the path or the initial posture is changed.
Or, dividing the singular region to plan the joint space in the singular region; when the path is planned, firstly, the path is divided in a Cartesian space to obtain discrete points and total movement time in the Cartesian space, then, angles of all axes are obtained by inverse solution according to the points in the Cartesian space, if five zero crossing points exist in the path, infinite speeds of four axes and six axes are caused, so that the paths cannot pass, and the middle mode is to re-plan the section of the overspeed starting position and the overspeed ending position of the four axes and the six axes in the joint space, so that part of position precision is sacrificed, and the path precision error in a singular area is overlarge.
Disclosure of Invention
In order to solve the problems, the invention provides a track planning method, a system, equipment and a medium for a mechanical arm to pass through a wrist singular point, which ensure the position accuracy of the tail end and simultaneously prevent the problems of four-six axes overspeed and large tail end accuracy error when the tail end of the mechanical arm passes through the singular position.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
in a first aspect, the present invention provides a trajectory planning method for a robot arm passing through a singular point of a wrist, including:
obtaining a position corresponding to each moment in a Cartesian space according to an initial path planned by the mechanical arm, and obtaining four-axis, five-axis and six-axis shaft angles corresponding to each moment in a four-axis, five-axis and six-axis constant speed state according to the total time of the initial path, the shaft angle of a starting point position and the shaft angle of an end point position;
and obtaining the shaft angles of the first shaft, the second shaft and the third shaft according to the shaft angles of the four shafts, the fifth shaft and the sixth shaft corresponding to each moment and the positions corresponding to each moment, so that the motion track of the mechanical arm passing through the wrist singular point is obtained according to the shaft angles of the first shaft to the sixth shaft.
As an alternative embodiment, the four-axis, five-axis and six-axis uniform shaft speeds are respectively:
wherein,,for the axle speed of four axles, +.>For the axle speed of five axles>For a six axis shaft speed, < >>、、/>The axle angles of four, five and six axles, respectively, of the starting position +.>、/>、/>The shaft angles of four shafts, five shafts and six shafts of the end position are respectively, and T is the total time of the initial path.
As an alternative embodiment, the shaft angles of four, five and six shafts corresponding to each moment are respectively:
wherein,,is the axis angle of four axes at the moment t +.>Is the axle angle of five axles at the moment t +.>Is the shaft angle of six shafts at the moment t, < >>Is the interpolation time.
Alternatively, the shaft angle of a shaft is:
wherein,,is the shaft angle of four shafts->Is the shaft angle of five shafts->An axis angle of an axis, (x, y) is a position coordinate corresponding to each moment,d 6 is the joint distance of the 6 th joint.
Alternatively, the axis angle of the triaxial is:
Alternatively, the two axes have an axis angle of:
wherein,,is the shaft angle of two shafts, +.>The axis angle of the three axes, z is the z coordinate value in the position coordinates corresponding to each moment,d 1 for joint distance of 1 st joint +.>Is the position coordinate after being transformed from the 3-axis coordinate system to the 6-axis coordinate system.
As an alternative embodiment, after obtaining the shaft angles of the first shaft, the second shaft and the third shaft, selecting the solution that minimizes the shaft angle change of all shafts as the optimal shaft angles of the first shaft, the second shaft and the third shaft, and obtaining the motion trail of the mechanical arm passing through the wrist singular point according to the optimal shaft angles of the first shaft to the sixth shaft.
In a second aspect, the present invention provides a trajectory planning system for a robot arm passing a singular point of a wrist, including:
the four-axis to six-axis angle determining module is configured to obtain a position corresponding to each moment in a Cartesian space according to an initial path planned for the mechanical arm, and obtain four-axis, five-axis and six-axis angles corresponding to each moment in a four-axis, five-axis and six-axis constant speed state according to the total time of the initial path, the axis angle of a starting point position and the axis angle of an ending point position;
the one-axis to three-axis angle determining module is configured to obtain the one-axis, two-axis and three-axis shaft angles according to the four-axis, five-axis and six-axis shaft angles corresponding to each moment and the positions corresponding to each moment, so that the motion track of the mechanical arm passing through the wrist singular point is obtained according to the one-axis to six-axis shaft angles.
In a third aspect, the invention provides an electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the method of the first aspect.
In a fourth aspect, the present invention provides a computer readable storage medium storing computer instructions which, when executed by a processor, perform the method of the first aspect.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a track planning method, a system, equipment and a medium for a robot arm passing through a wrist singular point, which are applied to the Cartesian space track planning of the robot arm, and according to the shaft angles of a starting point position and an end point position, the shaft speeds of four shafts, five shafts and six shafts are fixed, so that the shaft angles of four shafts, five shafts and six shafts corresponding to each moment in a four-shaft, five shafts and six shafts uniform speed state are obtained, and then the shaft angles of the four shafts, the five shafts and the six shafts are adopted to reversely solve the shaft angles of the first shaft, the second shaft and the three shafts, so that the problem that the overspeed of the four shafts and the six shafts and the problem that the error of the precision of the tail end of the robot arm is large can not occur when the tail end of the robot arm passes through the singular position while the precision of the tail end position is ensured.
The invention does not need to change the path and the initial and final gestures, does not need to bypass the singular point planning, realizes that the original path passes through the singular point, and has the key process that the shaft speeds of four shafts, five shafts and six shafts are fixed, and the shaft angles of a first shaft, a second shaft and three shafts are reversely solved by combining the positions; because the four-axis and the six-axis rotation axes are overlapped when the five-axis is 0 degrees, overspeed is caused to the shaft speeds of the four-axis and the six-axis rotation axes when the inverse solution is obtained, the problem is avoided when the shaft speeds of the four-axis rotation speed, the five-axis rotation speed and the six-axis rotation speed are fixed first, and therefore the position accuracy is ensured.
Additional aspects of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
Fig. 1 is a flowchart of a trajectory planning method for a robot arm passing through a singular point of a wrist according to embodiment 1 of the present invention.
Detailed Description
The invention is further described below with reference to the drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the 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 this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular forms also are intended to include the plural forms, and furthermore, it is to be understood that the terms "comprises" and "comprising" and any variations thereof are intended to cover non-exclusive inclusions, such as, for example, processes, methods, systems, products or devices that comprise a series of steps or units, are not necessarily limited to those steps or units that are expressly listed, but may include other steps or units that are not expressly listed or inherent to such processes, methods, products or devices.
Embodiments of the invention and features of the embodiments may be combined with each other without conflict.
Example 1
When a linear path is planned for the mechanical arm, the position corresponding to each moment is planned in a Cartesian space according to the positions of the starting point and the ending point of the planned path, and when the situation that five axes pass through 0 point and four six axes are overspeed occurs in the process of negating, the path is considered to pass through the wrist singular point. In order to ensure the position accuracy, the embodiment adopts the originally planned position, avoids overspeed by giving the shaft speeds of four shafts, five shafts and six shafts, changes the posture interpolation mode to ensure that the tail end of the mechanical arm smoothly passes through the singular point, and does not have the problems of overspeed of four shafts and six shafts and large tail end accuracy error.
As shown in fig. 1, the present embodiment provides a track planning method for a robot arm passing through a wrist singular point, including:
obtaining a position corresponding to each moment in a Cartesian space according to an initial path planned by the mechanical arm, and obtaining four-axis, five-axis and six-axis shaft angles corresponding to each moment in a four-axis, five-axis and six-axis constant speed state according to the total time of the initial path, the shaft angle of a starting point position and the shaft angle of an end point position;
and obtaining the shaft angles of the first shaft, the second shaft and the third shaft according to the shaft angles of the four shafts, the fifth shaft and the sixth shaft corresponding to each moment and the positions corresponding to each moment, so that the motion track of the mechanical arm passing through the wrist singular point is obtained according to the shaft angles of the first shaft to the sixth shaft.
In this embodiment, a path planning in cartesian space is first performed, a position corresponding to each moment in the cartesian space is obtained according to an initial path planned for the mechanical arm, and if a wrist singular point occurs, an inverse solution of the endpoint is recalculated, so that an axis angle of the start point position is set to beThe axial angle of the end position is。
In the embodiment, according to the total time T of the initial path planned for the first time, the shaft angles of the four shafts, the five shafts and the six shafts at the starting point position and the shaft angles of the four shafts, the five shafts and the six shafts at the end point position, the shaft speeds of the four shafts, the five shafts and the six shafts are obtained; then, by fixing the shaft speeds of four, five and six shafts, the interpolation time is setObtaining shaft angles of four shafts, five shafts and six shafts corresponding to each moment in a four-shaft, five-shaft and six-shaft constant speed state; the method comprises the following steps:
wherein,,shaft with four shaftsSpeed (I)>For the axle speed of five axles>For a six axis shaft speed, < >>Is the axis angle of four axes at the moment t +.>Is the axle angle of five axles at the moment t +.>The axis angle of the six axes at time t.
In this embodiment, the axis angles of the first axis, the second axis and the third axis are recalculated according to the axis angles of the four axes, the five axes and the six axes corresponding to each moment and the positions (i.e., x, y and z coordinate values) corresponding to each moment; the method comprises the following steps:
(1) Firstly, determining a homogeneous transformation matrix between coordinate systems according to DH parameters of a robot:
wherein a is the length of the rod piece,the torsion angle of the rod piece is d, the joint distance is d, and q is the joint torsion angle; i is the ith joint or rod.
(2) Obtaining a homogeneous transformation matrix of 4 to 6 according to the shaft angles of four shafts, five shafts and six shafts corresponding to each moment;
(3) The first three data of the fourth column of the homogeneous transformation matrix arePosition information of coordinate transformation is to be obtainedThe position of the transformation from the 3-axis coordinate system to the 6-axis coordinate system is marked +.>;
(4) From homogeneous transformation matricesAnd (3) making the data of the second row and the fourth column of the matrix on the left side of the equation equal to the data of the fourth column of the second row of the matrix on the right side of the equation to obtain the shaft angle of one shaft:
wherein,,d 6 is the joint distance of the 6 th joint.
(5) Based on homogeneous transformation matrixThe data of the fourth column of the first row of the matrix on the left side of the equation are equal to the data of the fourth column of the third row of the matrix on the right side of the equation, so that the axial angle of the triaxial is obtained;
wherein atan is an arctangent function used to calculate the angle value; c 3 、s 3 、K 3 Are all intermediate coefficients;d 1 the joint distance of the 1 st joint.
(6) According toAnd (3) making the data of the third row and the fourth column of the matrix on the left side of the equation equal to the data of the fourth column of the third row of the matrix on the right side of the equation to obtain the shaft angle of the two shafts:
in this embodiment, if there are multiple solutions for the shaft angles of the first, second and third shafts, the solution set that minimizes the angle change of all the shafts is selected from the starting point according to the shaft angles of the shafts of the robot at the previous time,/>The shaft angle is the shaft angle at the last moment; and calculating to obtain a group of solutions with the smallest angle change, namely an optimal solution, so as to obtain optimal axis angles of a first axis, a second axis and a third axis, and finally obtaining a motion track of the mechanical arm through the wrist singular point according to the axis angles of the first axis to the six axes.
Example 2
The embodiment provides a track planning system for a robot arm passing through a wrist singular point, which comprises the following steps:
the four-axis to six-axis angle determining module is configured to obtain a position corresponding to each moment in a Cartesian space according to an initial path planned for the mechanical arm, and obtain four-axis, five-axis and six-axis angles corresponding to each moment in a four-axis, five-axis and six-axis constant speed state according to the total time of the initial path, the axis angle of a starting point position and the axis angle of an ending point position;
the one-axis to three-axis angle determining module is configured to obtain the one-axis, two-axis and three-axis shaft angles according to the four-axis, five-axis and six-axis shaft angles corresponding to each moment and the positions corresponding to each moment, so that the motion track of the mechanical arm passing through the wrist singular point is obtained according to the one-axis to six-axis shaft angles.
It should be noted that the above modules correspond to the steps described in embodiment 1, and the above modules are the same as examples and application scenarios implemented by the corresponding steps, but are not limited to those disclosed in embodiment 1. It should be noted that the modules described above may be implemented as part of a system in a computer system, such as a set of computer-executable instructions.
In further embodiments, there is also provided:
an electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the method described in embodiment 1. For brevity, the description is omitted here.
It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general purpose processors, digital signal processors DSP, application specific integrated circuits ASIC, off-the-shelf programmable gate array FPGA or other programmable logic device, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may include read only memory and random access memory and provide instructions and data to the processor, and a portion of the memory may also include non-volatile random access memory. For example, the memory may also store information of the device type.
A computer readable storage medium storing computer instructions which, when executed by a processor, perform the method described in embodiment 1.
The method in embodiment 1 may be directly embodied as a hardware processor executing or executed with a combination of hardware and software modules in the processor. The software modules may be located in a random access memory, flash memory, read only memory, programmable read only memory, or electrically erasable programmable memory, registers, etc. as well known in the art. The storage medium is located in a memory, and the processor reads the information in the memory and, in combination with its hardware, performs the steps of the above method. To avoid repetition, a detailed description is not provided herein.
Those of ordinary skill in the art will appreciate that the elements of the various examples described in connection with the present embodiments, i.e., the algorithm steps, can be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
While the foregoing description of the embodiments of the present invention has been presented in conjunction with the drawings, it should be understood that it is not intended to limit the scope of the invention, but rather, it is intended to cover all modifications or variations within the scope of the invention as defined by the claims of the present invention.
Claims (10)
1. The track planning method for the robot arm passing through the singular points of the wrist is characterized by comprising the following steps:
obtaining a position corresponding to each moment in a Cartesian space according to an initial path planned by the mechanical arm, and obtaining four-axis, five-axis and six-axis shaft angles corresponding to each moment in a four-axis, five-axis and six-axis constant speed state according to the total time of the initial path, the shaft angle of a starting point position and the shaft angle of an end point position;
and obtaining the shaft angles of the first shaft, the second shaft and the third shaft according to the shaft angles of the four shafts, the fifth shaft and the sixth shaft corresponding to each moment and the positions corresponding to each moment, so that the motion track of the mechanical arm passing through the wrist singular point is obtained according to the shaft angles of the first shaft to the sixth shaft.
2. The method for planning the trajectory of the robot arm over the singular point of the wrist according to claim 1, wherein the four-axis, five-axis and six-axis uniform shaft speeds are respectively:
wherein,,for the axle speed of four axles, +.>For the axle speed of five axles>For a six axis shaft speed, < >>、/>、The axle angles of four, five and six axles, respectively, of the starting position +.>、/>、/>The shaft angles of four shafts, five shafts and six shafts of the end position are respectively, and T is the total time of the initial path.
3. The trajectory planning method for the robot arm passing through the singular points of the wrist according to claim 2, wherein the four-axis, five-axis and six-axis shaft angles corresponding to each moment are respectively:
4. The method for planning a trajectory of a robot arm over a singular point of a wrist of claim 1, wherein an axis angle of an axis is:
6. The trajectory planning method for the robot arm passing through the singular points of the wrist according to claim 1, wherein the axis angles of the two axes are:
wherein,,is the shaft angle of two shafts, +.>The axis angle of the three axes, z is the z coordinate value in the position coordinates corresponding to each moment,d 1 for joint distance of 1 st joint +.>Is the position coordinate after being transformed from the 3-axis coordinate system to the 6-axis coordinate system.
7. The trajectory planning method for the mechanical arm passing through the singular point of the wrist according to claim 1, wherein after the axis angles of the first axis, the second axis and the third axis are obtained, a solution for minimizing the axis angle change of all the axes is selected as the optimal axis angles of the first axis, the second axis and the third axis, and the motion trajectory for the mechanical arm passing through the singular point of the wrist is obtained according to the optimal axis angles of the first axis to the sixth axis.
8. The track planning system for the robot arm passing through the singular points of the wrist is characterized by comprising:
the four-axis to six-axis angle determining module is configured to obtain a position corresponding to each moment in a Cartesian space according to an initial path planned for the mechanical arm, and obtain four-axis, five-axis and six-axis angles corresponding to each moment in a four-axis, five-axis and six-axis constant speed state according to the total time of the initial path, the axis angle of a starting point position and the axis angle of an ending point position;
the one-axis to three-axis angle determining module is configured to obtain the one-axis, two-axis and three-axis shaft angles according to the four-axis, five-axis and six-axis shaft angles corresponding to each moment and the positions corresponding to each moment, so that the motion track of the mechanical arm passing through the wrist singular point is obtained according to the one-axis to six-axis shaft angles.
9. An electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the method of any one of claims 1-7.
10. A computer readable storage medium storing computer instructions which, when executed by a processor, perform the method of any of claims 1-7.
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