CN107980108B

CN107980108B - Robot motion trajectory planning method and related device

Info

Publication number: CN107980108B
Application number: CN201780002229.0A
Authority: CN
Inventors: 张志明
Original assignee: Shenzhen A&E Intelligent Technology Institute Co Ltd
Current assignee: Shenzhen A&E Intelligent Technology Institute Co Ltd
Priority date: 2017-01-04
Filing date: 2017-01-04
Publication date: 2021-07-09
Anticipated expiration: 2037-01-04
Also published as: CN107980108A; WO2018126355A1

Abstract

This scheme relates to the motion control field, especially relates to robot movement track planning technique. In the robot motion track planning method, characteristic points of Bezier curves for n times are determined according to a first CP motion track segment and a second CP motion track segment, wherein n is not less than 4 (401); and constructing an n-order Bezier curve according to the characteristic points to serve as a smooth transition track section (402) between the first CP motion track section and the second CP motion track section. Because the Bezier curve of n times is used as the smooth transition track section between the two CP motion track sections, the starting point of the smooth transition track section is tangent to the first CP motion track section and has the same curvature, and the ending point of the smooth transition track section is tangent to the second CP motion track section and has the same curvature, thereby realizing the smooth switching of continuous CP motion, simultaneously, the speed does not need to be reduced to 0, and the acceleration does not jump.

Description

Robot motion trajectory planning method and related device

Technical Field

The invention relates to the field of motion control, in particular to a robot motion trail planning technology.

Background

In the motion control of the robot, the trajectory motion of the controlled component (e.g., the operation arm) can be divided into CP motion (continuous motion including linear motion and circular motion) and PTP motion (point-to-point motion).

When planning the motion trail of the robot, multiple segments of CP motion may be required to be performed continuously. Taking an example that two CP motions are continuously performed, please refer to fig. 1a, a CP motion track segment 1 (also referred to as track segment 1) and a CP motion track segment 2 (also referred to as track segment 2) can be respectively a straight line segment, and in addition, an arc segment and an arc segment (fig. 1b), an arc segment and a straight line segment (fig. 1c and fig. 1d) can be continuously performed.

In the planning of the single-section CP movement, the initial speed and the final speed are both 0, if the initial speed and the final speed of each section of CP movement are both reduced to 0 in the continuous movement process of the multiple sections of CP, the working efficiency can be greatly reduced, and frequent acceleration and deceleration can also influence the service life of the motor and the reducer. Therefore, the motion trajectory rule tends not to decrease the speed of each CP motion in the continuous motion of the multiple CP segments to zero.

This faces another problem: still referring to FIG. 1a, if consecutive straight segments are not on the same line, there will be sharp corners. The apex of the sharp corner is O (point O is the intersection of the two trajectory segments). Similarly, referring to fig. 1b, if the tangents of two consecutive arc segments are not coincident, there is a sharp corner. Similarly, if the tangent of the straight line segment is not coincident with the tangent of the circular arc segment (see fig. 1c and fig. 1d), there will be a sharp corner. If the speed is not 0, the vibration is generated by the sharp corner.

For this purpose, a smooth transition track segment can be designed between two consecutive CP motion track segments. For example, referring to fig. 2, a smooth transition trajectory segment can be obtained by using a vector superposition method. In this way, the interpolation point from the turning point a to the intersection point O of the trajectory segment 1 in fig. 2 coincides with the interpolation point from the turning point B to the intersection point O of the trajectory segment 2 by the space vector addition. The superimposed interpolation points form an arc of space (i.e., an arc between points a and B in fig. 2), so that the trajectory is smooth.

That is, the finally planned running track runs from point C to point a, then turns out the track section 1, enters the smooth transition track section between point a and point B, turns into the track section 2 from point B, and finally reaches point D.

Of course, for continuous motion of more than two sections of CP motion, two consecutive CP motion trajectory sections may be so designed, respectively.

Although the vector superposition method smoothes the CP motion connected in front and back, in practical applications, as shown in fig. 1a to 1d, there are a straight line segment and a straight line segment, a straight line segment and a circular arc segment, and a circular arc segment. Although the vector superposition method can replace sharp corners with circular arcs, the vector superposition method is only certainly suitable for the scene of switching the straight line segment and the straight line segment, and circular arcs tangent to two tracks may not be found in the switching of the straight line segment and the circular arc segment and the switching of the circular arc segment and the circular arc segment. The reason is that the straight line segment and the straight line segment which are intersected in the space are definitely coplanar, but the straight line segment and the circular arc segment, and the circular arc segment are not necessarily coplanar, so that a common circular arc switching cannot be found out under the condition of non-coplanarity.

Therefore, there is a need for a technical solution for planning a motion trajectory of a robot, so that smooth transition can be performed regardless of whether continuous motion trajectory segments are coplanar or not, and the speed is continuous (i.e. the speed does not have to be reduced to 0) at an inflection point (an inflection point and an inflection point).

Disclosure of Invention

In view of the above, an object of the embodiments of the present invention is to provide a method and a related apparatus for planning a motion trajectory of a robot, so as to smoothly transit a continuous CP motion, and at the same time, the speed does not need to be reduced to 0.

The inventor of the application finds out in the research process that:

the Bezier curve is a mathematical curve consisting of line segments and nodes. The overall shape of the robot is not limited to circular arcs, and non-coplanar smooth tracks can be realized, so that the robot motion track planning method can be applied to the robot motion track planning aspect.

The Bezier curve can be used as a smooth transition track section between continuous motion track sections, the initial point of the Bezier curve coincides with the turning point of one motion track section (which can be called as lc track section), and the terminal point of the Bezier curve coincides with the turning point of the other motion track section (which can be called as ln track section).

The inventors have found that to achieve velocity continuity at the inflection points (the exit and entrance points), the Bezier curve needs to be tangent to the lc locus at its start point and tangent to the ln locus at its end point.

The formula of the Bezier curve of degree n (degree n) is as follows:

wherein b is_i,n(t) is called Bernstein basis function,

t-0 corresponds to the start point of the bezier curve, and t-1 corresponds to the end point of the bezier curve.

P₀-P_nThe n characteristic points or control points define an n-degree Bezier curve in a plane or in a three-dimensional space, and a polygon formed by the n characteristic points or control points is called a characteristic polygon or a control polygon. Wherein, P₀As a starting point, P_nIs an end point, P₁-P_n-1Is the middle point. See, for example, FIG. 3, P₀、P₁、P₂、P₃The four points define a cubic Bezier curve, which starts at P₀Trend P₁And from P₂Direction to P₃. It should be noted that the typical cubic Bezier curve does not pass through P₁、P₂These two points provide only directions.

According to the derivative function property of Bezier basis function, the tangent vector of the starting point and the ending point of the Bezier curve for n times can be obtained as

Then:

when t is 0, B' (0) is n (P)₁-P₀) B' (0) is the tangent vector of the Bezier curve at the starting point for n times;

when t is 1, B' (1) is n (P)_n-P_n-1) B' (1) is the tangent vector of the Bezier curve at the termination point n times.

Observing the tangent vector, the tangent directions (i.e. tangent vectors) of the n-order Bezier curve at the starting point and the ending point are consistent with the trends of the first edge and the last edge of the characteristic polygonal type. Taking the cubic Bezier curve shown in FIG. 3 as an example, B' (0) is 3 (P)₁-P₀)，B′(1)＝3(P₃-P₂) And the first side of FIG. 3 is P₁P₀The last edge is P₃P₂。

In order to make the tangential vector directions of the n-order Bezier curves at the initial point and the final point respectively the same as the tangential vector directions of the lc track segment and the ln track segment, a minimum of four characteristic points or control points are needed, so that the cubic Bezier curves can be selected as the smooth transition track segment.

However, the inventors of the present application found in the course of further research that:

the use of cubic Bezier curves as smooth transition trajectory segments allows smooth transition of continuous CP motion, while the velocity does not have to be reduced to 0, but only ensures continuous velocity at the inflection point, while the acceleration at the inflection point is not necessarily continuous. Along with the development of robot science and technology, the requirement on the planning of the robot track is higher and higher, and if the acceleration is discontinuous, the acceleration jumped at the inflection point can cause the motor to shake, and damage is caused to the motor and the speed reducer.

The inventor of the application finds that the reason of the acceleration jump is the sudden centripetal acceleration by analyzing the reason of the acceleration jump.

The essential condition for the acceleration to be continuous is that the curvature is continuous on the basis of the velocity continuity.

The centripetal acceleration at a certain point has a formula

Where v represents the velocity of the point and ρ represents the curvature of the point. In the case of v being continuous, ensuring the curvature is continuous ensures that the trajectory acceleration is continuous.

The formula for the curvature of the curve is:

where B '(t) represents the first derivative function of the Bezier curve and B' (t) represents the second derivative function of the Bezier curve. From the curvature formula, one can derive: ensuring the second order conductibility of the Bezier curve ensures the acceleration of any point on the Bezier curve to be continuous. So as long as the Bezier curve with the times larger than 1, the track has a certain curvature and is continuous.

On the other hand, in order to ensure no jump at the inflection point, the speed and the acceleration at the inflection point are required to be continuous, which requires that the Bezier curve is tangent to the lc track segment at the starting point (i.e. the inflection point) and has continuous curvature, and simultaneously, the Bezier curve is tangent to the ln track segment at the ending point (i.e. the inflection point) and has continuous curvature.

According to the derivative function property of the Bezier basis function, the second derivative vector of the beginning point and the end point of the Bezier curve for n times can be obtained:

obtaining: when t is 0, B ″ (0) ═ n (n-1) (P)₂-2P₁+P₀)

When t is 1, B ″ (1) ═ n (n-1) (P)_n-2P_n-1+P_n-2)

The above formula shows that the second derivative vector is only related to 3 adjacent control points.

In order to make the second derivative direction consistent with the second derivative direction of the lc track segment and the ln track segment, a minimum of five control points (or feature points) are required, so n-times (n is not less than 4) Bezier curve can be selected, and the quartic Bezier curve has the formula:

B(t)＝P₀(1-t)⁴+4P₁t(1-t)³+6P₂t²(1-t)²+4P₃t³(1-t)+P₄t⁴，t∈[0，1]

based on the research findings, the embodiment of the invention provides the following technical scheme:

on one hand, the embodiment of the application provides a robot motion trajectory planning method, which is at least used for realizing smooth switching between two continuous CP motion trajectory segments based on n times (n is not less than 4) of Bezier curves, wherein the two continuous CP motion trajectory segments comprise a first CP motion trajectory segment and a second CP motion trajectory segment; the method comprises the following steps: determining characteristic points of the Bezier curve for n times according to the first CP motion track segment and the second CP motion track segment; the characteristic points include P₀、P₁、P₂、P₃Wherein P is₀Is a starting point, P₃Is an end point, P₁、P₂Is the middle point; constructing a Bezier curve for n times (n is not less than 4) according to the characteristic points, wherein the Bezier curve is used as a smooth transition track section between the first CP motion track section and the second CP motion track section, the starting point of the smooth transition track section is the exit point of the first CP motion track section, and the ending point of the smooth transition track section is the exit point of the second CP motion track section; the smooth transition track segment and the first CP motion track segment have the same tangent vector direction and the same curvature on the starting point; and the smooth transition track section and the second CP motion track section have the same tangential vector direction and the same curvature at the termination point. In this embodiment, an n-th (n is not less than 4) Bezier curve is used as the smooth transition track segment between the first CP motion track segment and the second CP motion track segment, since the tangential directions of the smooth transition track segment at the start point and the end point are respectively equal to the first CP motion track segment and the second CP motion track segmentThe tangent vector directions of the track sections are the same, so that the smooth transition track section is tangent to the first CP motion track section at the starting point of the smooth transition track section and is tangent to the second CP motion track section at the ending point of the smooth transition track section, so that the continuous speed (the inflection point and the inflection point) at the inflection point can be realized, namely the continuous CP motion smooth switching can be realized, and meanwhile, the speed does not need to be reduced to 0. In addition, the curvature of the smooth transition track section at the starting point is the same as the curvature of the first CP motion track section at the inflection point (the starting point is coincident with the inflection point, or the starting point is also considered as the inflection point), and the curvature at the ending point is the same as the curvature of the second CP motion track section at the inflection point (the ending point is coincident with the inflection point, or the ending point is also considered as the inflection point), so that the continuous acceleration at the inflection point (the inflection point and the inflection point) can be realized without jumping.

In one possible design, before the determining the feature points of the Bezier curve n times (n is not less than 4), the method further includes: and planning continuous CP motion track segments.

In one possible design, where n is 4, the feature points include P₀、P₁、P₂、P₃And P₄Wherein P is₀Is a starting point, P₄Is an end point, P₁、P₂And P₃First to third intermediate points; the intersection point of the first CP motion track segment and the second CP motion track segment is represented as an O point; the determining the characteristic points of the Bezier curve for n times according to the first CP motion track segment and the second CP motion track segment comprises: determining the intersection point O as the second intermediate point P₂。

In one possible design, the determining the feature points of the Bezier curve for n times according to the first CP motion trajectory segment and the second CP motion trajectory segment further includes: if the first CP motion track section is a straight line section, selecting the intersection point O and the starting point P₀A point on the line segment therebetween as the first intermediate point P₁(ii) a If the first CP motion track segment is a circular arc segment, determining a first intermediate point P₁At a starting point P₀On a tangent line of, and, line segment P₁P₀Has a length of

Where r1 denotes a radius of the first CP motion trajectory segment, and α 1 denotes a central angle at the start point.

In one possible design, the determining the feature points of the Bezier curve for n times according to the first CP motion trajectory segment and the second CP motion trajectory segment further includes: if the second CP motion track section is a straight line section, selecting the intersection point O and the termination point P₄A point on the line segment therebetween as the third intermediate point P₃(ii) a If the second CP motion track segment is a circular arc segment, determining the third intermediate point P₃At the end point P₄On a tangent line of, and, line segment P₂P₄Has a length of

Where r2 denotes a radius of the second CP motion trajectory segment and α 2 denotes a central angle at the termination point.

In one possible design, where n is 5, the feature points include P₀、P₁、P₂、P₃、P₄And P₅Wherein P is₀Is a starting point, P₅Is an end point, P₁To P₄First to fourth intermediate points; and the intersection point of the first CP motion track segment and the second CP motion track segment is represented as an O point.

In one possible design, the determining the feature points of the Bezier curve for n times according to the first CP motion trajectory segment and the second CP motion trajectory segment includes: if the first CP motion track segment is a circular arc segment, determining the first intermediate point P₁Is located at the starting point P₀On a tangent line of, and, line segment P₁P₀Has a length of

Wherein r1 represents a radius of the first CP motion trajectory segment, α 1 represents a central angle at the start point; determining the second intermediate point P₂To take the starting point P₀Trisection on the arc segment with the intersection point O as the end pointAnd (4) point.

In one possible design, the determining the feature points of the Bezier curve for n times according to the first CP motion trajectory segment and the second CP motion trajectory segment includes: if the first CP motion track section is a straight line section, selecting the starting point P₀And trisection points on a straight line segment with the intersection point O as an endpoint are respectively taken as first intermediate points P₁And a second intermediate point P₂。

In one possible design, the determining the feature points of the Bezier curve for n times according to the first CP motion trajectory segment and the second CP motion trajectory segment further includes: if the second CP motion track segment is a circular arc segment, determining the third intermediate point P₃On a tangent to the termination point, and a line segment P₃P₅Has a length of

Wherein r2 represents the radius of the second CP motion trajectory segment, α 2 represents the central angle at the termination point; determining the fourth intermediate point P₄The end points are trisection points on the arc segment with the end point and the intersection point O as the end points.

In one possible design, the determining the feature points of the Bezier curve for n times according to the first CP motion trajectory segment and the second CP motion trajectory segment further includes: if the second CP motion track section is a straight line section, trisection points on the straight line section with the end point and the intersection point O as end points are selected as the third middle point P respectively₃And a fourth intermediate point P₄。

On the other hand, the embodiment of the invention provides a robot motion trail planning device which has the function of realizing the behavior of the robot motion trail planning device in the actual method. The functions can be realized by hardware, and the functions can also be realized by executing corresponding software by hardware. The hardware or software includes one or more modules corresponding to the above-described functions.

In one possible design, the structure of the robot motion trajectory planning device includes: the processor executes the method by running the software program stored in the memory and calling the data stored in the memory.

In another aspect, an embodiment of the present invention provides a robot, which includes the robot motion trajectory planning device, and a controlled device that operates according to two continuous CP motion trajectory segments and a smooth transition trajectory segment planned by the robot motion trajectory planning device. The control means may be, for example, an operating arm.

In another aspect, an embodiment of the present invention provides a computer storage medium for storing computer software instructions for the robot motion trajectory planning apparatus, which includes a program designed to execute the above aspects.

In still another aspect, an embodiment of the present invention provides a computer storage medium for storing computer software instructions for the robot, which includes a program designed to execute the above aspects.

Compared with the prior art, in the embodiment, the Bezier curve is used for n times (n is not less than 4) as the smooth transition track section between the first CP motion track section and the second CP motion track section, and since the tangential directions of the smooth transition track section at the starting point and the ending point are respectively the same as the tangential directions of the first CP motion track section and the second CP motion track section, the smooth transition track section is tangent to the first CP motion track section at the starting point and the second CP motion track section at the ending point, so that the continuous speed at the turning point (the turning point and the turning point) can be realized, that is, the continuous CP motion smooth transition can be realized, and meanwhile, the speed does not need to be reduced to 0. In addition, the curvature of the smooth transition track section at the starting point is the same as the curvature of the first CP motion track section at the inflection point (the starting point is coincident with the inflection point, or the starting point is also considered as the inflection point), and the curvature at the ending point is the same as the curvature of the second CP motion track section at the inflection point (the ending point is coincident with the inflection point, or the ending point is also considered as the inflection point), so that the continuous acceleration at the inflection point (the inflection point and the inflection point) can be realized without jumping.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIGS. 1a-1d are schematic diagrams of successive motion trajectory segments provided by embodiments of the present invention;

FIG. 2 is a schematic diagram of a smooth transition trajectory segment obtained by a vector superposition method according to an embodiment of the present invention;

FIG. 3 is a schematic diagram of an n-degree (n is not less than 4) Bezier curve according to an embodiment of the present invention;

4-5, 6a, 7a, 8a, 9a, 10a, 11a, 12a are exemplary flowcharts of a robot motion trajectory planning method provided by an embodiment of the present invention;

6b, 7b, 8b, 9b, 10b, 11b, 12b are schematic diagrams illustrating transition of two continuous motion trajectory segments by using smooth transition trajectory segments according to embodiments of the present invention;

FIGS. 6c, 7c, 9c, 10c, 11c, 12c are curvature diagrams provided by embodiments of the present invention;

FIG. 8c is a geometric schematic provided by an embodiment of the present invention;

fig. 13 is a schematic structural diagram of a robot motion trajectory planning device according to an embodiment of the present invention;

fig. 14 is a schematic diagram of a general computer architecture of a robot motion trajectory planning device according to an embodiment of the present invention.

Detailed Description

The technical terms, abbreviations or abbreviations that may be used in the present invention are as follows:

TCP point: a tool coordinate center point;

linear motion: the TCP point of the robot moves along a linear track in a Cartesian space;

circular arc motion: the CP point of the robot moves along an arc track in a Cartesian space;

and (3) CP: continuous motion, a trajectory motion mode in cartesian space, including linear motion and circular motion;

bezier curve n times: the formula of the Bezier curve for n times is as follows:

referred to as the Bernstein basis function,

The embodiment of the invention provides a robot motion trajectory planning method and a related device, which are used for enabling continuous CP motion to be smoothly switched, and meanwhile, the speed does not need to be reduced to 0 and the acceleration does not jump. The robot motion trajectory planning device related to the embodiment of the invention is applied to a robot, and can be specifically a controller/processor in the robot.

One embodiment of the invention provides a method for realizing robot motion trail planning and a robot motion trail planning device based on the method. The device can implement smooth switching between two continuous CP motion trajectory segments (a first CP motion trajectory segment and a second CP motion trajectory segment) by executing the method, please refer to fig. 4, and the specific operations include:

in section 401: determining characteristic points of the Bezier curve (n is not less than 4) for n times according to the first CP motion track segment and the second CP motion track segment;

taking n as an example, the characteristicsThe points may include P₀、P₁、P₂、P₃And P₄Wherein P is₀Is a starting point, P₄Is an end point, P₁、P₂、P₃Is the middle point.

And if n is 5, the feature point may include P₀、P₁、P₂、P₃、P₄And P₅Wherein P is₀Is a starting point, P₅The end points and the other points are intermediate points.

At part 402: and constructing the Bezier curve (n is not less than 4) for n times according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section.

After the feature points are determined, constructing the Bezier curve for n times (n is not less than 4) according to the feature points may use an existing construction method, which is not described herein again.

It should be noted that the start point of the smooth transition track segment coincides with the inflection point of the first CP motion track segment (or the start point of the smooth transition track segment may be regarded as the inflection point of the first CP motion track segment), and the end point of the smooth transition track segment coincides with the inflection point of the second CP motion track segment (or the end point of the smooth transition track segment may be regarded as the inflection point of the second CP motion track segment). This ensures that the path is continuous.

In addition, the smooth transition track section is at the starting point P₀The direction of the tangent vector is the same as the direction of the tangent vector of the first CP motion track segment at the inflection point, so that the smooth transition track segment is tangent to the first CP motion track segment at the starting point thereof, and the smooth transition track segment is tangent to the first CP motion track segment at the starting point P₀The curvature of the first CP motion track section is the same as the curvature of the first CP motion track section at the inflection point, so that the speed and the acceleration at the inflection point are ensured to be continuous.

Similarly, the tangent vector direction of the smooth transition track section at the ending point of the smooth transition track section is the same as the tangent vector direction of the second CP motion track section at the turning point. Thus, the smooth transition trajectory segment is tangent to the second CP motion trajectory segment at its termination point. And the curvature of the smooth transition track section at the termination point is the same as the curvature of the second CP motion track section at the turning point. Thus, the speed and acceleration at the turning point can be ensured to be continuous.

In one example, the point of inflection and the point of inflection may be determined according to a user's configuration. Specifically, the user may indicate a distance between the inflection point and the intersection point (the intersection point is an intersection point of the first CP motion trajectory segment and the second CP motion trajectory segment), and the distance between the inflection point and the intersection point is equal to the distance between the inflection point and the intersection point, so that the inflection point and the inflection point may be determined.

It should be noted that, for consecutive multiple CP motion track segments, the above-mentioned

parts

401 and 402 can be executed for every two consecutive CP motion track segments. For example, for the continuous three CP motion trajectory segments 1-3, a smooth transition trajectory segment between the CP motion trajectory segments 1-2 can be planned first, and then a smooth transition trajectory segment between the CP motion trajectory segments 2-3 can be planned.

The scheme provided by the embodiment of the invention is explained in the following with reference to fig. 5.

Fig. 5 is another exemplary flowchart of a robot motion trajectory planning method according to an embodiment of the present invention.

At part 500: and planning continuous CP motion track segments.

The continuous CP motion trajectory segments also need to be pre-planned. Section 500 is the basis for

subsequent sections

501 and 502.

In one example, all CP motion trajectory segments required may be planned at once. For example, if a total of 4 continuous CP motion trajectory segments are required to complete a certain operation of the robot, 4 continuous CP motion trajectory segments can be planned at one time.

In another example, all CP motion trajectory segments required may also be planned batch-wise. Still taking as an example that continuous CP motion trajectory segments 1-4 are needed to complete a certain operation of the robot, CP motion trajectory segments 1-2 may be planned first, and then

subsequent portions

501 and 502 are performed to obtain smooth transition trajectory segments between CP motion trajectory segments 1-2. Then, a CP motion trajectory segment 3 is planned, and the

subsequent portions

501 and 502 are executed to obtain a smooth transition trajectory segment between CP motion trajectory segments 2-3, and so on.

In yet another example, planning may also be done looking ahead for segment X, X typically taking 3. Taking an example that continuous CP motion trajectory segments 1-8 are needed to complete a certain operation of the robot, CP motion trajectory segments 1-2 may be planned first, and then

subsequent portions

501 and 502 are executed to obtain smooth transition trajectory segments between CP motion trajectory segments 1-2. Then, a CP motion track segment 3 is planned, and the

subsequent portions

501 and 502 are executed to obtain a smooth transition track segment between CP motion track segments 2-3. Then, after the CP motion track segment 1 runs, the CP motion track segment 4 is planned, and then the subsequent part 501 and part 502 are executed to obtain a smooth transition track segment between the CP motion track segments 3-4. And after the CP motion track section 2 runs, planning a CP motion track section 5, and then executing

subsequent parts

501 and 502 to obtain a smooth transition track section between the CP motion track sections 4-5, and so on.

In section 501: and determining the characteristic points of the Bezier curve for n times (n is not less than 4) according to the first CP motion track segment and the second CP motion track segment.

The portion 501 is similar to the portion 401, and is not described in detail here.

At element 502: and constructing a Bezier curve for n times (n is not less than 4) according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section.

Portion 502 is similar to portion 402 and will not be described in detail.

As mentioned above, when n is 4, there are five feature points, and when n is 5, there are six feature points. In the case where n is 4, the determination of the intermediate point is not the same as that in the case where n is 5. In practical applications, the first CP motion trajectory segment and the second CP motion trajectory segment may be respectively: straight line sections and straight line sections, straight line sections and circular arc sections, circular arc sections and straight line sections, and circular arc sections. The following examples will further illustrate the present invention in various cases.

Fig. 6a is an exemplary flowchart of another robot motion trajectory planning method provided in the embodiment of the present invention when n is 4 and the first CP motion trajectory segment and the second CP motion trajectory segment are straight line segments, respectively. Fig. 6b shows a first CP motion trajectory segment (lc) and a second CP motion trajectory segment (ln) and a smooth transition trajectory segment. The lc track segment and the ln track segment intersect at an intersection point O.

At part 601: determining the turning point of lc track segment as the starting point P of smooth transition track segment₀Determining the turning point of ln track segment as the ending point P of smooth transition track segment₄。

At element 602: determining the intersection point O as a (second) intermediate point P₂。

It has been previously demonstrated that the curvature of the Bezier curve of degree n (4) at the starting point is associated with 3 adjacent characteristic points (P)₀、P₁、P₂) In relation, the curvature at the termination point is also related to the adjacent 3 feature points (P)₂、P₃And P₄) In connection with, then P₂Point simultaneous need with P₀、P₁、P₃And P₄Coplanar, therefore, the intersection O is selected as P₂。

At 603: selecting a line segment P₀O (i.e. intersection O and starting point P)₀Line segment in between) as a (first) intermediate point P₁(ii) a Line segment P₀O is the intersection O and the starting point P₀The line segment in between.

In one example, the intermediate point P₁Distance to the intersection point O, equal to its starting point P₀The distance of (c). Thus, in solving for P₁When coordinates are obtained, P can be set₀P₁＝P₁And O, further obtaining the P1 point coordinate. P₀P₁＝P₁O can make the characteristic points uniformly distributed, and the uniform distribution of the characteristic points can make the parameters of the Beizer curve uniform and the change of the curvature of the track stable.

At element 604: selecting a line segment OP₄One point on as a (third) intermediate point P₃。

Line segment OP₄Is the intersection point O and the end point P₄The line segment in between.

In one example, the intermediate point P₃Distance to the point of intersection O, equal to the intermediate point P₃To a termination point P₄The distance of (c). Thus, in solving for P₃When coordinates are obtained, P can be set₃P₄＝P₃O, thereby obtaining P₃Point coordinates.

In section 605: and constructing a four-time Bezier curve according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section (the dotted line part in FIG. 6b is the smooth transition track section).

Section 605 is similar to

sections

402 and 502 described above and will not be described in detail.

Referring to fig. 6c, the curvature is 0 at both the start and end points by the method shown in fig. 6a, so that the acceleration is continuous at the inflection point.

Fig. 7a is an exemplary flowchart of another robot motion trajectory planning method provided in the embodiment of the present invention when n is 4, and the first CP motion trajectory segment is a straight line segment and the second CP motion trajectory segment is a circular arc segment. Fig. 7b shows a first CP motion trajectory segment (lc) and a second CP motion trajectory segment (ln) and a smooth transition trajectory segment.

In part 701: determining the turning point of lc track segment as the starting point P of smooth transition track segment₀Determining the turning point of ln track segment as the ending point P of smooth transition track segment₄。

The portion 701 is similar to the portion 601 and will not be described in detail here.

At element 702: determining the intersection point O as a (second) intermediate point P₂。

Portion 702 is similar to portion 602 and will not be described in detail.

At section 703: selecting a line segment P₀O (i.e. intersection O and starting point P)₀Line segment in between) as an intermediate point P₁。

The portion 703 is similar to the portion 603, and is not described in detail herein.

At element 704: determining an intermediate point P₃At the end point P₄On a tangent line of, and, line segment P₃P₄Has a length of

(see the figure for7b)。

Where r2 denotes the radius of the ln trajectory segment and α 2 denotes the termination point P₄The central angle of (d).

Formula (II)

Please refer to the embodiment shown in fig. 8 a.

In section 705: and constructing a four-time Bezier curve according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section (the dotted line part in FIG. 7b is the smooth transition track section).

Section 705 is similar to

sections

402, 502 and 605 described above and will not be described in detail.

Referring to fig. 7c, by the method shown in fig. 7a, the curvature is 0 at the starting point and 0.02 reciprocal of the radius (50) at the ending point, thereby realizing the acceleration continuity at the inflection point.

Fig. 8a is an exemplary flowchart of another robot motion trajectory planning method provided in the embodiment of the present invention when n is 4, the first CP motion trajectory segment is a circular arc segment, and the second CP motion trajectory segment is a straight line segment. Fig. 8b shows a first CP motion trajectory segment (lc) and a second CP motion trajectory segment (ln) and a smooth transition trajectory segment.

At 801, the turning point of lc track segment is determined as the starting point P of smooth transition track segment₀Determining the turning point of ln track segment as the ending point P of smooth transition track segment₄。

Portions 801 are similar to

portions

601 and 701 and are not described in detail herein.

At part 802: determining the intersection point O as a (second) intermediate point P₂。

Portions 802 are similar to

portions

602 and 702 and will not be described in detail.

At section 803: determining an intermediate point P₁At a starting point P₀On a tangent line of, and, line segment P₁P₀Has a length of

Where r1 denotes the radius of the lc trajectory segment and α 1 denotes the central angle of the starting point.

The following formula

And

the origin of (1).

Referring to fig. 8C, there are two continuous CP motion trajectory segments, the former segment is a circular arc segment, the latter segment is a straight line segment, point a is an intersection point, point C is an inflection point, the radius of the circular arc segment is r, and the central angle at the inflection point is α. And (4) root.

Point B is P1 point or P₃Point, point B, is located on the tangent of the arc at point C and satisfies that the n-fold Bezier curve has a curvature equal to the arc curvature at the starting point (i.e., point C). Knowing that the curvature of a circular arc segment is the inverse of the radius, the following equation:

wherein:

n is the Bezier curve times;

and the angle theta is the included angle between the vector AB and the vector BC.

A right triangle ABD is created to obtain | AB |, sin θ ═ AD ═ r-r · cos α.

Simplified equation two-sided derivation

At element 804: selecting a line segment OP₄One point on as an intermediate point P₃. Line segment OP₄Is the line segment between the intersection point O and the end point.

Portions 804 are similar to portions 604 and will not be described in detail.

At section 805: and constructing a four-time Bezier curve according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section (the dotted line part in FIG. 8b is the smooth transition track section).

Section 805 is similar to

sections

402, 502, 605 and 705 described above and will not be described in detail here.

Fig. 9a is an exemplary flowchart of another robot motion trajectory planning method provided in the embodiment of the present invention when n is 4 and both the first CP motion trajectory segment and the second CP motion trajectory segment are arc segments. Fig. 9b shows a first CP motion trajectory segment (lc) and a second CP motion trajectory segment (ln) and a smooth transition trajectory segment.

At the part 901, determining the turning point of the lc track segment as the starting point P of the smooth transition track segment₀Determining the turning point of ln track segment as the ending point P of smooth transition track segment₄。

The portion 901 is similar to the

portions

601, 701 and 801, and will not be described in detail here.

In section 902: determining the intersection point O as a (second) intermediate point P₂。

Portion 902 is similar to

portions

602, 702, and 802 and will not be described in detail herein.

At part 903: determining an intermediate point P₁At a starting point P₀On a tangent line of, and, line segment P₁P₀Has a length of

Portion 903 is similar to portion 803 and will not be described in detail herein.

At element 904: determining an intermediate point P₃At the end point P₄On a tangent line of, and, line segment P₂P₄Has a length of

(see also FIG. 9 b).

Portion 904 is similar to portion 704 and will not be described in detail.

In section 905: and constructing a four-time Bezier curve according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section (the dotted line part in FIG. 9b is the smooth transition track section).

Portion 905 is similar to

portions

402, 502, 605, 705, and 805 described above and will not be described herein.

Referring to fig. 9c, the curvature at the beginning and end points is the reciprocal of the radius (50) of 0.02 by the method shown in fig. 9a, so that the acceleration at the turning point is continuous.

Of the five control points considered for the quartic Bezier curve, P₂The point selection is performed on the intersection point of the two tracks, and the degree of freedom is not enough. To make the smooth trajectory adjustable, and to add more choices, the four Bezier curves may be upscaled to five Bezier curves.

The following describes a motion trajectory planning method based on five-time Bezier curves. The formula for the quintic Bezier curve is:

B(t)＝P₀(1-t)⁵+5P₁t(1-t)⁴+10P₂t2⁽1-t)³+10P₃t³(1-t)2...+5P₄t⁴(1-t)+P₅t⁵，t∈[0，1]

fig. 10a is an exemplary flowchart of another robot motion trajectory planning method provided in the embodiment of the present invention when n is 5 and the first CP motion trajectory segment and the second CP motion trajectory segment are arc segments, respectively. Fig. 10b shows a first CP motion trajectory segment (lc) and a second CP motion trajectory segment (ln) and a smooth transition trajectory segment, the lc trajectory segment and the ln trajectory segment intersecting at an intersection point O. The characteristic points include P₀、P₁、P₂、P₃、P₄And P₅Wherein P is₀Is a starting point, P₅Is an end point, P₁To P₄First to fourth intermediate points.

In part 1001: determining the turning point of lc track segment as the starting point P of smooth transition track segment₀Determining the turning point of ln track segment as the ending point P of smooth transition track segment₅。

The 1001 portion is similar to the 601, 701, 801 and 901 portions, and will not be described herein.

At element 1002: determining a (first) intermediate point P₁At a starting point P₀On a tangent line of, and, line segment P₁P₀Has a length of

Portion 1002 is similar to portion 803 and will not be described in detail.

In section 1003: determining a (second) intermediate point P₂To take a starting point P₀And a trisection point on a circular arc section (the circular arc section belongs to one part of the lc locus section) with the intersection point O as an end point.

Since there are two trisection points, in one example, the trisection point near the intersection point may be selected as the middle point P₂。

At element 1004: determining a fourth intermediate point P₄At the end point P₅On a tangent line of, and, line segment P₄P₅Has a length of

Where r2 denotes the radius of the ln trajectory segment and α 2 denotes the central angle at the termination point.

Portions 1004 are similar to portions 904 and will not be described in detail.

At section 1005: determining a (third) intermediate point P₃End point is, end point P₅And trisection points on a circular arc segment (the circular arc segment belongs to a part of the ln track segment) with the intersection point O as an end point.

Since there are two trisection points, in one example, the trisection point near the intersection point may be selected as the middle point P₃。

At section 1006: and constructing a quintic Bezier curve according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section (the dotted line part in FIG. 10b is the smooth transition track section).

Referring to fig. 10c, the curvature at the beginning and end points is the reciprocal of the radius (50) of 0.02 by the method shown in fig. 10a, so that the acceleration at the turning point is continuous.

Fig. 11a is an exemplary flowchart of another robot motion trajectory planning method provided in the embodiment of the present invention when n is 5, the first CP motion trajectory segment is a straight line segment, and the second CP motion trajectory segment is a circular arc segment. Fig. 11b shows a first CP motion trajectory segment (lc) and a second CP motion trajectory segment (ln) and a smooth transition trajectory segment, where the lc trajectory segment and the ln trajectory segment intersect at an intersection point O.

In section 1101: determining the turning point of lc track segment as the starting point P of smooth transition track segment₀Determining the turning point of ln track segment as the ending point P of smooth transition track segment₅。

Portions 1101 are similar to

portions

601, 701, 801, 901 and 1001 and are not described in detail herein.

At part 1102: is selected as the starting point P₀And trisection points on a straight line segment with the intersection point O as an endpoint are respectively taken as first intermediate points P₁And a second intermediate point P₂。

Since the curvature of the straight line is 0, P₀、P₁、P₂Co-linear.

Since there are two trisection points, in one example, the trisection point near the intersection point may be selected as the second intermediate point P₂Selecting a point close to the starting point P₀Is taken as a first intermediate point P₁。

At part 1103: determining a fourth intermediate point P₄At the end point P₅On a tangent line of, and, line segment P₄P₅Has a length of

Portions 1103 are similar to

portions

904 and 1004 and will not be described in detail here.

At part 1104: determining a third intermediate point P₃The end points are trisection points on the arc segment with the end point and the intersection point O as the end points.

Portion 1104 is similar to portion 1005 and will not be described in detail.

At part 1105: and constructing a fifth Bezier curve according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section (the dotted line part in FIG. 11b is the smooth transition track section).

Referring to fig. 11c, by the method shown in fig. 11a, the curvature is 0 at the starting point and 0.02 reciprocal of the radius (50) at the ending point, thereby realizing the acceleration continuity at the inflection point.

Fig. 12a is an exemplary flowchart of another robot motion trajectory planning method provided in the embodiment of the present invention when n is 5, the first CP motion trajectory segment is a straight line segment, and the second CP motion trajectory segment is a circular arc segment.

Fig. 12b shows a first CP motion trajectory segment (lc) and a second CP motion trajectory segment (ln) and a smooth transition trajectory segment, where the lc trajectory segment and the ln trajectory segment intersect at an intersection point O.

At part 1201: determining the turning point of lc track segment as the starting point P of smooth transition track segment₀Determining the turning point of ln track segment as the ending point P of smooth transition track segment₅。

Portion 1201 is similar to

portions

601, 701, 801, 901, 1001, and 1101 and will not be described in detail here.

At part 1202: is selected as the starting point P₀And the trisection points on the straight line segment with the intersection point O as the end point are respectively taken as (first) intermediate points P₁And a second intermediate point P₂。

Portion 1202 is similar to portion 1102 and will not be described in detail herein.

At part 1203: selecting to end point P₅And trisection points on a straight line segment with the intersection point O as an end point are respectively taken as third intermediate points P₃And a fourth intermediate point P₄。

Since the curvature of the straight line is 0, P₃、P₄、P₅Co-linear.

Since there are two trisection points, in one example, a trisection point near the intersection point may be selected as the third intermediate point P₃Selecting near the end point P₅Is taken as a fourth intermediate point P₄。

At element 1204: and constructing a quintic Bezier curve according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section (the dotted line part in FIG. 12b is the smooth transition track section).

Referring to fig. 12c, the curvature is 0 at both the start and end points by the method shown in fig. 12a, so that the acceleration is continuous at the inflection point.

When n is 5 and the first CP motion track section is a circular arc section and the second CP motion track section is a straight line section, the starting point P of the smooth transition track section₀End point P₅See

sections

601, 701, 801, 901, 1001 and 1201 for a first intermediate point P₁And a second intermediate point P₂See sections 1002 and 1003, and the third intermediate point P₃And a fourth intermediate point P₄The determination method can be seen in section 1203, and is not described herein again.

Fig. 13 shows a schematic structural diagram of a possible configuration of the robot motion trajectory planning apparatus according to the above embodiment, including:

a characteristic point determining unit 131, configured to determine a characteristic point of the Bezier curve n times (n is not less than 4) according to the first CP motion trajectory segment and the second CP motion trajectory segment.

A smooth transition track constructing unit 132, configured to construct an n-order (n is not less than 4) Bezier curve according to the feature point, where the n-order (n is not less than 4) Bezier curve is used as a smooth transition track section between the first CP motion track section and the second CP motion track section, a starting point of the smooth transition track section is an inflection point of the first CP motion track section, and a termination point of the smooth transition track section is an inflection point of the second CP motion track section; the smooth transition track segment and the first CP motion track segment have the same tangent vector direction and the same curvature on the starting point; and the smooth transition track section and the second CP motion track section have the same tangential vector direction and the same curvature at the termination point.

In addition, a planning unit 133 may be further included for planning consecutive CP motion trajectory segments before the feature point determining unit determines the feature points of the Bezier curve n times (n is not less than 4).

The feature point determination unit 131 can be used to execute the portion 401 shown in fig. 4, the portion 501 shown in fig. 5, the portion 601-604 shown in fig. 6a, the portion 701-704 shown in fig. 7a, the portion 801-804 shown in fig. 8a, the portion 901-904 shown in fig. 9a, the portion 1001-1005 shown in fig. 10a, the portion 1101-1104 shown in fig. 11a, and the portion 1201-1203 shown in fig. 12 a.

The smooth transition trajectory construction unit 132 may be configured to execute the part 402 shown in fig. 4, the part 502 shown in fig. 5, the part 605 shown in fig. 6a, the part 705 shown in fig. 7a, the part 805 shown in fig. 8a, the part 905 shown in fig. 9a, the part 1006 shown in fig. 10a, the part 1105 shown in fig. 11a, and the part 1204 shown in fig. 12 a.

The planning unit 133 may be used to perform the part 500 shown in fig. 5.

Fig. 14 shows a possible schematic structural diagram of the robot involved in the above embodiment, including:

a bus, a controller/processor 1, a memory 2, a communication interface 3, an input device 4, an output device 5, and a controlled device 6. The processor 1, the memory 2, the communication interface 3, the input device 4, the output device 5, and the controlled device 6 may be connected to each other by a bus. Wherein:

a bus may include a path that transfers information between components of a computer system.

The controller/processor 1 (robot motion trajectory planning device) may be a general-purpose processor, such as a general-purpose Central Processing Unit (CPU), a Network Processor (NP), a microprocessor, etc., or may be an application-specific integrated circuit (ASIC), or one or more integrated circuits for controlling the execution of the program according to the present invention. But may also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components. The controller/processor 1 may also be a combination of implementing computing functions, e.g., comprising one or more microprocessors, a combination of DSPs and microprocessors, or the like.

The memory 2 stores a program for executing the technical solution of the present invention, and may store an operating system and other application programs. In particular, the program may include program code including computer operating instructions. More specifically, memory 2 may be a read-only memory (ROM), other types of static storage devices that may store static information and instructions, a Random Access Memory (RAM), other types of dynamic storage devices that may store information and instructions, a disk storage device, and so forth.

The input device 4 may include means for receiving data and information input by a user, such as a keyboard, mouse, camera, scanner, light pen, voice input means, touch screen, etc.

The output device 5 may include means for allowing output of information to a user, such as a display screen, a printer, speakers, etc.

The communication interface 3 may comprise means for using any transceiver or the like for communicating with other devices or communication networks, such as ethernet, Radio Access Network (RAN), Wireless Local Area Network (WLAN) or the like.

The controller/processor 1 may be used to perform the processes of fig. 4, 5, 6a, 7a, 8a, 9a, 10a, 11a, 12a involving a robot motion trajectory planning device and/or other processes for the techniques described herein. The controller/processor may also be used to implement the functions of the aforementioned feature point determination unit 131, smooth transition trajectory construction unit 132, and planning unit 133.

The controlled device 6 can be used to run according to the two continuous CP motion trajectory segments and the smooth transition trajectory segment planned by the controller/processor 1.

It will be appreciated that figure 14 only shows a simplified design of the robot. In practice, the robot may comprise any number of transmitters, receivers, processors, controllers, memories, communication interfaces, etc., and all robots that may implement the present invention are within the scope of the present invention.

The method and the device disclosed by all the embodiments can be applied to mechanical arm control, and smooth switching of the mechanical arm in two continuous running tracks in a Cartesian space is realized. The method can be extended to any equipment needing path planning, such as a trolley, an aircraft and the like.

The steps of a method or algorithm described in connection with the disclosure herein may be embodied in hardware or in software instructions executed by a processor. The software instructions may consist of corresponding software modules that may be stored in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such the processor can read information from, and write information to, the storage medium. Of course, the storage medium may also be integral to the processor. The processor and the storage medium may reside in an ASIC.

Those skilled in the art will recognize that, in one or more of the examples described above, the functions described in this invention may be implemented in hardware, software, firmware, or any combination thereof. When implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a general purpose or special purpose computer.

The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made on the basis of the technical solutions of the present invention should be included in the scope of the present invention.

Claims

1. A robot motion trail planning method is characterized by at least being used for realizing smooth switching between two continuous CP motion trail sections, wherein the two continuous CP motion trail sections comprise a first CP motion trail section and a second CP motion trail section;

the method comprises the following steps:

determining characteristic points of the Bezier curve for n times according to the first CP motion track segment and the second CP motion track segment, wherein n is a positive integer not less than 4;

constructing an n-time Bezier curve according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section, wherein the starting point of the smooth transition track section is the inflection point of the first CP motion track section, and the ending point of the smooth transition track section is the inflection point of the second CP motion track section;

the smooth transition track segment and the first CP motion track segment have the same tangent vector direction and the same curvature on the starting point; the smooth transition track section and the second CP motion track section have the same tangential vector direction and the same curvature on the termination point;

if n is 4, the feature point includes a starting point P₀End point P₄And first to third intermediate points P₁、P₂、P₃(ii) a The intersection point of the first CP motion track segment and the second CP motion track segment is represented as an O point;

the determining the characteristic points of the Bezier curve for n times according to the first CP motion track segment and the second CP motion track segment comprises:

determining the intersection point O as the second intermediate point P₂；

If the first CP motion track section is a straight line section, selecting the intersection point O and the starting point P₀A point on the line segment therebetween as the first intermediate point P₁；

If the first CP motion track segment is a circular arc segment,determining a first intermediate point P₁At a starting point P₀On a tangent line of, and, line segment P₁P₀Has a length of

2. The method of claim 1, wherein prior to said determining feature points of an n-degree Bezier curve, further comprising: and planning continuous CP motion track segments.

3. The method of claim 1, wherein said determining characteristic points of an n-th order Bezier curve from said first CP motion trajectory segment and said second CP motion trajectory segment further comprises:

if the second CP motion track section is a straight line section, selecting the intersection point O and the termination point P₄A point on the line segment therebetween as the third intermediate point P₃；

If the second CP motion track segment is a circular arc segment, determining the third intermediate point P₃At the end point P₄On a tangent line of, and, line segment P₃P₄Has a length of

4. The method of claim 1 or 2,

if n is 5, the feature point includes a starting point P₀End point P₅And first to fourth intermediate points P₁、P₂、P₃、P₄(ii) a And the intersection point of the first CP motion track segment and the second CP motion track segment is represented as an O point.

5. The method as claimed in claim 4, wherein said determining the characteristic points of the Bezier curve for n times from the first CP motion trajectory segment and the second CP motion trajectory segment comprises:

if the first CP motion track segment is a circular arc segment, determining the first intermediate point P₁Is located at the starting point P₀On a tangent line of, and, line segment P₁P₀Has a length of

Wherein r1 represents a radius of the first CP motion trajectory segment, α 1 represents a central angle at the start point;

determining the second intermediate point P₂To take the starting point P₀And the intersection point O is the trisection point on the arc segment of the end point.

6. The method as claimed in claim 4, wherein said determining the characteristic points of the Bezier curve for n times from the first CP motion trajectory segment and the second CP motion trajectory segment comprises:

if the first CP motion track section is a straight line section, selecting the starting point P₀And trisection points on a straight line segment with the intersection point O as an endpoint are respectively taken as first intermediate points P₁And a second intermediate point P₂。

7. The method of claim 5 or 6, wherein said determining the characteristic points of the Bezier curve for n times from the first CP motion trajectory segment and the second CP motion trajectory segment further comprises:

if the second CP motion track segment is a circular arc segment, determining the third intermediate point P₃The trisection points on the arc segment with the termination point and the intersection point O as end points;

determining the fourth intermediate point P₄At the end point P₅On a tangent line of, and, line segment P₄P₅Has a length of

Wherein the content of the first and second substances,r2 represents the radius of the second CP motion trajectory segment, and α 2 represents the central angle at the termination point.

8. The method of claim 5 or 6, wherein said determining the characteristic points of the Bezier curve for n times from the first CP motion trajectory segment and the second CP motion trajectory segment further comprises:

if the second CP motion track section is a straight line section, trisection points on the straight line section with the end point and the intersection point O as end points are selected as the third middle point P respectively₃And a fourth intermediate point P₄。

9. A robot motion trail planning device is characterized by at least being used for realizing smooth switching between two continuous CP motion trail sections, wherein the two continuous CP motion trail sections comprise a first CP motion trail section and a second CP motion trail section; the device comprises:

a characteristic point determining unit, configured to determine a characteristic point of the Bezier curve for n times according to the first CP motion trajectory segment and the second CP motion trajectory segment, where n is a positive integer not less than 4;

a smooth transition track construction unit, configured to construct an n-order Bezier curve according to the feature point, where the n-order Bezier curve is used as a smooth transition track section between the first CP motion track section and the second CP motion track section, a starting point of the smooth transition track section is an inflection point of the first CP motion track section, and a termination point of the smooth transition track section is an inflection point of the second CP motion track section;

if n is 4, the feature point includes a starting point P₀End point P₄And first to third intermediate points P₁、P₂、P₃(ii) a The intersection point of the first CP motion track segment and the second CP motion track segment representsIs a point O;

in said aspect of determining feature points of a Bezier curve n times from said first and second CP motion trajectory segments, said smooth-transition trajectory construction unit is configured to: determining the intersection point O as the second intermediate point P₂；

If the first CP motion track segment is a circular arc segment, determining a first intermediate point P₁At a starting point P₀On a tangent line of, and, line segment P₁P₀Has a length of

10. The apparatus of claim 9, further comprising:

and the planning unit is used for planning continuous CP motion track segments before the characteristic point determining unit determines the characteristic points of the Bezier curve for n times.

11. The apparatus as recited in claim 9, wherein said smooth-transition-trajectory construction unit, in said determining feature points of an n-degree Bezier curve from said first CP motion-trajectory segment and said second CP motion-trajectory segment, is further configured to:

12. The apparatus according to claim 9 or 10, wherein if n-5, the feature point comprises a starting point P₀End point P₅And first to fourth intermediate points P₁、P₂、P₃、P₄(ii) a And the intersection point of the first CP motion track segment and the second CP motion track segment is represented as an O point.

13. The apparatus as recited in claim 12, wherein said smooth-transition-trajectory construction unit, in said determining feature points of an n-degree Bezier curve from said first CP motion-trajectory segment and second CP motion-trajectory segment, is configured to:

14. The apparatus as recited in claim 12, wherein said smooth-transition-trajectory construction unit, in said determining feature points of an n-degree Bezier curve from said first CP motion-trajectory segment and second CP motion-trajectory segment, is configured to: if the first CP motion track section is a straight line section, selecting the starting point P₀And trisection points on a straight line segment with the intersection point O as an endpoint are respectively taken as first intermediate points P₁And a second intermediate point P₂。

15. The apparatus according to claim 13 or 14, wherein in said determining feature points of a Bezier curve from said first and second CP motion trajectory segments for n times, said smooth-transition trajectory construction unit is further configured to:

Where r2 denotes a radius of the second CP motion trajectory segment, and α 2 denotes a central angle at the termination point.

16. The apparatus according to claim 13 or 14, wherein in said determining feature points of a Bezier curve from said first and second CP motion trajectory segments for n times, said smooth-transition trajectory construction unit is further configured to: if the second CP motion track section is a straight line section, trisection points on the straight line section with the end point and the intersection point O as end points are selected as the third middle point P respectively₃And a fourth intermediate point P₄。

17. A robot motion trail planning device is characterized by at least being used for realizing smooth switching between two continuous CP motion trail sections, wherein the two continuous CP motion trail sections comprise a first CP motion trail section and a second CP motion trail section;

the device comprises: a processor and a memory, the processor executing a software program stored in the memory, calling data stored in the memory, and performing at least the following steps:

n is 4, and the feature point includes a start point P₀End point P₄And first to third intermediate points P₁、P₂、P₃(ii) a The intersection point of the first CP motion track segment and the second CP motion track segment is represented as an O point;

determining the intersection point O as the second intermediate point P₂；

18. A robot is characterized by comprising a robot motion trail planning device and a controlled device, wherein:

the robot motion trail planning device is used for: determining characteristic points of the Bezier curve for n times according to the first CP motion track segment and the second CP motion track segment, wherein n is a positive integer not less than 4; constructing an n-time Bezier curve according to the characteristic points to serve as a smooth transition track section between the first CP motion track section and the second CP motion track section, wherein the starting point of the smooth transition track section is the inflection point of the first CP motion track section, and the ending point of the smooth transition track section is the inflection point of the second CP motion track section; the smooth transition track segment and the first CP motion track segment have the same tangent vector direction and the same curvature on the starting point; the smooth transition track section and the second CP motion track section have the same tangential vector direction and the same curvature on the termination point;

the controlled device is used for: running according to two continuous CP motion track sections and a smooth transition track section planned by the robot motion track planning device;

determining the intersection point O as the second intermediate point P₂；

Wherein r1 represents the radius of the first CP motion profile segmentAnd α 1 denotes a central angle at the starting point.

19. A robot as claimed in claim 18, wherein the controlled device is in particular: an operating arm.