CN116000940A - Constant force tracking method for realizing complex curved surface through FCPressNURBS instruction set - Google Patents
Constant force tracking method for realizing complex curved surface through FCPressNURBS instruction set Download PDFInfo
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Abstract
The invention provides a constant force tracking method for realizing a complex curved surface through an FCPressNURBS instruction set, and belongs to the technical field of robot control. The invention comprises the following steps: s10, acquiring a complex track plan of the robot by a track planning method of NURBS; s20, acquiring NURBS fitting track X based on T-type speed interpolation nurbs The method comprises the steps of carrying out a first treatment on the surface of the S30, acquiring the gesture of the robot by using a square gesture interpolation algorithm, and acquiring a robot gesture matrix { R (R) at a model value point i } i n ＝0 Conversion into corresponding quaternion representation { q } i } i n ＝0 Calculating the quaternion gesture of the corresponding discrete point to finish gesture interpolation of the robot; s40, determining the contact force between the tail end of the robot and the complex curved surface through an impedance control algorithm, correcting the motion trail of the tail end of the robot in real time by utilizing the output displacement quantity controlled by the impedance, and realizing constant force tracking contact with the complex curved surface. The invention can ensure the accuracy of the tail end track of the robot, the speed controllability and the contact during the contact operationStability of force.
Description
Technical Field
The invention belongs to the technical field of robot control, and relates to a constant force tracking method for realizing a complex curved surface through an FCPressNURBS instruction set.
Background
In the robot contact work, it is necessary to determine the surface profile of the curved surface to be contacted and sense the robot tip contact force through a multi-dimensional force sensor installed at the robot tip. For complex curved surfaces in an unknown environment, the accuracy of the fitting track influences the accuracy of track tracking when the robot contacts the work, and the constant force tracking algorithm of the robot directly influences the constant force tracking accuracy of the tail end of the robot.
At present, a constant force tracking strategy for curved surfaces is proposed in a plurality of documents, but most algorithms can only track simpler curved surfaces with constant force, and the tracking precision is low, so that the constant force tracking requirement of complex curved surfaces in the existing industrial scene can not be met; specifically, there are mainly the following problems:
1) The traditional track fitting method can only fit simpler shapes, such as straight lines, circular arcs or multi-section lines;
2) The traditional NURBS track planning method can only fit the motion track of the robot, but cannot control the motion speed of the robot;
3) When the robot contacts the operation, not only the motion track and the motion speed of the robot are required to be controlled, but also the contact force between the robot and an object is required to be controlled, in the prior art, the contact force between the tail end of the robot and the environment is unstable, and the constant force tracking is difficult to realize better.
Disclosure of Invention
The invention aims at: aiming at the problems, the invention improves the traditional single-position control or single-constant force control algorithm, provides a constant force tracking method for realizing a complex curved surface through an FCPressNURBS instruction set, fits a complex curved surface contour in a complex environment through a speed-controllable NURBS track planning algorithm, ensures constant force tracking precision and stability based on an impedance control algorithm, and further ensures the precision of a tail end track of a robot, the speed controllability and the stability of contact force during contact operation.
The technical content is as follows: a constant force tracking method for realizing complex curved surfaces through an FCPressNURBS instruction set comprises the following steps:
s10, acquiring complex track planning of the robot through a NURBS track planning method:
acquiring a space pose on a curved surface as a model value point of an FCPressNURBS instruction set, acquiring a track planning fitting curve of robot motion through the model value point, and establishing a u-s model between a fitting curve parameter u and an arc length parameter s;
s20, sampling the calculated u-S model based on a T-shaped speed interpolation algorithm model, and obtaining the arc length L to curve adjacent u i and ui+1 Performing speed interpolation to obtain NURBS fitting track X based on T-type speed interpolation nurbs； wherein ,ui and ui+1 Refers to the i and i+1th elements of the node vector;
s30, acquiring the gesture of the robot by using a square gesture interpolation algorithm, and acquiring a robot gesture matrix at a model value point
Conversion into the corresponding quaternion representation +.>
Calculating the quaternion gesture of the corresponding discrete point to finish gesture interpolation of the robot; />
S40, determining the contact force between the tail end of the robot and the complex curved surface through an impedance control algorithm, and correcting the motion track of the tail end of the robot in real time by utilizing the output displacement quantity controlled by the impedance, so that the contact force of the tail end of the robot can be kept in a set state, and constant force tracking contact with the complex curved surface is realized.
Further, the step S10 includes the following specific steps:
s1001, collecting the space pose of a complex curved surface in a plurality of groups of environments, and taking the space pose as a model value point of an FCPressNURBS instruction set, wherein a control point of a fitting track can be obtained through a model value point motion back calculation control point algorithm;
the number N of the collected model value points is more than or equal to 5, and the coordinates of the model value points are used
A representation; coordinates of control points->
A representation; all control points are obtained through a catch-up method;
s1002, acquiring a cubic B spline position track planning fitting curve meeting G2 continuity through a control point; the track planning fitting curve is represented by a k-degree B spline curve equation:
wherein ,
called k-th order B-spline basis function, k= 3,i =0, 1,2, …, n; p (P) i Represents a control point, i=0, 1,2, …, n; u= [ U ] 0 ,u 1 ,…,u n+k+1 ]Representing node vectors, u.epsilon.0, 1]；
S1003, sampling parameters such as the obtained k times of B spline curve equation c (u) and the like, wherein the sampling period is 1/n, and obtaining the discrete sample
Representing the discretized node vector, +.>
Representation->
The corresponding value of c (u);
s1004, calculating arc lengths of two parameter intervals [ a, b ] by using a Boolean formula, wherein the Boolean formula is as follows:
wherein f (x) is calculated by substituting |c' (u) | for x 0 ＝a，x 4 ＝b，
x 2 ＝x 1 +h，x 3 ＝x 2 +h，f i ＝f(x i )，i＝0,1,…,4；
Each arc length, namely two adjacent discrete points, can be obtained through a Boolean formula
Corresponding arc length
Total arc length->
Thereby the arc length parameter can be obtained>
Is that
S1005, generating a u-S model between the parameter u and the arc length parameter S by using a quintic polynomial fitting;
u＝k 0 +k 1 s+k 2 s 2 +k 3 s 3 +k 4 s 4 +k 5 s 5
wherein the method comprises the steps ofU represents the discrete in step S1003
s represents the arc length parameter +.>
By least square method
K＝(X T X) -1 X T Y
wherein ,
further, the step S20 includes the following specific steps:
s2001, adopting a T-type speed interpolation algorithm, and setting acceleration and maximum speed through the total arc length L and the total arc length
The time used by the acceleration section, the constant speed section and the deceleration section can be calculated respectively:
wherein ,v0 Representing the initial velocity, v 1 Representing the final speed; q 0 ＝s 0 ＝0，q 1 ＝s 1 ＝1；
The acceleration is represented, and T is the control period of the robot;
s2002, respectively calculating displacement amounts of an acceleration section, a constant speed section and a deceleration section by combining a speed planning algorithm, wherein the displacement calculation equations of different sections are as follows:
wherein ,Sa 、S v and Sd The displacement amounts of the acceleration, uniform velocity and deceleration sections are respectively represented.
Further, the step S30 includes the following specific steps:
s3001, by means of the determined arc length parameter S i And a discrete point u i Determining t value of a quaternion spherical linear interpolation algorithm:
s3002, calculating a multi-section smooth attitude change through a spherical linear interpolation algorithm:
Squad(q i ,s i ,s i+1 ,q i+1 ；t)＝Slerp(Slerp(q i ,q i+1 ；t),Slerp(s i ,s i+1 ；t)；2t(1-t))。
further, the step S40 includes the following specific steps:
s4001, deducing a control equation suitable for discrete points through an impedance control algorithm to obtain a robot displacement correction X based on force control c ：
Wherein M, B and K represent the mass coefficient, damping coefficient and stiffness coefficient of the impedance control, respectively;
and Xc Respectively representing acceleration, speed and displacement of the robot; t is the control period; f (F) e and Fd Representing the actual contact force and the desired contact force, respectively；
S4002, a fusion force/bit mixed control framework, and determining control modes of different dimensions through a selection matrix H;
fitting track X obtained in step S20 nurbs As the motion track of the robot, and the displacement X obtained by the impedance control algorithm c As the motion displacement correction quantity of the robot under the force control action, further obtaining the motion trail X of the robot under the constant force control robot ：
X robot ＝H·X nurbs +(1-H)·X c
Wherein the matrix is selected
h i ∈[0,1]，h i =0 denotes position control, h i =1 represents impedance control.
Compared with the prior art, the invention has the beneficial effects that:
(1) The track planning method based on NURBS can fit the profile of a more complex curved surface in the environment (such as the surface of an engine blade of an airplane, the surface of an automobile skin or the surface of other irregular objects), and the fitted curve is used as the motion track of a robot in Cartesian space, so that the precision of the tail end track of the robot during contact operation can be ensured.
(2) According to the invention, the motion speed of the robot can be controlled through a T-shaped speed interpolation algorithm on the basis of a complex curve based on NURBS track planning, so that the robot can work on the body surface according to a designated speed during contact type operation, and the controllability of the robot speed during contact operation is ensured.
(3) The invention can maintain stable contact force between the tail end of the robot and the environment through the active compliant control method.
Drawings
FIG. 1 is a flow chart of a constant force tracking method for complex curved surfaces;
FIG. 2A is a diagram of an experimental scenario of the present invention in an embodiment;
FIG. 2B shows the invention in an embodimentExplicitly fitted trajectory X nurbs And the actual motion trail of the robot based on FCPressNURBS instruction set control;
FIG. 3 is a graph showing a fitted trajectory X according to the present invention in an embodiment nurbs A speed profile of the robot tip and an actual speed profile when moving;
fig. 4 illustrates the contact force of the robot tip with a complex curved surface in the environment in an embodiment.
Detailed Description
The following detailed description of the technical solution of the present invention will be given with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the invention discloses a constant force tracking method for realizing complex curved surfaces by using an FCPressNURBS instruction set, which comprises the following steps:
s10, acquiring complex track planning of the robot through a NURBS track planning method:
and acquiring the space pose on the curved surface as a model value point of the FCPressNURBS instruction set, acquiring a track planning fitting curve of the robot motion through the model value point, and establishing a u-s model between a fitting curve parameter u and an arc length parameter s.
The step S10 comprises the following specific steps:
s1001, collecting the space pose of a complex curved surface in a plurality of groups of environments, and taking the space pose as a model value point of an FCPressNURBS instruction set, wherein a control point of a fitting track can be obtained through a model value point motion back calculation control point algorithm;
the number N of the model value points collected under the general condition is more than or equal to 5, and the coordinates of the model value points are used
A representation; coordinates of control points->
All control points can be found by the catch-up method:
wherein ,
s1002, acquiring a cubic B spline position track planning fitting curve meeting G2 continuity through a control point.
The track planning fitting curve is represented by a k-degree B spline curve equation:
wherein ,
called k times B-spline basis function (k=3 in the present invention), P i (i=0, 1,2, …, n) represents a control point; u= [ U ] 0 ,u 1 ,…,u n+k+1 ]Representing node vectors, u.epsilon.0, 1]；
The node vector is an indispensable parameter in computing NURBS curves, where C (u) and B (u) are both functions of u;
s1003, sampling parameters such as the obtained k times of B spline curve equation c (u) and the like, wherein the sampling period is 1/n, and obtaining the discrete sample
and />
Representing the discretized node vector, +.>
Representation->
The corresponding value of c (u); />
The B-spline curve equation c (u) is regarded as a function of the argument u,
represents the independent variable after the dispersion,
representing the discrete dependent variable;
s1004, calculating arc lengths of two parameter intervals [ a, b ] by using a Boolean formula:
wherein f (x) is calculated by substituting |c' (u) | for x 0 ＝a，x 4 ＝b，
x 2 ＝x 1 +h，x 3 ＝x 2 +h，f i ＝f(x i )，i＝0,1,…,4；
All adjacent two discrete points can be obtained through a Boolean formula
Corresponding arc length ∈>
Thereby finding the total arc length +.>
Thereby the arc length parameter can be obtained>
Is that
S1005, generating a u-S model between the parameter u and the arc length parameter S by using a quintic polynomial fitting;
u＝k 0 +k 1 s+k 2 s 2 +k 3 s 3 +k 4 s 4 +k 5 s 5
wherein u represents the discretized value in step S1003
s represents the arc length parameter +.>
By least square method
K＝(X T X) -1 X T Y
wherein K＝[k0 ,k 1 ,k 2 ,k 3 ,k 4 ,k 5 ] T ,Y＝[u 0 ,u 1 ,…,u n ] T ,
S20, sampling the calculated u-S model based on a T-shaped speed interpolation algorithm model, and obtaining the arc length L to curve adjacent u i and ui+1 Performing speed interpolation to obtain NURBS fitting track X based on T-type speed interpolation nurbs, wherein ui and ui+1 Refers to the i and i+1 elements of the node vector.
The step S20 comprises the following specific steps:
s2001, adopting a T-type speed interpolation algorithm to pass through a total arcLength L and acceleration and maximum speed set based on total arc length
The time used by the acceleration section, the constant speed section and the deceleration section can be calculated respectively:
wherein ,v0 Representing the initial velocity, v 1 Representing the final speed; q 0 ＝s 0 ＝0，q 1 ＝s 1 ＝1；
The acceleration is represented, and T is the control period of the robot;
s2002, respectively calculating displacement amounts of an acceleration section, a constant speed section and a deceleration section by combining a speed planning algorithm, wherein the displacement calculation equations of different sections are as follows:
wherein ,Sa 、S v and Sd Respectively representing the displacement amounts of the acceleration section, the constant speed section and the deceleration section;
through S2001 and S2002, NURBS planning track based on T-shaped speed planning, namely fitting track X, can be finally obtained nurbs 。
Fig. 2A is an actual scene diagram when experiments were performed in the present embodiment. The end effector of fig. 2A is a flexible roller that deforms under force, resulting in a large deviation between the actual motion curve and the fitted curve of fig. 2B.
Fig. 2B is a comparison of a fitted track and an actual motion track, where the fitted track in fig. 2B is a track fitted by collecting a surface profile of an object, and the actual track is a track of a robot end recorded in real time when the robot moves with a certain contact force between the robot and the surface of the object. The deviation between the fitted trajectory and the actual trajectory is mainly due to the deformation of the robotic end effector under stress. By comparing the profile of the fitted track and the profile of the actual track, the superposition of the two tracks can be found to be very high, which also indicates that the track fitted by the NURBS track planning algorithm with controllable speed is relatively fit with the actual track. Fig. 3 is a speed profile of the fitted trajectory and a speed profile of the robot when actually moving. From the figure, the motion speeds of the robot in different periods can be accurately controlled through a NURBS track planning algorithm with controllable speed.
S30, acquiring the gesture of the robot by using a square gesture interpolation algorithm; robot gesture matrix at model value point to be obtained
Conversion into the corresponding quaternion representation +.>
And then calculating the quaternion gesture of the corresponding discrete point to complete gesture interpolation of the robot.
The step S30 comprises the following specific steps:
s3001, by means of the determined arc length parameter S i And a discrete point u i Determining t value of a quaternion spherical linear interpolation algorithm:
s3002, calculating a multi-section smooth attitude change through a spherical linear interpolation algorithm:
Squad(q i ,s i ,s i+1 ,q i+1 ；t)＝Slerp(Slerp(q i ,q i+1 ；t),Slerp(s i ,s i+1 ；t)；2t(1-t))。
s40, determining the contact force between the tail end of the robot and the complex curved surface through an impedance control algorithm, and correcting the motion track of the tail end of the robot in real time by utilizing the output displacement quantity of the impedance control, wherein the method is an active compliance control method (the admittance control in the active compliance control is used in the invention), so that the contact force of the tail end of the robot can be kept in a set state, and constant force tracking contact with the complex curved surface is realized;
the step S40 comprises the following specific steps:
s4001, deducing a control equation suitable for discrete points through an impedance control algorithm to obtain a robot displacement correction X based on force control c ：
Wherein M, B and K represent the mass coefficient, damping coefficient and stiffness coefficient of the impedance control, respectively;
and Xc Respectively representing acceleration, speed and displacement of the robot; t is the control period; f (F) e and Fd Representing the actual contact force and the desired contact force, respectively;
s4002, fusing a force/bit mixed control framework, and determining control modes (position control or force control) of different dimensions through a selection matrix H.
Fitting track X obtained in step S20 nurbs As a motion trajectory of the robot, trajectory X nurbs The method is obtained by fitting based on NURBS algorithm, and has the characteristic of controllable speed; and the displacement X obtained by the impedance control algorithm c As the motion displacement correction quantity of the robot under the force control action, the actual motion trail X of the robot under the constant force control is obtained robot ：
X robot ＝H·X nurbs +(1-H)·X c
Wherein the matrix is selected
h i ∈[0,1]，h i =0 denotes position control, h i =1 represents impedance control;
X robot is a motion track X which is sent to the robot under the control of a constant force based on the FCPressNURBS instruction set control robot Which is substantially similar to the actual motion trajectory in fig. 2, if the error of the robot is ignored, it can be considered as X robot The actual motion profile in fig. 2.
The desired force of FIG. 4 is artificially set, fd in the admittance control equation; the actual stress in fig. 4 is the tip stress acquired in real time by the tip six-dimensional force sensor as the robot traverses objects in the environment based on the FCPressNURBS instruction set. The actual stress of the tail end of the robot basically floats in the upper and lower ranges of fd, and the floating range is in the range of +0.3 to-0.3, which shows that the constant force tracking algorithm based on the FCPressNURBS instruction set control has higher constant force tracking precision on complex curved surfaces in the environment.
The invention fits the complex curved surface contour in the complex environment through the NURBS track planning algorithm with controllable speed, ensures the constant force tracking precision and stability based on the impedance control algorithm, further ensures the precision of the tail end track of the robot, the speed controllability and the stability of the contact force during the contact operation, and is a speed-controllable constant force tracking method for complex curved surfaces.
As described above, although the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limiting the invention itself. Various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (5)
1. A constant force tracking method for realizing complex curved surfaces through an FCPressNURBS instruction set is characterized by comprising the following steps:
s10, acquiring complex track planning of the robot through a NURBS track planning method:
acquiring a space pose on a curved surface as a model value point of an FCPressNURBS instruction set, acquiring a track planning fitting curve of robot motion through the model value point, and establishing a u-s model between a fitting curve parameter u and an arc length parameter s;
s20, sampling the calculated u-S model based on a T-shaped speed interpolation algorithm model, and obtaining the arc length L to curve adjacent u i and ui+1 Performing speed interpolation to obtain NURBS fitting track X based on T-type speed interpolation nurbs； wherein ,ui and ui+1 Refers to the i and i+1th elements of the node vector;
s30, acquiring the gesture of the robot by using a square gesture interpolation algorithm, and acquiring a robot gesture matrix at a model value point
Conversion into the corresponding quaternion representation +.>
Calculating the quaternion gesture of the corresponding discrete point to finish gesture interpolation of the robot;
s40, determining the contact force between the tail end of the robot and the complex curved surface through an impedance control algorithm, and correcting the motion track of the tail end of the robot in real time by utilizing the output displacement quantity controlled by the impedance, so that the contact force of the tail end of the robot can be kept in a set state, and constant force tracking contact with the complex curved surface is realized.
2. The method for realizing constant force tracking of complex curved surfaces by using an FCPressNURBS instruction set according to claim 1, wherein the step S10 comprises the following specific steps:
s1001, collecting the space pose of a complex curved surface in a plurality of groups of environments, and taking the space pose as a model value point of an FCPressNURBS instruction set, wherein a control point of a fitting track can be obtained through a model value point motion back calculation control point algorithm;
the number N of the collected model value points is more than or equal to 5, and the coordinates of the model value points are used
A representation; coordinates of control points->
A representation; all control points are obtained through a catch-up method;
s1002, acquiring a cubic B spline position track planning fitting curve meeting G2 continuity through a control point; the track planning fitting curve is represented by a k-degree B spline curve equation:
wherein ,
called k-th order B-spline basis function, k= 3,i =0, 1,2, …, n; p (P) i Represents a control point, i=0, 1,2, …, n; u= [ U ] 0 ，u 1 ，…，u n+k+1 ]Representing node vectors, u.epsilon.0, 1]；
S1003, sampling parameters such as the obtained k times of B spline curve equation c (u) and the like, wherein the sampling period is 1/n, and obtaining the discrete sample
and />
Representing the discretized node vector, +.>
Representation->
The corresponding value of c (u);
s1004, calculating arc lengths of two parameter intervals [ a, b ] by using a Boolean formula, wherein the Boolean formula is as follows:
wherein f (x) is calculated by substituting |c' (u) | for x 0 ＝a，x 4 ＝b，
x 2 ＝x 1 +h，x 3 ＝x 2 +h，f i ＝f(x i )，i＝0，1，…，4；
Each arc length, namely two adjacent discrete points, can be obtained through a Boolean formula
Corresponding arc length ∈>
Total arc length->
Thereby the arc length parameter can be obtained>
Is that
S1005, generating a u-S model between the parameter u and the arc length parameter S by using a quintic polynomial fitting;
u＝k 0 +k 1 s+k 2 s 2 +k 3 s 3 +k 4 s 4 +k 5 s 5
wherein u represents the discretized value in step S1003
s represents the arc length parameter +.>
By least square method
K＝(X T X) -1 X T Y
Wherein k= [ K ] 0 ,k 1 ,k 2 ,k 3 ,k 4 ,k 5 ] T ,Y＝[u 0 ,u 1 ,…,u n ] T ,
3. The method for realizing constant force tracking of complex curved surfaces by using the FCPressNURBS instruction set according to claim 2, wherein the step S20 comprises the following specific steps:
s2001, adopting a T-type speed interpolation algorithm, and setting acceleration and maximum speed through the total arc length L and the total arc length
The time used by the acceleration section, the constant speed section and the deceleration section can be calculated respectively:
wherein ,v0 Representing the initial velocity, v 1 Representing the final speed; q 0 ＝s 0 ＝0，q 1 ＝s 1 ＝1；
The acceleration is represented, and T is the control period of the robot;
s2002, respectively calculating displacement amounts of an acceleration section, a constant speed section and a deceleration section by combining a speed planning algorithm, wherein the displacement calculation equations of different sections are as follows:
wherein ,Sa 、S v and Sd The displacement amounts of the acceleration, uniform velocity and deceleration sections are respectively represented.
4. A method for implementing constant force tracking of complex curved surfaces by FCPressNURBS instruction set according to claim 3, wherein said S30 comprises the following specific steps:
s3001, by means of the determined arc length parameter S i And a discrete point u i Determining t value of a quaternion spherical linear interpolation algorithm:
s3002, calculating a multi-section smooth attitude change through a spherical linear interpolation algorithm:
Squad(q i ，s i ，s i+1 ，q i+1 ；t)＝Slerp(Slerp(q i ，q i+1 ；t)，Slerp(s i ，s i+1 ；t)；2t(1-t))。
5. the method for realizing constant force tracking of complex curved surfaces by using the FCPressNURBS instruction set according to claim 4, wherein the step S40 comprises the following specific steps:
s4001, deducing a control equation suitable for discrete points through an impedance control algorithm to obtain a robot displacement correction X based on force control c ：
Wherein M, B and K represent the mass coefficient, damping coefficient and stiffness coefficient of the impedance control, respectively;
and Xc Respectively representing acceleration, speed and displacement of the robot; t is the control period; f (F) e and Fd Representing the actual contact force and the desired contact force, respectively;
s4002, a fusion force/bit mixed control framework, and determining control modes of different dimensions through a selection matrix H;
fitting track X obtained in step S20 nurbs As the motion track of the robot, and the displacement X obtained by the impedance control algorithm c As the motion displacement correction quantity of the robot under the force control action, further obtaining the motion trail X of the robot under the constant force control robot ：
X robot ＝H·X nurbs +(1-H)·X c
Wherein the matrix is selected
h i ∈[0，1]，h i =0 denotes position control, h i =1 represents impedance control. />
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