CN113103239B - Robot attitude trajectory generation method and device and storage medium - Google Patents
Robot attitude trajectory generation method and device and storage medium Download PDFInfo
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Abstract
The invention provides a robot gesture track generation method, a device and a storage medium, wherein the method comprises the following steps: acquiring a plurality of quaternion postures in the robot motion process, and grouping all the postures; determining a first quaternion corresponding to each group of quaternion postures according to the grouping result; converting the first quaternion corresponding to each group into a plurality of vectors of three-dimensional space, and interpolating each vector by adopting a cubic Bezier curve to obtain an interpolation curve; sampling the interpolation curve to obtain a plurality of sampling points; and fitting all the sampling points by adopting a cubic B-spline curve to generate a robot attitude track. The technical scheme of the invention can generate the gesture track of the whole C2 continuous robot, and reduce the track fluctuation among the gestures of the robot.
Description
Technical Field
The invention relates to the technical field of intelligent control, in particular to a robot posture trajectory generation method and device and a storage medium.
Background
When the tail end gesture track of the robot is sufficiently smooth, the track tracking performance of the robot can be improved. At present, the attitude of the robot is often described by a rotation matrix, an Euler angle, an RPY (Roll-Pitch-Yaw), a quaternion and the like, wherein when the attitude planning is carried out by utilizing the rotation matrix, the data redundancy is high, and the orthogonality of the data is directly damaged; the singularity exists when the posture is expressed by an RPY method; when the attitude is expressed by the Euler angle, the phenomenon of dead locking of the universal joint can occur, interpolation is difficult, and the requirements on smoothness and continuity in robot attitude planning cannot be well met.
The quaternion is widely applied due to the advantages of simple and visual description, small calculated amount and the like, when the robot posture is described, the problem of dead locking of a universal joint generated when an Euler angle rotates can be effectively solved, and the posture interpolation efficiency is higher than that based on the Euler angle and a rotation matrix. When the quaternion is adopted to describe the robot attitude, the quaternion attitude interpolation method mainly comprises quaternion linear interpolation, spherical linear interpolation and spherical spline interpolation.
However, the spherical linear interpolation has only C0 continuity, and the spherical spline interpolation also has only C1 continuity, and thus cannot meet the actual requirement. In order to obtain a quaternion spline curve with higher continuity, the prior art provides a quaternion spline curve with C2 continuity, which can meet the requirement of C2 continuity, but the adopted model is too complex, the track fluctuation is large, the mathematical model is complex, and the understanding is difficult.
Disclosure of Invention
The invention solves the problem of reducing the track fluctuation among the postures of the robot when the posture track of the robot meets the continuous requirement of C2.
In order to solve the above problems, the present invention provides a method, an apparatus, and a storage medium for generating a robot gesture trajectory.
In a first aspect, the present invention provides a method for generating a robot pose trajectory, including:
acquiring a plurality of quaternion postures in the robot motion process, and grouping all the quaternion postures;
determining a first quaternion corresponding to each group of quaternion postures according to grouping results;
converting the first quaternion corresponding to each group into a plurality of vectors of three-dimensional space, and interpolating each vector by adopting a cubic Bezier curve to obtain an interpolation curve;
sampling the interpolation curve for multiple times to obtain multiple sampling points;
and fitting all the sampling points by adopting a cubic B-spline curve to generate a robot attitude track.
Optionally, the grouping all the quaternion poses comprises:
and sequentially grouping every three quaternion postures into one group according to the action sequence of the robot, wherein every two adjacent groups comprise the same quaternion posture, and when the number of the remaining quaternion postures is less than three, dividing every two remaining quaternion postures into one group.
Optionally, the determining, according to the grouping result, a first quaternion corresponding to each group of quaternion attitudes includes:
for a group of three quaternion attitudes, determining a transformation matrix between two adjacent quaternion attitudes, and respectively converting the two obtained transformation matrices into the first quaternion;
and for the two quaternion attitudes which are in a group, keeping the quaternion attitudes unchanged, wherein the two quaternion attitudes respectively correspond to one first quaternion.
Optionally, the converting the first quaternion corresponding to each group into a plurality of vectors in three-dimensional space, and interpolating each vector by using a cubic bezier curve includes:
converting the two quaternions corresponding to each set of the quaternion attitudes into three first unit vectors of a three-dimensional space, wherein each unit vector corresponds to a first data point;
and for each group of three first data points, performing interpolation by using a cubic Bezier curve, wherein the interpolation curve between the first data points is generated by solving two middle control points of the cubic Bezier curve, wherein the first data point in the motion direction of the robot in the three first data points is a first control point of the cubic Bezier curve, the third first data point is a last control point of the cubic Bezier curve, and the second first data point is a point on the cubic Bezier curve.
Optionally, the sampling the interpolation curve multiple times, and obtaining multiple sampling points includes:
and sequentially sampling the interpolation curve for multiple times, and converting each sampling point obtained by sampling into a second quaternion respectively.
Optionally, the fitting all the sampling points by using a cubic B-spline curve comprises:
for the second quaternion corresponding to each sampling point, establishing a mapping relation between the second quaternion and a second unit vector, and converting the second quaternion into the second unit vector according to the mapping relation, wherein each second unit vector corresponds to one second data point;
and fitting all the second data points by adopting a cubic B-spline curve to generate the robot posture track.
In a second aspect, the present invention provides a robot posture trajectory generation apparatus, including:
the acquisition module is used for acquiring a plurality of quaternion postures in the motion process of the robot and grouping all the quaternion postures;
the grouping module is used for determining a first quaternion corresponding to each group of quaternion postures according to the grouping result;
the interpolation module is used for converting the first quaternion corresponding to each group into a plurality of vectors of three-dimensional space, and interpolating each vector by adopting a cubic Bezier curve to obtain an interpolation curve;
the sampling module is used for sampling the interpolation curve for multiple times to obtain multiple sampling points;
and the fitting module is used for fitting all the sampling points by adopting a cubic B-spline curve to generate a robot attitude track.
In a third aspect, the present invention provides an electronic device, including a memory and a processor;
the memory for storing a computer program;
the processor is configured to implement the robot pose trajectory generation method as described above when executing the computer program.
In a fourth aspect, the present invention provides a computer-readable storage medium having stored thereon a computer program, which, when executed by a processor, implements the robot pose trajectory generation method as described above.
The robot posture track generation method, the robot posture track generation device and the storage medium have the beneficial effects that: the method comprises the steps of obtaining a plurality of quaternion postures in the robot motion process, grouping the quaternion postures, calculating quaternion corresponding to each group of quaternion postures according to grouping results, and ensuring that each group corresponds to two quaternion. And then interpolating by adopting a cubic Bezier curve interpolation algorithm to generate an interpolation curve between quaternion postures, sampling for multiple times on the interpolation curve to obtain multiple sampling points, and fitting all the sampling points by adopting a cubic B spline curve fitting algorithm to generate a continuous robot posture track of the whole C2. Meanwhile, the technical scheme of the invention can reduce the track fluctuation among the postures of the robot and improve the smoothness of the track.
Drawings
Fig. 1 is a schematic flow chart of a robot posture trajectory generation method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a cubic Bezier curve according to another embodiment of the present invention;
fig. 3 is a schematic structural diagram of a robot pose trajectory generation apparatus according to an embodiment of 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 terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein.
As shown in fig. 1, an embodiment of the present invention provides a robot pose trajectory generation method, including:
and step S110, acquiring a plurality of quaternion postures in the movement process of the robot, and grouping all the quaternion postures.
In particular, the quaternion pose represents a quaternion representation of the robot pose.
Step S120, determining quaternions corresponding to the quaternion postures of each group according to grouping results;
step S130, converting the first quaternion corresponding to each group into a plurality of vectors of three-dimensional space, and interpolating each vector by adopting a cubic Bezier (Bezier) curve to obtain an interpolation curve;
step S140, sampling the interpolation curve for multiple times to obtain multiple sampling points;
and S150, fitting all the sampling points by adopting a cubic B-spline curve to generate a robot attitude track.
In this embodiment, a plurality of quaternion attitudes in the robot motion process are obtained, the quaternion attitudes are grouped, quaternion corresponding to each group of quaternion attitudes is calculated according to the grouping result, and it is ensured that each group corresponds to two quaternion. And then interpolating by adopting a cubic Bezier curve interpolation algorithm to generate an interpolation curve between quaternion postures, sampling for multiple times on the interpolation curve to obtain multiple sampling points, and fitting all the sampling points by adopting a cubic B spline curve fitting algorithm to generate a continuous robot posture track of the whole C2. Meanwhile, the technical scheme of the invention can reduce the track fluctuation among the postures of the robot and improve the smoothness of the posture track. The gesture track has more definite physical significance and is beneficial to popularization and application.
Optionally, the grouping all the quaternion poses includes:
and sequentially grouping every three quaternion postures into one group according to the action sequence of the robot, wherein every two adjacent groups comprise the same quaternion posture, and when the number of the remaining quaternion postures is less than three, dividing every two remaining quaternion postures into one group.
Specifically, assuming that the quaternion postures are A, B, C, D and E respectively in sequence according to the motion sequence of the robot, the quaternion postures can be divided into two groups, one group is A, B, C, the other group is C, D, E, the two groups include the same quaternion posture C, if the quaternion postures are A, B, C and D respectively in sequence, after A, B and C are first divided into one group, only one D is left, and the common C is added, and only two quaternion postures are left, the two quaternion postures C and D are used as one group.
Optionally, the determining, according to the grouping result, a first quaternion corresponding to each group of quaternion attitudes includes:
and determining a transformation matrix between two adjacent quaternion attitudes for a group of three quaternion attitudes, and then converting the two transformation matrices into the first quaternion respectively.
Specifically, the quaternion attitude is an attitude during the robot action, when three quaternion attitudes are in a group, the three quaternion attitudes are first converted into three attitude matrices, if the three attitude matrices are R matrices, respectively i-1 ,，R i ,，R i+1 Then determining a transformation matrix between two adjacent attitude matrices and finally converting the transformation matrix into a first quaternion, e.g.
Wherein R is i+1 R i -1 Is an attitude matrix R i ，R i+1 F denotes a mapping relation of the transformation matrix to the first quaternion, Q i Representing a first quaternion. Respectively converting the two transformation matrixes into first quaternions to obtain two first quaternions Q i ，Q i+1 。
And for the two quaternion attitudes which are in a group, keeping the quaternion attitudes unchanged, wherein the quaternion corresponding to the two quaternion attitudes is the first quaternion.
In this optional embodiment, when each group includes three quaternion attitudes, the first quaternion represents a transformation relationship between attitude matrices corresponding to the three quaternion attitudes, and when each group includes two quaternion attitudes, the first quaternion represents a transformation relationship between two quaternion attitudes from the base coordinate system.
Optionally, the converting the first quaternion corresponding to each group into a plurality of vectors in three-dimensional space, and interpolating each vector by using a cubic bezier curve includes:
converting the two first quaternions corresponding to each set of quaternion attitudes into three first unit vectors of a three-dimensional space, wherein each first unit vector corresponds to a first data point;
and for each group of three first data points, interpolating by using a cubic Bezier curve, wherein with the first data point in the motion direction of the robot in the three first data points as a first control point of the cubic Bezier curve, the third first data point as a last control point of the cubic Bezier curve and the second first data point on the cubic Bezier curve, two middle control points of the cubic Bezier curve are solved, and the two middle control points coincide to generate the interpolation curve between the quaternion postures.
In particular, since the unit quaternion can be expressed as the product of two three-dimensional unit vectors, and the two vectors follow the quaternion multiplication law, assume two first quaternions Q corresponding to an arbitrary set of quaternion poses i-1 ，Q i Two first quaternions Q are expressed by a first formula i-1 ，Q i The first formula includes:
then the process of the first step is carried out,
and the combination of (a) and (b),
where there are 9 unknowns and 9 equations, a unique set of first unit vectors can be found
Each first unit vector corresponds to a data point.
As shown in fig. 2, a cubic bezier curve is then used for interpolation:
defining a cubic Bezier curve over the interval [0,1] using a second formula comprising:
wherein, B 0,3 (t)＝(1-t) 3 ,B 1,3 (t)＝3t(1-t) 2 ,
B 2,3 (t)＝3t 2 (1-t),B 3,3 (t)＝t 3 。
Then s is determined using a third formula 1 Corresponding parameter t 1 The third formula includes:
a parameter t 1 Substituting into the second formula of cubic Bezier curve, and s (t) 1 )＝s 1 Solving a control point b of the cubic Bezier curve 1 、b 2 And then obtaining a cubic Bezier curve
Cubic Bezier curve
I.e. the interpolation curve, passes through s in fig. 2 0 、s 1 And s 2 The curve of (d) is the interpolation curve.
A fourth formula may be employed to convert points on a cubic Bezier curve to a second quaternion, the fourth formula including:
wherein q (t) represents a second quaternion,
a cubic Bezier curve is shown,
is a unit vector.
Optionally, the sampling the interpolation curve multiple times, and obtaining multiple sampling points includes:
and sequentially sampling the interpolation curve for multiple times, and converting each sampling point obtained by sampling into a second quaternion respectively.
Specifically, cubic Bezier curves are sequentially aligned
Sampling is carried out to obtain a plurality of sampling points, and the sampling points are all represented by the second quaternion because the points on the cubic Bezier curve are converted into the second quaternion.
Optionally, the fitting all the sampling points by using a cubic B-spline curve comprises:
for the second quaternion corresponding to each sampling point, the second quaternion can be expressed as
Wherein q is i0 、q i1 、q i2 And q is i3 In the case of a real number,
and
in units of imaginary numbers.
Establishing the second quaternion Q i And a second unit vector Q i ' mapping relationship Q between i →Q i ′，
Wherein q is i0 ≠0；
Converting the second quaternion into the second unit vectors according to the mapping relation, wherein each second unit vector corresponds to a second data point;
and fitting all the second data points by adopting a cubic B-spline curve to generate the robot posture track.
Specifically, fitting all the second data points by using the cubic B-spline curve comprises performing back calculation on a group of second data points on the curve to define a control vertex of the B-spline curve, and determining the cubic B-spline curve, namely the robot attitude trajectory. The determination of the control points of the cubic B-spline curve from the data points is known in the art, for example, see "journal of the university of post and telecommunications" paper 19, vol.3, a simple method for cubic B-spline back calculation ", which is not described herein again.
In this optional embodiment, the interpolation curve is sampled to obtain a plurality of sampling points, and then all the sampling points are fitted through cubic B-spline curve fitting algorithm, so that a whole C2 continuous robot attitude track can be obtained, wherein the robot attitude track speed and the acceleration are continuous, the smoothness of the robot motion is ensured, and compared with the prior art, the fluctuation of the generated robot attitude track is reduced, and the physical significance of the robot attitude track is more definite.
As shown in fig. 3, an embodiment of the present invention provides a robot pose trajectory generating apparatus, configured to execute the robot pose trajectory generating method described above, including:
the acquisition module is used for acquiring a plurality of quaternion postures in the motion process of the robot and grouping all the quaternion postures;
the grouping module is used for determining a first quaternion corresponding to each group of quaternion postures according to the grouping result, wherein each group of quaternion postures corresponds to two first quaternions;
the interpolation module is used for converting the first quaternion corresponding to each group into a plurality of vectors of three-dimensional space, and interpolating each vector by adopting a cubic Bezier curve to obtain an interpolation curve;
the sampling module is used for sampling the interpolation curve for multiple times to obtain multiple sampling points;
and the fitting module is used for fitting all the sampling points by adopting a cubic B-spline curve to generate a robot attitude track.
Another embodiment of the present invention provides an electronic device comprising a memory and a processor; the memory for storing a computer program; the processor is configured to implement the robot pose trajectory generation method as described above when executing the computer program. The device may be a computer or a server, etc.
Yet another embodiment of the present invention provides a computer program stored on a computer-readable storage medium, which when executed by a processor, implements the robot pose trajectory generation method as described above.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like. In this application, the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment of the present invention. In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit may be implemented in the form of hardware, or may also be implemented in the form of a software functional unit.
Although the present disclosure has been described above, the scope of the present disclosure is not limited thereto. Various changes and modifications may be effected therein by one of ordinary skill in the pertinent art without departing from the spirit and scope of the present disclosure, and these changes and modifications are intended to be within the scope of the present disclosure.
Claims (6)
1. A robot pose trajectory generation method is characterized by comprising the following steps:
acquiring a plurality of quaternion postures in the robot motion process, and grouping all the quaternion postures, wherein the method comprises the following steps: sequentially grouping every three quaternion postures into one group according to the action sequence of the robot, wherein every two adjacent groups comprise the same quaternion posture, and when the number of the remaining quaternion postures is less than three, dividing every two remaining quaternion postures into one group;
determining a first quaternion corresponding to each group of quaternion postures according to grouping results, wherein the determining comprises the following steps: for a group of three quaternion attitudes, determining a transformation matrix between two adjacent quaternion attitudes, and respectively converting the two obtained transformation matrices into the first quaternion; for a group of two quaternion attitudes, keeping the quaternion attitudes unchanged, wherein the two quaternion attitudes respectively correspond to one first quaternion;
converting the first quaternion corresponding to each group into a plurality of vectors of three-dimensional space, and interpolating each vector by adopting a cubic Bezier curve to obtain an interpolation curve, wherein the method comprises the following steps: converting each set of two corresponding first quaternions into three first unit vectors of a three-dimensional space, each first unit vector corresponding to one first data point; for each group of three first data points, performing interpolation by using a cubic Bezier curve, wherein the interpolation curve between the first data points is generated by solving two middle control points of the cubic Bezier curve and the two middle control points coincide with each other by taking the first data point in the robot motion direction as the first control point of the cubic Bezier curve, the third first data point is the last control point of the cubic Bezier curve and the second first data point is positioned on the cubic Bezier curve;
sampling the interpolation curve to obtain a plurality of sampling points;
and fitting all the sampling points by adopting a cubic B-spline curve to generate a robot attitude track.
2. The method of claim 1, wherein the sampling the interpolation curve to obtain a plurality of sampling points comprises:
and sequentially sampling the interpolation curve for multiple times, and converting each sampling point obtained by sampling into a second quaternion respectively.
3. The robot pose trajectory generation method of claim 2, wherein the fitting all the sample points with a cubic B-spline curve comprises:
for the second quaternion corresponding to each sampling point, establishing a mapping relation between the second quaternion and a second unit vector, and converting the second quaternion into the second unit vector according to the mapping relation, wherein each second unit vector corresponds to one second data point;
and fitting all the second data points by adopting a cubic B-spline curve to generate the robot posture track.
4. A robot pose trajectory generation apparatus, comprising:
the acquisition module is used for acquiring a plurality of quaternion postures in the motion process of the robot and grouping all the quaternion postures, and comprises the following steps: sequentially grouping every three quaternion postures into one group according to the action sequence of the robot, wherein every two adjacent groups comprise the same quaternion posture, and when the number of the remaining quaternion postures is less than three, dividing every two remaining quaternion postures into one group;
the grouping module is used for determining a first quaternion corresponding to each group of quaternion postures according to a grouping result, and comprises: for a group of three quaternion attitudes, determining a transformation matrix between two adjacent quaternion attitudes, and respectively converting the two obtained transformation matrices into the first quaternion; for a group of two quaternion attitudes, keeping the quaternion attitudes unchanged, wherein the two quaternion attitudes respectively correspond to one first quaternion;
an interpolation module, configured to convert the first quaternion corresponding to each group into a plurality of vectors in a three-dimensional space, and interpolate each vector by using a cubic bezier curve to obtain an interpolation curve, where the interpolation module includes: converting each set of two corresponding first quaternions into three first unit vectors of a three-dimensional space, each first unit vector corresponding to one first data point; for each group of three first data points, performing interpolation by using a cubic Bezier curve, wherein the interpolation curve between the first data points is generated by solving two middle control points of the cubic Bezier curve and the two middle control points coincide with each other by taking the first data point in the robot motion direction as the first control point of the cubic Bezier curve, the third first data point is the last control point of the cubic Bezier curve and the second first data point is positioned on the cubic Bezier curve;
the sampling module is used for sampling the interpolation curve for multiple times to obtain multiple sampling points;
and the fitting module is used for fitting all the sampling points by adopting a cubic B-spline curve to generate a robot attitude track.
5. An electronic device comprising a memory and a processor;
the memory for storing a computer program;
the processor, configured to, when executing the computer program, implement the robot pose trajectory generation method of any of claims 1 to 3.
6. A computer-readable storage medium, characterized in that the storage medium has stored thereon a computer program which, when being executed by a processor, carries out the robot pose trajectory generation method according to any of the claims 1 to 3.
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