CN109531573B - Robot posture smooth path generation method based on sample lines - Google Patents
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Abstract
The invention provides a method for generating a robot posture smooth path based on a spline, which comprises the following steps: step S1, converting a rotation matrix R for representing the robot posture into a quaternion q representation, and further converting the quaternion q into a three-dimensional vector psi representation in a Cartesian space; and step S2, planning the three-dimensional vector psi by adopting a spline curve planning technology, constructing a spline curve, and converting the spline curve into quaternion representation so as to generate a robot tail end attitude path. The invention converts the attitude points of the end effector of the robot into three-dimensional vectors of a Cartesian space, and obtains a smooth attitude path through spline interpolation, thereby improving the smoothness of the path and reducing the computation amount.
Description
Technical Field
The invention relates to the technical field of industrial robots, in particular to a method for generating a smooth path based on the posture of a spline robot.
Background
How to plan an available and smooth path is one of the difficulties in the path planning of the robot. For industrial robots, the requirements on the smoothness of the path are higher. One important reason for affecting the smoothness of the robot path is the unsmooth change in pose. Currently, the most industrial robots generate the gesture path by using a quaternion spherical linear interpolation (SLERP) method. However, this method is a linear interpolation method, which is continuous with C0, so the path planned by this method is continuous, but the smoothness cannot be guaranteed. And therefore, the accuracy and repeatability of the path of the robot are seriously affected.
At present, most robot manufacturers do not fundamentally eliminate the reason for the unsmooth path, but adopt some post-processing methods. For example, smoothing means such as filtering, but this method may have a great influence on the path accuracy of the robot, for example, the filtered path may have a certain drift with the target path, so that the disadvantage of this method is more and more prominent in the times of today having higher requirements on the accuracy of the robot.
In addition, in the prior art, various methods based on quaternion spline curve planning, such as a fast quaternion spline curve construction method, are proposed for the research on the attitude smooth path planning method. However, this method can only guarantee C1And the method is continuous and cannot be applied to the attitude path planning of the robot. Another way is to accumulate quaternion spline curves, which can guarantee C2Continuously, but in the robot path planning process, when the accumulated quaternion spline interpolation is applied, a closed solution form is not available, a numerical iteration method is needed, the consumed time is long, and the requirement of the real-time performance of the robot path planning is not met. There is also a risk of solution failure, and in academic studies most studies are still based on variations of these two methods, but these methods cannot be used directly in robotic path planning.
Disclosure of Invention
The object of the present invention is to solve at least one of the technical drawbacks mentioned.
Therefore, the invention aims to provide a method for generating a smooth path based on the posture of a spline robot.
In order to achieve the above object, an embodiment of the present invention provides a method for generating a smooth path based on a spline robot pose, including the following steps:
step S1, converting a rotation matrix R for representing the robot posture into a quaternion q representation, and further converting the quaternion q into a three-dimensional vector psi representation in a Cartesian space;
and step S2, planning the three-dimensional vector psi by adopting a spline curve planning technology, constructing a spline curve, and converting the spline curve into quaternion representation so as to generate a robot tail end attitude path.
Further, in the step S1, a rotation matrix R representing the robot pose is converted into a quaternion q, wherein,
q＝(n，Θ)
wherein n is a rotating shaft vector and is a three-dimensional unit vector, and theta is a rotating angle around the rotating shaft n.
Further, in the step S1, converting the quaternion q into a three-dimensional vector Ψ representation in the cartesian space includes:
the quaternion q is written as follows:
the following relationship is thus obtained from the quaternion operation:
wherein,
further, in step S2, the planning the three-dimensional vector Ψ by using a spline curve planning technique includes:
let phi be n theta, let t be a construction parameter of the attitude spline curve, and construct the following spline curve:
φ＝NP
wherein N is a base matrix of the spline curve,
m is the degree of the spline curve; p is a control point of the spline curve;
under the condition of giving the robot attitude point, solving phi NP to obtain a smooth spline curve by a spline interpolation method,
further, the obtained spline curve constructed in the Cartesian space is converted into a representation form of quaternion through the following formula for application,
according to the method for generating the smooth path based on the gesture of the spline robot, the gesture point of the end effector of the robot is converted into a three-dimensional vector of a Cartesian space, and a smooth gesture path is obtained through spline interpolation. Compared with a Slerp method, the constructed attitude spline is continuous in high order, and the smoothness of the path can be improved; compared with the quaternion spline curve in an accumulation form, the method has less calculation amount and can meet the real-time requirement of planning.
Additional aspects and advantages 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.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a flowchart of a spline-based robot pose smooth path generation method according to an embodiment of the present invention.
Fig. 2 is a schematic diagram illustrating comparison of the results of the pose spline path planning according to the embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The invention provides a robot posture smooth path generation method based on sample lines, which is characterized in that a sample line curve is constructed in a Cartesian space to obtain C2A continuous smooth state path.
As shown in fig. 1, the method for generating a smoothed path based on a spline robot pose according to the embodiment of the present invention includes the following steps:
in step S1, since the rotation matrix cannot be directly applied to path planning, the rotation matrix R for representing the robot posture is converted into a quaternion q, which is further converted into a three-dimensional vector Ψ in cartesian space.
First, a rotation matrix R representing the robot pose is converted into a quaternion q, wherein,
q＝(n，Θ) (1)
wherein n is a rotating shaft vector and is a three-dimensional unit vector, and theta is a rotating angle around the rotating shaft n.
The quaternion q is then converted to a three-dimensional vector Ψ representation in cartesian space, comprising:
the quaternion q is written as follows:
the following relationship is thus obtained from the quaternion operation:
wherein,
and step S2, planning the three-dimensional vector psi by adopting a spline curve planning technology, constructing a spline curve, and converting the spline curve into quaternion representation so as to generate a robot tail end attitude path.
In step S1, the quaternion q is converted into a three-dimensional vector Ψ in the cartesian space. In fact, Ψ is a four-dimensional vector, but the first term thereof is constantly 0, and thus, the vector Ψ can be regarded as a three-dimensional vector, so that the vector Ψ can be directly planned, and a pose path is constructed by using a spline curve planning technique.
Let phi be n Θ, apply spline planning technique to the vector. Let t be the construction parameter of the attitude spline curve, construct the following spline curve:
φ＝NP (5)
wherein N is a base matrix of the spline curve,
m is the degree of the spline curve; p is a control point of the spline curve;
under the condition of giving the robot attitude point, solving phi NP to obtain a smooth spline curve by a spline interpolation method,
then, the obtained spline curve constructed in the Cartesian space is converted into a representation form of quaternion through the formula (3) for application,
in this process, although the spline curve is constructed in cartesian space, the smoothness of the curve does not change during the conversion into quaternions. The spline curve is C2Continuous, therefore quaternion attitude spline path is also C2And (3) continuous. The smooth and available gesture path constructed in the above way can effectively improve the path smoothness and accuracy of the robot. Fig. 2 shows the pose path planning result.
According to the method for generating the smooth path based on the gesture of the spline robot, the gesture point of the end effector of the robot is converted into a three-dimensional vector of a Cartesian space, and a smooth gesture path is obtained through spline interpolation. Compared with a Slerp method, the constructed attitude spline is continuous in high order, and the smoothness of the path can be improved; compared with the quaternion spline curve in an accumulation form, the method has less calculation amount and can meet the real-time requirement of planning.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention. The scope of the invention is defined by the appended claims and their full range of equivalents.
Claims (2)
1. A method for generating a smooth path based on the posture of a spline robot is characterized by comprising the following steps:
step S1, converting a rotation matrix R for representing the robot posture into a quaternion q representation, and further converting the quaternion q into a three-dimensional vector psi representation in a Cartesian space;
step S2, planning the three-dimensional vector psi by adopting a spline curve planning technology, constructing a spline curve, and converting the spline curve into quaternion representation so as to generate a robot terminal attitude path;
in said step S1, the rotation matrix R representing the robot pose is converted into a quaternion q, wherein,
q＝(n，Θ)
wherein n is a rotating shaft vector and is a three-dimensional unit vector, and theta is a rotating angle around the rotating shaft;
in the step S1, converting the quaternion q into a three-dimensional vector Ψ representation in cartesian space includes:
the quaternion q is written as follows:
the following relationship is thus obtained from the quaternion operation:
wherein,
in step S2, the planning of the three-dimensional vector Ψ by using a spline curve planning technique includes the following steps:
let phi be n theta, let t be a construction parameter of the attitude spline curve, and construct the following spline curve:
φ＝NP
wherein N is a base matrix of the spline curve,
m is the degree of the spline curve; p is a control point of the spline curve, and n is a numerical value;
under the condition of giving the robot attitude point, solving phi NP to obtain a smooth spline curve by a spline interpolation method,
2. the spline-based robot pose smooth path generation method of claim 1, wherein the spline curve constructed in Cartesian space is converted to a representation of quaternion for application by the following equation,
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