CN110757454A - Path planning method and device for cooperative rotation of double robots - Google Patents
Path planning method and device for cooperative rotation of double robots Download PDFInfo
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Abstract
The invention relates to a path planning method and a device for cooperative rotation of two robots, wherein the method is used for a circular arc path interpolation method of six axes at the tail end of the robot relative to a workpiece; the two robots are oppositely arranged relative to a world coordinate z axis, the path arc radius is set according to the size of a clamped workpiece, the path deflection angle is set, and a cooperative rotation working condition is executed; acquiring a homogeneous transformation matrix of the coordinates of the end groups of the two robots according to the relative relation of the arrangement of the robot platforms and the standard D-H parameters of the robots; respectively carrying out coordinate rotation interpolation and control point coordinate vector interpolation based on space geometry on the two robots to generate a homogeneous transformation matrix of the control points relative to the robot base coordinate; and solving joint coordinate angle variables corresponding to the control point homogeneous transformation matrix according to inverse dynamics. The invention can accurately control the double-robot end effector to execute the circular arc path under each deflection angle according to the size of the workpiece to be processed, has small track roundness error and has universal applicability.
Description
Technical Field
The invention relates to the technical field of multi-robot cooperative path planning, in particular to a method and a device for path planning of two-robot cooperative rotation.
Background
The multi-robot system is an important direction for the robot research, and can realize more complex working conditions and has stronger robustness compared with a single-robot system. The double-robot cooperative operation is an important branch of a multi-robot system, and is used as an important motion working condition of the double-robot cooperation, and the double robots cooperatively rotate around a central point to realize flexible multi-posture change of a workpiece in space, so that various complex operation requirements are met. Such as arc bending of steel plates, welding of spatial three-dimensional complex welding seams and the like.
The serial robot path planning comprises a large number of posture transformation of the robot end effector, the robot posture is described with quaternion, a rotation matrix and an Euler angle, the quaternion is used for representing rotation, any rotation shaft and any rotation angle in a calibration coordinate system can be flexibly matched, and the problem of universal joint locking is effectively avoided. The rotation matrix and the quaternion have a simple equivalent transformation relation, and are widely applied to interpolation calculation.
Disclosure of Invention
In view of the above, there is a need to provide a method and an apparatus for planning a path by cooperative rotation of two robots, which are suitable for all the above, and can precisely control the end effector of the two robots to execute a cooperative rotation condition with respect to the arc center point of the path under the actual working condition of cooperative work of the two robots, and have general applicability.
A path planning method for cooperative rotation of two robots is applied to a cooperative system of two robots, the system comprises two robots, the two robots both comprise end effectors used for clamping workpieces to be processed together, the method is used for path planning of multi-angle cooperative rotation motion around a central point in space for a sixth axis at the tail end of the robot, and the method comprises the following steps:
on the basis of independent modeling of a single robot, establishing a mutual position relation of robot platforms, and constructing a kinematic system with relative coordinate transformation;
setting a world coordinate system according to a robot platform arrangement strategy, and calibrating a base coordinate system and a tail end coordinate system of the two robots;
taking each base coordinate system of the two robots as a central coordinate, and solving a homogeneous transformation matrix basic form of the terminal coordinates of the robots according to the standard D-H parameters as basic kinematic parameters;
establishing a path arc model on the cooperative rotation working condition of the robot system, and setting a symmetrical center coordinate system as a path base as an origin;
calculating a homogeneous transformation matrix of the path initial control points according to the known path deflection angle and the path arc radius;
extracting a three-dimensional rotation matrix from the homogeneous transformation matrix of the path initial control point to perform coordinate rotation interpolation based on quaternion;
extracting an initial coordinate vector from the homogeneous transformation matrix of the path initial control point to perform control point coordinate vector interpolation based on space geometry;
and obtaining the joint control angle of the final control point based on homogeneous transformation matrix conversion of inverse dynamics.
Further, the influence of the arc axial offset is considered in the interpolation process of the three-position rotation coordinate, and the maximum interval angle value of the control point is solved according to the limitation of the arc axial offset.
Further, a homogeneous transition from the initial control pointMatrix extraction three-dimensional rotation matrix
Let cos be c, sin be s, and the coordinate vector of the point P coordinate system relative to the control point is generally in the form of
r is the path arc radius; the path circular interpolation can be expressed as two interpolation links of rotation and coordinate vectors:
(1) will T3Q converted to quaternion form0＝q0+q1i+q2j+q3k, where i, j, k are imaginary units, q0、q1、q2、q3Is a specific variable value, and sets the quaternion expression of the control point to Qi＝[wi,(xi,yi,zi)]T，wiIs the value of the real variable, xi,yi,ziIs the value of the imaginary variable, according to Qi-Q'. Q0*Q′-1Substituting a calculation formula of quaternion multiplication into the maximum arc maximum angle of the control point to obtain quaternion of each rotated control point, and converting the quaternion into a rotation matrix at any control point;
(2) the coordinate offset of the control point relative to the coordinate system P can be determined by the offset vector P in each coordinate axis directionx，py，pzExpressing, the coordinate vector of the control point as
In general form (1).
Further, the solving method of the initial control homogeneous transformation matrix comprises the following steps: relative rotation path xpzpThe plane deflection angle is α, the radius of the path arc is r, and the coordinate P of the starting point of the path is0First by ypRotate 90 degrees clockwise, then rotate clockwise (α +90 degrees) relative to the z-axis, and translate along the z-axis axially to-r m (m is more than or equal to 0)<360)；P0The homogeneous transformation matrix relative to the P-point coordinate system is represented as:
further, the maximum angle value of the arc control point satisfies:
the interval angle between the two control points is less than
Accordingly, a specific n value is taken to satisfyIndicating that adjacent control points are spaced by n, the control point rotation angle should be set to n,2n, … kn.
Further, an initial control point Q0The quaternion representation of (a) is generally of the form:
the quaternion is n around the axis rotation angle, and the associated quaternion for the axis of rotation is expressed as:
quaternion Qi＝[wi,(xi,yi,zi)]TThe general form of gesture rotation is represented as:
the formula for converting quaternion to rotation matrix is:
further, the control points satisfy the relationship with respect to each element of the coordinate vector of the point P coordinate system:
v is the number of path control points.
Further, the homogeneous transformation matrix of the two robot control points with respect to the robot base standard is represented as:
l is the distance between two robots in the x-axis direction, b is the distance between two robots in the y-axis direction, and h1The height of the base of the left robot is h2The height of the base of the right robot.
A path planning device with double robots rotating cooperatively comprises a robot coordinate calibration module, a control point interpolation module and an inverse dynamics solving module;
the robot coordinate calibration module is used for calibrating the attributes of the base coordinate and the tail end axis coordinate of the unit robot and establishing a relative coordinate relation in the robot cooperative system;
the control point interpolation module is used for executing circular arc path interpolation of the two robots according to the homogeneous transformation matrix at the tail end of the robot and aiming at the interpolation requirement of the path circular arc;
and the inverse dynamics solving module is used for combining the homogeneous transformation matrixes of the control points and solving the joint angle variation corresponding to six axes.
Furthermore, the control point interpolation module comprises an initial control point unit, a coordinate rotation interpolation unit and a coordinate vector position interpolation unit;
the initial control point unit comprises a path circular arc modeling module and a homogeneous transformation matrix solving module of an initial control point coordinate system, and is used for modeling a path circular arc and solving a homogeneous transformation matrix of an initial control point;
the coordinate rotation interpolation solving unit comprises a circular arc axial deviation solving module and a quaternion interpolation module of which a rotation matrix rotates around an axis, and is used for calculating the maximum control point interval angle meeting the circular arc axial deviation requirement and solving the coordinate rotation matrix of the control point according to the maximum control point interval angle;
the coordinate vector position interpolation unit comprises a control point axial offset solving module and a control point position interpolation module, and is used for calculating the axial offset of the control point relative to the rotation center and generating the position vector of the control point.
The invention discloses a path planning method and a path planning device for cooperative rotation of double robots, which are provided with a path circular interpolation method and a path circular interpolation device based on quaternion and rotation matrix. The multi-angle centering rotation of the double-robot coordinated conveying workpiece in the space can be realized, and the universal applicability is realized.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic platform diagram of a dual-robot system of the present invention;
FIG. 2 is a simplified structural diagram of a two-robot collaboration platform of the present invention;
FIG. 3 is a flow chart of path arc interpolation according to the present invention;
FIG. 4 is a graph of the path arc axial offset of the present invention;
fig. 5 is a schematic diagram of control points for path circular interpolation according to the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. It should be noted that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and all other embodiments obtained by those skilled in the art without any inventive work based on the embodiments of the present invention belong to the protection scope of the present invention.
The invention provides a path planning method for double-robot cooperative rotation, which is applied to a double-robot cooperative system, wherein the system comprises two robots, the two robots respectively comprise an end effector which is used for clamping a workpiece to be machined together, and the method is used for performing coordinate interpolation of control points of circular motion on six axes at the tail end of the robot so as to realize multi-angle center-to-center rotation of the workpiece clamped by the double robots in a coordinated manner in space. Specifically, the method provided by the invention comprises the following steps:
the two robots are oppositely arranged relative to a world coordinate z axis, the path arc radius is set according to the size of a clamped workpiece, the path deflection angle is set, and the cooperative rotation working condition is executed.
And acquiring a homogeneous transformation matrix of the coordinates of the end groups of the two robots according to the relative relation of the arrangement of the robot platforms and the standard D-H parameters of the robots.
And respectively carrying out coordinate rotation interpolation and control point coordinate vector interpolation based on space geometry on the two robots to generate a homogeneous transformation matrix of the control points relative to the robot base coordinate.
And solving joint coordinate angle variables corresponding to the control point homogeneous transformation matrix according to inverse dynamics.
Specifically, in the method, the terminal group coordinate homogeneous transformation matrix is divided into two parts, namely a three-dimensional rotating coordinate and a position vector. And adopting rotation interpolation based on quaternion for the three-dimensional rotation coordinate, adopting coordinate interpolation based on space geometry for the position vector, and integrating the three-dimensional rotation coordinate and the position vector into a homogeneous transformation matrix of the control point relative to the corresponding robot base coordinate. And (5) carrying out inverse dynamics solution on the alignment secondary transformation matrix, and outputting the angle value of each axis joint of the robot at the control point.
Furthermore, the influence of the arc axial offset is considered in the interpolation process of the three-position rotation coordinate, and the maximum interval angle value of the control point is solved according to the limitation of the arc axial offset.
Referring to fig. 1-5, a preferred embodiment of the application of the method of the present invention is shown.
Fig. 1 is a schematic diagram of a platform of a cooperative system of the present invention, in which a master robot and a slave robot (schematically, a master robot 1 and a slave robot 2) are industrial robots loaded with 20kg and 5kg, respectively. The two robots are arranged oppositely in space according to the z axis of a world coordinate system, and the tail ends of the robots are loaded with end effectors (specifically, pneumatic suction cups in the embodiment) and simultaneously clamp workpieces to execute working conditions.
Fig. 2 shows a simplified structural diagram of a two-robot cooperative platform. The plane simplified structure mainly describes the relative position relationship and the D-H parameter attribute of the double robots in a world coordinate system. There is an x-axis spacing l and a y-axis spacing b. The height of the base of the robot 1 is h1The height of the base of the robot 2 is h2(ii) a The length of the joint connecting rod of the left and right robots is aiAnd a'iThe offset is diAnd d'i。
Fig. 3 shows a path arc interpolation flowchart of the present invention, in which a homogeneous transformation matrix of initial control points is calculated from a path arc radius determined by a predetermined path deflection angle and a workpiece size.
FIG. 4 is a schematic view of the maximum axial offset of the arc of the path. When the movej linear motion instruction is adopted to plan the circular arc path, the axial deviation of the path circular arc exists. The tail end of the experiment platform adopts a flexible elastic air claw, and the elastic limit is 0.01 m. The maximum axial offset of the path arc is set to 0.005 m. The control points equally divide the path arc, with the maximum axial offset occurring on the centerline of two adjacent control points.
Fig. 5 is a schematic diagram of control points for path circular interpolation. Extracting three-dimensional rotation matrix from homogeneous transformation matrix of initial control points
Let cos be c, sin be s, and the coordinate vector of the point P coordinate system relative to the control point is generally in the form of
And r is the radius of the path arc. The path circular interpolation can be expressed as two interpolation links of rotation and coordinate vectors:
(1) will T3Q converted to quaternion form0＝q0+q1i+q2j+q3k, where i, j, k are imaginary units, q0、q1、q2、q3Is a specific variable value, and sets the quaternion expression of the control point to Qi＝[wi,(xi,yi,zi)]T，wiIs the value of the real variable, xi,yi,ziIs the value of the imaginary variable, according to Qi-Q'. Q0*Q′-1And substituting a calculation formula of quaternion multiplication into the maximum arc maximum angle of the control point to obtain quaternion of each rotated control point, and converting the quaternion into a rotation matrix at any control point.
(2) The coordinate offset of the control point relative to the coordinate system P can be determined by the offset vector P in each coordinate axis directionx，py，pzExpressing, the coordinate vector of the control point as
In general form (1).
Preferably, the solving method of the initial control homogeneous transformation matrix comprises the following steps: relative rotation path xpzpThe plane deflection angle is α, the radius of the path arc is r, and the coordinate P of the starting point of the path is0First by ypRotate 90 degrees clockwise, then rotate clockwise (α +90 degrees) relative to the z-axis, and translate along the z-axis axially to-r m (m is more than or equal to 0)<360)。P0The homogeneous transformation matrix relative to the P-point coordinate system is represented as:
preferably, the maximum angle value of the arc control point satisfies:
the interval angle between the two control points is less than
Accordingly, a specific n value is taken to satisfy
Indicating that adjacent control points are spaced by n, the control point rotation angle should be set to n,2n, … kn.
Preferably, the initial control point Q0The quaternion representation of (a) is generally of the form:
preferably, the quaternion has an angle of rotation n around the axis, and the quaternion associated with the axis of rotation is expressed as:
preferably, quaternion Qi＝[wi,(xi,yi,zi)]TThe general form of gesture rotation is represented as:
the formula for converting quaternion to rotation matrix is:
preferably, the control points satisfy the relationship with respect to each element of the coordinate vector of the point P coordinate system:
v is the number of path control points.
Preferably, the homogeneous transformation matrix of the two robot control points with respect to the robot base coordinates can be expressed as:
l is the distance between two robots in the x-axis direction, b is the distance between two robots in the y-axis direction, and h1The height of the base of the left robot is h2The height of the base of the right robot.
The invention correspondingly provides a path planning device for cooperative rotation of two robots, which comprises a robot coordinate calibration module, a control point interpolation module and an inverse dynamics solving module;
the robot coordinate calibration module is used for calibrating the attributes of the base coordinate and the tail end axis coordinate of the unit robot and establishing a relative coordinate relation in the robot cooperative system;
the control point interpolation module is used for executing circular arc path interpolation of the two robots according to the uniform transformation matrix of the tail end of the robot and aiming at the interpolation requirement of the path circular arc;
the control point interpolation module comprises an initial control point unit, a coordinate rotation interpolation unit and a coordinate vector position interpolation unit.
The initial control point solver comprises a path circular arc modeling module and a homogeneous transformation matrix solving module of an initial control point coordinate system. And the homogeneous transformation matrix is used for modeling the path circular arc and solving the initial control point.
The coordinate rotation interpolation solving unit comprises a circular arc axial deviation solving module and a quaternion interpolation module of which a rotation matrix rotates around an axis. And the method is used for calculating the maximum control point spacing angle meeting the requirement of the arc axial deviation and solving the coordinate rotation matrix of the control points according to the maximum control point spacing angle.
The coordinate vector position interpolation unit comprises a control point axial offset solving module and a control point position interpolation module. For calculating the axial offset of the control point from the center of rotation and generating a position vector for the control point.
And the inverse dynamics solving module is used for combining the homogeneous transformation matrixes of the control points and solving the joint angle variation corresponding to six axes.
The path planning method and the device for the cooperative rotation of the double robots are a path circular interpolation method with or without difference suitable for quaternions and rotation matrixes of various robots, can calculate interpolation control points of path circular arc tracks, have smooth interpolation paths, meet joint angle limitation and have low roundness error. The multi-angle centering rotation of the double robots cooperatively carrying the workpiece in the space is realized, and the universal applicability is realized.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A path planning method for cooperative rotation of two robots is applied to a cooperative system of two robots, the system comprises two robots, the two robots both comprise end effectors used for clamping workpieces to be processed together, the method is used for path planning of a sixth axis at the tail end of the robot in multi-angle cooperative rotation motion around a central point in space, and the method is characterized by comprising the following steps:
on the basis of independent modeling of a single robot, establishing a mutual position relation of robot platforms, and constructing a kinematic system with relative coordinate transformation;
setting a world coordinate system according to a robot platform arrangement strategy, and calibrating a base coordinate system and a tail end coordinate system of the two robots;
taking each base coordinate system of the two robots as a central coordinate, and solving a homogeneous transformation matrix basic form of the terminal coordinates of the robots according to the standard D-H parameters as basic kinematic parameters;
establishing a path arc model on the cooperative rotation working condition of the robot system, and setting a symmetrical center coordinate system as a path base as an origin;
calculating a homogeneous transformation matrix of the path initial control points according to the known path deflection angle and the path arc radius;
extracting a three-dimensional rotation matrix from the homogeneous transformation matrix of the path initial control point to perform coordinate rotation interpolation based on quaternion;
extracting an initial coordinate vector from the homogeneous transformation matrix of the path initial control point to perform control point coordinate vector interpolation based on space geometry;
and obtaining the joint control angle of the final control point based on homogeneous transformation matrix conversion of inverse dynamics.
2. The method for planning a path through cooperative rotation of two robots as claimed in claim 1, wherein the maximum interval angle value of the control points is solved according to the limitation of the arc axial offset by considering the effect of the arc axial offset in the interpolation process of the three-dimensional rotation coordinate.
3. The dual-robot cooperative rotation path planning method according to claim 1, wherein a three-dimensional rotation matrix is extracted from a homogeneous transformation matrix of the initial control points
Let cos be c, sin be s, and the coordinate vector of the point P coordinate system relative to the control point is generally in the form of
r is the path arc radius; the path circular interpolation can be expressed as two interpolation links of rotation and coordinate vectors:
(1) will T3Q converted to quaternion form0＝q0+q1i+q2j+q3k, where i, j, k are imaginary units, q0、q1、q2、q3Is a specific variable value, and sets the quaternion expression of the control point to Qi＝[wi,(xi,yi,zi)]T，wiIs the value of the real variable, xi,yi,ziIs the value of the imaginary variable, according to Qi-Q'. Q0*Q′-1Substituting a calculation formula of quaternion multiplication into the maximum arc maximum angle of the control point to obtain quaternion of each rotated control point, and converting the quaternion into a rotation matrix at any control point;
(2) the coordinate offset of the control point relative to the coordinate system P can be determined by the offset vector P in each coordinate axis directionx，py，pzExpressing, the coordinate vector of the control point as
In general form (1).
4. The method for planning a path through cooperative rotation of two robots according to claim 3, wherein the solution method for initially controlling the homogeneous transformation matrix comprises: relative rotation path xpzpThe plane deflection angle is α, the radius of the path arc is r, and the coordinate P of the starting point of the path is0First by ypRotate 90 degrees clockwise, then rotate clockwise (α +90 degrees) relative to the z-axis, and translate-rm along the z-axis axially (m is more than or equal to 0)<360)；P0The homogeneous transformation matrix relative to the P-point coordinate system is represented as:
5. the method for planning a path through cooperative rotation of two robots according to claim 4, wherein the maximum angle value of the arc control point satisfies:
the interval angle between the two control points is less than
Accordingly, a specific n value is taken to satisfy
Indicating that adjacent control points are spaced by n, the control point rotation angle should be set to n,2n, … kn.
6. The dual-robot cooperative rotation path planning method according to claim 5, wherein an initial control point Q is set0The quaternion representation of (a) is generally of the form:
the quaternion is n around the axis rotation angle, and the associated quaternion for the axis of rotation is expressed as:
quaternion Qi＝[wi,(xi,yi,zi)]TThe general form of gesture rotation is represented as:
the formula for converting quaternion to rotation matrix is:
7. the dual-robot co-rotating path gauge of claim 6The method is characterized in that the control points satisfy the following relations with respect to each element of the coordinate vector of the point P coordinate system:
v is the number of path control points.
8. The method for path planning with cooperative rotation of two robots as claimed in claim 7, wherein the homogeneous transformation matrix of the two robot control points with respect to the robot base target is represented as:
l is the distance between two robots in the x-axis direction, b is the distance between two robots in the y-axis direction, and h1The height of the base of the left robot is h2The height of the base of the right robot.
9. A path planning device with two robots rotating cooperatively is characterized by comprising a robot coordinate calibration module, a control point interpolation module and an inverse dynamics solving module;
the robot coordinate calibration module is used for calibrating the attributes of the base coordinate and the tail end axis coordinate of the unit robot and establishing a relative coordinate relation in the robot cooperative system;
the control point interpolation module is used for executing circular arc path interpolation of the two robots according to the homogeneous transformation matrix at the tail end of the robot and aiming at the interpolation requirement of the path circular arc;
and the inverse dynamics solving module is used for combining the homogeneous transformation matrixes of the control points and solving the joint angle variation corresponding to six axes.
10. The dual-robot cooperative rotation path planning apparatus according to claim 9, wherein the control point interpolation module includes an initial control point unit, a coordinate rotation interpolation unit, and a coordinate vector position interpolation unit;
the initial control point unit comprises a path circular arc modeling module and a homogeneous transformation matrix solving module of an initial control point coordinate system, and is used for modeling a path circular arc and solving a homogeneous transformation matrix of an initial control point;
the coordinate rotation interpolation solving unit comprises a circular arc axial deviation solving module and a quaternion interpolation module of which a rotation matrix rotates around an axis, and is used for calculating the maximum control point interval angle meeting the circular arc axial deviation requirement and solving the coordinate rotation matrix of the control point according to the maximum control point interval angle;
the coordinate vector position interpolation unit comprises a control point axial offset solving module and a control point position interpolation module, and is used for calculating the axial offset of the control point relative to the rotation center and generating the position vector of the control point.
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