CN1288601C - Method for conducting path planning based on three-dimensional scatter point set data of free camber - Google Patents

Abstract

The invention relates to a method for path planning based on the three-dimensional scattered point set data of the free-form surface. The method uses the interpolation and reconstruction of the scattered data of the free-form surface to fit the three-dimensional discrete data points into a triangular Bernstein-Bézier surface, and then uses the triangular Bernstein -Bézier surface performs six-dimensional trajectory planning on the obtained interpolation surface; for trajectory planning along any direction, the trajectory planning can be obtained by transforming the coordinates of this direction into the xy coordinate direction; the triangular Bernstein-Bézier surface is a cubic triangular Bernstein -Bézier surfaces. The method of the invention utilizes the triangular Bernstein-Bézier surface to fit the free-form surface of the three-dimensional scattered point set data and plans the six-dimensional processing trajectory on the interpolation surface, thereby realizing the path planning of the three-dimensional scattered point set data on the arbitrary free-form surface.

Description

Method of Path Planning Based on 3D Scattered Point Set Data of Freeform Surface

technical field

The invention relates to the field of computer control of integrated laser processing, in particular to a method for path planning based on three-dimensional scattered point set data of a free-form surface.

Background technique

In the prior art, laser surface strengthening requires that the laser optical axis, that is, the laser processing head, be perpendicular to the processing surface. In this way, when planning the processing path, not only the three-dimensional spatial position of the processing point, but also the normal vector corresponding to the processing point must be obtained. At present, the three-dimensional discrete data of the free-form surface is used as the data source of the system, and the main method to realize the path planning of the laser surface enhancement of the free-form surface is to use the B-Spline or NURBS surface as the basis to fit the free-form surface of the spatially scattered data, and then , correspondingly use B-Spline or NURBS surface to complete the planning of the six-dimensional trajectory; however, the spatially scattered data used when fitting the free-form surface based on the B-Spline or NURBS surface must be equidistant and uniform, and cannot handle any three-dimensional Scattered point set data. Therefore, path planning using B-Spline or NURBS surface as the basis of fitting surface has great limitations.

For example, Patent No. US5363479, titled "SYSTEM AND METHOD FOR RENDERING BEZIER SPLINES", describes a system and method for simulating Bézier curves in a computer graphics system. Curve, this method is limited to the processing of the curve, and the obtained discrete straight line segments are non-equal, and cannot be applied to the strengthening of the laser surface; Patent No. US5818459, the description of the US patent titled "DATA CONVERSION APPARATUS AND METHODUSING CONTROLPOINTS OF ACURVE" An instrument that automatically converts the three-time fitting curve into the two-time fitting curve is a device for curve processing, which also does not meet the requirements of laser surface strengthening; patent No. JP10198812, titled "APPROXIMATING METHOD FOR FREE-FORMSURFACE" The patent describes a method for optimizing free-form surfaces with NURBS surfaces approaching arbitrary boundaries. This method transforms the four boundary curves of the original surface into cubic B-Spline curves to realize the approach of free-form surfaces to a NURBS surface. The patent combines a node vector The corresponding two cubic B-Spline curves mesh the approximate free-form surface, and each grid is approximated by a cubic C1 continuous Besizer surface, so that all cubic Besizer surfaces are connected into a NURBS surface, and the surface fitting The procedure does not address the path planning problem.

Contents of the invention

The purpose of the present invention is: to overcome the existing free-form surface laser surface enhanced path planning method can only use equidistant uniform space scattered data as a basis to fit the curved surface for path planning, can not handle any three-dimensional scattered point set data, Therefore, the use of B-Spline or NURBS surface to fit the free-form surface of three-dimensional scattered points in space has great limitations in use, so as to provide a laser surface processing system based on the three-dimensional scattered point set data of free-form surface. method of path planning.

The object of the present invention is achieved like this: a kind of method of the present invention carries out path planning based on the three-dimensional scattered point set data of free-form surface, this method, in the laser surface processing system, reconstructs the scattered data interpolation of free-form surface by industrial control computer, Fit the three-dimensional discrete data points into a triangular Bernstein-Bézier surface, and then use the triangular Bernstein-Bézier surface to plan the six-dimensional trajectory of the obtained interpolation surface. Finally, the industrial control computer outputs the six-dimensional trajectory data of the free-form surface to control the movement of the robot.

In this method, in the laser surface processing system, the six-dimensional trajectory data obtained through industrial computer processing is output to the robot, and the robot is controlled to drive the laser processing head fixed on its arm to move according to the six-dimensional trajectory data. The steps include:

(1) After the industrial control computer receives the three-dimensional scattered point set data of the free-form surface, the triangular Bernstein-Bézier surface is used to fit the interpolation surface of the three-dimensional scattered point set data, and the spatial triangular mesh surface is obtained;

(2) Project the spatial triangular mesh surface to the xy plane, and the industrial control computer takes the (x, y) coordinates of each point on the spatial triangular mesh surface, and determines the rectangular area (x _min , y _min ) , (x _max , y _max );

(3) Starting from the point p′ ₁ = (x _min , y _min ), take points in sequence along the y-axis to form a point set {p′ _k }, p′ _k = (x _min , y _min + (k-1 )×d), (k=1, 2, ..., n), wherein, d is the distance between two points determined according to different requirements, until the point (x _min , y _max ); then according to the step ( 1) The obtained spatial triangular mesh surface, obtain the corresponding point p _k (x _k , y _k , z _k ) of p′ _k on the triangular mesh surface, and form a point set {p _k };

(5) According to each point in the {p _k } point set and its calculated barycenter parameters (u, v, w) in the corresponding triangle domain of the {p _k } point set, use the triangular Bernstein-Bézier surface to calculate the corresponding triangle Six-dimensional point set {l _k }={(x _k , y _k , z _k , ax _k , ay _k , az _z )} on the surface;

(6) When the number of corresponding points p _k on the triangular mesh surface is n≥4, the six-dimensional point set {l _k } is used as the type value point, and the chord length parametric spline curve is constructed with d as the step size, and Six-dimensional point set {m _k (x _k , y _k , z _k , ax _k , ay _k , az _k )}, as a trajectory line;

When 0<n≤3, the industrial control computer takes {m _k }={l _k }(k=1, 2, 3) as a trajectory;

When n=0, the industrial control computer ends the operation;

(7) Take the trajectory line {m _k } obtained above as the reference trajectory line, project it onto the xy plane, and obtain the distance from it along the x-axis direction on the xy plane as d(x _k+1 =x _k +d) point set, then, get the corresponding point q _k (x _k , y _k , z _k ) on the triangular mesh surface; and after projecting the point set {q _k } onto the xy plane, along the y-axis direction Take points sequentially with step size d until the boundary of the smallest rectangular area (x _min , y _min ), (x _max , y _max ), and then calculate the point set {q′ of each point of the extended line segment on the triangular mesh surface _k }, then combine {q _k } and {q′ _k } to get the point set {p _k (x _k , y _k , z _k )} on the triangular mesh surface;

(8) Repeat the above steps (5)-(7) to obtain the next track line, until x _k+1 > x _max , the industrial computer ends the calculation;

(9) The industrial computer outputs the obtained six-dimensional trajectory data to the robot control cabinet, and controls the laser processing head on the robot to process the free-form surface.

For trajectory planning along any direction, the trajectory planning along any direction can be obtained by transforming the coordinates of this direction to the x-y coordinate direction, and then generating the trajectory in the x-y coordinate system and then undergoing inverse transformation.

The triangular Bernstein-Bézier surface described in the above step (5) is a cubic triangular Bernstein-Bézier surface.

Advantages of the present invention: the method for path planning based on free-form surface three-dimensional scattered point set data of the present invention uses triangular Bernstein-Bézier surface to realize free-form surface fitting of any three-dimensional scattered point set data and interpolation surface Six-dimensional processing trajectory planning, so that path planning can be performed on any free-form surface.

Description of drawings

Fig. 1 is a schematic flow chart of the method for path planning of three-dimensional scattered point set data of the present invention

Figure 2 is a schematic flow chart of trajectory planning for interpolation surfaces using triangular Bernstein-Bézier surfaces

Fig. 3 is a schematic diagram of a laser processing system according to an embodiment of the present invention

Fig. 4 is the laser processing trajectory of the automobile mold part area of the present invention

Fig. 5 is the actual processing effect of the automobile mold of the present invention

Figures

1. Laser 2. Industrial computer 3. Multi-axis linkage frame robot

4. Laser processing head

Detailed ways

Describe the specific embodiment of the present invention in detail with reference to accompanying drawing 1-3.

The laser processing control system used in this embodiment is a laser processing device with flexible transmission and multi-axis linkage, patent No. 98101217.5 of the Institute of Mechanics, Chinese Academy of Sciences. As shown in Figure 3, the laser processing head 4 and the frame robot 3 The arm is fixedly connected, the output end of the laser 1 is connected to the laser processing head 4 with an optical fiber, the input end of the laser 1 is connected to the industrial control computer 2 through the field bus, and the frame robot 3 is a high-precision, large-scale five-axis robot. The control cabinet of the type robot 3 is also connected to the industrial control computer 2 through the serial port. In this example, a 500W YAG pulse laser 1 (peak power can reach 7KW) is used to strengthen the surface of the automobile mold. The laser parameters: pulse width 24ms, pulse repetition rate 4Hz; The specific process is as follows:

1. As shown in Figure 1, after the industrial control computer 2 receives the three-dimensional scattered point set data of the automobile mold, it triangulates the three-dimensional scattered point set data through the three-dimensional data projection domain segmentation method, and obtains the triangle of the three-dimensional space data points The grid is subdivided, the vertices of the triangulation grid are P ₁ , P ₂ ,..., and the point set {P _i } is obtained, and then the normal vector and tangent vector of the vertex P _i are calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

S _ik =|(P _ik -P _i )×(P _i(k+1) -P ₀ )|/2 (2)

$\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula, m is the number of triangles adjacent to P _i , P _ik and P _i(k+1) are the vertices of the kth triangle adjacent to P _i , Ni _ik is the kth triangle adjacent to P _i The normal vector of the triangle, the area of the kth triangle adjacent to S _ik and P _i , the normal vector N(P _i ) and the tangent vector D _i,i+1 and D _i,i+2 of each vertex are obtained.

Finally, use the normal vector N(P _i ) of each vertex and the tangent vector D _{i, i+1} , D _{i, i+2} to perform cubic triangular Bernstein-Bézier construction on each triangle to obtain the cubic interpolation of the three-dimensional scattered point set data curved surface to obtain a spatial triangular mesh surface;

2. As shown in Figure 2, the trajectory of the robot for laser processing is further planned on the triangular Bernstein-Bézier surface through the industrial computer 2, and the specific steps are as follows:

(1) Project the spatial triangular mesh surface obtained in step 1 onto the xy plane, and determine the minimum rectangular area (x _min , y _min ), (x _max , y _max ) containing the surface projection on the xy plane;

(2) Instruct the industrial control computer to take p′ ₁ = (x _min , y _min ) as the starting point, and take points p′ _k = (x _min , y _min + (k-1) sequentially at intervals of d=1.26mm along the y-axis ×d), until the boundary end point (x _min , y _max ), where d is the interval between the centers of the two processing points, and then according to the corresponding point P _k of p′ _k on the triangular mesh surface (k=1, 2, ..., n)=(x _k , y _k , z _k );

(3) Calculate the center of gravity parameters (u, v, w) in the corresponding triangular domain of p _k according to the following calculation formula:

p _k =ua+vb+wc

u+v+w=1

In the formula, a, b, c are the coordinates of the three vertices of the triangle domain corresponding to the point p _k .

(4) According to each point in the {p _k } point set and its center of gravity parameters (u, v, w) in the corresponding triangular domain, combined with the fitted triangular Bernstein-Bézier surface to obtain the six-dimensional points on the corresponding triangular surface Set {l _k }={(x _k , y _k , z _k , ax _k , ay _k , az _z )};

(5) When the number of corresponding points p _k on the triangular mesh surface is n≥4, the chord length parametric spline curve is constructed with the six-dimensional point set {l _k } as the value point and the step size as d, and obtained as The six-dimensional point set of the first trajectory {m _k (x _k , y _k , z _k , ax _k , ay _k , az _k )};

When the number of corresponding points p _k on the triangular mesh surface is 0<n≤3, then take {m _k }={l _k }, (k=1, 2, 3) as the first track;

When the number n=0 of the corresponding point _pk on the triangular mesh surface, the industrial control computer ends the operation;

(6) Take the trajectory line {m _k } obtained above as the reference trajectory line, project it onto the xy plane, and obtain the distance from it along the x-axis direction on the xy plane as d(x _k+1 =x _k +d) point set, then, get the corresponding point q _k (x _k , y _k , z _k ) on the triangular mesh surface; and after projecting the point set {q _k } onto the xy plane, along the y-axis direction Take points sequentially with step size d until the boundary of the minimum rectangular area (x _min , y _min ), (x _max , y _max ), and then calculate the point set {q′ of each point of the extended line segment on the triangular mesh surface _k }, then combine {q _k } and {q′ _k } to get the point set {p _k (x _k , y _k , z _k )} on the triangular mesh surface;

(7) Repeat the above steps (3)-(6) to obtain the next trajectory until x _k+1 >x _max , the industrial computer ends the operation.

3. The industrial control computer 2 converts the obtained trajectory data into robot motion instructions, and then outputs it to the control cabinet of the robot 3 through the serial port of the industrial control computer 2, and the robot control cabinet controls the laser processing head 4 to carry out the automobile mold according to the planned trajectory data. processing.

Figure 4 shows the results of laser surface processing path planning in some areas of the automobile mold, and Figure 5 shows the effect after laser processing.

Claims (3)

1, a kind of method of carrying out path planning based on the 3 d discrete point collection data of free form surface, this method is in the Laser Surface Treatment system, obtain sextuple track data by the industrial computer processing and output to robot, and control robot drives the laser instrument processing head be fixed on its arm and moves according to sextuple track data, and its step comprises:

(1) after industrial computer receives the 3 d discrete point collection data of free form surface, utilizes triangle Bernstein-B é zier curved surface to carry out the interpolation curved surface that match obtains 3 d discrete point collection data, obtain the space triangular topological relations;

(2) this space triangular topological relations is projected to the xy plane, get on the triangular topological relations of space (x, the y) coordinate, and determine rectangular area (x that point is concentrated every bit with this by industrial computer _Min, y _Min), (x _Max, y _Max);

(3) with a p ₁'=(x _Min, y _Min) be starting point, get a formation point set { p successively along the y direction of principal axis _k', p _k'=(x _Min, y _Min+ (k-1) * d), (k=1,2 ..., n), wherein, d is the distance between two points that requirement is determined according to difference, until point (x _Min, y _Max); According to the resulting space of step (1) triangular topological relations, obtain p again _k' corresponding point p on triangular topological relations _k(x _k, y _k, z _k), form point set { p _k;

(4) according to { p _kEach point of concentrating of point and calculate with { p _k(u, v w), utilize triangle Bernstein-B é zier curved surface to calculate sextuple point set { l on the corresponding triangular surface for center of gravity parameter in the corresponding triangular domain of point set _k}={ (x _k, y _k, z _k, ax _k, ay _k, az _z);

(5) the corresponding point p on triangular topological relations _kNumber n 〉=4, with sextuple point set { l _kBe data point, and be step-length structure chord length parametric spline curve with d, obtain sextuple point set { m _k(x _k, y _k, z _k, ax _k, ay _k, az _k), as a trajectory;

When 0＜n≤3, industrial computer is with { m _k}={ l _k, (k=1,2,3) are as a track;

Work as n=0, industrial computer finishes computing;

(6) with the above-mentioned trajectory { m that obtains _kBe with reference to trajectory, it is projected on the x-y plane, and to obtain with it on the x-y plane be d (x along the axial distance of x _K+1=x _k+ d) point set then, obtains the respective point q on the triangular topological relations _k(x _k, y _k, z _k); And with point set { q _kProject on the x-y plane after, get successively a little until minimum rectangular area (x with step-length d along the y direction of principal axis _Min, y _Min), (x _Max, y _Max) the border, then, calculate the point set { q of each point on triangular topological relations that extends line segment _k', again with { q _kAnd { q _k' merge the point set { p obtain on the triangular topological relations _k(x _k, y _k, z _k);

(7) repeat above-mentioned steps (5)-(6) and obtain next bar trajectory, up to x _K+1＞x _MaxThe time, industrial computer finishes computing;

(8) the sextuple track data that will be obtained by industrial computer outputs to the robot switch board, and the laser instrument processing head on the control robot is processed this free form surface.

2, by the described method of carrying out path planning based on the 3 d discrete point collection data of free form surface of claim 1, it is characterized in that, for trajectory planning along any direction, can by with this direction coordinate transform to the x-y coordinate direction, in the x-y coordinate system, generate again behind the track through inverse transformation and obtain trajectory planning along any direction.

3, carry out the method for path planning by claim 1 is described based on the 3 d discrete point collection data of free form surface, it is characterized in that the described triangle Bernstein-B of step (4) é zier curved surface is three triangle Bernstein-B é zier curved surfaces.

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