CN112659126A - Industrial robot track segment transition method based on non-uniform B-spline curve - Google Patents

Industrial robot track segment transition method based on non-uniform B-spline curve Download PDF

Info

Publication number
CN112659126A
CN112659126A CN202011544185.4A CN202011544185A CN112659126A CN 112659126 A CN112659126 A CN 112659126A CN 202011544185 A CN202011544185 A CN 202011544185A CN 112659126 A CN112659126 A CN 112659126A
Authority
CN
China
Prior art keywords
curve
point
straight line
spline
transition
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202011544185.4A
Other languages
Chinese (zh)
Other versions
CN112659126B (en
Inventor
刘建群
杨轶焬
高伟强
刘洋
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guangdong University of Technology
Original Assignee
Guangdong University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Guangdong University of Technology filed Critical Guangdong University of Technology
Priority to CN202011544185.4A priority Critical patent/CN112659126B/en
Publication of CN112659126A publication Critical patent/CN112659126A/en
Application granted granted Critical
Publication of CN112659126B publication Critical patent/CN112659126B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

The invention discloses an industrial robot track segment transition method based on a non-uniform B-spline curve, which utilizes a multi-track segment transition method to process a motion track specified by a user: calculating curve control points by using a curve transition model; estimating the speed of a track transition region by using a speed constraint model; and outputting a track interpolation point sequence of the robot in a Cartesian space by using the speed planning curve to realize the processing of the robot. The invention ensures the G of the overall track3The continuous acceleration is continuous, the connection speed of the corners of the multiple sections of continuous tracks is improved, the sudden change of the acceleration is avoided, and the smooth motion of the center point of the robot tool is realized.

Description

Industrial robot track segment transition method based on non-uniform B-spline curve
Technical Field
The invention relates to the technical field of industrial robots, in particular to an industrial robot track segment transition method based on a non-uniform B-spline curve.
Background
When an industrial robot carries out Cartesian space continuous track planning, the motion track of the industrial robot is generally composed of multiple sections of tracks, and the quality of track connection processing affects the processing quality and the working efficiency. If the robot does not process the corner, the robot directly decelerates and stops, working time is increased, and large-scale acceleration and deceleration of the motor, time consumption and energy consumption are caused; if the holding speed passes directly through the inflection point, machine vibration may be generated, resulting in unpredictable accuracy errors and affecting workpiece quality.
At present, the conventional method for track connection transition is curve fitting, a section of miniature curve is inserted into a connection position, the curve does not pass through an inflection point, and the transition is smooth by sacrificing position precision. For example, corner transition is realized through arc switching, but there is abrupt change of normal acceleration of a connecting point, which causes machine vibration; method for constructing real-time fitting curve through Bezier curve, but track can only reach G2Continuously; moreover, the above method does not consider the connection between the straight circular arc tracks, which will seriously affect the efficiency when the robot processes the complex curved surface workpiece.
Disclosure of Invention
The invention aims to overcome the problem of corner transition of a robot and provides a method for constructing a connection curve model of a 'straight line-straight line' track and a 'straight line-circular arc' track, which is used for realizing the G-shaped non-uniform track of the whole track by splicing a section of miniature non-uniform B-spline curve in a corner area on the basis of the original track3The continuous acceleration is continuous, and when meeting the precision requirement, the connection speed of continuous orbit of promotion multistage shortens the motion time.
In order to achieve the purpose, the technical scheme provided by the invention is as follows:
a transition method of an industrial robot track section based on a non-uniform B-spline curve utilizes a multi-track section transition method to process a motion track appointed by a user: calculating curve control points by using a curve transition model; estimating the speed of a track transition region by using a speed constraint model; and outputting a track interpolation point sequence of the robot in a Cartesian space by using the speed planning curve to realize high-speed smooth processing of the robot.
Further, the specific process of the multi-segment trajectory transition method includes:
s1, setting various parameters of the industrial robot, including respective performance parameters of six joints of the industrial robot and planning parameters of a Cartesian space; creating a cache group, wherein the cache group comprises a track queue cache, a speed planning cache and a transition track information cache of the industrial robot, and all the caches are set to be empty after being created;
s2, analyzing the 'straight line-straight line' track type and the 'straight line-circular arc' track type, and determining the position of a control point of the non-uniform B-spline curve by using a corresponding curve transition model;
s3, limiting the corner speed according to the size of the current corner;
and S4, calculating a curve interpolation point according to the calculated spline curve control point position.
Further, in step S2, when the trajectory type is "straight line-straight line", the running trajectory is composed of two adjacent straight line segments, and assuming B, A, C is an end point of the two straight lines, the two straight lines intersect at a point a, and an included angle between the two straight lines is α, a specific process for determining the position of the control point of the non-uniform B-spline curve is as follows:
a, constructing a spline curve, and obtaining a curve control point di；
To achieve the engagement curve with G3Continuity, number of spline curves is 5, control point diThe number is 7, corresponding to d0，d1，...，d6(ii) a In order to ensure that the starting point and the end point of the curve can coincide with the head and tail control points, the head and tail vector nodes are set with the repetition degree of 6 times, namely u0＝...＝u5＝0；u7＝...＝u 121 is ═ 1; to ensure symmetry of the curve, u60.5, the node vector of the model is set to U ═ 0000000.5111111]T(ii) a Control point d for the tangent of the spline curve to the line at the junction0，d1，d2On a straight line AB, control point d3Is positioned at the inflection point A; similarly, control point d4，d5，d6Lies on a straight line AC; in order to make the curve at the control point d0And d6Is connected with a straight line and has G3The second and third derivatives of the curve p (u) with respect to the arc length s are zero when u is 0 and u is 1; after derivation, the proportional relation among the control points can be obtained:
Figure BDA0002855244940000031
assuming a unit transition length d1d2By simplifying the above formula, one can obtain:
Figure BDA0002855244940000032
b. calculating unit transition length l according to a given error;
because the node vectors of the spline curve are centrosymmetric, the obtained curve also has the characteristic of centrosymmetry; when the curve parameter u is 0.5, the distance between the highest point F of the spline curve and the inflection point A is the farthest, and the position error of the curve is the largest, so that the position accuracy of the transition curve can be ensured by controlling the maximum error of AF at the inflection point; the model error equation δ is derived as follows:
Figure BDA0002855244940000033
in the formula, delta is a given upper limit of position error, and alpha is an included angle between two straight lines; setting the curve transition length not to exceed one fourth of the original straight line length, wherein the unit transition length l formula is as follows:
Figure BDA0002855244940000034
c. calculating the space coordinates of the control points through a linear equation;
equation of a space line as Pi＝Ps-Li·VL(ii) a Wherein P issIs a straight line starting point, VLUnit vector pointing from start to end, LiThe distance from the starting point to the corresponding control point; finding control point d on AB section1When the temperature of the water is higher than the set temperature,
Figure BDA0002855244940000035
further, in step S2, when the trajectory type is "straight line-circular arc", the moving trajectory is composed of a spatial straight line and a spatial circular arc, and assuming that B, A is an end point of the straight line, A, C is an end point of the circular arc with a radius R, the two end points intersect at a point a, the straight line AD is a tangent of the circular arc at the point a, and an included angle between the straight line BA and the straight line AD is α, a specific process of determining the position of the control point of the non-uniform B spline curve is as follows:
a. establishing a curved surface;
translating the straight line from the point A to a point O at the center of the circle to obtain a straight line EO, and constructing a circle with a plurality of layers of radiuses R, parallel to the bottom surface circle and with the center on the straight line; when the constructed circular arcs are dense enough, a cylindrical curved surface can be formed; constructing a transition curve on the cylindrical curved surface by using known information; cutting off the curved surface from the straight line BA by using three-dimensional software to obtain an unfolded drawing; the tangent line AD corresponds to the straight line AD in the development figure, the included angle between the tangent line AD and the straight line BA is alpha, and the passing point D is perpendicular to the arc line
Figure BDA0002855244940000041
The foot is D';
b. constructing a transition model;
using "straight-line" type transition models, subtending arcs
Figure BDA0002855244940000042
Constructing a spline curve between the straight line BA and the straight line BA; wherein, according to the idea of 'replacing curve with straight', the tangent line AD is approximated to be an arc line
Figure BDA0002855244940000043
Directly constructing a spline curve in the DAB;
c. establishing a mapping relation between an expansion surface and a space curved surface;
because the actual space curved surface is formed by splicing innumerable layers of arcs, points on the expansion surface can be mapped to the points on the actual space curved surface, each dot-dash line substantially corresponds to the expansion line of the corresponding layer of arcs in the space curved surface, and the position of the point on the space curved surface can be calculated at any point P on the expansion surface as long as the point P is located on the expansion line of which arc; in the construction of the transition model, the determination of the transition model is simplified by a method of approximating an arc line by a tangent line, and a point in the transition curve is calculated:
making a straight line parallel to the tangent line AD at the passing point P, and intersecting the straight line AD at the point A'; the position of the point A 'on the straight line can be determined, the position of the circle center of the arc layer corresponding to the space curved surface on the axis EO can be determined, the length d of the straight line PA' is approximately equal to the length of the arc line on the corresponding expansion line, and the corresponding central angle theta is obtained in the corresponding space curved surface through the relation theta which is d/R.
Further, the corner speed is determined by the minimum value of three constraint speeds, and a speed V is set for a user respectivelyuserString height error limit allowable speed VerrCentripetal acceleration limiting allowable speed VcirThe maximum allowable corner speed is calculated as follows:
a. calculating chordal height error limit allowable velocity Verr；
When the curvature of the curve track is large and the running speed is high, the actual interpolation track and the theoretical track generate a large track error; since the curvature of the curve of the model is the largest in the area where u is 0.5, and the chord height error is the largest, the chord height error of the whole section of the curve is controlled by performing curve approximate chord height error analysis on the point;
will PiAnd Pi+1The curve between them is similar to an arc with equal curvature, the radius of curvature is R, PiPi+1The interpolation distance is L, and a chord height error model is obtained; according to the geometrical relationship, the estimation formula of the chord height error epsilon when the curve u is 0.5 is as follows:
Figure BDA0002855244940000051
wherein, PiRadius of curvature of
Figure BDA0002855244940000052
P '(u) and P' (u) are the first and second derivatives of P (u), respectively, and the interpolation length L is approximately PiIs multiplied by the interpolation period TcSubstitution intoFrom the above equation, the allowable velocity V under the string height error limit is knownerrComprises the following steps:
Figure BDA0002855244940000053
b. calculating the centripetal acceleration limit allowable speed Vcir；
As the curvature of the spline curve is higher and the curvature radius is smaller, the motor needs larger normal acceleration to change the motion direction, and the acceleration at the joint point needs to be ensured to exceed the set value amax(ii) a Centripetal acceleration limits allowable speed VcirComprises the following steps:
Figure BDA0002855244940000054
c. taking the minimum value; maximum allowable corner velocity vcorThe following can be obtained:
vcor＝min{Vuser，Verr，Vcir}。
further, in step S4, when the current trajectory segment is "straight-line", the trajectory B → a → C is followed by optimization using the curve transition model, and the trajectory of the current segment is changed to B → F → C, and two straight lines and a spline curve are spliced, i.e. the straight line Bd is followed0Spline d0d6Straight line d6C；
The specific process of calculating the curve interpolation point is as follows:
calculating the actual length of a splicing curve, then carrying out S-shaped speed planning on the splicing curve according to the calculated corner speed so as to obtain a position-time sequence of a fixed interpolation period, and finally calculating interpolation points by using a non-uniform B-spline curve formula;
the construction formula of the non-uniform B-spline curve is as follows:
Figure BDA0002855244940000061
Figure BDA0002855244940000062
wherein k is the spline curve frequency, and the spline parameter u belongs to [0,1 ]]，diAs spline curve control points, Ni,k(u) is a k-th order B-spline basis function; and calculating a spline parameter u corresponding to each period by planning the position according to the speed of each period, and further determining a space interpolation point corresponding to each period.
Further, in step S4, when the current trajectory segment type is "straight line-circular arc", the trajectory B → a → C is followed by optimization using the curve transition model, and then the trajectory of the current segment is changed to B → F → C, and the current segment is spliced by a straight line, a spline curve and a circular arc, i.e. the straight line Bd0Spline d0d6Arc d6C；
The specific process of calculating the curve interpolation point is as follows;
calculating the actual length of a splicing curve, performing S-shaped speed planning on the splicing curve according to the calculated corner speed to obtain a position-time sequence of a fixed interpolation period, constructing a curve between a tangent line AD and a straight line AB by using a non-uniform B-spline curve formula, calculating interpolation points, and finally utilizing the mapping relation between an expansion surface and a space curved surface, wherein each interpolation point on the expansion surface has a corresponding space circle center position and a corresponding space circle center angle theta, and the space circular arc equation C (theta) is O + R (V)tsinθ+Vrcos theta), where O is the position of the center of the spatial arc, R is the radius of the spatial arc, and VtA tangent unit vector which is the interpolation direction at the starting point of the circular arc, namely the direction of the straight line AD, VrThe unit vector of which the circle center points to the circular arc starting point is the direction of a straight line OA, theta is the size of a circle center angle corresponding to a circular arc which is interpolated from the circular arc starting point according to a given interpolation direction, and by the method, mapping conversion of the expansion surface interpolation point and the space circular arc is realized, so that the space interpolation point of each period in the curved surface space is obtained.
Compared with the prior art, the principle and the advantages of the scheme are as follows:
at present, the mainstream arc transition method is to realize smooth transition by joining a small section of tangent arc, but because the transition arc and the straight line are only in tangent relation, acceleration at the joint point is suddenly changed, and machine vibration is caused.
According to the scheme, on the basis of the original track, a section of miniature non-uniform B-spline curve is spliced in the corner area, so that the G of the whole track is guaranteed3The continuous acceleration is continuous, the connection speed of the corners of the multiple sections of continuous tracks is improved, the sudden change of the acceleration is avoided, and the smooth motion of the center point of the robot tool is realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the services required for the embodiments or the technical solutions in 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 these drawings without creative efforts.
FIG. 1 is a schematic flow diagram of a multi-segment trajectory transition method;
FIG. 2 is a schematic view of a "straight-line" trajectory;
FIG. 3 is one of the schematic diagrams of a "straight-arc" trajectory;
FIG. 4 is a schematic view of a constructed curved surface;
FIG. 5 is a schematic view of a cylindrical curved surface formed on the basis of FIG. 4;
FIG. 6 is a developed view of FIG. 5 taken along line BA;
FIG. 7 is a view showing the tangent line AD of FIG. 6 approximated by an arc line
Figure BDA0002855244940000071
A schematic diagram of (a);
FIG. 8 is a schematic diagram of a chord height error model;
FIG. 9 is a second schematic diagram of a "straight-circular arc" trajectory;
fig. 10 is a schematic view of the motion space trajectory of a given industrial robot;
FIG. 11 is a graphical comparison of tip spatial trajectory velocities without and with spline filtering;
FIG. 12 is a schematic illustration of curvature analysis of a circular arc transition trajectory and a spline curve transition trajectory;
FIG. 13 is a schematic diagram of transition region spline curves and corresponding straight line trajectory position errors.
Detailed Description
The invention will be further illustrated with reference to specific examples:
the industrial robot track segment transition method based on the non-uniform B-spline curve, disclosed by the embodiment of the invention, utilizes a multi-track segment transition method to process a motion track specified by a user: calculating curve control points by using a curve transition model; estimating the speed of a track transition region by using a speed constraint model; and outputting a track interpolation point sequence of the robot in a Cartesian space by using the speed planning curve to realize high-speed smooth processing of the robot.
As shown in fig. 1, the specific process of the multi-segment trajectory transition method includes:
s1, setting various parameters of the six-degree-of-freedom industrial robot, including the performance parameters of the six joints of the industrial robot and the planning parameters of a Cartesian space; creating a cache group, wherein the cache group comprises a track queue cache, a speed planning cache and a transition track information cache of the industrial robot, and all the caches are set to be empty after being created;
s2, analyzing the 'straight line-straight line' track type and the 'straight line-circular arc' track type, and determining the position of a control point of the non-uniform B-spline curve by using a corresponding curve transition model;
when the trajectory type is "straight line-straight line", the running trajectory is composed of two adjacent straight line segments, as shown in fig. 2, B, A, C is the end points of the two straight lines, the two straight lines intersect at point a, wherein the included angle between the two straight lines is α, then the specific process of determining the position of the control point of the non-uniform B-spline curve is as follows:
a. constructing a spline curve, and finding a curve control point di；
To realize the connectionCurve having G3Continuity, number of spline curves is 5, control point diThe number is 7, corresponding to d0，d1，...，d6(ii) a In order to ensure that the starting point and the end point of the curve can coincide with the head and tail control points, the head and tail vector nodes are set with the repetition degree of 6 times, namely u0＝...＝u5＝0；u7＝...＝u 121 is ═ 1; to ensure symmetry of the curve, u60.5, the node vector of the model is set to U ═ 0000000.5111111]T(ii) a Control point d for the tangent of the spline curve to the line at the junction0，d1，d2On a straight line AB, control point d3Is positioned at the inflection point A; similarly, control point d4，d5，d6Lies on a straight line AC; in order to make the curve at the control point d0And d6Is connected with a straight line and has G3The second and third derivatives of the curve p (u) with respect to the arc length s are zero when u is 0 and u is 1; after derivation, the proportional relation among the control points can be obtained:
Figure BDA0002855244940000091
assuming a unit transition length d1d2By simplifying the above formula, one can obtain:
Figure BDA0002855244940000092
b. calculating unit transition length l according to a given error;
because the node vectors of the spline curve are centrosymmetric, the obtained curve also has the characteristic of centrosymmetry; when the curve parameter u is 0.5, the distance between the highest point F of the spline curve and the inflection point A is the farthest, and the position error of the curve is the largest, so that the position accuracy of the transition curve can be ensured by controlling the maximum error of AF at the inflection point; the model error equation δ is derived as follows:
Figure BDA0002855244940000093
in the formula, delta is a given upper limit of position error, and alpha is an included angle between two straight lines; setting the curve transition length not to exceed one fourth of the original straight line length, wherein the unit transition length l formula is as follows:
Figure BDA0002855244940000094
c. calculating the space coordinates of the control points through a linear equation;
equation of a space line as Pi＝Ps-Li·VL(ii) a Wherein P issIs a straight line starting point, VLUnit vector pointing from start to end, LiThe distance from the starting point to the corresponding control point; to find the control point d on the AB section1For the purpose of example only,
Figure BDA0002855244940000095
when the track type is "straight line-circular arc", the running track is formed by a space straight line and a space circular arc different surface, as shown in fig. 3, B, A is an end point of the straight line, A, C is an end point of the circular arc with the radius R, the two end points intersect at a point a, the straight line AD is a tangent line of the circular arc at the point a, and an included angle between the straight line BA and the straight line AD is α, then a specific process for determining the position of the control point of the non-uniform B spline curve is as follows:
a. establishing a curved surface;
because the straight line and the circular arc are in a non-coplanar relationship, it is difficult to directly construct a transition curve communicated with the non-coplanar relationship in a three-dimensional space, but if the transition curve can be constructed on a determined plane or curved surface, the difficulty of constructing the curve can be reduced. The method for constructing the curved surface comprises the following steps:
translating the straight line from the point A to the point O at the center of the circle to obtain a straight line EO, and constructing a circle with countless layers of radiuses of R, parallel to the bottom surface circle and the center of the circle on the straight line, as shown in FIG. 4; when the constructed circular arcs are dense enough, a cylindrical curved surface can be formed, as shown in fig. 5; using the known information, willThe transition curve is constructed on the cylindrical curved surface; cutting the curved surface from the line BA by using three-dimensional software to obtain an expanded view as shown in FIG. 6; the tangent line AD in FIG. 4 corresponds to the straight line AD in the expanded view of FIG. 6, and also has an angle α with the straight line BA, and the passing point D is perpendicular to the arc line
Figure BDA0002855244940000101
The foot is D';
b. constructing a transition model;
using "straight-line" type transition models, subtending arcs
Figure BDA0002855244940000102
And a spline curve is constructed between the straight line BA and the straight line BA. According to the idea of 'replacing curve with straight', the tangent line AD is approximated to be an arc line
Figure BDA0002855244940000103
As shown in FIG. 7, when the spline curve is directly constructed in DAB, the deviation is generated from the actual curve constructed in D' AB, the actual curve is closer to the inflection point A, and the accuracy requirement can still be met. Since the embodiment aims at space planning of the industrial robot and is suitable for the working condition of large stroke, the arc with large radius corresponds to smaller curvature, and the length of the transition curve replacing the straight line segment is 3 times of the position error, the corresponding DD' is almost very small, and the theoretical curve is close to the actual curve.
c. Establishing a mapping relation between an expansion surface and a space curved surface;
since the actual space curved surface is formed by splicing innumerable layers of arcs, points on the unfolded surface can be mapped to points on the actual space curved surface, each dot-dash line in fig. 6 substantially corresponds to the unfolded line of the corresponding layer of arc in the space curved surface, and the position of the point on the space curved surface can be calculated at any point P on the unfolded surface as long as the point P is located on the unfolded line of which arc; in the construction of the transition model, the determination of the transition model is simplified by a method of approximating an arc line by a tangent line, and a point in the transition curve is calculated:
the passing point P is a straight line parallel to the tangent line AD, and the straight line AD is intersected with the point A' as shown in FIG. 7; the position of the point A 'on the straight line can determine the position of the circle center of the corresponding arc layer on the axial lead EO on the space curved surface graph 4, the length d of the straight line PA' is approximately equal to the length of the arc line on the corresponding expansion line, and the corresponding central angle theta is obtained in the corresponding space curved surface through the relation theta which is d/R.
S3, limiting the corner speed according to the size of the current corner;
the corner speed is determined by the minimum value of three constraint speeds, and the speed V is set for the user respectivelyuserString height error limit allowable speed VerrCentripetal acceleration limiting allowable speed VcirThe maximum allowable corner speed is calculated as follows:
calculating chordal height error limit allowable velocity Verr；
a. When the curvature of the curve track is large and the running speed is high, the actual interpolation track and the theoretical track generate a large track error; since the curvature of the curve of the model is the largest in the area where u is 0.5, and the chord height error is the largest, the chord height error of the whole section of the curve is controlled by performing curve approximate chord height error analysis on the point; will PiAnd Pi+1The curve between them is similar to an arc with equal curvature, the radius of curvature is R, PiPi+1The interpolation distance is L, and a chord height error model is obtained and is shown in FIG. 8; according to the geometrical relationship, the estimation formula of the chord height error epsilon when the curve u is 0.5 is as follows:
Figure BDA0002855244940000111
wherein, PiRadius of curvature of
Figure BDA0002855244940000112
P '(u) and P' (u) are the first and second derivatives of P (u), respectively, and the interpolation length L is approximately PiIs multiplied by the interpolation period TcBy substituting the above formula, the allowable velocity V under the string height error limit can be obtainederrComprises the following steps:
Figure BDA0002855244940000113
b. calculating the centripetal acceleration limit allowable speed Vcir；
As the curvature of the spline curve is higher and the curvature radius is smaller, the motor needs larger normal acceleration to change the motion direction, and the acceleration at the joint point needs to be ensured to exceed the set value amax(ii) a Centripetal acceleration limits allowable speed VcirComprises the following steps:
Figure BDA0002855244940000121
c. taking the minimum value; maximum allowable corner velocity vcorThe following can be obtained:
vcor＝min{Vuser，Verr，Vcir}。
and S4, calculating a curve interpolation point according to the calculated spline curve control point position.
When the current track segment type is "straight line-straight line" as shown in fig. 1, the moving track B → a → C, after the optimization is performed by using the curve transition model, the moving track of the current segment is changed into B → F → C, and the two segments of straight lines and the spline curve are spliced, namely, the straight line Bd0Spline d0d6Straight line d6C；
The specific process of calculating the curve interpolation point is as follows:
calculating the actual length of a splicing curve, then carrying out S-shaped speed planning on the splicing curve according to the calculated corner speed so as to obtain a position-time sequence of a fixed interpolation period, and finally calculating interpolation points by using a non-uniform B-spline curve formula;
the construction formula of the non-uniform B-spline curve is as follows:
Figure BDA0002855244940000122
Figure BDA0002855244940000123
wherein k is the spline curve frequency, and the spline parameter u belongs to [0,1 ]]，diAs spline curve control points, Ni,k(u) is a k-th order B-spline basis function; and calculating a spline parameter u corresponding to each period by planning the position according to the speed of each period, and further determining a space interpolation point corresponding to each period.
When the current trajectory segment type is "straight-circular arc" as shown in fig. 9, the trajectory B → a → C is followed by optimization using the curve transition model, and the trajectory of the current segment is changed to B → F → C, and the current segment is spliced by a straight line, a spline curve and a circular arc, that is, a straight line Bd0Spline d0d6Arc d6C；
The specific process of calculating the curve interpolation point is as follows;
calculating the actual length of a splicing curve, performing S-shaped speed planning on the splicing curve according to the calculated corner speed to obtain a position-time sequence of a fixed interpolation period, constructing a curve between a tangent line AD and a straight line AB by using a non-uniform B-spline curve formula as shown in FIG. 7, calculating interpolation points, and finally calculating interpolation points by using the mapping relation between an expansion surface and a space curved surface, wherein each interpolation point on the expansion surface has a corresponding space circle center position and a corresponding space circle center angle theta, and the space circular arc equation C (theta) is O + R (V)tsinθ+Vrcos theta), where O is the position of the center of the spatial arc, R is the radius of the spatial arc, and VtA tangent unit vector which is the interpolation direction at the starting point of the circular arc, namely the direction of the straight line AD, VrThe unit vector of which the circle center points to the circular arc starting point is the direction of a straight line OA, theta is the size of a circle center angle corresponding to a circular arc which is interpolated from the circular arc starting point according to a given interpolation direction, and by the method, mapping conversion of the expansion surface interpolation point and the space circular arc is realized, so that the space interpolation point of each period in the curved surface space is obtained.
To prove the effectiveness and superiority of this embodiment, the spatial trajectory of fig. 10 is tested and the set motion parameters are as follows: the maximum speed of the Cartesian space motion planning is 1000mm/s and the maximum speed isAcceleration of 2000mm/s2The interpolation period is 1ms, and the maximum position error of the corner is 0.1 mm. Under the conditions of the same motion track and the same motion parameters, the time consumed by using a curve transition method for motion is 5607ms, the time consumed by not using the transition method for motion is 6844ms, the time is reduced by 1237ms, and the optimization efficiency reaches 20%. The end space trajectory speed pair is such as shown in fig. 11, which shows the corner transition region, and the curve transition method can keep the speed at a higher level, which is the main reason for improving the efficiency. Curvature analysis of the arc transition trajectory and the spline curve transition trajectory using analysis software as shown in fig. 12 shows that the arc has an obvious abrupt change in curvature at the junction point, while the spline curve has a uniform change in curvature at the junction point. The spline curve and the corresponding straight line trajectory position error in the transition region are shown in fig. 13, and it can be seen that the set trajectory error requirement (less than 0.1mm) is satisfied.
The above-mentioned embodiments are merely preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, so that variations based on the shape and principle of the present invention should be covered within the scope of the present invention.

Claims (7)

1. A transition method for a track section of an industrial robot based on a non-uniform B-spline curve is characterized in that a multi-track section transition method is used for processing a motion track specified by a user: calculating curve control points by using a curve transition model; estimating the speed of a track transition region by using a speed constraint model; and outputting a track interpolation point sequence of the robot in a Cartesian space by using the speed planning curve to realize high-speed smooth processing of the robot.
2. The method for transition of the track segment of the industrial robot based on the non-uniform B-spline curve is characterized in that the specific process of the multi-segment track transition method comprises the following steps:
s1, setting various parameters of the industrial robot, including respective performance parameters of six joints of the industrial robot and planning parameters of a Cartesian space; creating a cache group, wherein the cache group comprises a track queue cache, a speed planning cache and a transition track information cache of the industrial robot, and all the caches are set to be empty after being created;
s2, analyzing the 'straight line-straight line' track type and the 'straight line-circular arc' track type, and determining the position of a control point of the non-uniform B-spline curve by using a corresponding curve transition model;
s3, limiting the corner speed according to the size of the current corner;
and S4, calculating a curve interpolation point according to the calculated spline curve control point position.
3. The method for transitioning the trajectory section of the industrial robot based on the non-uniform B-spline curve as claimed in claim 2, wherein in step S2, when the trajectory type is "straight line-straight line", the operation trajectory is composed of two adjacent straight line sections, assuming B, A, C is the end points of the two straight lines, and the two straight lines intersect at the point A, and the included angle between the two straight lines is α, the specific process for determining the position of the control point of the non-uniform B-spline curve is as follows:
a. constructing a spline curve, and finding a curve control point di；
To achieve the engagement curve with G3Continuity, number of spline curves is 5, control point diThe number is 7, corresponding to d0，d1，...，d6(ii) a In order to ensure that the starting point and the end point of the curve can coincide with the head and tail control points, the head and tail vector nodes are set with the repetition degree of 6 times, namely u0＝...＝u5＝0；u7＝...＝u121 is ═ 1; to ensure symmetry of the curve, u60.5, the node vector of the model is set to U ═ 0000000.5111111]T(ii) a Control point d for the tangent of the spline curve to the line at the junction0，d1，d2On a straight line AB, control point d3Is positioned at the inflection point A; similarly, control point d4，d5，d6Lies on a straight line AC; in order to make the curve at the control point d0And d6Is connected with a straight line and has G3Is 0 and u is 1, the curve p (u) is of second order with respect to the arc length sAnd the third derivative is zero; after derivation, the proportional relation among the control points can be obtained:
Figure FDA0002855244930000021
assuming a unit transition length d1d2To simplify the above formula, | | can be given as:
Figure FDA0002855244930000022
b. calculating unit transition length l according to a given error;
because the node vectors of the spline curve are centrosymmetric, the obtained curve also has the characteristic of centrosymmetry; when the curve parameter u is 0.5, the distance between the highest point F of the spline curve and the inflection point A is the farthest, and the position error of the curve is the largest, so that the position accuracy of the transition curve can be ensured by controlling the maximum error of AF at the inflection point; the model error equation δ is derived as follows:
Figure FDA0002855244930000023
in the formula, delta is a given upper limit of position error, and alpha is an included angle between two straight lines; setting the curve transition length not to exceed one fourth of the original straight line length, wherein the unit transition length l formula is as follows:
Figure FDA0002855244930000024
c. calculating the space coordinates of the control points through a linear equation;
equation of a space line as Pi＝Ps-Li·VL(ii) a Wherein P issIs a straight line starting point, VLUnit vector pointing from start to end, LiThe distance from the starting point to the corresponding control point; on the AB sectionControl point d1When the temperature of the water is higher than the set temperature,
Figure FDA0002855244930000025
4. the method for transitioning the trajectory section of the industrial robot based on the non-uniform B-spline curve as claimed in claim 3, wherein in step S2, when the trajectory type is "straight line-arc", the operation trajectory is composed of a space straight line and a space arc different surface, assuming that B, A is the end point of the straight line, A, C is the end point of the arc with radius R, the two ends intersect at point A, the straight line AD is the tangent line of the arc at point A, and the included angle between the straight line BA and the straight line AD is α, the specific process of determining the position of the control point of the non-uniform B-spline curve is as follows:
a. establishing a curved surface;
translating the straight line from the point A to a point O at the center of the circle to obtain a straight line EO, and constructing a circle with a plurality of layers of radiuses R, parallel to the bottom surface circle and with the center on the straight line; when the constructed circular arcs are dense, a cylindrical curved surface can be formed; constructing a transition curve on the cylindrical curved surface by using known information; cutting off the curved surface from the straight line BA by using three-dimensional software to obtain an unfolded drawing; the tangent line AD corresponds to the straight line AD in the development figure, the included angle between the tangent line AD and the straight line BA is alpha, and the passing point D is perpendicular to the arc line
Figure FDA0002855244930000031
The foot is D';
b. constructing a transition model;
using "straight-line" type transition models, subtending arcs
Figure FDA0002855244930000032
Constructing a spline curve between the straight line BA and the straight line BA; wherein, according to the idea of 'replacing curve with straight', the tangent line AD is approximated to be an arc line
Figure FDA0002855244930000033
Directly constructing a spline curve in the DAB;
c. establishing a mapping relation between an expansion surface and a space curved surface;
because the actual space curved surface is formed by splicing innumerable layers of arcs, points on the expansion surface can be mapped to the points on the actual space curved surface, each dot-dash line substantially corresponds to the expansion line of the corresponding layer of arcs in the space curved surface, and the position of the point on the space curved surface can be calculated at any point P on the expansion surface as long as the point P is located on the expansion line of which arc; in the construction of the transition model, the determination of the transition model is simplified by a method of approximating an arc line by a tangent line, and a point in the transition curve is calculated:
making a straight line parallel to the tangent line AD at the passing point P, and intersecting the straight line AD at the point A'; the position of the point A 'on the straight line can be determined, the position of the circle center of the arc layer corresponding to the space curved surface on the axis EO can be determined, the length d of the straight line PA' is approximately equal to the length of the arc line on the corresponding expansion line, and the corresponding central angle theta is obtained in the corresponding space curved surface through the relation theta which is d/R.
5. The method for transitioning trajectory segments of an industrial robot based on non-uniform B-spline curves as claimed in claim 4, wherein the corner velocity is determined by the minimum of three constraint velocities, each of which is a user-defined velocity VuserString height error limit allowable speed VerrCentripetal acceleration limiting allowable speed VcirThe maximum allowable corner speed is calculated as follows:
a. calculating chordal height error limit allowable velocity Verr；
When the curvature of the curve track is large and the running speed is high, the actual interpolation track and the theoretical track generate a large track error; since the curvature of the curve of the model is the largest in the area where u is 0.5, and the chord height error is the largest, the chord height error of the whole section of the curve is controlled by performing curve approximate chord height error analysis on the point;
will PiAnd Pi+1The curve between them is similar to an arc with equal curvature, the radius of curvature is R, PiPi+1The interpolation distance is L, and a chord height error model is obtained; estimation of the chord height error epsilon at 0.5 in curve u according to the geometrical relationThe formula is as follows:
Figure FDA0002855244930000041
wherein, PiRadius of curvature of
Figure FDA0002855244930000042
P '(u) and P' (u) are the first and second derivatives of P (u), respectively, and the interpolation length L is approximately PiIs multiplied by the interpolation period TcBy substituting the above formula, the allowable velocity V under the string height error limit can be obtainederrComprises the following steps:
Figure FDA0002855244930000043
b. calculating the centripetal acceleration limit allowable speed Vcir；
As the curvature of the spline curve is higher and the curvature radius is smaller, the motor needs larger normal acceleration to change the motion direction, and the acceleration at the joint point needs to be ensured to exceed the set value amax(ii) a Centripetal acceleration limits allowable speed VcirComprises the following steps:
Figure FDA0002855244930000044
c. taking the minimum value; maximum allowable corner velocity vcorThe following can be obtained:
vcor＝min{Vuser，Verr，Vcir}。
6. the method as claimed in claim 5, wherein in step S4, when the current trajectory segment type is "straight-line", the moving trajectory B → A → C, and after using the curve transition model for optimization, the moving trajectory of the current segment is changed to B → F → C, and the two types are selected fromSplicing of line segments and spline curves, i.e. straight line Bd0Spline d0d6Straight line d6C；
The specific process of calculating the curve interpolation point is as follows:
calculating the actual length of a splicing curve, then carrying out S-shaped speed planning on the splicing curve according to the calculated corner speed so as to obtain a position-time sequence of a fixed interpolation period, and finally calculating interpolation points by using a non-uniform B-spline curve formula;
the construction formula of the non-uniform B-spline curve is as follows:
Figure FDA0002855244930000051
Figure FDA0002855244930000052
wherein k is the spline curve frequency, and the spline parameter u belongs to [0,1 ]]，diAs spline curve control points, Ni,k(u) is a k-th order B-spline basis function; and calculating a spline parameter u corresponding to each period by planning the position according to the speed of each period, and further determining a space interpolation point corresponding to each period.
7. The method for transitioning the trajectory segment of the industrial robot based on the non-uniform B-spline curve as claimed in claim 5, wherein in step S4, when the type of the current trajectory segment is "straight line-arc", the trajectory B → A → C is followed by using the curve transition model to optimize, the trajectory of the current segment is changed to B → F → C, and the current segment is spliced by a straight line, a spline curve and an arc, i.e. the straight line Bd0Spline d0d6Arc d6C；
The specific process of calculating the curve interpolation point is as follows;
calculating the actual length of the spliced curve, and then carrying out S-shaped speed planning on the spliced curve according to the calculated corner speed so as to obtain a fixed interpolationThe method comprises the steps of constructing a curve between a tangent line AD and a straight line AB by using a non-uniform B-spline curve formula, calculating interpolation points, and finally utilizing the mapping relation between an expansion surface and a space curved surface, wherein each interpolation point on the expansion surface has a corresponding space circle center position and a corresponding space circle center angle theta, and the space circular arc equation C (theta) is O + R (V)tsinθ+Vrcos theta), where O is the position of the center of the spatial arc, R is the radius of the spatial arc, and VtA tangent unit vector which is the interpolation direction at the starting point of the circular arc, namely the direction of the straight line AD, VrThe unit vector of which the circle center points to the circular arc starting point is the direction of a straight line OA, theta is the size of a circle center angle corresponding to a circular arc which is interpolated from the circular arc starting point according to a given interpolation direction, and by the method, mapping conversion of the expansion surface interpolation point and the space circular arc is realized, so that the space interpolation point of each period in the curved surface space is obtained.
CN202011544185.4A 2020-12-23 2020-12-23 Industrial robot track segment transition method based on non-uniform B spline curve Active CN112659126B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011544185.4A CN112659126B (en) 2020-12-23 2020-12-23 Industrial robot track segment transition method based on non-uniform B spline curve

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011544185.4A CN112659126B (en) 2020-12-23 2020-12-23 Industrial robot track segment transition method based on non-uniform B spline curve

Publications (2)

Publication Number Publication Date
CN112659126A true CN112659126A (en) 2021-04-16
CN112659126B CN112659126B (en) 2023-05-16

Family

ID=75409711

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011544185.4A Active CN112659126B (en) 2020-12-23 2020-12-23 Industrial robot track segment transition method based on non-uniform B spline curve

Country Status (1)

Country Link
CN (1) CN112659126B (en)

Cited By (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113246143A (en) * 2021-06-25 2021-08-13 视比特(长沙)机器人科技有限公司 Mechanical arm dynamic obstacle avoidance trajectory planning method and device
CN113276116A (en) * 2021-05-21 2021-08-20 武汉瀚迈科技有限公司 Error-controllable robot track synchronous transition method
CN113442142A (en) * 2021-07-14 2021-09-28 江南大学 Smoothing method for Cartesian space motion trail of six-axis serial industrial robot
CN113733099A (en) * 2021-09-28 2021-12-03 广州大学 Robot smooth track planning method, computer and storage medium
CN113997277A (en) * 2022-01-04 2022-02-01 广东工业大学 Photovoltaic power supply system for wearable lower limb exoskeleton robot
CN114184206A (en) * 2021-12-03 2022-03-15 北京车慧达科技有限公司 Method and device for generating driving route based on vehicle track points
CN114227672A (en) * 2021-11-26 2022-03-25 北京工业大学 Mechanical arm safety collision trajectory planning method and device, storage medium and equipment
CN114296400A (en) * 2021-11-16 2022-04-08 中南大学 Self-adaptive look-ahead processing method for laser cutting high-speed interpolation
CN114536337A (en) * 2022-02-24 2022-05-27 上海交通大学 Method and system for smoothing linear motion track of mechanical arm and storage medium
CN116551457A (en) * 2023-07-11 2023-08-08 济南邦德激光股份有限公司 Method and equipment for connecting and processing straight line segment and circular arc segment through spline curve
CN117315198A (en) * 2023-10-09 2023-12-29 中微智创(北京)软件技术有限公司 Smooth optimization method and system for smooth fine adjustment of moving target track corner

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105500354A (en) * 2016-02-02 2016-04-20 南京埃斯顿机器人工程有限公司 Transitional track planning method applied by industrial robot
CN106313047A (en) * 2016-09-28 2017-01-11 华中科技大学 Robot real-time corner transition method based on Bezier spline
CN109623820A (en) * 2018-12-25 2019-04-16 哈工大机器人（合肥）国际创新研究院 A kind of robot space tracking transition method
CN109664303A (en) * 2019-02-28 2019-04-23 武汉工程大学 A kind of four smooth orbit generation methods of shaft industrial robot B-spline transition type that error is controllable
CN111791236A (en) * 2020-07-17 2020-10-20 广东拓斯达科技股份有限公司 Industrial robot Cartesian space trajectory transition method
CN111897216A (en) * 2020-07-16 2020-11-06 华中科技大学 Multi-motion-segment speed planning and interpolation method

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105500354A (en) * 2016-02-02 2016-04-20 南京埃斯顿机器人工程有限公司 Transitional track planning method applied by industrial robot
CN106313047A (en) * 2016-09-28 2017-01-11 华中科技大学 Robot real-time corner transition method based on Bezier spline
CN109623820A (en) * 2018-12-25 2019-04-16 哈工大机器人（合肥）国际创新研究院 A kind of robot space tracking transition method
CN109664303A (en) * 2019-02-28 2019-04-23 武汉工程大学 A kind of four smooth orbit generation methods of shaft industrial robot B-spline transition type that error is controllable
CN111897216A (en) * 2020-07-16 2020-11-06 华中科技大学 Multi-motion-segment speed planning and interpolation method
CN111791236A (en) * 2020-07-17 2020-10-20 广东拓斯达科技股份有限公司 Industrial robot Cartesian space trajectory transition method

Cited By (20)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113276116A (en) * 2021-05-21 2021-08-20 武汉瀚迈科技有限公司 Error-controllable robot track synchronous transition method
CN113276116B (en) * 2021-05-21 2022-01-18 武汉瀚迈科技有限公司 Error-controllable robot track synchronous transition method
CN113246143A (en) * 2021-06-25 2021-08-13 视比特(长沙)机器人科技有限公司 Mechanical arm dynamic obstacle avoidance trajectory planning method and device
CN113442142A (en) * 2021-07-14 2021-09-28 江南大学 Smoothing method for Cartesian space motion trail of six-axis serial industrial robot
CN113442142B (en) * 2021-07-14 2022-08-23 杭州泛海科技有限公司 Smoothing method for Cartesian space motion trail of six-axis serial industrial robot
CN113733099A (en) * 2021-09-28 2021-12-03 广州大学 Robot smooth track planning method, computer and storage medium
CN114296400B (en) * 2021-11-16 2024-03-12 中南大学 Self-adaptive look-ahead processing method for laser cutting high-speed interpolation
CN114296400A (en) * 2021-11-16 2022-04-08 中南大学 Self-adaptive look-ahead processing method for laser cutting high-speed interpolation
CN114227672A (en) * 2021-11-26 2022-03-25 北京工业大学 Mechanical arm safety collision trajectory planning method and device, storage medium and equipment
CN114227672B (en) * 2021-11-26 2022-07-26 北京工业大学 Mechanical arm safety collision track planning method and device, storage medium and equipment
CN114184206A (en) * 2021-12-03 2022-03-15 北京车慧达科技有限公司 Method and device for generating driving route based on vehicle track points
CN114184206B (en) * 2021-12-03 2024-04-19 北京车慧达科技有限公司 Method and device for generating driving route based on vehicle track points
CN113997277B (en) * 2022-01-04 2022-04-15 广东工业大学 Photovoltaic power supply system for wearable lower limb exoskeleton robot
CN113997277A (en) * 2022-01-04 2022-02-01 广东工业大学 Photovoltaic power supply system for wearable lower limb exoskeleton robot
CN114536337A (en) * 2022-02-24 2022-05-27 上海交通大学 Method and system for smoothing linear motion track of mechanical arm and storage medium
CN114536337B (en) * 2022-02-24 2023-06-23 上海交通大学 Mechanical arm linear motion track smoothing method and system and storage medium
CN116551457B (en) * 2023-07-11 2023-10-27 济南邦德激光股份有限公司 Method and equipment for connecting and processing straight line segment and circular arc segment through spline curve
CN116551457A (en) * 2023-07-11 2023-08-08 济南邦德激光股份有限公司 Method and equipment for connecting and processing straight line segment and circular arc segment through spline curve
CN117315198A (en) * 2023-10-09 2023-12-29 中微智创(北京)软件技术有限公司 Smooth optimization method and system for smooth fine adjustment of moving target track corner
CN117315198B (en) * 2023-10-09 2024-04-16 中微智创(北京)软件技术有限公司 Smooth optimization method and system for smooth fine adjustment of moving target track corner

Also Published As

Publication number Publication date
CN112659126B (en) 2023-05-16

Similar Documents

Publication Publication Date Title
CN112659126A (en) Industrial robot track segment transition method based on non-uniform B-spline curve
CN109571473B (en) Error-controllable small line segment trajectory fairing method
CN107263484B (en) Robot joint space point-to-point motion trajectory planning method
CN111791236B (en) Industrial robot Cartesian space trajectory transition method
CN111897216B (en) Multi-motion-segment speed planning and interpolation method
CN105500354B (en) Transitional track planning method applied by industrial robot
CN111061213B (en) Processing method based on Bezier curve corner smooth transition algorithm
Zhang et al. A G4 continuous B-spline transition algorithm for CNC machining with jerk-smooth feedrate scheduling along linear segments
CN112975992B (en) Error-controllable robot track synchronous optimization method
CN111966047B (en) Triaxial micro-line segment direct speed transition method based on trigonometric function acceleration and deceleration control
CN111897290A (en) Smooth corner transition smoothing method for axial acceleration
CN111913441B (en) Corner smooth transition method based on track mode
Zhang et al. An optimal curvature-smooth transition algorithm with axis jerk limitations along linear segments
WO2022057155A1 (en) Transition method for five-axis tool path transfer smoothing, medium, and numerical control device for five-axis machine tool
CN110147077B (en) Cosine interpolation method of industrial robot under space linear operation
CN111633668B (en) Motion control method for robot to process three-dimensional free-form surface
KR20070027921A (en) Transition trajectory generation between non-smoothly connected paths for industrial robots
CN113290558A (en) NURBS curve speed interpolation method based on parameter densification
CN116430796A (en) Machining path local fairing method based on geometric clipping
CN109991921B (en) Smooth B spline track direct generation method
Li et al. Error constraint optimization for corner smoothing algorithms in high-speed CNC machine tools
CN106444636A (en) Speed planning parameter selection method suitable for continuous mixing curve
CN113433889B (en) Tool path planning method for five-axis machine tool machining based on three-section type claw curve
CN113985805A (en) Electronic cam generation method and terminal
CN113276116A (en) Error-controllable robot track synchronous transition method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant