CN109571473B - Error-controllable small line segment trajectory fairing method - Google Patents

Error-controllable small line segment trajectory fairing method Download PDF

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CN109571473B
CN109571473B CN201811468150.XA CN201811468150A CN109571473B CN 109571473 B CN109571473 B CN 109571473B CN 201811468150 A CN201811468150 A CN 201811468150A CN 109571473 B CN109571473 B CN 109571473B
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track
point
error
fairing
curve
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CN109571473A (en
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何姗姗
颜昌亚
李振瀚
黄昆涛
邓炎超
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Wuhan Institute of Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q15/00—Automatic control or regulation of feed movement, cutting velocity or position of tool or work
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path

Abstract

An error-controllable small-line-segment track fairing method comprises the following steps: step 1, preprocessing a robot track point: traversing all track points of the whole track, segmenting according to the distance and included angle between the track points, and dividing the whole track into a plurality of segment set; step 2, tracing point fairing: and (3) traversing the set of broken line segments generated in the step (1), and calculating the fairing track of each broken line segment according to the track point error threshold, the chord height error threshold, the continuity requirement and the fairing requirement. The invention generates the small line segment track fairing into the fairing track meeting the requirements of continuity, shape preservation and error, and improves the working efficiency and the working quality of numerical control processing or industrial robot application; the fairing curve is suitable for requirements of different continuities and execution efficiency; compared with the existing transition method, the fairing curve can control track point errors to achieve the interpolation effect, so that the track point characteristics can be reserved.

Description

Error-controllable small line segment trajectory fairing method
Technical Field
The invention belongs to the field of numerical control machining and track optimization of industrial robots, and particularly relates to an error-controllable small line segment track fairing method.
Background
The linear trajectory represented by the small line segment is widely applied to numerical control machining and industrial robot applications. In the field of numerical control machining, small line segments are the most widely expressed forms of machining paths of complex curved surface parts such as impellers, blades and molds. The small-line-segment-track multi-axis machining is one of the core technologies for high-speed and high-precision machining of complex curved surface parts. However, the track of the small line segment has the problem of discontinuous first-order and second-order derivatives, so that the machine tool is frequently accelerated and decelerated and vibrates, and the working efficiency and the machining precision are greatly reduced. In the technical field of industrial robot application, the robot controls the robot to move by recognizing a motion command. The motion instructions recognizable by the existing industrial robot comprise a linear motion instruction, an arc motion instruction and an axis coordinate motion instruction. Most complex trajectories consist of straight-line motion commands (small-segment trajectories) and a small number of circular-arc motion commands. However, the motion trajectories represented by the small line segments and the circular arcs have the problem of discontinuous first-order and second-order derivatives at the joints, so that the robot is accelerated and decelerated frequently, and the working efficiency is reduced. In addition, industrial robots are not as rigid as numerically controlled machines, resulting in a vibration phenomenon more easily occurring.
In the field of numerical control machining, in order to optimize the discontinuity problem of small segment tracks, a NURBS (non-uniform rational B-spline) can be adopted to approach the small segment tracks, and the continuity of the tracks is further improved. For example, in a non-patent document (a chord error relating tool path B-spline fitting method for NC machining based on energy development and LSPIA), a triaxial machining path is subjected to fairing processing by using a cubic B-spline curve, so that the continuity of the segment G2 can be achieved, and the chord height error can be ensured to meet the error requirement. Non-patent document "A real-time approximation scheme and motion planning for CNC machining of short line segments" proposes a method for performing G on a triaxial numerical control machining track by adopting a quartic B spline curve3Continuous bridging algorithm, can obtain smooth transition of track points and G3A continuous real-time conformal interpolation trajectory. The expression of the quartic B-spline trajectory is complex and requires a large memory consumption.
In the field of industrial robots, in order to improve the continuity of motion tracks, most robots add a first-order continuous transition command (such as a CNT command) to a motion command. Individual robots have added SPLINE transition instructions, such as SPLINE by KUKA and MOMOVES by MOTOMAN. Such commands can more easily maintain the programmed speed, but cannot control the chordal height error between the trace points to meet the error requirements. Patent document 201710097192.6 has already been accepted to propose a method for generating a smooth motion trajectory of an industrial robot, which can control errors of data points and chord heights simultaneously, but the transition curve only provides two curves, namely cubic B-spline and quartic B-spline, and the linear trajectory represented by a small line segment has low continuity and does not meet the requirement of errors, resulting in the reduction of working efficiency and working quality.
Disclosure of Invention
The invention aims to solve the technical problems that in the existing numerical control machining or industrial robot application, the continuity of a linear track represented by a small line segment is low and the requirement of an error is not met, and provides an error-controllable small line segment track fairing method which is simple in calculation, capable of improving the continuity, guaranteeing the precision and suitable for various fairing curves.
The technical scheme adopted by the invention for solving the technical problems is as follows:
an error-controllable small-line-segment track fairing method comprises the following steps:
step 1, preprocessing a robot track point: traversing all track points of the whole track, segmenting according to the distance and included angle between the track points, and dividing the whole track into a plurality of segment set;
step 2, tracing point fairing: and (3) traversing the set of broken line segments generated in the step (1), and calculating the fairing track of each broken line segment according to the track point error threshold, the chord height error threshold, the continuity requirement and the fairing requirement.
According to the scheme, the step 1 is to preprocess the input track points, and specifically comprises the following steps:
step 1.1, distance segmentation, wherein the distance between track points is used as a first segmentation condition: if the distance between the adjacent track points is smaller than a distance threshold value, segmenting the two track points; the track points are divided into three sections of broken line segments;
step 1.2, segmenting an included angle, wherein in a segmented third segment (namely, the third segment in the three segments of the broken line segment in the step 1.1), an included angle between adjacent track segments is used as a second segmentation condition: if the included angle between two adjacent track sections is larger than the angle threshold value, segmenting at the middle point of the two track sections;
step 1.3, the broken line segments segmented twice in the step 1.1 and the step 1.2 are sorted, the broken line segments with the number of track points smaller than 3 in the broken line segments are not smoothed, and the broken line segments which do not participate in smoothing are output in the smoothed tracks according to linear tracks; and smoothing the broken line segments with the number of the track points more than or equal to 3 in the broken line segments.
According to the scheme, in the step 1.1, the two segmented track points are not subjected to fairing, namely, the line segment with the distance smaller than the distance threshold value does not need to be faired.
According to the scheme, the step 2 traverses the broken line segment set generated in the step 1, and each segmented broken line segment can be subjected to fairing, taking the fairing of one broken line segment as an example, the method comprises the following specific steps:
step 2.1, determining initial iteration parameters, and setting the original track points contained in the current broken line segment as
Figure BDA0001890312380000021
The error threshold of the trace point is marked as epsilonmax(ii) a The chord height error threshold is recorded as deltamaxRequires epsilonmax≤δmaxThe trace point error is the trace point error between the smooth curve and the original trace point; the chord height error is the chord height error between a curve after fairing and a broken line segment formed by original track points, and the maximum iteration number is recorded as kmaxSetting the current iteration number as k equal to 0, and recording the iteration track point as
Figure BDA0001890312380000022
Setting an iteration chord height error threshold value for the internal track points except the head and the tail, and recording the iteration chord height error threshold value as
Figure BDA0001890312380000023
The iteration chord height error is the chord height error between a broken line segment consisting of iteration track points and a transition curve, and because the maximum chord height error point appears at a track point, the maximum iteration chord height error is also the maximum track point error between the iteration track point and the transition curve;
step 2.2, iteration track points
Figure BDA0001890312380000031
According to iterative chord height error threshold
Figure BDA0001890312380000032
Generating a (N-1) section symmetrical transition curve (one is generated at every three iteration track points, the symmetry of the transition curve is to ensure that the maximum point of the chord height error is positioned at the middle point of the curve) according to the continuity requirement and the shape-preserving requirement, and recording the transition curve as the middle point
Figure BDA0001890312380000033
Wherein the continuity requirement means that the continuity of the junction of the transition curve and the linear portion meets the continuity requirement;
step 2.3, calculating the maximum error point of the trace point on the (N-1) section transition curve, and recording the maximum error point as the maximum error point
Figure BDA0001890312380000034
Because of the adoption of the symmetrical transition curve, the maximum error point of the track point is as follows:
Figure BDA0001890312380000035
and traversing j to 1, … N-1, and further calculating the maximum trace point error:
Figure BDA0001890312380000036
step 2.4, if the maximum track point error deltakError threshold epsilon less than track pointmaxOr k ═ kmaxTerminating the iteration and outputting the fairing track
Figure BDA0001890312380000037
Here, the track point error threshold epsilonmaxChordal height error threshold set for step 2.1
Figure BDA0001890312380000038
For deciding whether the iteration terminates; otherwise, turning to step 2.5;
step 2.5, traversing j to 1, … N-1 according to the original track point PjMaximum point of sum track point error
Figure BDA0001890312380000039
Calculating an offset vector
Figure BDA00018903123800000310
Then, updating the iteration track points:
Figure BDA00018903123800000311
Figure BDA00018903123800000312
and calculating an iterative chordal height error threshold
Figure BDA00018903123800000313
Wherein
Figure BDA00018903123800000314
Is a vector
Figure BDA00018903123800000315
And
Figure BDA00018903123800000316
half of the included angle between the two parts; then, changing k to k +1, and turning to step 2.2;
step 2.6, the fairing track output in the step 2.4 is arranged, the track after fairing is formed by combining N straight line sections and (N-1) fairing curve sections, and the method sequentially comprises the following steps: straight line segment
Figure BDA00018903123800000317
Smooth curve
Figure BDA00018903123800000318
Straight line segment
Figure BDA00018903123800000319
Smooth curve
Figure BDA00018903123800000320
… smooth curve
Figure BDA00018903123800000321
Straight line segment
Figure BDA00018903123800000322
According to the scheme, in the step 2.2, the continuity requirement is determined according to practical application and is G1Continuous, G2Continuous or G3Any one of the above; selection of a transition curve, G, according to the continuity requirement1The continuous time transition curve selects a circular arc curve, a parabola or a cubic B-spline curve of four control points G2Selecting cubic B-spline curves of five control points or quintic B-spline curves of four control points or other polynomial curves continuously; the shape-preserving requirement means that no folding occurs between two adjacent transition curves and the whole transition curve is smooth after smoothing.
Through the technical scheme, compared with the prior art, the invention has the advantages that:
(1) the small line segment track can be smoothened to generate a smoothening track meeting the requirements of continuity, shape preservation and error, so that the working efficiency and the working quality of numerical control machining or industrial robot application are improved;
(2) compared with the existing transition method, the fairing curve of the invention is suitable for various transition curves: circular arc curves, B-spline curves of different times, PH curves or other polynomial curves and the like can be suitable for requirements of different continuities and execution efficiencies.
(3) Compared with the existing transition method, the fairing curve can control track point errors to achieve an interpolation effect, so that track point characteristics can be reserved, and the fairing curve not only meets a chord height error threshold, but also is uniform in distribution of chord height errors of the whole fairing track, and can ensure a shape-preserving and uniform fairing effect.
Drawings
FIG. 1 is a schematic diagram of track point preprocessing according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of trace point transition according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of trace point iteration according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a smooth track according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention discloses an error-controllable small line segment track fairing method, which comprises the following steps:
step 1, preprocessing a robot track point: traversing all track points of the whole track, segmenting according to the distance and included angle between the track points, and dividing the whole track into a plurality of segment set. Taking the 9 trace points in FIG. 1 as an example, all trace points are marked as
Figure BDA0001890312380000041
First, a distance threshold is determined, and for m 0,1, … 7, a length | P is calculatedmPm+1If PmPm+1If | is less than the distance threshold, then at PmAnd Pm+1Two points are segmented; the distance threshold is determined according to the specific application, and the line segments with the distance less than the distance threshold do not need to be smooth. As in this example, the distance threshold is set at 0.5 mm. If the line segment distance | P1P2And | ═ 0.4 mm. Then at P1And P2And (3) segmenting, wherein the track points are divided into three sections: { P0P1},{P1P2},{P2～P8}。
Then, segmenting according to the included angle, and regarding the third section of track { P2～P8H, calculating angle Pn-1PnPn+1(n is 3,4,5,6,7), if the angle is greater than the angle threshold, then at PnIs segmented. The angle threshold needs to be determined according to specific application, and track points with angles close to 180 degrees do not need to be smooth. As in the case of fig. 1, the angle threshold is set to 179.5 °, if ≈ P4P5P6179.7 deg. is at P5Is segmented.
The segment broken line segment obtained finally is as follows: { P0P1},{P1P2},{P2P3P4P5},{P5P6P7P8}. According to the requirement that the fairing treatment is carried out only at three points, only { P }2P3P4P5},{P5P6P7P8Is fairing.
Step 2, tracing point fairing: traversing the set of broken line segments which are generated in the step 1 and need fairing, and calculating fairing tracks of each broken line segment according to a track point error threshold, a chord height error threshold, continuity requirements and fairing requirements; by a broken line segment
Figure BDA0001890312380000042
The smoothing is as an example, and the specific steps are as follows:
step 2.1, determining initial iteration parameters, and setting the original track points contained in the current broken line segment as
Figure BDA0001890312380000043
The error threshold of the trace point is marked as epsilonmax(ii) a The chord height error threshold is recorded as deltamaxRequires epsilonmax≤δmaxAnd is epsilonmax、δmaxAll decide according to actual processing demand: if the requirement on the precision of the track point is higher, epsilon can be setmax0.001-0.1 mm; in robot trajectory applications, δmaxGenerally within 1 mm;
the maximum number of iterations is denoted kmaxSetting the current iteration number as k equal to 0, and recording the iteration track point as
Figure BDA0001890312380000051
Setting an iterative chordal height error threshold for the internal track points except the head and the tail, and recording the iterative chordal height error threshold as 0 to … N
Figure BDA0001890312380000052
Figure BDA0001890312380000053
The iteration chord height error is the chord height error between a broken line segment formed by the iteration track points and a transition curve, and the maximum iteration chord height error is also the maximum track point error between the iteration track points and the transition curve because the maximum chord height error appears at the track points;
step 2.2, iteration track points
Figure BDA0001890312380000054
Generating a (N-1) segment symmetric transition curve according to the iteration chord height error threshold, the continuity requirement and the shape-preserving requirement, namely
Figure BDA0001890312380000055
According to iterative chord height error threshold
Figure BDA0001890312380000056
The transition is carried out by adopting a symmetrical fairing curve to obtain a transition curve of a section (N-1), which is marked as
Figure BDA0001890312380000057
The transition curve adopts a symmetrical curve, needs to meet the requirements of error, continuity and shape preservation, and firstly selects a curve according to the continuity requirement, such as G1When continuous, the cubic B-spline curve of the arc curve, the parabola or four control points can be selected, G2A cubic B-spline curve of five control points or a quintic B-spline curve of four control points may be selected in succession.
With G2The continuously required cubic B-spline curve transition is taken as an example:
first the transition curve uses a cubic B-spline curve with five control points:
Figure BDA0001890312380000058
Figure BDA0001890312380000059
in order to be the basis function(s),
Figure BDA00018903123800000510
five control points; the node vector is P ═ {0,0,0,0,0.5,1,1,1,1 }.
With 3 locus points P of FIG. 2i-1PiPi+1The transition curve between is calculated as an example: to satisfy G2Continuity, requirement Q0,Q1,Q2Is located on line segment Pi-1PiUpper, Q2,Q3,Q4Is located on line segment PiPi+1The above step (1); let Q2＝PiWhile simultaneously setting Q1＝Pi-d2T1,Q0＝Pi-(1+c)d2T1,Q3＝Pi+d2T2,Q4＝Pi+(1+c)d2T2,d1＝cd2Wherein
Figure BDA00018903123800000511
To determine 5 control points, two unknowns c, d need to be solved2And calculating a data point error constraint, wherein the data point error is maximum at the midpoint due to the construction of the bilateral symmetry of the B spline, and based on the B spline constructed above,
Figure BDA00018903123800000512
Figure BDA00018903123800000513
by derivation, the data point error ε can be expressed as:
Figure BDA00018903123800000514
because the maximum point of the chord height difference of the transition curve constructed above appears at the locus point, the error epsilon of the data point is required to be smaller than the threshold value of the chord height error
Figure BDA00018903123800000515
Is required to
Figure BDA00018903123800000516
Wherein
Figure BDA00018903123800000517
＜T1,T2Is > T1,T2The included angle therebetween.
In order to meet the shape-preserving requirement, the margin distance of two adjacent bridging curves is set as lmThus is desirable
Figure BDA00018903123800000518
Wherein li-1＝|Pi-1Pi|,li＝|PiPi+1|，lm＝a·min{li-1,liAnd a is a constant coefficient.
In conclusion, it is preferable
Figure BDA00018903123800000519
Wherein c, a is a constant between 0 and 1, and c is 0.25, and a is 0.25. To obtain d2Five control points of the transition curve can be obtained
Figure BDA00018903123800000520
Step 2.3, calculating the maximum error point of the trace point on the (N-1) section transition curve, and recording the maximum error point as the maximum error point
Figure BDA0001890312380000061
Because of the adoption of the symmetrical transition curve, the maximum error point of the track point is
Figure BDA0001890312380000062
And traversing j to 1, … N-1, and further calculating the maximum trace point error:
Figure BDA0001890312380000063
step 2.4, if the maximum track point error deltakError threshold epsilon less than track pointmaxOr k ═ kmaxTerminating the iteration and outputting the fairing track
Figure BDA0001890312380000064
Otherwise, go to step 2.5, where the trace pointError threshold epsilonmaxChordal height error threshold set for step 2.1
Figure BDA0001890312380000065
To decide whether the iteration terminates.
Step 2.5, traversing j to 1, … N-1 according to the original track point PjMaximum point of sum track point error
Figure BDA0001890312380000066
Calculating an offset vector
Figure BDA0001890312380000067
Then, updating the iteration track points:
Figure BDA0001890312380000068
Figure BDA0001890312380000069
and calculating an iterative chordal height error threshold
Figure BDA00018903123800000610
Wherein
Figure BDA00018903123800000611
Is a vector
Figure BDA00018903123800000612
And
Figure BDA00018903123800000613
the included angle is half of the included angle, and the chord height error distribution of the transition curve obtained by the method is more uniform; then, changing k to k +1, and turning to step 2.2; as shown in fig. 3, the round points are original trace points, the pentagram points are maximum trace point errors, and the square points are iterative trace points; through continuous iteration, the five-pointed star point gradually approaches the round point until the iteration stops.
Step 2.6, the fairing track output in the step 2.4 is arranged, the track after fairing is formed by combining N straight line sections and (N-1) fairing curve sections, and the method sequentially comprises the following steps: straight lineSegment of
Figure BDA00018903123800000615
Smooth curve
Figure BDA00018903123800000614
Straight line segment
Figure BDA00018903123800000616
Smooth curve
Figure BDA00018903123800000617
… smooth curve
Figure BDA00018903123800000618
Straight line segment
Figure BDA00018903123800000619
As shown in fig. 4, the solid line is a broken line segment formed by original track points, and the dotted line is a smooth track, and is formed by a straight line segment and a smooth curve. The triangular point is the connection point of the straight line segment and the smooth curve.

Claims (4)

1. An error-controllable small line segment track fairing method is characterized by comprising the following steps:
step 1, preprocessing a robot track point: traversing all track points of the whole track, segmenting according to the distance and included angle between the track points, and dividing the whole track into a plurality of segment set;
step 2, tracing point fairing: traversing the set of broken line segments generated in the step 1, and calculating the fairing track of each broken line segment according to the track point error threshold, the chord height error threshold, the continuity requirement and the fairing requirement; taking the fairing of a broken line segment as an example, the method comprises the following specific steps:
step 2.1, determining initial iteration parameters, and setting the original track points contained in the current broken line segment as
Figure FDA0003155983580000011
The error threshold of the trace point is marked as epsilonmax(ii) a Error in chord heightThe difference threshold is denoted as deltamaxRequires epsilonmax≤δmaxThe trace point error is the trace point error between the smooth curve and the original trace point; the chord height error is the chord height error between a curve after fairing and a broken line segment formed by original track points, and the maximum iteration number is recorded as kmaxSetting the current iteration number as k equal to 0, and recording the iteration track point as
Figure FDA0003155983580000012
Setting an iteration chord height error threshold value for the internal track points except the head and the tail, and recording the iteration chord height error threshold value as
Figure FDA0003155983580000013
The iteration chord height error is the chord height error between a broken line segment consisting of iteration track points and a transition curve, and because the maximum chord height error point appears at a track point, the maximum iteration chord height error is also the maximum track point error between the iteration track point and the transition curve;
step 2.2, iteration track points
Figure FDA0003155983580000014
According to iterative chord height error threshold
Figure FDA0003155983580000015
Continuity requirements and conformality requirements generate a (N-1) segment symmetric transition curve, i.e.
Figure FDA0003155983580000016
According to iterative chord height error threshold
Figure FDA0003155983580000017
The transition is carried out by adopting a symmetrical fairing curve to obtain a transition curve of a section (N-1), which is marked as
Figure FDA0003155983580000018
Wherein the continuity requirement means that the continuity of the junction of the transition curve and the linear portion satisfies the continuityRequiring;
step 2.3, calculating the maximum error point of the trace point on the (N-1) section transition curve, and recording the maximum error point as the maximum error point
Figure FDA0003155983580000019
Because of the adoption of the symmetrical transition curve, the maximum error point of the track point is as follows:
Figure FDA00031559835800000110
and traversing j to 1, … N-1, and further calculating the maximum trace point error:
Figure FDA00031559835800000111
step 2.4, if the maximum track point error deltakError threshold epsilon less than track pointmaxOr k ═ kmaxTerminating the iteration and outputting the fairing track
Figure FDA00031559835800000112
Here, the track point error threshold epsilonmaxChordal height error threshold set for step 2.1
Figure FDA00031559835800000113
For deciding whether the iteration terminates; otherwise, turning to step 2.5;
step 2.5, traversing j to 1, … N-1 according to the original track point PjMaximum point of sum track point error
Figure FDA00031559835800000114
Calculating an offset vector
Figure FDA00031559835800000115
Then, updating the iteration track points:
Figure FDA00031559835800000116
Figure FDA00031559835800000117
and calculating an iterative chordal height error threshold
Figure FDA00031559835800000118
Wherein
Figure FDA00031559835800000119
Is a vector
Figure FDA00031559835800000120
And
Figure FDA00031559835800000121
half of the included angle between the two parts; then, changing k to k +1, and turning to step 2.2;
step 2.6, the fairing track output in the step 2.4 is arranged, the track after fairing is formed by combining N straight line sections and (N-1) fairing curve sections, and the method sequentially comprises the following steps: straight line segment
Figure FDA0003155983580000021
Smooth curve
Figure FDA0003155983580000022
Straight line segment
Figure FDA0003155983580000023
Smooth curve
Figure FDA0003155983580000024
… smooth curve
Figure FDA0003155983580000025
Straight line segment
Figure FDA0003155983580000026
2. The error-controllable small-segment trajectory fairing method as claimed in claim 1, wherein step 1 is to preprocess the input trajectory points, and specifically comprises the following steps:
step 1.1, distance segmentation, wherein the distance between track points is used as a first segmentation condition: if the distance between the adjacent track points is smaller than a distance threshold value, segmenting the two track points; the track points are divided into three sections of broken line segments;
step 1.2, included angle segmentation, wherein in a third segment of broken line segment after segmentation, an included angle between adjacent track segments is used as a second segmentation condition: if the included angle between two adjacent track sections is larger than the angle threshold value, segmenting at the middle point of the two track sections;
step 1.3, the broken line segments segmented twice in the step 1.1 and the step 1.2 are sorted, the broken line segments with the number of track points smaller than 3 in the broken line segments are not smoothed, and the broken line segments which do not participate in smoothing are output in the smoothed tracks according to linear tracks; and smoothing the broken line segments with the number of the track points more than or equal to 3 in the broken line segments.
3. The method according to claim 2, wherein in step 1.1, the two segmented trace points are not faired, that is, the line segment with a distance smaller than the distance threshold value does not need to be faired.
4. The method according to claim 1, wherein in step 2.2, the continuity requirement is determined according to practical application and is G1Continuous, G2Continuous or G3Any one of the above; selection of a transition curve, G, according to the continuity requirement1The continuous time transition curve selects a circular arc curve, a parabola or a cubic B-spline curve of four control points G2Selecting cubic B-spline curves of five control points or quintic B-spline curves of four control points or other polynomial curves continuously; the shape-preserving requirement means that no folding occurs between two adjacent transition curves and the whole transition curve is smooth after smoothing.
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