CN105563482A - Rotation movement planning method for end effector of industrial robot - Google Patents

Abstract

The invention provides a rotation movement planning method for an end effector of an industrial robot. The method comprises the following steps: the initial and final postures of the rotation movement of the end effector are input and are converted into quaternions for expression; the end effector is judged to be at a rotation movement turning area or not; if the end effector is not at the turning area, the initial and final postures are interpolated by adopting a quaternion spherical linear interpolation method; rotary shaft vector quantities are calculated and expressed according to the quaternions of the initial and final postures; the angular speed and angular acceleration of the rotation movement of the end effector are calculated according to the rotary shaft vector quantities and the turning angle of the end effector around the equivalent shaft; if the end effector is at the turning area, two rotation tracks at the turning area are interpolated successively for twice by adopting the quaternion spherical linear interpolation method; and the angular speed and angular acceleration are calculated. According to the method, the postures of the end of the robot are described by using quaternions; the problem of eulerian angle singularity is avoided; the rotation movement planning is converted to an initial and final quaternion interpolation problem; and the rotation process around the single shaft is more visible.

Description

Method for planning the rotational movement of an end effector of an industrial robot

Technical Field

The invention relates to the technical field of industrial robots, in particular to a rotary motion planning method for an end effector of an industrial robot.

Background

Industrial robots are often used with tools, i.e. end effectors, that are oriented towards a specific application. The motion of the tool can be described in terms of rigid body motion, including translation of the center point of the tool and rotation of the tool. Since the control of the industrial robot takes place on axes, the rotational movement of the tool is mapped to the axis space as well as the translation of the center point of the tool, so that the rotational movement also needs to be performed smoothly. The existing method for planning the rotary motion of the end effector of the industrial robot mainly comprises the following steps:

(1) simultaneous attitude interpolation for three axes

The robot tip pose is expressed in the form of euler angles, i.e. equivalent to a rotational movement from a unit pose about three axes. And interpolating Euler angles of three axes of the initial attitude and the final attitude to obtain a tail end rotation motion track. The method decomposes the posture into three independent variables for interpolation, and is easy to process when two rotary motions are smoothly connected. However, the euler angle indicates that the posture is singular, and the rotational motion interpolated by the method rotates around three axes, so that the method is not intuitive.

(2) Interpolation by the angle of axis method

And changing the tail end posture of the robot is equivalent to rotating the robot by a certain angle around an equivalent rotating shaft. The rotating shaft of the rotary motion formed by the interpolation method is not changed, and the rotary motion planning is converted into the single-degree-of-freedom planning problem of a certain angle, so that the problem is solved. However, when the two rotational motions are smoothly connected, the rotational angular velocity direction of the end of the robot is suddenly changed, so that a large acceleration is caused, and the robot shakes.

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 rotary motion planning method for an end effector of an industrial robot, wherein quaternions are used for describing the tail end posture of the robot, the problem of singularity of Euler angles is avoided, the rotary motion planning is converted into the interpolation problem of initial and final quaternions, and the rotary process is more visual around single-axis motion.

In order to achieve the above object, an embodiment of the present invention provides a rotational motion planning method for an end effector of an industrial robot, including the steps of:

step S1, inputting the initial and final postures of the rotation motion of the end effector, and converting the initial and final postures into quaternion representation;

step S2, judging whether the end effector is in a turning area of rotary motion;

step S3, if the end effector is not in the turning area, interpolating the initial and final postures by a quaternion spherical linear interpolation method, calculating quaternion of the initial and final postures to represent and calculate a rotating shaft vector, and calculating the angular velocity and the angular acceleration of the rotation motion of the end effector according to the rotating shaft vector and the rotation angle of the end effector around the equivalent rotating shaft;

step S4, if the end effector is in the turning area, two rotation tracks of the turning area are continuously interpolated twice by adopting a quaternion spherical linear interpolation method, the attitude data of the end effector is calculated, the first derivative of the attitude data is calculated, and the angular velocity of the rotation motion of the end effector is calculated according to the first derivative of the attitude data; and calculating a second derivative of the attitude data, and calculating the angular acceleration of the rotary motion of the end effector according to the second derivative of the attitude data.

Further, in step S1, the quaternion q of the first and last attitude transformation is expressed as:

$q_w=\sqrt{\left(trace\right(R\left)\right)/2};$

q_x＝(R₃₂-R₂₃)/4q_w；

q_y＝(R₁₃-R₃₁)/4q_w；

q_z＝(R₂₁-R₁₂)/4q_w；

wherein trace (R) is a trace of a rotation matrix of the end effector rotational motion.

Further, in step S3, the interpolating the initial and final postures by using a quaternion spherical linear interpolation method includes:

firstly, according to the initial and final postures q₀,q₁Calculating the included angle between the two postures,

θ₀＝arccos(q₀q₁)；

interpolating the initial attitude and the final attitude by adopting the quaternion spherical linear interpolation algorithm to obtain attitude quaternion at the moment t as follows:

$q=slerp(q_0,q_1,\mathrm{\θ}(t)/{\mathrm{\θ}}_0)=q_0{\left({q_0}^{-1}{q}_1\right)}^{\mathrm{\θ}\left(t\right)/{\mathrm{\θ}}_0};$

and theta (t) is the rotation angle of the end effector around the equivalent rotating shaft at the moment t.

Further, in step S3, the quaternion expression of the initial and final postures is calculated as follows:

r＝log(q₀ ^-1q₁)/arccos(q₀q₁)。

further, in the step S3, the calculating the angular velocity of the end effector rotation motion is:

$\mathrm{\ω}=r\stackrel{\·}{\mathrm{\θ}}\left(t\right),$

wherein,is the first derivative of the angle of rotation θ (t) of the end effector about the equivalent axis of rotation;

the calculating the angular acceleration of the rotational motion of the end effector is:

$\mathrm{\α}=r\stackrel{\·\·}{\mathrm{\θ}}\left(t\right)$

wherein,the second derivative of the angle of rotation θ (t) of the end effector about the equivalent pivot axis.

Further, the method for continuously interpolating the two rotation tracks of the turning area twice by adopting a quaternion spherical linear interpolation method comprises the following steps:

setting the parameter of the turning area rotation track as h, and when h changes, the quaternion of the two rotation tracks is as follows:andthe first interpolation of the quaternion spherical linear interpolation method is adopted for both the first and the second parameters, the second interpolation of the quaternion spherical linear interpolation method is adopted for both the first and the second parameters, and the third parameter is changed into a control function of p (h);

$q\left(h\right)=slerp\left(\widetilde{q_1}\right(h),\widetilde{q_2}(h),p(h\left)\right)=\widetilde{q_1}\left(h\right){(\widetilde{q_1}{\left(h\right)}^{-1},\widetilde{q_2}(h\left)\right)}^{p\left(h\right)}$

wherein p (h) is satisfied,

further, in step S4, the pose data of the end effector is calculated as:

wherein,

according to the rotary motion planning method for the end effector of the industrial robot, quaternions are used for describing the tail end posture of the robot, the problem of singularity of an Euler angle is solved, rotary motion planning is converted into the interpolation problem of initial and final quaternions, and the rotary process moves around a single axis more intuitively. The method is characterized in that the smooth connection of the rotary motion is realized by utilizing two times of quaternion spherical surface linear interpolation in a turning area from the previous track to the next track at the tail end of the robot, and a posture, angular velocity and angular acceleration algorithm of the full rotary motion process is calculated and output by utilizing a second derivative of the quaternion of the rotary motion, so that the method can be used for the dynamic feedforward control and the operation space control of the industrial robot.

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.

Drawings

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 flow chart of a method of planning a rotational movement of an end effector for an industrial robot according to an embodiment of the present invention;

fig. 2 is a flow chart of a method of planning a rotational movement of an end effector for an industrial robot according to another embodiment of the invention;

fig. 3 is a schematic diagram of a pose trajectory of an end effector according to an 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.

As shown in fig. 1, a method for planning a rotational motion of an end effector of an industrial robot according to an embodiment of the present invention includes the steps of:

in step S1, the initial and final postures of the rotational motion of the end effector are input, and the initial and final postures are converted into a quaternion representation.

The quaternion q of the first and last attitude transformations is expressed as:

$q_w=\sqrt{\left(trace\right(R\left)\right)/2};$

q_x＝(R₃₂-R₂₃)/4q_w；

q_y＝(R₁₃-R₃₁)/4q_w；

q_z＝(R₂₁-R₁₂)/4q_w；

where trace (R) is the trace of the rotation matrix R of the end effector rotational motion.

In step S2, it is determined whether or not the end effector is in the turning region of the rotational motion.

And step S3, if the end effector is not in the turning area, interpolating the initial attitude and the final attitude by a quaternion spherical linear interpolation method, calculating quaternion of the initial attitude and the final attitude to represent a calculation rotating shaft vector, and calculating the angular velocity and the angular acceleration of the rotation motion of the end effector according to the rotating shaft vector and the rotation angle of the end effector around the equivalent rotating shaft.

The initial attitude and the final attitude are interpolated by adopting a quaternion spherical linear interpolation method, and the method comprises the following steps:

firstly, according to the initial and final postures q₀,q₁Calculating the included angle between the two postures,

θ₀＝arccos(q₀q₁)；(1)

and (3) interpolating the initial attitude and the final attitude by adopting a quaternion spherical linear interpolation algorithm to obtain attitude quaternion at the moment t as follows:

$q=slerp(q_0,q_1,\mathrm{\θ}(t)/{\mathrm{\θ}}_0)=q_0{\left({q_0}^{-1}{q}_1\right)}^{\mathrm{\θ}\left(t\right)/{\mathrm{\θ}}_0};---\left(2\right)$

and theta (t) is the rotation angle of the end effector around the equivalent rotating shaft at the moment t. The general S-shaped speed planning method can be called for planning by the boundary condition that the initial angle and the final angle and the angular speed are zero.

After interpolation is finished, the direction of a rotating shaft in the linear interpolation of the quaternion spherical surface is unchanged, and the quaternion for calculating the initial attitude and the final attitude represents and calculates a rotating shaft vector as follows:

r＝log(q₀ ^-1q₁)/arccos(q₀q₁)；(3)

wherein log is the logarithm of the difference of the quaternions of the initial attitude and the final attitude.

And calculating the angular velocity and the angular acceleration of the rotation motion of the end effector according to the rotation shaft vector and the rotation angle of the end effector around the equivalent rotation shaft.

Specifically, the angular velocity of the end effector rotational motion is calculated as:

$\mathrm{\ω}=r\stackrel{\·}{\mathrm{\θ}}\left(t\right),---\left(4\right)$

wherein,the first derivative of the angle of rotation θ (t) of the end effector about the equivalent axis of rotation.

Calculating the angular acceleration of the end effector rotational motion as:

$\mathrm{\α}=r\stackrel{\·\·}{\mathrm{\θ}}\left(t\right),---\left(5\right)$

wherein,the second derivative of the angle of rotation θ (t) of the end effector about the equivalent pivot axis.

Step S4, if the end effector is in the turning area, two rotating tracks of the turning area are continuously interpolated twice by adopting a quaternion spherical linear interpolation method, the attitude data of the end effector is calculated, the first derivative of the attitude data is calculated, and the angular velocity of the rotating motion of the end effector is calculated according to the first derivative of the attitude data; and calculating a second derivative of the attitude data, and calculating the angular acceleration of the rotary motion of the end effector according to the second derivative of the attitude data.

The method for continuously interpolating the two rotation tracks of the turning area twice by adopting a quaternion spherical linear interpolation method comprises the following steps:

the track of the rotation motion is determined by connecting two rotation tracks, the parameter of the rotation track of the turning area is set as h, and the range of the parameter is [0,1 ]]When h varies, the quaternion of the two rotation trajectories is:andthe two are obtained by the first interpolation of the quaternion spherical linear interpolation method, then the second interpolation of the quaternion spherical linear interpolation method is adopted for the two, and the third parameter is changed into the control function of p (h). Under such conditions a smooth transition of the two rotational movements that are smoothly connected can be achieved.

$q\left(h\right)=slerp\left(\widetilde{q_1}\right(h),\widetilde{q_2}(h),p(h\left)\right)=\widetilde{q_1}\left(h\right){(\widetilde{q_1}{\left(h\right)}^{-1},\widetilde{q_2}(h\left)\right)}^{p\left(h\right)}$

Wherein p (h) is satisfied,。

during turning, the rotating shaft is in smooth transition, so that the angular velocity needs to be calculated by calculating the change rate of the posture along with the time. The attitude at any time during the turn zone can be written in the following form:

calculating pose data for the end effector as:

wherein,

then, a first derivative of the pose data is calculated, and an angular velocity of the end effector rotational motion is calculated based on the first derivative of the pose data.

$\stackrel{\·}{q}=\stackrel{\·}{a}{\tilde{q}}_1+a\stackrel{~\·}{q_1}+\stackrel{\·}{b}\widetilde{q_2}+b\stackrel{~\·}{q_2},---\left(7\right)$

Let, c_a＝cos((1-p)θ)，s_a＝sin((1-p)θ)，c_b＝cos(pθ)，s_b＝sin(pθ)

So as to obtain the compound with the characteristics of,

$\stackrel{\·}{a}=\frac{Ca\left(\stackrel{\·}{\mathrm{\θ}}\right(1-p)-\stackrel{\·}{p}\mathrm{\θ})}{\sin \mathrm{\θ}}-\frac{\stackrel{\·}{\mathrm{\θ}}\cos \left(\mathrm{\θ}\right)Sa}{\sin 2\mathrm{\θ}},\stackrel{\·}{b}=\frac{C_b({\stackrel{\·}{\mathrm{\θ}}}_p+\stackrel{\·}{p}\mathrm{\θ})}{\sin \mathrm{\θ}}-\frac{\stackrel{\·}{\mathrm{\θ}}\cos \left(\mathrm{\θ}\right)Sb}{\sin 2\mathrm{\θ}},$

wherein the angular velocity of the end effector rotational motion is as follows:

$\mathrm{\θ}=\arccos (\widetilde{q_1}\·\widetilde{q_2}),---\left(8\right)$

$\stackrel{\·}{\mathrm{\θ}}=-\frac{\stackrel{~\·}{q_1}\·\widetilde{q_2}+\widetilde{q_1}\·\stackrel{~\·}{q_2}}{sin\left(\mathrm{\θ}\right)},---\left(9\right)$

and calculating a second derivative of the attitude data, and calculating the angular acceleration of the rotary motion of the end effector according to the second derivative of the attitude data.

$\stackrel{\·\·}{q}=\stackrel{\·\·}{a}\widetilde{q_1}+2\stackrel{\·}{a}\stackrel{~\·}{q_1}+a\stackrel{~\·\·}{q_1}+\stackrel{\·\·}{b}\widetilde{q_2}+2\stackrel{\·}{b}\stackrel{~\·}{q_2}+b\stackrel{~\·\·}{q_2},---\left(10\right)$

Wherein,

$\stackrel{\·}{a}=\frac{\stackrel{\·}{\mathrm{\φ}}cos\left(\mathrm{\φ}\right)-a\stackrel{\·}{\mathrm{\θ}}cos\left(\mathrm{\θ}\right)}{\sin \left(\mathrm{\θ}\right)},\stackrel{\·}{b}=\frac{\stackrel{\·}{\mathrm{\ψ}}cos\left(\mathrm{\ψ}\right)-b\stackrel{\·}{\mathrm{\θ}}cos\left(\mathrm{\θ}\right)}{\sin \left(\mathrm{\θ}\right)},$

$\stackrel{\·\·}{a}=-a({\stackrel{\·}{\mathrm{\φ}}}^2+{\stackrel{\·}{\mathrm{\θ}}}^2)+\frac{\stackrel{\·\·}{\mathrm{\φ}}cos\left(\mathrm{\φ}\right)-a\stackrel{\·\·}{\mathrm{\θ}}cos\left(\mathrm{\θ}\right)}{\sin \left(\mathrm{\θ}\right)},2\·\frac{a{\stackrel{\·}{\mathrm{\θ}}}^2-\stackrel{\·}{\mathrm{\φ}}\stackrel{\·}{\mathrm{\θ}}cos\left(\mathrm{\φ}\right)\cos \left(\mathrm{\θ}\right)}{{\sin }^2\left(\mathrm{\θ}\right)},$

$\stackrel{\·\·}{b}=-b({\stackrel{\·}{\mathrm{\ψ}}}^2+{\stackrel{\·}{\mathrm{\θ}}}^2)+\frac{\stackrel{\·\·}{\mathrm{\ψ}}cos\left(\mathrm{\ψ}\right)-b\stackrel{\·\·}{\mathrm{\θ}}cos\left(\mathrm{\θ}\right)}{\sin \left(\mathrm{\θ}\right)},2\·\frac{b{\stackrel{\·}{\mathrm{\θ}}}^2-\stackrel{\·}{\mathrm{\ψ}}\stackrel{\·}{\mathrm{\θ}}cos\left(\mathrm{\ψ}\right)\cos \left(\mathrm{\θ}\right)}{{\sin }^2\left(\mathrm{\θ}\right)},$

the angular acceleration of the end effector rotational motion is as follows:

$\mathrm{\φ}=(1-p(h\left)\right)\mathrm{\θ}\left(h\right),\stackrel{\·}{\mathrm{\φ}}=(1-p(h\left)\right)\stackrel{\·}{\mathrm{\θ}}\left(h\right)-\stackrel{\·}{p}\left(h\right)\mathrm{\θ}\left(h\right),\stackrel{\·\·}{\mathrm{\φ}}=(1-p)\stackrel{\·\·}{\mathrm{\θ}}-2\stackrel{\·}{p}\stackrel{\·}{\mathrm{\θ}}-\stackrel{\·\·}{p}\mathrm{\θ}$

$\mathrm{\ψ}=p\left(h\right)\mathrm{\θ}\left(h\right),\stackrel{\·}{\mathrm{\ψ}}=\stackrel{\·}{p}\mathrm{\θ}+p\stackrel{\·}{\mathrm{\θ}},$

$\stackrel{\·\·}{\mathrm{\ψ}}=\stackrel{\·\·}{p}\mathrm{\θ}+2\stackrel{\·}{p}\stackrel{\·}{\mathrm{\θ}}+p\stackrel{\·\·}{\mathrm{\θ}}-sin\left(\mathrm{\θ}\right)\stackrel{\·\·}{\mathrm{\θ}}-cos\left(\mathrm{\θ}\right)\stackrel{\·}{\mathrm{\θ}}=\stackrel{~\·\·}{q_1}\·\widetilde{q_2}+2\stackrel{~\·}{q_1}\·\stackrel{~\·}{q_2}+\widetilde{q_1}\·\stackrel{~\·\·}{q_2}.$

fig. 2 is a flow chart of a method of planning a rotational movement of an end effector for an industrial robot according to another embodiment of the invention.

Step S201, inputting the initial and final postures of the rotary motion.

In step S202, the initial and final postures are converted into a quaternion representation.

The quaternion q of the first and last attitude transformations is expressed as:

$q_w=\sqrt{\left(trace\right(R\left)\right)/2};$

q_x＝(R_32-R₂₃)/4q_w；

q_y＝(R₁₃-R₃₁)/4q_w；

q_z＝(R₂₁-R₁₂)/4q_w。

step S203, determining whether the vehicle is in the turning area of the rotational motion.

And step S204, calling a first and last slerp and a rate planning subprogram to perform interpolation by using a general quaternion spherical linear interpolation subprogram and a general one-dimensional rate planning subprogram.

And S205, calculating the logarithm of the difference value of the initial quaternion and the final quaternion to obtain a rotating shaft vector.

r＝log(q₀ ^-1q₁)/arccos(q₀q₁)

In step S206, the velocity direction and the velocity are combined into a velocity, and the acceleration direction and the acceleration rate are combined into an acceleration.

And step S207, calling the initial and final slerp twice to interpolate the connected rotary motion postures.

In step S208, the first derivative of the attitude quaternion is calculated.

In step S209, the second derivative of the attitude quaternion is calculated.

Step S210, the angular velocity and the angular acceleration of the rotational motion are directly obtained according to a second derivative of the attitude.

The angular velocities of the end effector rotational motion are as follows:

the angular acceleration of the end effector rotational motion is as follows:

$\mathrm{\φ}=(1-p(h\left)\right)\mathrm{\θ}\left(h\right),\stackrel{\·}{\mathrm{\φ}}=(1-p(h\left)\right)\stackrel{\·}{\mathrm{\θ}}\left(h\right)-\stackrel{\·}{p}\left(h\right)\mathrm{\θ}\left(h\right),\stackrel{\·\·}{\mathrm{\φ}}=(1-p)\stackrel{\·\·}{\mathrm{\θ}}-2\stackrel{\·}{p}\stackrel{\·}{\mathrm{\θ}}-\stackrel{\·\·}{p}\mathrm{\θ}$

$\mathrm{\ψ}=p\left(h\right)\mathrm{\θ}\left(h\right),\stackrel{\·}{\mathrm{\ψ}}=\stackrel{\·}{p}\mathrm{\θ}+p\stackrel{\·}{\mathrm{\θ}},$

$\stackrel{\·\·}{\mathrm{\ψ}}=\stackrel{\·\·}{p}\mathrm{\θ}+2\stackrel{\·}{p}\stackrel{\·}{\mathrm{\θ}}+p\stackrel{\·\·}{\mathrm{\θ}}-sin\left(\mathrm{\θ}\right)\stackrel{\·\·}{\mathrm{\θ}}-cos\left(\mathrm{\θ}\right)\stackrel{\·}{\mathrm{\θ}}=\stackrel{~\·\·}{q_1}\·\widetilde{q_2}+2\stackrel{~\·}{q_1}\·\stackrel{~\·}{q_2}+\widetilde{q_1}\·\stackrel{~\·\·}{q_2}.$

fig. 3 is a schematic diagram of a pose trajectory of an end effector according to an embodiment of the present invention.

In step S211, the attitude, angular velocity, and angular acceleration of the rotational motion are output.

According to the rotary motion planning method for the end effector of the industrial robot, quaternions are used for describing the tail end posture of the robot, the problem of singularity of an Euler angle is solved, rotary motion planning is converted into the interpolation problem of initial and final quaternions, and the rotary process moves around a single axis more intuitively. The method is characterized in that the smooth connection of the rotary motion is realized by utilizing two times of quaternion spherical surface linear interpolation in a turning area from the previous track to the next track at the tail end of the robot, and a posture, angular velocity and angular acceleration algorithm of the full rotary motion process is calculated and output by utilizing a second derivative of the quaternion of the rotary motion, so that the method can be used for the dynamic feedforward control and the operation space control of the industrial robot.

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 (7)

1. A method for planning a rotational movement of an end effector of an industrial robot, characterized by the steps of:

step S1, inputting the initial and final postures of the rotation motion of the end effector, and converting the initial and final postures into quaternion representation;

step S2, judging whether the end effector is in a turning area of rotary motion;

step S3, if the end effector is not in the turning area, interpolating the initial and final postures by a quaternion spherical linear interpolation method, calculating quaternion of the initial and final postures to represent and calculate a rotating shaft vector, and calculating the angular velocity and the angular acceleration of the rotation motion of the end effector according to the rotating shaft vector and the rotation angle of the end effector around the equivalent rotating shaft;

step S4, if the end effector is in the turning area, two rotation tracks of the turning area are continuously interpolated twice by adopting a quaternion spherical linear interpolation method, the attitude data of the end effector is calculated, the first derivative of the attitude data is calculated, and the angular velocity of the rotation motion of the end effector is calculated according to the first derivative of the attitude data; and calculating a second derivative of the attitude data, and calculating the angular acceleration of the rotary motion of the end effector according to the second derivative of the attitude data.

2. A method of planning the rotational movement of an end effector for an industrial robot according to claim 1, characterized in that in step S1 the quaternion q of the first and last pose transformation is expressed as:

q_x＝(R₃₂-R₂₃)/4q_w；

q_y＝(R₁₃-R₃₁)/4q_w；

q_z＝(R₂₁-R₁₂)/4q_w；

wherein trace (R) is a trace of a rotation matrix of the end effector rotational motion.

3. A method for planning the rotational movement of an end effector for an industrial robot according to claim 1, wherein in step S3, the interpolating the initial and final poses according to the linear interpolation method using quaternion sphere comprises the following steps:

firstly, according to the initial and final postures q₀,q₁Calculating the included angle between the two postures,

θ₀＝arccos(q₀q₁)；

interpolating the initial attitude and the final attitude by adopting the quaternion spherical linear interpolation algorithm to obtain attitude quaternion at the moment t as follows:

and theta (t) is the rotation angle of the end effector around the equivalent rotating shaft at the moment t.

4. A method for planning the rotational movement of an end effector for an industrial robot according to claim 3, wherein in said step S3, said calculating the quaternion representation of the first and last postures calculates the rotation axis vector as:

r＝log(q₀ ^-1q₁)/arccos(q₀q₁)。

5. the method for planning the rotational motion of an end effector for an industrial robot according to claim 4, wherein in said step S3, said calculating the angular velocity of the rotational motion of said end effector is:

wherein,is the first derivative of the angle of rotation θ (t) of the end effector about the equivalent axis of rotation;

the calculating the angular acceleration of the rotational motion of the end effector is:

wherein,the second derivative of the angle of rotation θ (t) of the end effector about the equivalent pivot axis.

6. A method for planning the rotational movement of an end effector for an industrial robot according to claim 1, wherein in step S4, the interpolation of the two rotational trajectories of the turning zone is performed twice consecutively by using a quaternion sphere linear interpolation method, comprising the steps of:

setting the parameter of the turning area rotation track as h, and when h changes, the quaternion of the two rotation tracks is as follows:andthe first interpolation of the quaternion spherical linear interpolation method is adopted for both the first and the second parameters, the second interpolation of the quaternion spherical linear interpolation method is adopted for both the first and the second parameters, and the third parameter is changed into a control function of p (h);

wherein p (h) satisfies, p (0) ═ 0, p (1) ═ 1,

7. the rotational motion planning method for an end effector for an industrial robot according to claim 6, wherein in said step S4, the attitude data of the end effector is calculated as:

wherein,