CN116330302B - Motion planning method based on standard space curve - Google Patents
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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
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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
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Abstract
The present application relates toThe technical field of super-redundancy robot motion planning solves the technical problems that the existing super-redundancy robot has large space motion gait calculated amount and further causes non-real-time motion planning of the super-redundancy robot, and particularly relates to a motion planning method based on a standard frame space curve, which comprises the following steps: s1, constructing a space parameter curve C (t) as a ridge curve of the super-redundancy robot, and calculating a unit tangent vector at the initial position of the ridge curveNormal vector of unitUnit auxiliary normal vectorCoordinate system forming initial part of space parameter curve. The application carries out discretization by calculating the minimum rotation standard frame, avoids the calculation of curvature flexibility rate, has no requirement on the shape and the type of the back curve, and can improve the calculation efficiency by avoiding a large amount of curvature flexibility rate and integral calculation for discretization of the back curve of the super-redundancy robot.
Description
Technical Field
The application relates to the technical field of super-redundancy robot motion planning, in particular to a motion planning method based on a standard-frame space curve.
Background
Super redundant robot has wide application in narrow space detection and other fields because of containing more motion redundancy. At present, super-redundant robots mostly adopt a back curve discretization method to conduct motion planning. The joint angle is calculated by adopting a curve discretization method and a curvature and deflection rate integration mode, wherein the curvature and deflection rate of a ridge curve equation are calculated firstly, and for a complex curve, the calculation amount is very large, so that the discretization efficiency is greatly reduced.
Disclosure of Invention
Aiming at the defects of the prior art, the application provides a motion planning method based on a standard-frame space curve, which solves the technical problems that the existing super-redundancy robot space motion planning is large in calculated amount, and the super-redundancy robot motion planning is not real-time.
In order to solve the technical problems, the application provides the following technical scheme: a motion planning method based on a standard space curve comprises the following steps:
s1, constructing a space parameter curve C (t) as a ridge curve of the super-redundancy robot, and calculating a unit tangent vector at the initial position of the ridge curveUnit normal vector->Unit auxiliary normal vector->Coordinate system of minimum rotation frame forming initial position of space parameter curve>；
S2, according to a coordinate system of the initial position of the space parameter curveBefore calculation->Length of individual connecting rod->Unit tangent vector at the corresponding arc>Unit normal vector->Unit auxiliary normal vector->Form the minimum rotary frame->；
S3 based on the firstMinimum rotation frame->First->Minimum rotation frame->And generating a motion plan of the super-redundant robot.
Further, in step S1, the specific process includes the following steps:
s11, discretizing curve parameters t of a space parameter curve C (t), wherein the interval is，/>The curve parameter t takes the value +.>；
S12, according to the curve parameter t and the intervalCalculating the arc length of the dorsal curve +.>；
S13, making the arc lengthEqual to the front +.>Length of individual connecting rod->And calculates the front +/for super redundant robot>Length of individual connecting rod->Corresponding curve parameters>；
S14, calculating curve parametersTangential vector of the place->；
S15, calculating the starting of the ridge curveUnit tangent vector at->Unit normal vector->Unit auxiliary normal vector->。
Further, in step S12, the arc lengthThe calculation formula of (2) is as follows:
；
in the above, n refers to the number of discrete summation intervals of the arc length of the curve segment, m refers to the number of discrete curve segment sequences,the interval is indicated as such,representing that the spatial parameter curve C (t) is +.>Derivative of t>And (5) pointing to perform modular arithmetic.
Further, in step S13, specifically including:
by spacing at intervalsAccumulating the arc length of the discrete curve segments for the integration interval cycles until the arc length +.>Equal to front->Length of individual connecting rod->Further determining the curve parameters satisfying the condition +.>。
Further, in step S14, the curve parametersTangential vector of the place->The calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,for the spatial parameter curve C (t) versus curve parameter +.>1 st derivative of (c).
Further, in step S2, the specific process includes the following steps:
s21, setting the arc length of the distance starting position on the known curveIs->The minimum rotary frame at the position is +.>And arc length +.>Is->Unit tangent vector at->；
S22, calculating minimum rotation standard frameUnit tangent vector +.>Based on plane->Symmetry vector ∈>Wherein plane->For->And (4) point->Is divided into two halves;
s23, rotating the minimum mark frameUnit auxiliary normal vector->Based on plane->Mirror image is symmetry vector->The symmetry vector is further->Based on plane->Mirror symmetry and calculating the unit auxiliary normal vector +.>In a plane ofFor->Symmetry vector ∈>And unit tangent vector->Is divided into two halves;
s24, adopting a right-handed spiral rule to base on unit tangent vectorAnd unit auxiliary normal vector->Calculating the unit normal vector->；
S25, according to the unit tangent vectorUnit auxiliary normal vector->And unit normal vector->Form the minimum rotary frame->。
Further, in step S22, the symmetry vectorThe calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,indicate->Is the starting point->Is the position vector of the end point, +.>Is a unit tangent vector +.>Dot +.>About plane->Is a symmetric vector of (a).
Further, the method comprises the steps of,in step S23, a unit auxiliary normal vectorThe calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,is->About plane->Mirror symmetry vector, ">Is a unit tangent vector +.>And symmetry vector->Vector difference of>To form a minimum rotary frame->And a unit sub-normal vector of the gesture matrix.
Further, in step S3, the specific process includes the following steps:
s31, calculate the firstMinimum rotation frame->First->Minimum rotary frame/>Is +.>；
S32, based on attitude difference valueCalculating joint angle of orthogonal joint of super-redundant robot>；
S33, according to joint anglesAnd generating a motion plan of the super-redundant robot.
By means of the technical scheme, the application provides a motion planning method based on a standard-structured space curve, which has at least the following beneficial effects:
the application carries out discretization by calculating the minimum rotation standard frame, avoids the calculation of curvature flexibility rate, has no requirement on the shape and the type of the back curve, and can improve the calculation efficiency by avoiding a large amount of curvature flexibility rate and integral calculation for discretization of the back curve of the super-redundancy robot.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a schematic diagram of the application with a ridge curve based on minimum rotation frame discretization;
FIG. 2 is a schematic diagram of a method for calculating a minimum rotation frame based on a double reflection method of space geometry according to the present application;
FIG. 3 is a schematic diagram of the present application for generating a super-redundant robot motion plan.
In the figure: 1. super redundant robot links; 2. a minimum rotary frame; 3. a dorsal curve.
Detailed Description
In order that the above-recited objects, features and advantages of the present application will become more readily apparent, a more particular description of the application will be rendered by reference to the appended drawings and appended detailed description. Therefore, the realization process of how to apply the technical means to solve the technical problems and achieve the technical effects can be fully understood and implemented.
Those of ordinary skill in the art will appreciate that all or a portion of the steps in a method of implementing an embodiment may be implemented by a program to instruct related hardware and thus that the application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
Referring to fig. 1-3, a specific implementation manner of the present embodiment is shown, in which the minimum rotation frame is calculated for discretization, so that calculation of curvature flexibility rate is avoided, no requirement is made on shape and type of the back curve, and a large amount of curvature flexibility rate and integral calculation are avoided for discretization of the back curve of the super redundancy robot, so that calculation efficiency can be improved.
Referring to fig. 1, the present embodiment provides a motion planning method based on a standard space curve, which includes the following steps:
s1, constructing a space parameter curve C (t) as a ridge curve of the super-redundancy robot, and calculating a unit tangent vector at the initial position of the ridge curveUnit normal vector->Unit auxiliary normal vector->Coordinate system of the initial part of the formation of the spatial parameter curve +.>；
；
In this embodiment, the specific process of step S1 includes the following steps:
s11, discretizing curve parameters t of a space parameter curve C (t), wherein the interval is，/>The curve parameter t takes the value +.>；
S12, according to the curve parameter t and the intervalCalculating the arc length of the dorsal curve +.>；
Arc lengthThe calculation formula of (2) is as follows:
；
in the above, n refers to the number of discrete summation intervals of the arc length of the curve segment, m refers to the number of discrete curve segment sequences,the interval is indicated as such,representing that the spatial parameter curve C (t) is +.>Derivative of t>And (5) pointing to perform modular arithmetic.
S13, making the arc lengthEqual to the front +.>Length of individual connecting rod->And calculates the front +/for super redundant robot>Length of individual connecting rod->Corresponding curve parameters>；
By spacing at intervalsAccumulating the arc length of the discrete curve segments for the integration interval cycles until the arc length +.>Equal to front->Length of individual connecting rod->Further determining the curve parameters satisfying the condition +.>；
；
In the above-mentioned method, the step of,for the 1 st derivative of the spatial parameter curve C (t) with respect to the curve parameter t,/>Representing the number of links for length-accumulating summation, +.>Represents the length of the ith link, +.>Representing derivative symbols.
S14, calculating curve parametersTangential vector of the place->；
Curve parametersTangential vector of the place->The calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,for the spatial parameter curve C (t) versus curve parameter +.>1 st derivative of (c).
S15, calculating the starting of the ridge curveUnit tangent vector at->Unit normal vector->Unit auxiliary normal vector->Thus forming a coordinate system +.>。
Unit tangent vectorThe calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,is->The first derivative of the spatial parameter curve C (t) with respect to the curve parameter t.
Unit auxiliary normal vectorThe calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,is->Second derivative of the spatial parameter curve C (t) at the point with respect to the curve parameter t, +.>Representing a vector cross-product operation.
Unit normal vectorThe calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,is the unit auxiliary normal vector at the start of the back curve,>is the unit tangent vector at the start of the ridge curve.
S2, according to a coordinate system of the initial position of the space parameter curveBefore calculation->Length of individual connecting rod->Corresponding to the arc length, i.e. point +.>Unit tangent vector at->Unit normal vector->Unit auxiliary normal vector->Forming the minimum rotary frame。
In this embodiment, the specific process of step S2 includes the following steps:
s21, setting the arc length of the distance starting position on the known curveIs->The minimum rotary frame at the position is +.>And arc length +.>Is->Unit tangent vector at->；
S22, calculating minimum rotation standard frameUnit tangent vector +.>Based on plane->Symmetry vector ∈>Wherein plane->For->And (4) point->Is divided into two halves;
s23, rotating the minimum mark frameUnit auxiliary normal vector->Based on plane->Mirror image is symmetry vector->The symmetry vector is further->Based on plane->Mirror symmetry and calculating the unit auxiliary normal vector +.>In a plane ofFor->Symmetry vector ∈>And unit tangent vector->Is divided into two halves;
s24, adopting a right-handed spiral rule to base on unit tangent vectorAnd unit auxiliary normal vector->Calculating the unit normal vector->；
S25, according to the unit tangent vectorUnit auxiliary normal vector->And unit normal vector->Form the minimum rotary frame->。
Referring to fig. 2, a minimum rotation frame is calculated by a dual reflection method based on space geometryThe process of (2) is as follows:
first assume that points on a known curveThe minimum rotary frame at the position is +.>；
；
In the above-mentioned method, the step of,for the dotted line +.>Unit tangent vector at->For the dotted line +.>Unit normal vector at->For the dotted line +.>Unit sub-normal vector at.
To determine the starting pointMinimum rotation frame->The minimum rotation frame can be calculated>Unit tangent vector +.>Based on plane->Symmetry vector ∈>Wherein plane->For->And (4) point->The bisecting plane of (2) is:
；
in the above-mentioned method, the step of,indicate->Is the starting point->Is the position vector of the end point, +.>Is a unit tangent vector +.>Dot +.>About plane->Is a symmetric vector of (a).
Minimum rotary standard frame in the same wayUnit auxiliary normal vector->Based on plane->Mirror image as symmetrical vectorThe symmetry vector is further->Based on plane->Mirror symmetry and calculating the unit auxiliary normal vector +.>。
Wherein the plane isFor->Symmetry vector ∈>And unit tangent vector->Is equal to (1) bisecting plane (B),>is a curve of +.>The unit tangent vector at (5) can be calculated by the formula, regarding the unit auxiliary normal vector +.>The calculation formula is as follows:
；
in the above-mentioned method, the step of,is->About plane->Mirror symmetry vector, ">Is a unit tangent vector +.>And symmetry vector->Vector difference of>To form a minimum rotary frame->And a unit sub-normal vector of the gesture matrix.
Finally, the right-handed spiral rule is adopted to base on the unit tangent vectorAnd unit auxiliary normal vector->Calculating the unit normal vector->Unit normal vector->The calculation formula of (2) is as follows:
；
wherein the method comprises the steps ofTo form a minimum rotary frame->Gesture matrix->Further constitute the minimum rotation frame +.>。
S3 based on the firstMinimum rotation frame->First->Minimum rotation frame->Generating a motion plan of the super-redundant robot;
specifically, the firstMinimum rotation frame->The expression of (2) is:
；
first, theMinimum rotation frame->The expression of (2) is:
；
in this embodiment, the specific process of step S3 includes the following steps:
s31, calculate the firstMinimum rotation frame->First->Minimum rotation frame->Is +.>；
Specifically, the attitude differenceThe calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,。
s32, based on attitude difference valueCalculating joint angle of orthogonal joint of super-redundant robot>；
Specifically, the joint angleThe calculation formula of (2) is as follows:
；
wherein, because the super redundant robot joint is an orthogonal joint, the odd joint performs side swinging motion and the even joint performs pitching motion, the calculation modes of the odd joint angle and the even joint angle are different, and the joint angle is calculated by the stepAnd further generating a motion plan of the super-redundant robot.
S33, according to joint anglesAnd generating a motion plan of the super-redundant robot.
Referring to fig. 3, curve 1 changes slowly to curves 2 and 3, based on the minimum rotation frameCalculating corresponding joint angle with time according to formula (18)>Completing the motion planning of the super-redundant robot, X, Y, Z in fig. 3 is the three-dimensional coordinate direction of the coordinate system describing the ridge curve。
As an example, curve 1, curve 2 and curve 3 in fig. 3 are all spatial four-time bezier curves, and their parameter equations are respectively:
the parametric equation for curve 1 is:
；
the parametric equation for curve 2 is:
；
the parametric equation for curve 3 is:
；
wherein,,unit tangent vector of them at the start of the ridge curve +.>，
Unit normal vector，
Unit auxiliary normal vector，
Setting the length of the connecting rod of the super redundant robot0.1m;
thus, the example spine curve is based on the connecting rod lengthBased on minimum rotation frame->Discretizing to calculate joint angles of super redundant robot orthogonal joints corresponding to curves 1, 2 and 3 respectively>The method comprises the following steps:
joint angle of super redundant robot orthogonal joint corresponding to curve 1The method comprises the following steps:
[0.067, -0.470,0.052, -0.594,0.060, -0.389,0.0983, -0.187,0.182, -0.083,0.343, -0.0241,0.471,0.022,0.342,0.079,0.181,0.177,0.097,0.364,0.059,0.577,0.048,0.490,0.059,0.266,0.086,0.138,0.127,0.077,0.185,0.046] radians.
Joint angle of super redundant robot orthogonal joint corresponding to curve 2The method comprises the following steps:
[0.064, -0.643,0.046, -0.730,0.061, -0.348,0.108, -0.146,0.190, -0.063,0.304, -0.019,0.363,0.012,0.286,0.046,0.182,0.094,0.114,0.173,0.076,0.294,0.056,0.413,0.051,0.399,0.062,0.273,0.093,0.163,0.159,0.095,0.296,0.056] radians.
Joint angle of super redundant robot orthogonal joint corresponding to curve 3The method comprises the following steps:
[0.064, -0.646,0.045, -0.746,0.058, -0.360,0.096, -0.155,0.158, -0.073,0.236, -0.033,0.290, -0.008,0.269,0.014,0.200,0.0440,0.138,0.089,0.096,0.168,0.070,0.303,0.057,0.451,0.060,0.430,0.096,0.270,0.240,0.142] radians.
Thereby obtaining corresponding joint angles which change with timeAnd then, completing the motion planning of the super-redundant robot.
The embodiment avoids a large amount of curvature flexibility and integral calculation for the discretization of the super-redundancy robot back curve, and can improve the calculation efficiency.
In this specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different manner from other embodiments, so that the same or similar parts between the embodiments are referred to each other. For each of the above embodiments, since it is substantially similar to the method embodiment, the description is relatively simple, and reference should be made to the description of the method embodiment for relevant points.
The foregoing embodiments have been presented in a detail description of the application, and are presented herein with a particular application to the understanding of the principles and embodiments of the application, the foregoing embodiments being merely intended to facilitate an understanding of the method of the application and its core concepts; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present application, the present description should not be construed as limiting the present application in view of the above.
Claims (8)
1. The motion planning method based on the standard space curve is characterized by comprising the following steps of:
s1, constructing a space parameter curveC(t) As a ridge curve of the super redundant robot, and calculate a unit tangent vector at the start of the ridge curveUnit normal vector->Unit auxiliary normal vector->Coordinate system forming initial part of space parameter curve；
S2, according to a coordinate system of the initial position of the space parameter curveBefore calculation->Length of individual connecting rod->Unit tangent vector at the corresponding arc>Unit normal vector->Unit auxiliary normal vector->Form the minimum rotary frame->；
In step S2, the specific process includes the following steps:
s21, setting the arc length of the distance starting position on the known curveIs->The minimum rotary frame at the position is +.>And arc length +.>Is->Unit tangent vector at->；
S22, calculating minimum rotation standard frameUnit tangent vector +.>Based on plane->Symmetry vector being mirror imageWherein plane->For->And (4) point->Is divided into two halves;
s23, rotating the minimum mark frameUnit auxiliary normal vector->Based on plane->Mirror image as symmetrical vectorThe symmetry vector is further->Based on plane->Mirror symmetry and calculating the unit auxiliary normal vector +.>In a plane ofFor->Symmetry vector ∈>And unit tangent vector->Is divided into two halves;
s24, adopting a right-handed spiral rule to base on unit tangent vectorAnd unit auxiliary normal vector->Calculating unit normal vector；
S25, according to the unit tangent vectorUnit auxiliary normal vector->And unit normal vector->Forming the minimum rotary frame；
S3 based on the firstMinimum rotation frame->First->Minimum rotation frame->And generating a motion plan of the super-redundant robot.
2. A method of motion planning according to claim 1, characterized in that: in step S1, the specific process includes the following steps:
s11, the space parameter curveDiscretizing the curve parameter t of (2), wherein the interval is +.>，/>The curve parameter t takes the value +.>；
S12, according to the curve parameter t and the intervalCalculating the arc length of the dorsal curve +.>；
S13, making the arc lengthEqual to the front +.>Length of individual connecting rod->And calculates the front +/for super redundant robot>Length of individual connecting rod->Corresponding curve parameters>；
S14, calculating curve parametersTangential vector of the place->；
S15, calculating the starting of the ridge curveUnit tangent vector at->Unit normal vector->Unit auxiliary normal vector。
3. A method of motion planning according to claim 2, characterized in that: in step S12, arc lengthThe calculation formula of (2) is as follows:
；
in the above, n refers to the number of discrete summation intervals of the arc length of the curve segment, m refers to the number of discrete curve segment sequences,the interval is indicated as such,representing that the spatial parameter curve C (t) is +.>Derivative of t>And (5) pointing to perform modular arithmetic.
4. A method of motion planning according to claim 2, characterized in that: in step S13, specifically, the method includes:
by spacing at intervalsAccumulating the arc length of the discrete curve segments for the integration interval cycles until the arc length +.>Equal to front->Length of individual connecting rod->Further determining the curve parameters satisfying the condition +.>。
5. A method of motion planning according to claim 2, characterized in that: in step S14, curve parametersTangential vector of the place->The calculation formula of (2) is as follows:
；
in the method, in the process of the application,for the spatial parameter curve C (t) versus curve parameter +.>1 st derivative of (c).
6. A method of motion planning according to claim 1, characterized in that: in step S22, the symmetry vectorThe calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,indicate->Is the starting point->Is the position vector of the end point, +.>Is a unit tangent vector +.>Dot +.>About plane->Is a symmetric vector of (a).
7. A method of motion planning according to claim 1, characterized in that: in step S23, a unit auxiliary normal vectorThe calculation formula of (2) is as follows:
；
in the above-mentioned method, the step of,is->About plane->Mirror symmetry vector, ">Is a unit tangent vector +.>And symmetry vector->Vector difference of>To form a minimum rotary frame->And a unit sub-normal vector of the gesture matrix.
8. A method of motion planning according to claim 1, characterized in that: in step S3, the specific process includes the following steps:
s31, calculate the firstMinimum rotation frame->First->Minimum rotation frame->Is the attitude difference of (2)；
S32, based on attitude difference valueCalculating joint angle of orthogonal joint of super-redundant robot>；
S33, according to joint anglesAnd generating a motion plan of the super-redundant robot.
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