CN110488758B - Trajectory transition method based on PLCopen specification - Google Patents
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Abstract
The invention discloses a trajectory transition method based on PLCopen specification, which is applied to the field of motion control and adopts a circular interpolation mode to realize trajectory transition; the method specifically comprises the following steps of S1: acquiring the curve types of a current instruction and a next instruction from an instruction buffer area of the motion controller to form a curve type combination between adjacent tracks, wherein the adjacent tracks are connected by adopting a transition circular arc; s2: establishing a constraint equation related to the transition circular arc parameters according to the curve type combination; s3: solving a constraint equation to obtain a transition arc parameter; s4: and planning the track of the transition circular arc in an S-curve mode, and mapping the transition circular arc to each independent axis of a Cartesian coordinate system to realize circular interpolation between adjacent tracks. The invention realizes track transition by adopting a circular interpolation mode, has controllable profile precision of a transition curve, continuous curvature and smooth interpolation speed transition, strictly conforms to PLCopen specification, and has excellent universality and wide application range.
Description
Technical Field
The invention belongs to a motion track transition mode, and particularly relates to a track transition method based on PLCopen specifications.
Background
With the development of the general motion control industry, the standardization requirements are more and more emphasized, and various standards are increasingly enriched and perfected, wherein IEC61131-3 becomes the international standard of the standardized programming language of the industrial control system, the applicable market field is continuously expanded, and products adopting or applying the programming language standard also become the mainstream trend of the industrial control field.
The PLCopen organization is an international organization which is consistent with the standardization of a programming language, 5 standards for customizing a motion control function are added on the basis of the IEC standard, the development of software of a programmable controller is further promoted, and meanwhile, the market in the field of motion control is also greatly standardized. At present, a plurality of manufacturers have provided products meeting the standards of functional modules, and the standards are widely accepted by the market. The standard specifies 5 ways of trajectory transition: TMNone, TMStartVelocity, TMConnstantVelocity, TMCornerVelocity, and TMCornerVectivity; at present, the 5 transition modes can be completely supported, and particularly, the number of TMCornerDev manufacturers is very small, and the maturity of products is short.
Moreover, the research aiming at the track transition is mostly embodied in the special machine, for example, in the chinese patent of "a speed change curve circular arc fast interpolation method encapsulated into a PLCopen command", the granted publication number is CN103454979B, which is only discussed from the angle of circular arc interpolation, and the content of the track transition is not reflected; in the Chinese patent of the high-speed high-precision numerical control processing small segment real-time smooth transition interpolation method, the granted publication number is CN103699056B, and a cubic B-spline curve is used for realizing the transition of the maximum error constraint of a track. In chinese patent application, published under CN107291047A, the NURBS curve is used to fit the specified contour, but this does not meet the specification of trajectory transition of plcopenn.
Disclosure of Invention
The invention aims to provide a trajectory transition method based on PLCopen specification, which aims to solve the problems and the defects, realizes trajectory transition by adopting a circular interpolation mode, has controllable profile precision of a transition curve, continuous curvature and smooth transition of interpolation speed, strictly conforms to the PLCopen specification, and has excellent universality and wide application range.
In order to achieve the purpose, the invention adopts the technical scheme that: a trajectory transition method based on PLCopen specification is applied to the field of motion control, and a circular interpolation mode is adopted to realize trajectory transition; the method specifically comprises the following steps:
s1: acquiring the curve types of a current instruction and a next instruction from an instruction buffer area of the motion controller to form a curve type combination between adjacent tracks, wherein the adjacent tracks are connected by adopting a transition circular arc;
s2: establishing a constraint equation related to the transition circular arc parameters according to the curve type combination;
s3: solving a constraint equation to obtain a transition arc parameter;
s4: and planning the track of the transition circular arc in an S-curve mode, and mapping the transition circular arc to each independent axis of a Cartesian coordinate system to realize circular interpolation between adjacent tracks.
Further, the curve type combinations of step S1 include straight line to straight line, straight line to curve, curve to straight line and curve to curve combinations;
when the curve types are combined into straight lines and straight lines, namely the current command represents a straight line with a starting point of S1 and an end point of E1, the next command represents a straight line with a starting point of S2 and an end point of E2, and the E1 and the S2 are the same point and are curve transition corners; at this time, the constraint equation of step S2 is:
dist (CenP, transition arc) Radius; (1)
Dist(CenP,E1)＝Radius+MaxDev； (2)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, transition arc) is the distance from the center CenP of the transition arc to any point on the transition arc, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and MaxDev is the maximum allowable corner deviation;
when the curve types are combined into a straight line and a curve, namely the current command represents a straight line with a starting point of S1 and an end point of E1, the next command represents an arc with a centre of PostCenP, a radius of Postradius, a starting point of S2 and an end point of E2, and E1 and S2 are the same point and are curve transition corners;
at this time, the constraint equation of step S2 is:
dist (CenP, transition arc) Radius; (3)
Dist(CenP,PostCenP)＝Radius+PostRadius； (4)
Dist(CenP,E1)＝Radius+MaxDev； (5)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, transition arc) is the distance from the center CenP of the transition arc to any point on the transition arc, Dist (CenP, PostCenP) is the distance from the center CenP of the transition arc to the center PostCenP of the next section of instruction, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and maxd is the maximum allowable corner deviation;
when the curve type combination is a curve and a straight line, namely the current command represents an arc with the circle center PrevCenP, the radius Prevradius, the starting point S1 and the end point E1, the next command represents a straight line with the starting point S2 and the end point E2, and the E1 and the S2 are the same point and are curve transition corners;
at this time, the constraint equation of step S2 is:
dist (CenP, transition arc) Radius; (7)
Dist(CenP,PrevCenP)＝Radius+PrevRadius； (8)
Dist(CenP,E1)＝Radius+MaxDev； (9)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, transition arc) is the distance from the center CenP of the transition arc to any point on the transition arc, Dist (CenP, PrevCenP) is the distance from the center CenP of the transition arc to the center PrevCenP of the current command, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and MaxDev is the maximum allowable corner deviation;
when the curve type combination is a curve and a curve, namely the current command represents an arc with the circle center PrevCenP, the radius Prevradius, the starting point S1 and the end point E1, the next command represents an arc with the circle center PostCenP, the radius Postradius, the starting point S2 and the end point E2, and the E1 and the S2 are the same point and are curve transition corners;
at this time, the constraint equation in step S2 is:
Dist(CenP,PrevCenP)＝Radius+PrevRadius； (10)
Dist(CenP,PostCenP)＝Radius+PostRadius； (11)
Dist(CenP,E1)＝Radius+MaxDev； (12)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, PrevCenP) is the distance from the center CenP of the transition arc to the current instruction center PrevCenP, Dist (CenP, PostCenP) is the distance from the center CenP of the transition arc to the center PostCenP of the next instruction, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and MaxDev is the maximum allowable corner deviation.
Further, when the curve types are combined into a straight line and a curve, a curve and a straight line, and a curve, the constraint equation about the transition arc is solved in a manner of combining an analytic method and an iterative method, specifically:
establishing a multivariable nonlinear equation system F (X) 0 about a transition circular arc center Cenp according to a constraint equation, wherein X (CenP [0], CenP [1], CenP [2]), Cenp [0], Cenp [1] and Cenp [2] respectively represent coordinates of an X axis, a Y axis and a Z axis of the transition circular arc center Cenp;
iterative calculations were performed using the following iterative method:
x(k+1)＝x(k)-F'(x(k))-1F(x(k)),k＝0,1,...., (6)
wherein F' is the Jacobian matrix of F; setting an initial value x of an iteration(0)Coordinates of curve transition corners of adjacent tracks; thus, the numerical solution of the center Cenp of the transition arc is solved, as well as the starting point E1 'and the end point S2'.
The invention has the beneficial effects that: (1) based on the constraint on the track transition mode in the PLCopen specification, the maximum allowable corner deviation is set in a circular arc transition mode, the distance between a transition circular arc and a corner between track sections is not more than the set maximum allowable deviation, the stable transition between tracks is realized, and the controllable profile precision, continuous curvature and smooth interpolation speed without sudden change of the transition circular arc are ensured.
(2) The invention can support smooth transition between straight lines, straight lines and circular arcs, circular arcs and straight lines, and circular arcs, and can be widely applied to track transition of application scenes such as cutting, carving, welding, carrying and the like.
(3) According to the method, different constraint conditions are limited through combined classification of curves between adjacent tracks, an equation set is built, the starting point, the terminal point and the circle center of a transition circular arc are obtained through combination of an analytic method and a numerical method, the track transition problem is converted into a simple circular interpolation problem, the track can be visually pre-judged, and engineering application is facilitated.
Drawings
FIG. 1 is a flow chart of a trajectory transition method based on PLCopen specification according to the present invention;
FIG. 2 is a schematic view of the line and line transition of the present invention;
FIG. 3 is a schematic diagram of the transition between straight and curved lines according to the present invention;
FIG. 4 is a schematic diagram of a curve and line transition according to the present invention;
FIG. 5 is a schematic diagram of curves and curve transitions according to the present invention;
FIG. 6 is a schematic diagram showing a comparison between a target profile curve of example 1 of the present invention and a profile curve obtained by the trajectory transition method of the present invention;
fig. 7 is a schematic diagram of a synthesized interpolation speed according to embodiment 1 of the present invention.
Detailed Description
In order to make the content of the invention clearer, the following detailed description of the embodiments of the invention is made with reference to the accompanying drawings. It should be noted that for the sake of clarity, the figures and the description omit representation and description of parts known to those skilled in the art that are not relevant to the inventive concept.
Example 1:
the invention provides a trajectory transition method based on PLCopen specification, which is applied to the field of motion control and adopts a circular interpolation mode to realize trajectory transition; the method specifically comprises the following steps:
s1: acquiring the curve types of a current instruction and a next instruction from an instruction buffer area of the motion controller to form a curve type combination between adjacent tracks, wherein the adjacent tracks are connected by adopting a transition circular arc;
s2: establishing a constraint equation related to the transition circular arc parameters according to the curve type combination;
s3: solving a constraint equation to obtain a transition arc parameter;
s4: and planning the track of the transition circular arc in an S-curve mode, and mapping the transition circular arc to each independent axis of a Cartesian coordinate system to realize circular interpolation between adjacent tracks.
The curve type combination of the step S1 includes a combination of a straight line and a straight line, a combination of a straight line and a curve, a combination of a curve and a straight line, and a combination of a curve and a curve;
as shown in fig. 2, when the curve types are combined into a straight line and a straight line, i.e. the current command represents a straight line with a starting point of S1 and an end point of E1, the next command represents a straight line with a starting point of S2 and an end point of E2, and E1 and S2 are the same point and are curve transition corners; at this time, the constraint equation of step S2 is:
dist (CenP, transition arc) Radius; (1)
Dist(CenP,E1)＝Radius+MaxDev； (2)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, transition arc) is the distance from the center CenP of the transition arc to any point on the transition arc, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and MaxDev is the maximum allowable corner deviation;
as shown in fig. 3, when the curve types are combined into a straight line and a curve, that is, the current command represents a straight line having a starting point of S1 and an end point of E1, the next command represents an arc having a center of a circle of PostCenP, a radius of PostRadius, a starting point of S2, and an end point of E2, and E1 and S2 are the same point and are curve transition corners;
at this time, the constraint equation of step S2 is:
dist (CenP, transition arc) Radius; (3)
Dist(CenP,PostCenP)＝Radius+PostRadius； (4)
Dist(CenP,E1)＝Radius+MaxDev； (5)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, transition arc) is the distance from the center CenP of the transition arc to any point on the transition arc, Dist (CenP, PostCenP) is the distance from the center CenP of the transition arc to the center PostCenP of the next section of instruction, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and maxd is the maximum allowable corner deviation;
as shown in fig. 4, when the curve type is combined into a curve and a straight line, that is, the current command represents an arc with a center PrevCenP, a radius PrevRadius, a starting point S1, and an end point E1, the next command represents a straight line with a starting point S2 and an end point E2, and E1 and S2 are the same point and are curve transition corners;
at this time, the constraint equation of step S2 is:
dist (CenP, transition arc) Radius; (7)
Dist(CenP,PrevCenP)＝Radius+PrevRadius； (8)
Dist(CenP,E1)＝Radius+MaxDev； (9)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, transition arc) is the distance from the center CenP of the transition arc to any point on the transition arc, Dist (CenP, PrevCenP) is the distance from the center CenP of the transition arc to the center PrevCenP of the current command, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and MaxDev is the maximum allowable corner deviation;
as shown in fig. 5, when the curve type is combined into a curve and a curve, that is, the current command represents an arc with a center PrevCenP, a radius PrevRadius, a starting point S1, and an end point E1, the next command represents an arc with a center PostCenP, a radius PostRadius, a starting point S2, and an end point E2, and E1 and S2 are the same point and are curve transition corners;
at this time, the constraint equation in step S2 is:
Dist(CenP,PrevCenP)＝Radius+PrevRadius； (10)
Dist(CenP,PostCenP)＝Radius+PostRadius； (11)
Dist(CenP,E1)＝Radius+MaxDev； (12)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, PrevCenP) is the distance from the center CenP of the transition arc to the current instruction center PrevCenP, Dist (CenP, PostCenP) is the distance from the center CenP of the transition arc to the center PostCenP of the next instruction, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and MaxDev is the maximum allowable corner deviation.
In this embodiment, assume the center of the transition arc CenP as CenP [3]]Respectively representing X-axis, Y-axis and Z-axis coordinates, Dist (a, b) representing the distance between a and b, wherein a and b can be points or curves; taking a two-dimensional space as an example, when a and b are both points,
when a is a point and b is a straight line, let b expressWhen the formula Ax + By + C is 0, then
fabs represent absolute values.
When the curve types are combined into straight lines and straight lines, substituting the formula (1) into the formula (2), and directly obtaining a closed solution of the center CenP of the transition arc, a starting point E1 'and a terminal point S2' by using a unitary quadratic root-solving formula;
when the curve type combination is a straight line and a curve, a curve and a straight line, and a curve, the constraint equation about the transition arc is solved by adopting a mode of combining an analytic method and an iterative method, and taking the straight line and the curve type combination as an example, the method specifically comprises the following steps:
substituting formula (3) into formula (4) and formula (5) to establish a multivariable nonlinear equation set f (X) 0 about a transition circular arc center Cenp, where X (Cenp [0], Cenp [1], Cenp [2]), Cenp [0], Cenp [1], and Cenp [2] respectively represent coordinates of an X axis, a Y axis, and a Z axis of the transition circular arc center Cenp;
iterative calculations were performed using the following iterative method:
x(k+1)＝x(k)-F'(x(k))-1F(x(k)),k＝0,1,...., (6)
wherein F' is the Jacobian matrix of F; setting an initial value x of an iteration(0)Coordinates of curve transition corners (E1/S2) for adjacent tracks; thus, the numerical solution of the center Cenp of the transition arc is solved, as well as the starting point E1 'and the end point S2'. Similarly, when the curve types are curve and straight line and curve, the solving mode of the constraint equation is the same as that of the straight line and curve, and the corresponding constraint equation and the formula (6) are used for solving.
In step S4, a speed constraint Velocity, an Acceleration constraint Acceleration, a Deceleration constraint Deceleration, and an Acceleration constraint Jerk for S-curve planning need to be set to plan the trajectory of the solved transition arc; meanwhile, the input numerical value (transition arc parameter) may be optimized according to other constraints, such as prospective processing, maximum bow height error and the like, and no range limitation is made at the position.
As shown in FIG. 6, the present invention provides an embodiment of the trajectory transition method of the present invention, where curve 1 is the target profile curve and curve 2 is the profile curve obtained by using the trajectory transition equation of the present invention; wherein the coordinates of each corner point are as follows:
P0[3]＝{0.0,0.0,0.0,}，P1[3]＝{10000.0,10000.0,0.0}，P2[3]＝{15000.0,5000.0,0.0}，P3[3]＝{25000.0,5000.0,0.0}，P4[3]＝{30000.0,5000.0,0.0}，P5[3]＝{40000.0,10000.0,0.0}，P6＝{50000.0,0.0,0.0}。
the maximum allowable corner deviations MaxDev are both set to 1000.0, i.e. the input parameters Transition Parameter (Transition range) are both 1000.0.
And (3) constructing a two-dimensional equation according to the formula (1) and the formula (2), obtaining a closed solution C1[3] ═ 10000.0, 6585.7864 and 0.0} of the center CenP of the transition arc, and further obtaining S1[3] ═ 8292.8932,8292.8932 and 0.0}, and E1[3] ═ 11707.1068,9292.8932 }.
Constructing a multivariable nonlinear equation system of C2 according to formulas (3), (4) and (5), and solving a numerical solution of the multivariable nonlinear equation system by using a method of a formula (6); in the initial iteration value of C2, a P2 value is selected, and C2[3] = {14434.2434,6742.6591,0.0} is iteratively obtained, so that S2[3] = {13845.7926,6154.2078,0.0} and E2[3] } {15228.4210,6493.9991,0.0} are obtained.
Building a multivariable nonlinear equation system of C3 according to equations (10), (11) and (12), and using an equation (6) method, wherein an iteration initial value of C3 selects a P3 value, and then C3[3] = {25000.0,6215.0,0.0}, S3[3] = {24878.0488,6097.5610,0.0}, and E3[3] } {25121.9512,6097.5610,0.0}, are obtained.
Building a multivariable nonlinear equation system of C4 according to equations (7), (8) and (9), using the method of equation (6), wherein the iteration initial value of C4 selects a P4 value, and then, C4[3] = {35565.7566,6742.6591,0.0}, S4[3] = {34771.5790,6493.9991,0.0}, and E4[3] } {36154.2078,6154.2078,0.0}, are obtained.
The same method as C1 is used to obtain C5[3] = {40000.0,6585.7864,0.0}, S5[3] }, {38292.8932,8292.8932,0.0}, and E5[3] }, {41707.1068,8292.8932,0.0 }. And (4) solving the coordinates of the circle center, the starting point and the end point of the 5-section transition arc.
The input parameters of the standard linear interpolation module (MC _ MoveLinear relative) are all set as follows: velocity 100.0, Acceleration 10.0, Deceleration 10.0, Jerk 0.2; the input parameters of the standard circular arc interpolation module (MC _ Movecircular relative) are set as follows: velocity 80.0, Acceleration 5.0, Deceleration 5.0, Jerk 0.1; and planning the track of the transition circular arc by adopting an S curve mode, and mapping the contour curve to a Cartesian coordinate system by adopting a linear interpolation and circular interpolation mode to realize the final position interpolation.
As shown in fig. 7, the synthesized interpolation speed of the present embodiment smoothly transitions without abrupt changes.
The above description is only intended to illustrate the embodiments of the present invention, and the description is more specific and detailed, but not to be construed as limiting the scope of the invention. It should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the inventive concept, and these changes and modifications are within the scope of the invention. Therefore, the protection scope of the invention should be subject to the appended claims.
Claims (2)
1. A trajectory transition method based on PLCopen specification is applied to the field of motion control, and a circular interpolation mode is adopted to realize trajectory transition; the method is characterized by comprising the following steps:
s1: acquiring the curve types of a current instruction and a next instruction from an instruction buffer area of the motion controller to form a curve type combination between adjacent tracks, wherein the adjacent tracks are connected by adopting a transition circular arc;
s2: establishing a constraint equation related to the transition circular arc parameters according to the curve type combination;
s3: solving a constraint equation to obtain a transition arc parameter;
s4: planning the track of the transition circular arc in an S-curve mode, and mapping the transition circular arc to each independent axis of a Cartesian coordinate system to realize circular interpolation between adjacent tracks;
the curve type combination of the step S1 includes straight line and straight line, straight line and curve, curve and straight line, and curve combination;
when the curve types are combined into straight lines and straight lines, namely the current command represents a straight line with a starting point of S1 and an end point of E1, the next command represents a straight line with a starting point of S2 and an end point of E2, and the E1 and the S2 are the same point and are curve transition corners; at this time, the constraint equation of step S2 is:
dist (CenP, transition arc) Radius; (1)
Dist(CenP,E1)＝Radius+MaxDev； (2)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, transition arc) is the distance from the center CenP of the transition arc to any point on the transition arc, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and MaxDev is the maximum allowable corner deviation;
when the curve types are combined into a straight line and a curve, namely the current command represents a straight line with a starting point of S1 and an end point of E1, the next command represents an arc with a centre of PostCenP, a radius of Postradius, a starting point of S2 and an end point of E2, and E1 and S2 are the same point and are curve transition corners;
at this time, the constraint equation of step S2 is:
dist (CenP, transition arc) Radius; (3)
Dist(CenP,PostCenP)＝Radius+PostRadius； (4)
Dist(CenP,E1)＝Radius+MaxDev； (5)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, transition arc) is the distance from the center CenP of the transition arc to any point on the transition arc, Dist (CenP, PostCenP) is the distance from the center CenP of the transition arc to the center PostCenP of the next section of instruction, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and maxd is the maximum allowable corner deviation;
when the curve type combination is a curve and a straight line, namely the current command represents an arc with the circle center PrevCenP, the radius Prevradius, the starting point S1 and the end point E1, the next command represents a straight line with the starting point S2 and the end point E2, and the E1 and the S2 are the same point and are curve transition corners;
at this time, the constraint equation of step S2 is:
dist (CenP, transition arc) Radius; (7)
Dist(CenP,PrevCenP)＝Radius+PrevRadius； (8)
Dist(CenP,E1)＝Radius+MaxDev； (9)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, transition arc) is the distance from the center CenP of the transition arc to any point on the transition arc, Dist (CenP, PrevCenP) is the distance from the center CenP of the transition arc to the center PrevCenP of the current command, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and MaxDev is the maximum allowable corner deviation;
when the curve type combination is a curve and a curve, namely the current command represents an arc with the circle center PrevCenP, the radius Prevradius, the starting point S1 and the end point E1, the next command represents an arc with the circle center PostCenP, the radius Postradius, the starting point S2 and the end point E2, and the E1 and the S2 are the same point and are curve transition corners;
at this time, the constraint equation in step S2 is:
Dist(CenP,PrevCenP)＝Radius+PrevRadius； (10)
Dist(CenP,PostCenP)＝Radius+PostRadius； (11)
Dist(CenP,E1)＝Radius+MaxDev； (12)
wherein, CenP is the center of the transition arc, and Radius is the Radius of the transition arc; dist (CenP, PrevCenP) is the distance from the center CenP of the transition arc to the current instruction center PrevCenP, Dist (CenP, PostCenP) is the distance from the center CenP of the transition arc to the center PostCenP of the next instruction, Dist (CenP, E1) is the distance from the center CenP of the transition arc to the curve transition corner E1, and MaxDev is the maximum allowable corner deviation.
2. The PLCopen specification-based track transition method as claimed in claim 1, wherein: when the curve types are combined into straight lines and curves, curves and straight lines, curves and curves, the constraint equation about the transition arc is solved by adopting a mode of combining an analytic method and an iterative method, and the method specifically comprises the following steps:
establishing a multivariable nonlinear equation system F (X) 0 about a transition circular arc center Cenp according to a constraint equation, wherein X (CenP [0], CenP [1], CenP [2]), Cenp [0], Cenp [1] and Cenp [2] respectively represent coordinates of an X axis, a Y axis and a Z axis of the transition circular arc center Cenp;
iterative calculations were performed using the following iterative method:
x(k+1)＝x(k)-F'(x(k))-1F(x(k)),k＝0,1,...., (6)
wherein F' is the Jacobian matrix of F; setting an initial value x of an iteration(0)Coordinates of curve transition corners of adjacent tracks; thus, the numerical solution of the center Cenp of the transition arc is solved, as well as the starting point E1 'and the end point S2'.
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| CN112547425B (en) * | 2020-12-08 | 2022-11-18 | 深圳市华成工业控制股份有限公司 | Track look-ahead-based dispenser motion planning method and system |
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