CN113485370A - Parallel robot dynamic pick-and-place trajectory planning method and system - Google Patents

Parallel robot dynamic pick-and-place trajectory planning method and system Download PDF

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CN113485370A
CN113485370A CN202110918087.0A CN202110918087A CN113485370A CN 113485370 A CN113485370 A CN 113485370A CN 202110918087 A CN202110918087 A CN 202110918087A CN 113485370 A CN113485370 A CN 113485370A
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curve
pick
track
polynomial
place
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苏婷婷
梁旭
曾翔
何广平
郜一凡
赵全亮
赵磊
黄灿
张萌颖
狄杰建
袁俊杰
章杰
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North China University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle

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Abstract

The invention relates to a parallel robot dynamic pick-and-place track planning method and a system. The invention takes the shortest obstacle avoidance distance as the geometric constraint for solving the PH curve, realizes the obstacle avoidance function under the basic requirement of reducing the impact oscillation as much as possible, and only needs to calculate half of the path by utilizing the symmetry of the door-shaped pick-and-place track, thereby improving the calculation efficiency of obstacle avoidance track planning.

Description

Parallel robot dynamic pick-and-place trajectory planning method and system
Technical Field
The invention relates to the technical field of robot path planning, in particular to a parallel robot dynamic pick-and-place trajectory planning method and system.
Background
More and more work in the modern times replaces traditional manual operation through a robot, so that the industrial efficiency is improved, and particularly in scenes with high repetitive work ratio, such as cargo sorting, stacking and stacking, the efficiency advantage of the robot is more obvious. In various robot types, the Delta parallel robot is widely applied due to the advantages of simple structure, easy analysis and positive solution calculation and the like.
When the Delta robot is used for grabbing and carrying, the Delta robot generally moves according to a door-shaped path, and in an actual working scene, the Delta robot often has obstacles in the moving path or the possibility of collision with other objects, but the existing track planning method for avoiding obstacles of the Delta parallel robot often emphasizes the geometric problem and has poor calculation real-time performance.
Disclosure of Invention
The invention aims to provide a method and a system for planning a dynamic pick-and-place track of a parallel robot so as to improve the calculation efficiency of obstacle avoidance track planning.
In order to achieve the purpose, the invention provides the following scheme:
a method for planning a dynamic pick-and-place trajectory of a parallel robot, the method comprising:
solving the PH curve by taking the shortest obstacle avoidance distance as a geometric constraint to obtain a PH curve polynomial equation and a first intersection point and a second intersection point of the PH curve and the door-shaped pick-and-place track;
replacing a right-angle transition section between the first intersection point and the second intersection point in the door-shaped pick-and-place track with a PH curve between the first intersection point and the second intersection point;
taking the central axis of the portal pick-and-place track before replacement as a symmetry axis, replacing the other right-angle transition section with a symmetrical PH curve of the PH curve between the first intersection point and the second intersection point, and obtaining the portal pick-and-place track after replacement;
based on the symmetry of the replaced door-shaped pick-and-place track, the parallel robot moves according to the replaced door-shaped pick-and-place track according to the movement rule.
Optionally, the method for solving the PH curve by using the shortest obstacle avoidance distance as the geometric constraint to obtain a PH curve polynomial equation specifically includes:
establishing a relation equation between the coefficient of a PH curve polynomial equation and the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
according to the shortest obstacle avoidance distance, determining the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve by using a formula d which is 0.17064 m; wherein d is the shortest obstacle avoidance distance, and m is the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
and substituting the right-angle side length of the right-angle transition section in the portal pick-and-place track to be replaced by the PH curve into the relation equation to obtain the coefficient of the PH curve polynomial equation.
Optionally, the relation equation between the coefficient of the constructed PH curve polynomial equation and the right-angle side length of the right-angle transition section in the portal pick-and-place track to be replaced by the PH curve is
Figure BDA0003206400440000021
Wherein u is0、u2And v2Respectively, a first coefficient, a second coefficient and a third coefficient of a PH curve polynomial equation.
Optionally, the PH curve polynomial equation is
Figure BDA0003206400440000022
Wherein, x (gamma) and y (gamma) are respectively the abscissa and the ordinate of the PH curve, and gamma is the parameter of the PH curve.
Optionally, based on the symmetry of the replaced door-shaped pick-and-place track, the parallel robot moves according to the replaced door-shaped pick-and-place track according to the motion rule, and the method specifically includes the following steps:
according to a first polynomial motion rule, moving according to a first straight line track from a picking operation point of the parallel robot to a first intersection point;
according to the motion rule of the pH curve parameter dependence, the motion is carried out according to the pH curve track between the first intersection point and the second intersection point;
according to a second polynomial motion law, moving according to a second straight line track from a second intersection point to a symmetrical demarcation point;
and according to the symmetry of the replaced door-shaped pick-and-place track, moving according to the door-shaped pick-and-place track from the symmetrical dividing point to the parallel robot placing operation point according to the second polynomial motion law, the motion law depending on the PH curve parameters and the first polynomial motion law.
Optionally, the moving is performed according to a first polynomial law according to a first linear trajectory from a picking operation point of the parallel robot to the first intersection point, and the method further includes:
obtaining a first polynomial motion law expression as v1(Φ1)＝v10+v11Φ1+v12Φ1 2+v13Φ1 3+v14Φ1 4+v15Φ1 5(ii) a Wherein v is1(Φ1) To follow a first linear trajectory of speed, phi1Is a first variable, phi1＝t1/T1，Φ1∈[0,1]，T1For parallel robot slave pick-upTotal time required from operating point to first intersection, t1For real time, v10Is a first constant term, v11、v12、v13、v14And v15Respectively are coefficients of a polynomial in the first polynomial law of motion;
according to v1(0)＝0,v1(1)＝VB,v′1(0)＝0,v′1(1)＝0,v″1(0)＝0,v″1(1) Solving the first polynomial motion law expression under the boundary condition of 0 to obtain a polynomial motion law of a first linear track as v1(Φ1)＝10VBΦ1 3-15VBΦ1 4+6VBΦ1 5(ii) a Wherein, VBIs the speed, v, at which the parallel robot moves to the first intersection point1(0)、v′1(0)、v″1(0) Velocity, acceleration and acceleration rate of change, v, respectively, of the parallel robot at the pick-up operation point1(1)、v′1(1)、v″1(1) Respectively the speed, acceleration and acceleration rate of the parallel robot at the first intersection point.
Optionally, the moving according to the PH curve trajectory between the first intersection point and the second intersection point according to the PH curve parameter-dependent movement law further includes:
uniformly dividing the PH curve track into a plurality of time periods, and determining a motion rule expression v which depends on PH curve parameters when the motion is carried out according to the PH curve track2(γi)＝VB+16(VN-VB)γi 2+32(VB-VN)γi 3+16(VN-VB)γi 4(ii) a Wherein v is2(γi) Speed of movement in i-th time period, γiIs the value of the PH curve parameter, V, of the ith time periodBIs the speed, V, at which the parallel robot moves to the first intersection pointNThe minimum speed of the parallel robot moving according to the PH curve track;
motion law expression combined with PH curve parameter dependence and PH curveThe relation between the parameters and time in the line is obtained as the equation for solving the parameters
Figure BDA0003206400440000041
Wherein, F (gamma)i) Solving functions for the parameters, zeta, beta, delta,
Figure BDA0003206400440000042
Eta is respectively a third polynomial, a fourth polynomial, a fifth polynomial, a sixth polynomial and a seventh polynomial, m is the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve, and delta t is a time interval;
according to the formula
Figure BDA0003206400440000043
Determining the value of the parameter of each time period by using a Newton iteration method; wherein the content of the first and second substances,
Figure BDA0003206400440000044
as the value of the initial parameter(s),
Figure BDA0003206400440000045
values of the parameter, γ, for r-1 and r iterations, respectively, at the ith time periodi-1Is the value of the parameter at the i-1 th time period, v2(γi-1) The speed of motion along the PH curve path in the i-th time period, σ (γ)i-1) For the arc length of the PH curve versus the parameter gammai-1The derivative of (a) of (b),
Figure BDA0003206400440000046
the function is solved for the parameters at r-1 iterations,
Figure BDA0003206400440000047
is composed of
Figure BDA0003206400440000048
A derivative with respect to time;
and substituting the value of the parameter of each time period into a motion rule expression dependent on the PH curve parameter to obtain the motion rule dependent on the PH curve parameter.
Optionally, the moving is performed according to a second linear trajectory from the second intersection point to the symmetric dividing point according to a second polynomial law of motion, and the method further includes:
determining a second polynomial motion law of a second straight line track as v3(Φ3)＝v30+v31Φ3+v32Φ3 2+v33Φ3 3(ii) a Wherein v is3(Φ3) Velocity of the second linear track, phi3Is a second variable, [ phi ]3＝t3/T3，Φ3∈[0,1]，T3Total time, t, required for the parallel robots to pass from the second point of intersection to the symmetrical demarcation point3Real time, v, for movement according to a second rectilinear trajectory30Is a third constant term, v31、v32、v33Respectively are coefficients of a polynomial in the second polynomial law of motion;
according to v3(0)＝VB,v3(1)＝Vmax,v3'(0)＝0,v3'(1)＝0,s3(0) Solving a second polynomial motion law of the second linear track under the boundary condition of 0 to obtain a polynomial motion law of the second linear track as v3(Φ3)＝VB+3(Vmax-VB)Φ3 2+2(VB-Vmax)Φ3 3(ii) a Wherein, VBIs the speed, V, at which the parallel robot moves to the first intersection pointmaxIs the maximum speed, v, of movement according to a second rectilinear trajectory3(0)、v3'(0)、s3(0) Velocity, acceleration and displacement, v, of the parallel robot at the second intersection point, respectively3(1)、v3' 1 is the speed and acceleration of the parallel robot at the symmetrical dividing point respectively.
A parallel robot dynamic pick-and-place trajectory planning system, the system comprising:
the PH curve solving module is used for solving the PH curve by taking the shortest obstacle avoidance distance as a geometric constraint to obtain a PH curve polynomial equation and a first intersection point and a second intersection point of the PH curve and the door-shaped pick-and-place track;
the replacing module is used for replacing a PH curve between the first intersection point and the second intersection point with a right-angle transition section between the first intersection point and the second intersection point in the door-shaped pick-and-place track;
the replaced door-shaped pick-and-place track obtaining module is used for replacing the other right-angle transition section with a symmetrical PH curve of the PH curve between the first intersection point and the second intersection point by taking the central axis of the door-shaped pick-and-place track before replacement as a symmetrical axis to obtain the replaced door-shaped pick-and-place track;
and the execution module is used for enabling the parallel robot to move according to the replaced door-shaped pick-and-place track according to the movement rule based on the symmetry of the replaced door-shaped pick-and-place track.
Optionally, the PH curve solving module specifically includes:
the relation equation constructing submodule is used for constructing a relation equation between the coefficient of a PH curve polynomial equation and the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
the right-angle side length determining submodule is used for determining the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve according to the shortest obstacle avoidance distance by using a formula d which is 0.17064 m; wherein d is the shortest obstacle avoidance distance, and m is the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
and the coefficient obtaining submodule is used for substituting the right-angle side length of the right-angle transition section in the portal pick-and-place track to be replaced by the PH curve into the relational equation to obtain the coefficient of the PH curve polynomial equation.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a parallel robot dynamic pick-and-place track planning method and a system. The invention takes the shortest obstacle avoidance distance as the geometric constraint for solving the PH curve, realizes the obstacle avoidance function under the basic requirement of reducing the impact oscillation as much as possible, and only needs to calculate half of the path by utilizing the symmetry of the door-shaped pick-and-place track, thereby improving the calculation efficiency of obstacle avoidance track planning.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a flowchart of a method for planning a dynamic pick-and-place trajectory of a parallel robot according to an embodiment of the present invention;
FIG. 2 is a geometric path diagram of a pick-and-place operation according to a second embodiment of the present invention;
fig. 3 is a PH graph of the PPO path provided in the second embodiment of the present invention;
fig. 4 is a schematic diagram of coordinate point calculation according to a second embodiment of the present invention;
fig. 5 is a schematic diagram of a Delta parallel robot according to a second embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for planning a dynamic pick-and-place track of a parallel robot so as to improve the calculation efficiency of obstacle avoidance track planning.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example one
The invention provides a parallel robot dynamic pick-and-place trajectory planning method, as shown in figure 1, the method comprises the following steps:
step 101, solving a PH curve by taking the shortest obstacle avoidance distance as a geometric constraint to obtain a PH curve polynomial equation and a first intersection point and a second intersection point of the PH curve and the door-shaped pick-and-place track;
102, replacing a right-angle transition section between a first intersection point and a second intersection point in the door-shaped pick-and-place track with a PH curve between the first intersection point and the second intersection point;
103, taking the central axis of the portal pick-and-place track before replacement as a symmetry axis, replacing the other right-angle transition section with a symmetrical PH curve of the PH curve between the first intersection point and the second intersection point, and obtaining the portal pick-and-place track after replacement;
and step 104, based on the symmetry of the replaced door-shaped pick-and-place track, the parallel robot moves according to the replaced door-shaped pick-and-place track according to the movement rule.
The specific implementation process is as follows:
step 101, solving the PH curve by using the shortest obstacle avoidance distance as a geometric constraint to obtain a PH curve polynomial equation, which specifically includes:
establishing a relation equation between the coefficient of a PH curve polynomial equation and the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
according to the shortest obstacle avoidance distance, determining the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve by using a formula d which is 0.17064 m; wherein d is the shortest obstacle avoidance distance, and m is the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
and substituting the right-angle side length of the right-angle transition section in the portal pick-and-place track to be replaced by the PH curve into the relational equation to obtain the coefficient of the PH curve polynomial equation.
In the portal pick-and-place track before replacement, the lengths of the rectangular sides are known, so that the equation of the straight line of the rectangular sides in the rectangular coordinate system can be determined. Therefore, the intersection point of the PH curve polynomial equation and the equation of the right-angle side of the portal pick-and-place track before replacement is solved in the same rectangular coordinate system, and the intersection point of the two right-angle sides of one right angle in the portal pick-and-place track before replacement and the PH curve can be obtained.
Wherein the relation equation of the coefficient of the constructed PH curve polynomial equation and the right-angle side length of the right-angle transition section in the portal pick-and-place track to be replaced by the PH curve is
Figure BDA0003206400440000081
Wherein u is0、u2And v2Respectively, a first coefficient, a second coefficient and a third coefficient of a PH curve polynomial equation.
The pH curve polynomial equation is
Figure BDA0003206400440000082
Wherein, x (gamma) and y (gamma) are respectively the abscissa and the ordinate of the PH curve, and gamma is the parameter of the PH curve.
At step 102, the right angle is replaced with the PH curve, so that the right angle transition is replaced with the PH curve transition.
And 103, directly utilizing a PH curve replaced by a right angle and replacing another right angle by a symmetrical PH curve based on the symmetry principle because the pick-and-place trajectory of the door shape before replacement is symmetrical and has two right angles, so that the pick-and-place trajectory of the door shape after replacement is still in a symmetrical structure.
Step 104, based on the symmetry of the replaced door-shaped pick-and-place track, the parallel robot moves according to the replaced door-shaped pick-and-place track according to the motion rule, and the method specifically comprises the following steps:
according to a first polynomial motion rule, moving according to a first straight line track from a picking operation point of the parallel robot to a first intersection point;
according to the motion rule of the pH curve parameter dependence, the motion is carried out according to the pH curve track between the first intersection point and the second intersection point;
according to a second polynomial motion law, moving according to a second straight line track from a second intersection point to a symmetrical demarcation point;
and according to the symmetry of the replaced door-shaped pick-and-place track, moving according to the door-shaped pick-and-place track from the symmetrical dividing point to the parallel robot placing operation point according to the second polynomial motion law, the motion law depending on the PH curve parameters and the first polynomial motion law.
The step of determining the first polynomial law of motion is:
obtaining a first polynomial motion law expression as v1(Φ1)＝v10+v11Φ1+v12Φ1 2+v13Φ1 3+v14Φ1 4+v15Φ1 5(ii) a Wherein v is1(Φ1) To follow a first linear trajectory of speed, phi1Is a first variable, phi1＝t1/T1，Φ1∈[0,1]，T1Total time, t, required for the parallel robot to reach the first intersection from the pick-up operation point1For real time, v10Is a first constant term, v11、v12、v13、v14And v15Respectively are coefficients of a polynomial in the first polynomial law of motion;
according to v1(0)＝0,v1(1)＝VB,v′1(0)＝0,v′1(1)＝0,v″1(0)＝0,v″1(1) Solving the first polynomial motion law expression under the boundary condition of 0 to obtain a polynomial motion law of a first linear track as v1(Φ1)＝10VBΦ1 3-15VBΦ1 4+6VBΦ1 5(ii) a Wherein, VBIs the speed, v, at which the parallel robot moves to the first intersection point1(0)、v′1(0)、v″1(0) Velocity, acceleration and acceleration rate of change, v, respectively, of the parallel robot at the pick-up operation point1(1)、v′1(1)、v″1(1) Respectively the speed, acceleration and acceleration rate of the parallel robot at the first intersection point.
The steps for determining the motion rule depending on the PH curve parameter are as follows:
uniformly dividing the PH curve track into a plurality of time periods, and determining a motion rule expression v which depends on PH curve parameters when the motion is carried out according to the PH curve track2(γi)＝VB+16(VN-VB)γi 2+32(VB-VN)γi 3+16(VN-VB)γi 4(ii) a Wherein v is2(γi) Speed of movement in i-th time period, γiIs the value of the PH curve parameter, V, of the ith time periodBIs the speed, V, at which the parallel robot moves to the first intersection pointNThe minimum speed of the parallel robot moving according to the PH curve track;
combining a motion rule expression dependent on the PH curve parameters and a relational expression of the parameters and time in the PH curve to obtain a parameter solving equation of
Figure BDA0003206400440000091
Wherein, F (gamma)i) Solving functions for the parameters, zeta, beta, delta,
Figure BDA0003206400440000101
Eta is respectively a third polynomial, a fourth polynomial, a fifth polynomial, a sixth polynomial and a seventh polynomial, m is the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve, and delta t is a time interval;
according to the formula
Figure BDA0003206400440000102
Determining the value of the parameter of each time period by using a Newton iteration method; wherein the content of the first and second substances,
Figure BDA0003206400440000103
as the value of the initial parameter(s),
Figure BDA0003206400440000104
values of the parameter, γ, for r-1 and r iterations, respectively, at the ith time periodi-1Is the value of the parameter at the i-1 th time period, v2(γi-1) The speed of motion along the PH curve path in the i-th time period, σ (γ)i-1) For the arc length of the PH curve versus the parameter gammai-1The derivative of (a) of (b),
Figure BDA0003206400440000105
the function is solved for the parameters at r-1 iterations,
Figure BDA0003206400440000106
is composed of
Figure BDA0003206400440000107
A derivative with respect to time;
and substituting the value of the parameter of each time period into a motion rule expression dependent on the PH curve parameter to obtain the motion rule dependent on the PH curve parameter.
The step of determining the second polynomial law of motion is:
determining a second polynomial motion law of a second straight line track as v3(Φ3)＝v30+v31Φ3+v32Φ3 2+v33Φ3 3(ii) a Wherein v is3(Φ3) Velocity of the second linear track, phi3Is a second variable, [ phi ]3＝t3/T3，Φ3∈[0,1]，T3Total time, t, required for the parallel robots to pass from the second point of intersection to the symmetrical demarcation point3Real time, v, for movement according to a second rectilinear trajectory30Is a third constant term, v31、v32、v33Respectively are coefficients of a polynomial in the second polynomial law of motion;
according to v3(0)＝VB,v3(1)＝Vmax,v3'(0)＝0,v3'(1)＝0,s3(0) Solving a second polynomial motion law of the second linear track under the boundary condition of 0 to obtain a polynomial motion law of the second linear track as v3(Φ3)＝VB+3(Vmax-VB)Φ3 2+2(VB-Vmax)Φ3 3(ii) a Wherein, VBIs the speed, V, at which the parallel robot moves to the first intersection pointmaxIs the maximum speed, v, of movement according to a second rectilinear trajectory3(0)、v3'(0)、s3(0) Velocity, acceleration and displacement, v, of the parallel robot at the second intersection point, respectively3(1)、v3' 1 is the speed and acceleration of the parallel robot at the symmetrical dividing point respectively.
The invention discloses a novel track planning method of a pick-and-place Delta parallel robot with constraint, which realizes an obstacle avoidance function under the basic requirement of reducing impact oscillation as much as possible, and improves the calculation efficiency, reduces the calculation time and improves the real-time performance of a system compared with the prior method.
Example two
The trajectory planning method of the present invention is further described in detail with reference to fig. 2-5.
Interpretation of terms
pH curve: the Pythagorean-Hodograph curve is a polynomial curve with parameter speed and can be used for solving the problem of calculating the arc length and the equidistant line of the curve.
PPO path: i.e., pick-and-place operation path, refers to the path that the robot travels while performing the set of pick-and-place actions.
Delta robot: the robot structure is shown in fig. 5, and comprises a fixed platform, a movable platform, a driving rod and a driven rod, wherein three branched chains are symmetrically distributed.
The basic idea of the planning method for the dynamic picking track of the parallel robot is as follows:
1. constructing a basic pick-up action door-shaped path;
2. calculating a PH curve under the condition of meeting geometric constraint;
3. different motion laws are applied to plan the track in different stages, namely a polynomial motion law and a motion law depending on PH curve parameters, so as to obtain the smoothing performance in a Cartesian space and a joint space.
The method comprises the following specific steps:
step 1: in order to realize the pick-and-place operation of the parallel robot in a complex environment with constraints, the Delta robot is subjected to the planning of a pick-and-place operation track with a door-shaped track, wherein the deviation of a smooth curve (such as a BC arc of FIG. 2) of the pick-and-place operation track from a right-angle vertex (such as a BHC right angle of FIG. 2) does not exceed a specified geometric constraint d, namely a parameter d in FIG. 2 represents the maximum deviation of a right angle and a PH curve in a PPO path and is called as a specified geometric constraint, d is generally known in the practical situation, and d can be understood as the diameter of an obstacle.
Step 2: the gate-shaped trajectory described in step 1 is shown in fig. 2, and the Delta robot first grasps the object at point a and reaches the target point G along the sequence ABCDEFG. Where AB, CD, DE, FG segments are straight lines, BC and EF are quintic PH curves. H. The point I is the vertex of the door track under the condition of no transition, and in order to avoid obstacles and avoid oscillation, a curve BC is taken from the point B to the point C without taking a straight path of BH and HC. The length of each straight line is represented by AG | ═ w, | HC | ═ EI |, k, | BH | ═ FI |, m, | AB | ═ GF |, j, | AH | ═ GI |, h.
In a typical pick-and-place operation, the values of | AG | and | AH | in the track path, i.e., the values of w and h, are generally known.
And step 3: this step will determine the relationship of d to m and thus the PH curve. The curve of the transition is shown in figure 3.
The arc segments BC and EF in the step 1 adopt a fifth PH curve, and the PH curve formula is as follows:
Figure BDA0003206400440000121
equation (1) expands as:
Figure BDA0003206400440000122
wherein, γ is a parameter of the curve, and since the present invention adopts 5 PH curves to form the transition section of the path, n is 5; pi＝(xi,yi) The control points of the curve are indicated, i is 0, …, 5.
The X, Y coordinates of the curve can be calculated according to equation (1), expressed as γ:
Figure BDA0003206400440000123
u is known from the definition of PH curve0、u2、v2All are polynomial, and are specifically as follows:
Figure BDA0003206400440000124
according to the calculation, when the distance between the right-angle vertex H and the curve BC is the largest in the portal-shaped locus as shown in fig. 3, the point on the curve is taken as N, and γ is 0.5. On the PPO path, to simplify the calculation and meet the real-time requirement, this patent will assume that m is k, so equation 3 can be:
Figure BDA0003206400440000131
as can be seen from the equation (4),
Figure BDA0003206400440000132
next, d is calculated, and the calculated N point coordinates can be expressed as:
Figure BDA0003206400440000133
according to fig. 4, the x-coordinate value of the H point is a sum of the Y-coordinate value of the N point and the Y-coordinate value of the N point, and the x-coordinate value of the H point is 0 because the H point is on the Y axis, that is:
Figure BDA0003206400440000134
the geometric constraint d described in step 1 can be determined from the coordinates of the H and N points, i.e.
Figure BDA0003206400440000135
In order for the pick-and-place operation to satisfy the geometric constraint d described in step 1, as long as m in the pick-and-place operation trajectory is designed to satisfy m ═ d/0.17064, the requirement that the deviation of the smooth curve (e.g., BC arc of fig. 2) of the pick-and-place operation trajectory from the right angle vertex (e.g., BHC right angle of fig. 2) does not exceed the specified geometric constraint d is satisfied, and the PH curve is determined.
And 4, step 4: in the AB section in the pick-and-place operation in the step 1, the motion rule of the robot end effector is adopted
v1(Φ)＝v10+v11Φ+v12Φ2+v13Φ3+v14Φ4+v15Φ5 (8)
Wherein v is1Representing the velocity, v, of the end effector in the segment AB10To v15Is a coefficient, phi is defined as phi ═ t1/T1，Φ∈[0,1]，T1Expressed as the total time required for the end effector to move from point A to point B, t1Expressed as real time; simultaneously with VBRepresenting the velocity at which the end effector moves to point B. Next, the respective coefficients are calculated based on the initial conditions. From the boundary conditions, it can be seen that at the initial time, the velocity, acceleration, and acceleration rate of change of the end effector are all 0, and at T1At the moment, the velocity becomes VBAcceleration and acceleration rate of change are also 0, i.e. v1(0)＝0,v1(1)＝VB,v′1(0)＝0,v′1(1)＝0,v″1(0)＝0,v″1(1) 0, so equation 8 can be expressed as
v1(Φ)＝10VBΦ3-15VBΦ4+6VBΦ5 (9)
The displacement can be obtained according to the speed, and then the corresponding position of the corresponding time can be obtained, so that the track planning of the AB section is completed.
And 5: in the BC section in the pick-and-place operation in step 1, the PH curve shown in step 3 is used, and the motion law on which the parameters depend adopts the formula 10, that is:
v2(γ)＝v20+v21γ+v22γ2+v23γ3+v24γ4+v25γ5 (10)
wherein v is2Representing the velocity, v, of the end effector at segment BC20To v25Are coefficients. Next, the respective coefficients are calculated based on the initial conditions. V is obtained according to step 42(0)＝VBSince the PPO tracks are symmetrical, v can be obtained2(1)＝VBTo ensure the continuity of acceleration, v is2'(0)＝0,v2Where 0 is equal to '1', the velocity at point N should be minimal, so equation 10 is:
v2(γ)＝VB+16(VN-VB)γ2+32(VB-VN)γ3+16(VN-VB)γ4 (11)
to know the parameter gammaiTime dependence, defining the real time t of motion at segment BC2I Δ t, Δ t being the time interval, i 1,2, 3.. N,
Figure BDA0003206400440000141
T2representing the total time of the BC segment motion. The relationship between the parameters and time in the PH curve is:
Figure BDA0003206400440000142
wherein s represents the arc length of the curve, and σ (γ) is the result of derivation of the arc length s on the parameter γ;
Figure BDA0003206400440000151
the parameter value corresponding to each time can be obtained by the derivation from equation 12 to equation 14:
Figure BDA0003206400440000152
wherein
Figure BDA0003206400440000153
Figure BDA0003206400440000154
Collate equation 14 into function F (γ)i)：
Figure BDA0003206400440000155
Analysis F (. gamma.) (i) The PH curve parameter gamma under the function can be knowniHaving a unique solution, the pH curve parameter γ is then solved according to Newton's iterative method by equation 16i：
Figure BDA0003206400440000156
Solving for gamma using newton iteration methodiThe idea of the iterative method is to calculate continuously, the calculation times are larger and can only be completed by a computer,
Figure BDA0003206400440000157
denotes an initial value given by the second line of equation (16), and (r) at the upper right corner denotes the r-th γ obtained after r-times of calculationi. Since i represents the segmented several-segment motion, γ 00. Using equation 16, it can be calculated
Figure BDA0003206400440000158
Then, new gamma can be obtained continuously according to the formula 16iThe significance of the iterative method is that after a sufficient number of operations, the previous one is
Figure BDA0003206400440000159
And the latter one
Figure BDA0003206400440000161
The difference between the two will be smaller and smaller, and the final error will be negligibly small, so that the value that stabilizes is gammaiThe value of (c).
From equation 16, gammaiThe speed value at the current time can be obtained, i.e. equation 10 is determined. In the same step 4, the displacement can be obtained from the speed, and then the corresponding position of the corresponding time can be obtained, so that the track planning of the BC section is completed.
Step 6: in the CD section in the pick-and-place operation in the step 1, the motion rule of the robot end effector is adopted
v3(Φ)＝v30+v31Φ+v32Φ2+v33Φ3 (17)
Wherein v is3Representing the velocity, v, of the end effector in the CD segment30To v33Is a coefficient, phi is defined as phi ═ t3/T3，Φ∈[0,1]，T3Expressed as the total time required for the end effector to move from point C to point D, t3Expressed as real time. Next, the respective coefficients are calculated based on the initial conditions. Determining respective coefficients, v, based on boundary conditions3(0)＝VB,v3(1)＝Vmax,v3'(0)＝0,v3'(1)＝0,s3(0)＝0，s3Representing the real-time displacement of CD segments, equation 17 can be expressed as
v3(Φ)＝VB+3(Vmax-VB)Φ2+2(VB-Vmax)Φ3 (18)
Wherein s is3(1) So that T is obtained when the ratio is (w-2k)/23＝(w-2k)/(VB+Vmax) And D isThe point speed reaches the maximum, i.e. VD＝VmaxThe displacement can be obtained from the speed, and then the corresponding position of the corresponding time can be obtained, so that the track planning of the CD section is completed.
And 7: in the DE segment in the pick-and-place operation in step 1, the calculation method is similar to that of the CD segment.
And 8: in the EF segment in the pick-and-place operation in step 1, the calculation method is similar to that of the BC segment.
And step 9: in the FG segment in the pick-and-place operation in step 1, the calculation method is similar to that of the AB segment.
Compared with the prior art, the invention has the advantages that:
the invention is helpful to avoid the collision of the robot with the surrounding environment in the execution process, thereby improving the safety of the robot system;
the computational efficiency can be increased in steps 7, 8, 9, which helps to achieve real-time interpolation. If two PPO tracks need to meet the same specified geometric constraint, the PH curves of the two PPO tracks in the XOY coordinate system shown in FIG. 3 are the same, so that the pH value curve does not need to be solved again, the time is saved, and the real-time property of the system is improved;
since both the PPO trace and the PH curve are symmetrical, the calculation can be simplified using symmetry to save time.
EXAMPLE III
The invention also provides a system for planning the dynamic pick-and-place track of the parallel robot, which comprises:
the PH curve solving module is used for solving the PH curve by taking the shortest obstacle avoidance distance as a geometric constraint to obtain a PH curve polynomial equation and a first intersection point and a second intersection point of the PH curve and the door-shaped pick-and-place track;
the replacing module is used for replacing a PH curve between the first intersection point and the second intersection point with a right-angle transition section between the first intersection point and the second intersection point in the door-shaped pick-and-place track;
the replaced door-shaped pick-and-place track obtaining module is used for replacing the other right-angle transition section with a symmetrical PH curve of the PH curve between the first intersection point and the second intersection point by taking the central axis of the door-shaped pick-and-place track before replacement as a symmetrical axis to obtain the replaced door-shaped pick-and-place track;
and the execution module is used for enabling the parallel robot to move according to the replaced door-shaped pick-and-place track according to the movement rule based on the symmetry of the replaced door-shaped pick-and-place track.
The PH curve solving module specifically includes:
the relation equation constructing submodule is used for constructing a relation equation between the coefficient of a PH curve polynomial equation and the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
the right-angle side length determining submodule is used for determining the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve according to the shortest obstacle avoidance distance by using a formula d which is 0.17064 m; wherein d is the shortest obstacle avoidance distance, and m is the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
and the coefficient obtaining submodule is used for substituting the right angle side length of the right angle transition section in the portal pick-and-place track to be replaced by the PH curve into the relational equation to obtain the coefficient of the PH curve polynomial equation.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A parallel robot dynamic pick-and-place trajectory planning method is characterized by comprising the following steps:
solving the PH curve by taking the shortest obstacle avoidance distance as a geometric constraint to obtain a PH curve polynomial equation and a first intersection point and a second intersection point of the PH curve and the door-shaped pick-and-place track;
replacing a right-angle transition section between the first intersection point and the second intersection point in the door-shaped pick-and-place track with a PH curve between the first intersection point and the second intersection point;
taking the central axis of the portal pick-and-place track before replacement as a symmetry axis, replacing the other right-angle transition section with a symmetrical PH curve of the PH curve between the first intersection point and the second intersection point, and obtaining the portal pick-and-place track after replacement;
based on the symmetry of the replaced door-shaped pick-and-place track, the parallel robot moves according to the replaced door-shaped pick-and-place track according to the movement rule.
2. The method for planning the dynamic pick-and-place trajectory of the parallel robot according to claim 1, wherein the PH curve is solved by taking the shortest obstacle avoidance distance as a geometric constraint to obtain a PH curve polynomial equation, which specifically comprises:
establishing a relation equation between the coefficient of a PH curve polynomial equation and the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
according to the shortest obstacle avoidance distance, determining the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve by using a formula d which is 0.17064 m; wherein d is the shortest obstacle avoidance distance, and m is the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
and substituting the right-angle side length of the right-angle transition section in the portal pick-and-place track to be replaced by the PH curve into the relation equation to obtain the coefficient of the PH curve polynomial equation.
3. The method as claimed in claim 2, wherein the equation of the relationship between the coefficients of the polynomial equation of the PH curve and the length of the right-angle side of the right-angle transition section in the Menu-shaped pick-and-place trajectory to be replaced by the PH curve is
Figure FDA0003206400430000021
Wherein u is0、u2And v2Respectively, a first coefficient, a second coefficient and a third coefficient of a PH curve polynomial equation.
4. The method of claim 3, wherein the PH curve polynomial equation is
Figure FDA0003206400430000022
Wherein, x (gamma) and y (gamma) are respectively the abscissa and the ordinate of the PH curve, and gamma is the parameter of the PH curve.
5. The method for planning the dynamic pick-and-place trajectory of the parallel robot according to claim 1, wherein the parallel robot moves according to the replaced pick-and-place trajectory according to the motion rule based on the symmetry of the replaced pick-and-place trajectory, specifically comprising:
according to a first polynomial motion rule, moving according to a first straight line track from a picking operation point of the parallel robot to a first intersection point;
according to the motion rule of the pH curve parameter dependence, the motion is carried out according to the pH curve track between the first intersection point and the second intersection point;
according to a second polynomial motion law, moving according to a second straight line track from a second intersection point to a symmetrical demarcation point;
and according to the symmetry of the replaced door-shaped pick-and-place track, moving according to the door-shaped pick-and-place track from the symmetrical dividing point to the parallel robot placing operation point according to the second polynomial motion law, the motion law depending on the PH curve parameters and the first polynomial motion law.
6. The method for planning the dynamic pick-and-place trajectory of the parallel robot according to claim 5, wherein the motion is performed according to a first linear trajectory from the pick-up operation point of the parallel robot to the first intersection point according to a first polynomial motion law, and the method further comprises:
obtaining a first polynomial motion law expression as v1(Φ1)＝v10+v11Φ1+v12Φ1 2+v13Φ1 3+v14Φ1 4+v15Φ1 5(ii) a Wherein v is1(Φ1) To follow a first linear trajectory of speed, phi1Is a first variable, phi1＝t1/T1，Φ1∈[0,1]，T1Total time, t, required for the parallel robot to reach the first intersection from the pick-up operation point1For real time, v10Is a first constant term, v11、v12、v13、v14And v15Respectively are coefficients of a polynomial in the first polynomial law of motion;
according to v1(0)＝0,v1(1)＝VB,v′1(0)＝0,v′1(1)＝0,v″1(0)＝0,v″1(1) Solving the first polynomial motion law expression under the boundary condition of 0 to obtain a polynomial motion law of a first linear track as v1(Φ1)＝10VBΦ1 3-15VBΦ1 4+6VBΦ1 5(ii) a Wherein, VBIs the speed, v, at which the parallel robot moves to the first intersection point1(0)、v′1(0)、v″1(0) Velocity, acceleration and acceleration rate of change, v, respectively, of the parallel robot at the pick-up operation point1(1)、v′1(1)、v″1(1) Respectively the speed, acceleration and acceleration rate of the parallel robot at the first intersection point.
7. The method for planning a dynamic pick-and-place trajectory of a parallel robot according to claim 1, wherein the motion is performed according to a PH curve trajectory between a first intersection point and a second intersection point according to a PH curve parameter-dependent motion law, and the method further comprises:
uniformly dividing the PH curve track into a plurality of time periods, and determining a motion rule expression v which depends on PH curve parameters when the motion is carried out according to the PH curve track2(γi)＝VB+16(VN-VB)γi 2+32(VB-VN)γi 3+16(VN-VB)γi 4(ii) a Wherein v is2(γi) Speed of movement in i-th time period, γiIs the value of the PH curve parameter, V, of the ith time periodBIs the speed, V, at which the parallel robot moves to the first intersection pointNThe minimum speed of the parallel robot moving according to the PH curve track;
combining a motion rule expression dependent on the PH curve parameters and a relational expression of the parameters and time in the PH curve to obtain a parameter solving equation of
Figure FDA0003206400430000031
Wherein, F (gamma)i) Solving functions for the parameters, zeta, beta, delta,
Figure FDA0003206400430000032
Eta is respectively a third polynomial, a fourth polynomial, a fifth polynomial, a sixth polynomial and a seventh polynomial, m is the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve, and delta t is a time interval;
according to the formula
Figure FDA0003206400430000041
Determining the value of the parameter of each time period by using a Newton iteration method; wherein the content of the first and second substances,
Figure FDA0003206400430000042
as the value of the initial parameter(s),
Figure FDA0003206400430000043
values of the parameter, γ, for r-1 and r iterations, respectively, at the ith time periodi-1Is the value of the parameter at the i-1 th time period, v2(γi-1) The speed of motion along the PH curve path in the i-th time period, σ (γ)i-1) For the arc length of the PH curve versus the parameter gammai-1The derivative of (a) of (b),
Figure FDA0003206400430000044
the function is solved for the parameters at r-1 iterations,
Figure FDA0003206400430000045
is composed of
Figure FDA0003206400430000046
A derivative with respect to time;
and substituting the value of the parameter of each time period into a motion rule expression dependent on the PH curve parameter to obtain the motion rule dependent on the PH curve parameter.
8. The method for planning the dynamic pick-and-place trajectory of the parallel robot according to claim 5, wherein the second polynomial law of motion is used to move along a second straight line trajectory from the second intersection point to the symmetrical dividing point, and the method further comprises:
determining a second polynomial motion law of a second straight line track as v3(Φ3)＝v30+v31Φ3+v32Φ3 2+v33Φ3 3(ii) a Wherein v is3(Φ3) Velocity of the second linear track, phi3Is a second variable, [ phi ]3＝t3/T3，Φ3∈[0,1]，T3Total time, t, required for the parallel robots to pass from the second point of intersection to the symmetrical demarcation point3Real time, v, for movement according to a second rectilinear trajectory30Is a third constant term, v31、v32、v33Are respectively a second polynomialCoefficients of polynomials in law;
according to v3(0)＝VB,v3(1)＝Vmax,v3'(0)＝0,v3'(1)＝0,s3(0) Solving a second polynomial motion law of the second linear track under the boundary condition of 0 to obtain a polynomial motion law of the second linear track as v3(Φ3)＝VB+3(Vmax-VB)Φ3 2+2(VB-Vmax)Φ3 3(ii) a Wherein, VBIs the speed, V, at which the parallel robot moves to the first intersection pointmaxIs the maximum speed, v, of movement according to a second rectilinear trajectory3(0)、v3'(0)、s3(0) Velocity, acceleration and displacement, v, of the parallel robot at the second intersection point, respectively3(1)、v3' 1 is the speed and acceleration of the parallel robot at the symmetrical dividing point respectively.
9. A system for planning a dynamic pick-and-place trajectory for a parallel robot, the system comprising:
the PH curve solving module is used for solving the PH curve by taking the shortest obstacle avoidance distance as a geometric constraint to obtain a PH curve polynomial equation and a first intersection point and a second intersection point of the PH curve and the door-shaped pick-and-place track;
the replacing module is used for replacing a PH curve between the first intersection point and the second intersection point with a right-angle transition section between the first intersection point and the second intersection point in the door-shaped pick-and-place track;
the replaced door-shaped pick-and-place track obtaining module is used for replacing the other right-angle transition section with a symmetrical PH curve of the PH curve between the first intersection point and the second intersection point by taking the central axis of the door-shaped pick-and-place track before replacement as a symmetrical axis to obtain the replaced door-shaped pick-and-place track;
and the execution module is used for enabling the parallel robot to move according to the replaced door-shaped pick-and-place track according to the movement rule based on the symmetry of the replaced door-shaped pick-and-place track.
10. The system for planning the dynamic pick-and-place trajectory of the parallel robot according to claim 9, wherein the PH curve solving module specifically comprises:
the relation equation constructing submodule is used for constructing a relation equation between the coefficient of a PH curve polynomial equation and the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
the right-angle side length determining submodule is used for determining the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve according to the shortest obstacle avoidance distance by using a formula d which is 0.17064 m; wherein d is the shortest obstacle avoidance distance, and m is the right-angle side length of a right-angle transition section in the portal pick-and-place track to be replaced by the PH curve;
and the coefficient obtaining submodule is used for substituting the right-angle side length of the right-angle transition section in the portal pick-and-place track to be replaced by the PH curve into the relational equation to obtain the coefficient of the PH curve polynomial equation.
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