CN115922721A - Trajectory planning method and system for parallel Delta robots with different pick-and-place heights - Google Patents
Trajectory planning method and system for parallel Delta robots with different pick-and-place heights Download PDFInfo
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Abstract
The invention belongs to the technical field of robot trajectory planning, and particularly relates to a trajectory planning method and system for parallel Delta robots at different pick-and-place heights, aiming at solving the problems that the existing parallel Delta robots have relatively few researches on flexible control of trajectories and rarely research the trajectory planning of pick-up positions and placing positions on different horizontal planes. The invention comprises the following steps: dividing a robot operation path into a straight line segment moving upwards, horizontally and downwards and a curve segment moving upwards to the horizontal and horizontally to the downwards; the straight line section and the curve section are subjected to motion constraint through cubic polynomial motion laws and cubic polynomial motion laws respectively; obtaining a total execution time function of picking and placing operations of the parallel Delta robot based on the distances of different sections and the speed of the end effector of the parallel Delta robot; constructing an optimization objective function with the energy consumption and the total execution time of the parallel Delta robot as optimization indexes; and solving to obtain the parallel Delta robot pick-and-place track. The invention has flexible control of operation tracks with different pick-and-place heights and smooth motion track.
Description
Technical Field
The invention belongs to the technical field of robot trajectory planning, and particularly relates to a trajectory planning method and system for parallel Delta robots with different pick-and-place heights.
Background
The motion track and motion rule of the robot affect the dynamic precision of the mechanism, so that a track planning method needs to be researched to improve the dynamic precision of the robot. The picking and placing operation is a basic step of the robot for carrying out product classification assembly on an assembly line, the demand is large, and the scene is usually carried out by adopting a parallel Delta robot for corresponding operation.
The parallel Delta robot has the advantages of high precision, high speed, good dynamic performance, compact structure and the like, is widely applied to picking, placing, sorting and stacking in the industries of food, electronics, biology and the like, and plays an important role in the aspects of precision positioning devices, assembly operation, medicine, bioengineering and the like. Therefore, the method for planning the pick-and-place operation track of the Delta robot needs to be researched. The pick-and-place operation track is usually a door-shaped track and can be divided into three parts, namely a vertical section, a horizontal section and a vertical section. In some practical work tasks, the picking position and the placing position are on different horizontal planes, so that the rising and falling distances of the picking and placing work are different, and meanwhile, barriers such as a partition plate and the like may exist between the picking position and the placing position, and the difficulty of the picking and placing operation of the robot is increased.
Therefore, a trajectory planning method meeting different picking heights and placing heights of the parallel Delta robot is needed in the field, so that flexible control over the picking and placing operation trajectory is realized, and the robot meets different requirements under various actual scenes.
Disclosure of Invention
In order to solve the above problems in the prior art, that is, the existing parallel Delta robot has relatively few research on flexible control of the trajectory, and rarely has the problem of researching the trajectory planning of the picking position and the placing position on different horizontal planes, the invention provides a trajectory planning method for the parallel Delta robot with different picking and placing heights, which comprises the following steps:
step S10, acquiring a parallel Delta robot pick-and-place operation path, dividing the operation path, and acquiring a straight line segment L moving upwards 1 Up to horizontal movement curve segment L 2 Straight line segment L of horizontal motion 3 And L 4 Horizontal to downward motion curve segment L 5 And a downward moving straight line segment L 6 ；
Step S20, L 1 、L 3 、L 4 And L 6 Segment constraint parallel Delta robot end effector speed, L, by cubic polynomial motion law 2 And L 5 Constraining the speed of the end effector of the parallel Delta robot through a fourth-order polynomial motion law;
s30, obtaining a total execution time function of the pick-and-place operation of the parallel Delta robot based on the distances of different sections and the speed of the parallel Delta robot end effector;
and S40, constructing an optimization objective function with the energy consumption and the total execution time of the parallel Delta robot as optimization indexes, and solving the optimization objective function to obtain the pick-and-place track of the parallel Delta robot.
In some preferred embodiments, the parallel Delta robot pick and place operation path is represented as:
L＝L 1 +L 2 +L 3 +L 4 +L 5 +L 6
wherein L represents the parallel Delta robot pick-and-place operation path ABCDEFG, L 1 Paths AB, L representing straight line segments of upward motion 2 Path BC, L representing a curved segment of upward to horizontal movement 3 And L 4 Representing straight line segments of horizontal motionPath CDE, L 5 Paths EF, L representing curved segments of horizontal to downward motion 6 A path FG representing a straight line segment moving downward.
In some preferred embodiments, the intersection point of the vertical tangent and the horizontal tangent of the path BC is H, the intersection point of the vertical tangent and the horizontal tangent of the path EF is I, and the intersection point of the horizontal straight line passing through the point B of the path AB and the parallel Delta robot pick-and-place operation path ABCDEFG is L;
let the distance | AB | of the path AB be denoted as j 1 Let the distance | FG | of the path FG be denoted as j 2 The distance | HB | of HB is denoted as m 1 Let the distance of HC | be denoted as k 1 The distance of IF is denoted as m 2 Let the distance of IE | be denoted as k 2 Let the distance | CD | of the CD be denoted as w k1 The distance of DE | is denoted as w k2 The distance | AH | of AH is denoted by h 1 Let the distance | GI | of GI be h 2 The linear distance | AG | of AG is denoted as w.
In some preferred embodiments, the curve segment L of the upward to horizontal movement 2 And said horizontal to downward motion curve segment L 5 All are PH curves, with lengths:
wherein l BC Representing a curved segment L of upward to horizontal movement 2 Length of (l) EF Representing a curve segment L of horizontal to downward motion 5 Length of (d).
In some preferred embodiments, the cubic polynomial law of motion, which is expressed as:
v i (Φ i )＝v 0i +v 1i Φ i +v 2i (Φ i ) 2 +v 3i (Φ i ) 3
wherein phi i ＝t i /T i And phi i ∈[0，1]，i＝L 1 ，L 3 ，L 4 ，L 3 L respectively corresponding to pick-and-place operation paths of parallel Delta robots 1 、L 3 、L 4 And L 6 Segment, T i For the total time of execution of the i-th segment, t i Current time, v, of execution for segment i i (Φ i ) Is the speed of the i-th section, v 0i ，v 1i ，v 2i ，v 3i Respectively, to be solved parameters of a cubic polynomial motion law.
In some preferred embodiments, the fourth-order polynomial law of motion, which is expressed as:
v j (Φ j )＝v 0j +v 1j Φ j +v 2j (Φ j ) 2 +v 3j (Φ j ) 3 +v 4j (Φ j ) 4
wherein phi j ＝t j /T j And phi j ∈[0，1]，j＝L 2 ，L 5 L respectively corresponding to pick-and-place operation paths of parallel Delta robots 2 And L 5 Segment, T j For the total time of execution of the j-th segment, t j Current time, v, of execution for the jth segment k (Φ j ) Is the speed of the j-th section, v 0j ，v 1j ，v 2j ，v 3j ，v 4j Respectively, to be solved parameters of a fourth-order polynomial motion law.
In some preferred embodiments, the total execution time function of the parallel Delta robot pick-and-place operation is expressed as:
wherein, T all Total execution time, V, for parallel Delta robot pick-and-place operations B For the speeds, V, of the parallel Delta robot end effector at points B and C of the operational path ABCDEFG F For parallel connection Delta robot end effector located on operation pathVelocity, V, at points E and F of path ABCDEFG mid1 Positioning a parallel Delta robot end effector at a curved segment L of an up-to-horizontal motion of an operational path ABCDEFG 2 Speed of the midpoint of (1) BC Is a curve segment L 2 Length of (V) mid Positioning the parallel Delta robot end effector at the curve segment L of the horizontal to downward motion of the operational path ABCDEFG 5 Speed of the midpoint of (1) EF Is a curve segment L 5 Length of (V) max The velocity of the parallel Delta robot end effector at point D of the operational path ABCDEFG.
In some preferred embodiments, the energy consumption and the total execution time of the parallel Delta robot are optimization objective functions of an optimization index, which are expressed as:
f is an optimization objective function between energy consumption and total execution time of the parallel Delta robot, m represents the mth of 3 total joint numbers of the parallel Delta robot, N represents the nth of the joint angle numbers N in one pick-and-place operation period of the joints of the parallel Delta robot, and theta is theta mn Value, θ, representing the nth joint angle of the mth joint of the parallel Delta robot mn+1 Value, ω, representing the n +1 joint angle of the mth joint of the parallel Delta robot 1 Weight, omega, corresponding to total execution time optimization index of parallel Delta robots 2 And optimizing the weight corresponding to the index for the total energy consumption of the parallel Delta robot.
In some preferred embodiments, if the parallel Delta robot pick-and-place operation path does not include the straight line segment L of horizontal motion 3 And L 4 Then L is 1 And L 6 Segment constraint parallel Delta robot end effector speed, L, through first law of motion 2 And L 5 And the speed of the end effector of the parallel Delta robot is constrained by the second motion law.
In another aspect of the invention, a trajectory planning system for parallel Delta robots with different pick-and-place heights is provided, the trajectory planning system comprising:
a path dividing module configured to acquire a parallel Delta robot pick-and-place operation path, divide the operation path, and acquire a straight line segment L moving upwards 1 Up to horizontal movement curve segment L 2 Straight line segment L of horizontal motion 3 And L 4 Horizontal to downward motion curve segment L 5 And a downward moving straight line segment L 6 ；
A speed constraint module configured as L 1 、L 3 、L 4 And L 6 The speed, L, of the end effector of the parallel Delta robot is constrained by the motion law of a cubic polynomial 2 And L 5 Constraining the speed of the end effector of the parallel Delta robot through a fourth-order polynomial motion law;
the execution time calculation module is configured to obtain a total execution time function of the pick-and-place operation of the parallel Delta robot based on the distances of different segments and the speed of the parallel Delta robot end effector;
and the picking and placing track acquisition module is configured to construct an optimization objective function with the energy consumption and the total execution time of the parallel Delta robot as optimization indexes, and solve the optimization objective function to obtain the picking and placing track of the parallel Delta robot.
The invention has the beneficial effects that:
(1) The invention relates to a trajectory planning method for different pick-and-place heights of a parallel Delta robot, which divides the motion trajectories of the parallel Delta robot into a vertical straight-line segment, a horizontal straight-line segment and a PH curve transition segment, considers the motion trajectories of the parallel Delta robot with different pick-and-place heights under various conditions of only the vertical straight-line segment and the PH curve transition segment, plans corresponding paths and motion rules for different segments according to different conditions, constructs an optimized objective function containing energy consumption and total execution time performance indexes of the parallel Delta robot, and solves the optimized objective function to obtain the pick-and-place trajectory of the parallel Delta robot. The method is easy to realize, and meets the safety, optimality, flexibility and stability of the robot, namely, the obstacle avoidance, the optimal time, the flexible control of the picking and placing operation track and the smooth motion of the track are realized.
(2) The track planning method for the parallel Delta robot with different pick-and-place heights can realize quick, accurate and safe operation in the intelligent manufacturing fields of stacking, grabbing, warehousing and the like, meet the requirements of various actual scenes, and provide a research direction for the track planning of pick-and-place operations of other robots through a research route.
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Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings in which:
FIG. 1 is a schematic flow chart of a trajectory planning method for different pick-and-place heights of a parallel Delta robot according to the present invention;
FIG. 2 is a schematic diagram of a pick-and-place operation path of the parallel Delta robot according to an embodiment of the method for planning the trajectories of different pick-and-place heights of the parallel Delta robot of the invention;
FIG. 3 is a diagram of a PH curve transition section in a pick-and-place operation path according to an embodiment of a trajectory planning method for different pick-and-place heights of a parallel Delta robot according to the invention;
FIG. 4 is a schematic diagram of a pick-and-place operation path without a horizontal straight line segment according to an embodiment of the method for planning the trajectories of the parallel Delta robots with different pick-and-place heights.
Detailed Description
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not to be construed as limiting the invention. It should be noted that, for convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
The invention discloses a trajectory planning method for different pick-and-place heights of parallel Delta robots, which comprises the following steps:
step S10, acquiring a parallel Delta robot pick-and-place operation path, dividing the operation path, and acquiring a straight line segment L moving upwards 1 Up to horizontal movement curve segment L 2 Straight line segment L of horizontal motion 3 And L 4 Horizontal to downward motion curve segment L 5 And a downward moving straight line segment L 6 ；
Step S20, L 1 、L 3 、L 4 And L 6 Segment constraint parallel Delta robot end effector speed, L, by cubic polynomial motion law 2 And L 5 Constraining the speed of the end effector of the parallel Delta robot through a fourth-order polynomial motion law;
s30, obtaining a total execution time function of the pick-and-place operation of the parallel Delta robot based on the distances of different sections and the speed of the parallel Delta robot end effector;
and S40, constructing an optimization objective function with the energy consumption and the total execution time of the parallel Delta robot as optimization indexes, and solving the optimization objective function to obtain the pick-and-place track of the parallel Delta robot.
In order to more clearly describe the trajectory planning method for different pick-and-place heights of the parallel Delta robot, the following describes the steps in the embodiment of the invention in detail with reference to fig. 1.
The trajectory planning method for the parallel Delta robots with different pick-and-place heights in the first embodiment of the invention comprises the following steps S10-S40, wherein the following steps are described in detail:
step S10, acquiring a parallel Delta robot pick-and-place operation path, dividing the operation path, and acquiring a straight line segment L moving upwards 1 Curve segment L of upward to horizontal movement 2 Straight line segment L of horizontal motion 3 And L 4 Horizontal to downward motion curve segment L 5 And a downward moving straight line segment L 6 。
As shown in fig. 2, a schematic diagram of a pick-and-place operation path according to an embodiment of the trajectory planning method for different pick-and-place heights of a parallel Delta robot of the present invention is shown, where the pick-and-place operation path of the parallel Delta robot is represented by the following formula (1):
L＝L 1 +L 2 +L 3 +L 4 +L 5 +L 6 (1)
wherein L represents the parallel Delta robot pick-and-place operation path ABCDEFG, L 1 Paths AB, L representing straight line segments moving upwards 2 Path BC, L representing a curved segment of up-to-horizontal motion 3 And L 4 Path CDE, L representing straight line segment of horizontal motion 5 Paths EF, L representing curved segments of horizontal to downward motion 6 A path FG representing a straight line segment moving downwards.
The intersection point of the vertical tangent line and the horizontal tangent line of the path BC is H, the intersection point of the vertical tangent line and the horizontal tangent line of the path EF is I, and the intersection point of the horizontal straight line passing through the point B of the path AB and the parallel Delta robot pick-and-place operation path ABCDEFG is L; HL indicates that a baffle barrier exists, the horizontal line of the highest point of the baffle barrier is HL, so the heights of B point and L point of a vertical motion segment of the parallel Delta robot must be at least HL.
Let the distance | AB | of the path AB be denoted as j 1 Let the distance | FG | of the path FG be written as j 2 The distance | HB | of HB is denoted as m 1 Let the distance of HC | be denoted as k 1 The distance of IF is denoted as m 2 Let the distance of IE | be denoted as k 2 Let the distance | CD | of CD be written as w k1 The distance of DE | is denoted as w k2 The distance | AH | of AH is denoted by h 1 Let the distance | GI | of GI be h 2 The linear distance | AG | of AG is denoted as w.
As shown in FIG. 3, a diagram of a PH curve transition section in a pick-and-place operation path according to an embodiment of the method for planning trajectories of parallel Delta robots with different pick-and-place heights according to the invention is shown, wherein the curve section L moves upwards to the horizontal 2 And said horizontal to downward motion curve segment L 5 Both are pH curves, the lengths of which are shown in formula (2) and formula (3):
wherein l BC Representing a curved segment L of upward to horizontal movement 2 Length of (l) EF Representing a curve segment L of horizontal to downward motion 5 Length of (d).
Step S20, L 1 、L 3 、L 4 And L 6 The speed, L, of the end effector of the parallel Delta robot is constrained by the motion law of a cubic polynomial 2 And L 5 And the speed of the end effector of the parallel Delta robot is constrained by a fourth-order polynomial motion law.
When the parallel Delta robot picks and places the straight line segment L including horizontal movement in the operation path 3 And L 4 I.e. w ≧ k 1 +k 2 ＝m 1 +m 2 When m is 1 ＝|HB|＝m 2 = | IF |, the total length of the pick-and-place operation path in this case is as shown in equation (4):
wherein l all Represents a straight line segment L including horizontal motion in the pick-and-place operation path of the parallel Delta robot 3 And L 4 The total length of the pick-and-place operation path.
L 1 、L 3 、L 4 And L 6 The speed of the end effector of the parallel Delta robot is constrained by a cubic polynomial motion law, which is shown as the formula (5):
v i (Φ i )＝v 0i +v 1i Φ i +v 2i (Φ i ) 2 +v 3i (Φ i ) 3 (5)
wherein phi i ＝t i /T i And phi i ∈[0，1]，i＝L 1 ，L 3 ，L 4 ，L 6 L respectively corresponding to pick-and-place operation paths of parallel Delta robots 1 、L 3 、L 4 And L 6 Segment, T i For the total time of execution of the i-th segment, t i Current time, v, of execution for segment i i (Φ i ) Is the speed of the i-th section, v 0i ，v 1i ，v 2i ，v 3i Respectively, to be solved parameters of a cubic polynomial motion law.
L when in parallel Delta robot pick-and-place operation path 1 In the paragraph, the boundary constraint condition is shown in equation (6):
wherein, V B For the speeds, v, of the parallel Delta robot end effectors at points B and C of the operational path ABCDEFG 1 (0) Is L 1 Speed of start of segment, v 1 (1) Is L 1 End point velocity of stage, v' 1 (0) Is L 1 Starting acceleration of segment, v' 1 (1) Is L 1 End point acceleration of the segment, s 1 (0) Is L 1 Displacement of the start of the segment, s 1 (1) Is L 1 Displacement of the end of the segment.
Based on the above constraints, equation (7) can be obtained:
wherein v is 1 (Φ 1 ) Is L 1 Velocity function of the segment, s 1 (Φ 1 ) Is L 1 Displacement function of the segment, phi 1 ＝t 1 /T 1 ，T 1 Is L 1 Total execution time of the segment, t 1 Is L 1 The current execution time of the segment.
L when in parallel Delta robot pick-and-place operation path 3 In the segment, the boundary constraint condition is shown as equation (8):
wherein, V max Velocity, v, at point D of the operational path ABCDEFG for a parallel Delta robot end effector 3 (0) Is L 3 Speed of start of segment, v 3 (1) Is L 3 End point velocity of stage, v' 3 (0) Is L 3 Origin acceleration of segment, v' 3 (1) Is L 3 End point acceleration of the segment, s 3 (0) Is L 3 Displacement of the start of the segment, s 3 (1) Is L 3 Displacement of the end point of the segment.
Based on the above constraints, equation (9) can be obtained:
wherein v is 3 (Φ 3 ) Is L 3 Velocity function of the segment, s 3 (Φ 3 ) Is L 3 Displacement function of the segment, phi 3 ＝t 3 /T 3 ，T 3 Is L 3 Total execution time of the segment, t 3 Is L 3 The current execution time of the segment.
L when in parallel Delta robot pick-and-place operation path 4 In the segment, the boundary constraint condition is as shown in equation (10):
wherein, V F For the speeds, v, of the parallel Delta robot end effector at points E and F of the operational path ABCDEFG 4 (0) Is L 4 Speed of start of segment, v 4 (1) Is L 4 End point velocity of stage, v' 4 (0) Is L 4 Starting acceleration of segment, v' 4 (1) Is L 4 End point acceleration of segment, s 4 (0) Is L 4 Displacement of the start of the segment, s 4 (1) Is L 4 Displacement of the end of the segment.
Based on the above constraints, equation (11) can be obtained:
wherein v is 4 (Φ 4 ) Is L 4 Velocity function of the segment, s 4 (Φ 4 ) Is L 4 Displacement function of the segment, Φ 4 ＝t 4 /T 4 ，T 4 Is L 4 Total execution time of the segment, t 4 Is L 4 The current execution time of the segment.
L when in parallel Delta robot pick-and-place operation path 6 In the paragraph, the boundary constraint is as shown in equation (12):
wherein v is 6 (0) Is L 6 Speed of start of segment, v 6 (1) Is L 6 End point velocity of stage, v' 6 (0) Is L 6 Starting acceleration of segment, v' 6 (1) Is L 6 End point acceleration of the segment, s 6 (0) Is L 6 Displacement of the start of the segment, s 6 (1) Is L 6 Displacement of the end point of the segment.
Based on the above constraints, equation (13) can be obtained:
wherein v is 6 (Φ 6 ) Is L 6 Velocity function of the segment, s 6 (Φ 6 ) Is L 6 Displacement function of the segment, phi 6 ＝t 6 /T 6 ，T 6 Is L 6 Total execution time of segments, t 6 Is L 6 The current execution time of the segment.
L 2 And L 5 The speed of the end effector of the parallel Delta robot is restrained by a fourth-order polynomial motion rule, wherein the fourth-order polynomial motion rule is shown as a formula (14):
v j (Φ j )＝v 0j +v 1j Φ j +v 2j (Φ j ) 2 +v 3j (Φ j ) 3 +v 4j (Φ j ) 4 (14)
wherein phi is j ＝t j /T j And phi j ∈[0，1]，j＝L 2 ，L 5 L respectively corresponding to pick-and-place operation paths of parallel Delta robots 2 And L 5 Segment, T j For the total time of execution of the j-th segment, t j Current time, v, of execution for the jth segment j (Φ j ) Is the speed of the j-th section, v 0j ，v 1j ，v 2j ，v 3j ，v 4j Respectively, to be solved parameters of a fourth-order polynomial motion law.
L when in parallel Delta robot pick-and-place operation path 2 In the segment, the boundary constraint condition is as shown in equation (15):
wherein, V mid1 Positioning a parallel Delta robot end effector at a curved segment L of an up-to-horizontal motion of an operational path ABCDEFG 2 Velocity of the midpoint of (v) 2 (0) Is L 2 Speed of start of segment, v 2 (0.5) i.e. t 2 /T 2 Is L =0.5 2 Speed of the segment at intermediate time v 2 (1) Is L 2 End point velocity of stage, v' 2 (0) Is L 2 Starting acceleration of segment, v' 2 (1) Is L 2 End point acceleration of segment, s 2 (0) Is L 2 Displacement of the start of the segment, s 2 (1) Is L 2 Displacement of the end point of the segment.
Based on the above constraints, equation (16) can be obtained:
wherein v is 2 (Φ 2 ) Is L 2 Velocity function of the segment, s 2 (Φ 2 ) Is L 2 Displacement function of the segment, phi 2 ＝t 2 /T 2 ，T 2 Is L 2 Total execution time of the segment, t 2 Is L 2 Current execution time of segment, l BC Is a curve segment L 2 Length of (d).
L when in parallel Delta robot pick-and-place operation path 5 In the paragraph, the boundary constraint is as shown in equation (17):
wherein, V mid2 Is a curve segment L 2 Length of (V) mid2 Positioning the parallel Delta robot end effector at the curve segment L of the horizontal to downward motion of the operational path ABCDEFG 5 Velocity of the midpoint of (v) 5 (0) Is L 5 Speed of start of segment, v 5 (0.5) i.e. t 5 /T 5 Is L =0.5 5 Speed of the segment at the middle time v 5 (1) Is L 5 End point velocity of stage, v' 5 (0) Is L 5 Origin acceleration of segment, v' 5 (1) Is L 5 End point acceleration of the segment, s 5 (0) Is L 5 Displacement of the start of the segment, s 5 (1) Is L 5 Displacement of the end point of the segment.
Based on the above constraints, equation (18) can be obtained:
wherein v is 5 (Φ 5 ) Is L 5 Velocity function of the segment, s 5 (Φ 5 ) Is L 5 Displacement function of the segment, phi 5 ＝t 5 /T 5 ，T 5 Is L 5 Total execution time of segments, t 5 Is L 5 Current execution time of segment, l EF Is a curve segment L 5 Length of (d).
Step S30, based on the distances of different segments and the speed of the parallel Delta robot end effector, obtaining a total execution time function of the parallel Delta robot pick-and-place operation, as shown in formula (19):
wherein, T all Total execution time for parallel Delta robot pick-and-place operations.
The constraint condition of the total execution time of the parallel Delta robot pick-and-place operation in the above case is shown as the formula (20):
wherein,
q i is the ith joint angle, τ i Is the ith motor torque.
Definition a imax Is L i The maximum acceleration of the segment(s) is,
it can be seen that once j is determined 1 、j 2 、a 1max And a 6max Then V can be calculated B And V F 。
By
And w k1 +w k2 ＝w-2m 1 If a is 3max ＝a 4max And it is a known definite value, V can be calculated max And w k1 And w k2 。
L when in parallel Delta robot pick-and-place operation path 2 In sections, assume V mid1 ＝p 1 ·V B ，V mid2 ＝p 2 ·V F And 0 < p 1 ＜1，0＜p 2 < 1, and assume a 1max ＝a 6max ，a 3max ＝a 4max The total execution time T of the pick-and-place operation of the parallel Delta robot at this time all As shown in equation (21):
once the pick-and-place operation point is determined, j 1 、j 2 、m 1 And w, the maximum acceleration can be determined once the servo system of the robot is determined. a is a 1max The larger, T all Smaller but a 1max Too large results in too poor dynamic performance of the robotic system, a 3max Condition (a) and 1max similarly. The maximum acceleration can generally be determined from the system performance of the robot, so a 1max And a 3max Can generally be determined in advance. When p is 1 Increase, T all Decrease, but dynamic performance will be deteriorated, but p 1 Increase, T all Not much reduced. p is a radical of 2 Condition (1) and p 1 Similarly.
And S40, constructing an optimization objective function with the energy consumption and the total execution time of the parallel Delta robot as optimization indexes, and solving the optimization objective function to obtain the pick-and-place track of the parallel Delta robot.
The optimization objective function with the energy consumption and the total execution time of the parallel Delta robot as the optimization index is shown as the formula (22):
f is an optimization objective function between the energy consumption and the total execution time of the parallel Delta robot, m represents the mth of 3 total joints of the parallel Delta robot, and n represents the current parallel Delta machineThe nth, theta, of the joint angle numbers N in a pick-and-place cycle of operation of the human joint mn Value, θ, representing the nth joint angle of the mth joint of the parallel Delta robot mn+1 Value, ω, representing the n +1 joint angle of the mth joint of the parallel Delta robot 1 Weight, omega, corresponding to total execution time optimization index of parallel Delta robots 2 And optimizing the weight corresponding to the index for the total energy consumption of the parallel Delta robot.
Solving this optimization problem by interior point method, by solving for p 1 To optimize the objective function and the pick-and-place operation trajectory is determined.
As shown in FIG. 4, a schematic diagram of a pick-and-place operation path without a horizontal straight line segment is shown, in which if the pick-and-place operation path of the parallel Delta robot does not include a horizontal straight line segment L, the method for planning the trajectories of the parallel Delta robots with different pick-and-place heights is provided in the present invention 3 And L 4 I.e. w < m 1 +m 2 Then L is 1 And L 6 Segment constraint parallel Delta robot end effector speed, L, through first law of motion 2 And L 5 And constraining the speed of the end effector of the parallel Delta robot through a second motion law, wherein the total execution time of the pick-and-place operation of the parallel Delta robot is as shown in a formula (23):
the constraint condition of the total execution time of the parallel Delta robot pick-and-place operation in the above case is shown as the formula (24):
wherein,
q i is the ith joint angle, τ i Is the ith motor torque.
Total execution time T of parallel Delta robot pick-and-place operation at the moment all As shown in equation (25):
once the pick-and-place operation point is determined, j 1 、j 2 And w are determined, the optimization problem is solved by the interior point method by substituting equation (25) into the optimization objective function equation (22), and p is solved 1 To optimize the objective function and the pick-and-place operation trajectory is determined.
Although the foregoing embodiments describe the steps in the above sequential order, those skilled in the art will understand that, in order to achieve the effect of the present embodiments, the steps may not be executed in such an order, and may be executed simultaneously (in parallel) or in an inverse order, and these simple variations are within the scope of the present invention.
The trajectory planning system of the parallel Delta robot with different pick-and-place heights in the second embodiment of the invention comprises:
a path dividing module configured to acquire a parallel Delta robot pick-and-place operation path, divide the operation path, and acquire a straight line segment L moving upwards 1 Up to horizontal movement curve segment L 2 Straight line segment L of horizontal motion 3 And L 4 Horizontal to downward motion curve segment L 5 And a downward moving straight line segment L 6 ；
A speed constraint module configured as L 1 、L 3 、L 4 And L 6 The speed, L, of the end effector of the parallel Delta robot is constrained by the motion law of a cubic polynomial 2 And L 5 The speed of the end effector of the parallel Delta robot is restrained by a fourth-order polynomial motion rule;
the execution time calculation module is configured to obtain a total execution time function of the pick-and-place operation of the parallel Delta robot based on the distances of different segments and the speed of the parallel Delta robot end effector;
and the picking and placing track acquisition module is configured to construct an optimization objective function with the energy consumption and the total execution time of the parallel Delta robot as optimization indexes, and solve the optimization objective function to obtain the picking and placing track of the parallel Delta robot.
It can be clearly understood by those skilled in the art that, for convenience and simplicity of description, the specific working process and related description of the system described above may refer to the corresponding process in the foregoing method embodiment, and details are not described herein again.
It should be noted that, the trajectory planning system for different pick-and-place heights of the parallel Delta robot provided in the above embodiment is only illustrated by the division of the above functional modules, and in practical applications, the above functions may be allocated to different functional modules according to needs, that is, the modules or steps in the embodiment of the present invention are further decomposed or combined, for example, the modules in the above embodiment may be combined into one module, or may be further split into a plurality of sub-modules, so as to complete all or part of the above described functions. Names of the modules and steps related in the embodiments of the present invention are only for distinguishing the modules or steps, and are not to be construed as unduly limiting the present invention.
An electronic apparatus according to a third embodiment of the present invention includes:
at least one processor; and
a memory communicatively coupled to at least one of the processors; wherein,
the memory stores instructions executable by the processor for performing a method of trajectory planning for different pick-and-place heights of a parallel Delta robot as described above.
A computer-readable storage medium of a fourth embodiment of the present invention stores computer instructions for execution by the computer to implement the trajectory planning method for different pick-and-place heights of the parallel Delta robot described above.
It can be clearly understood by those skilled in the art that, for convenience and brevity of description, the specific working processes and related descriptions of the storage device and the processing device described above may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
Those of skill in the art would appreciate that the various illustrative modules, method steps, and modules described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that programs corresponding to the software modules, method steps may be located in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. To clearly illustrate this interchangeability of electronic hardware and software, various illustrative components and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as electronic hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The terms "first," "second," and the like are used for distinguishing between similar elements and not necessarily for describing or implying a particular order or sequence.
The terms "comprises," "comprising," or any other similar term are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
So far, the technical solutions of the present invention have been described in connection with the preferred embodiments shown in the drawings, but it is easily understood by those skilled in the art that the scope of the present invention is obviously not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the invention, and the technical scheme after the changes or substitutions can be within the protection scope of the invention.
Claims (10)
1. A trajectory planning method for different pick-and-place heights of parallel Delta robots is characterized by comprising the following steps:
step S10, acquiring a parallel Delta robot pick-and-place operation path, dividing the operation path, and acquiring a straight line segment L moving upwards 1 Up to horizontal movement curve segment L 2 Straight line segment L of horizontal motion 3 And L 4 Horizontal to downward motion curve segment L 5 And a downward moving straight line segment L 6 ；
Step S20, L 1 、L 3 、L 4 And L 6 Segment constraint parallel Delta robot end effector speed, L, by cubic polynomial motion law 2 And L 5 Constraining the speed of the end effector of the parallel Delta robot through a fourth-order polynomial motion law;
s30, obtaining a total execution time function of the pick-and-place operation of the parallel Delta robot based on the distances of different sections and the speed of the parallel Delta robot end effector;
and S40, constructing an optimization objective function with the energy consumption and the total execution time of the parallel Delta robot as optimization indexes, and solving the optimization objective function to obtain the pick-and-place track of the parallel Delta robot.
2. The method for planning trajectories of different pick-and-place heights of parallel Delta robots according to claim 1, wherein the pick-and-place operation path of the parallel Delta robot is expressed as:
L＝L 1 +L 2 +L 3 +L 4 +L 5 +L 6
wherein L represents the parallel Delta robot pick-and-place operation path ABCDEFG, L 1 Paths AB, L representing straight line segments moving upwards 2 Path representing a curved segment of up-to-horizontal motionBC，L 3 And L 4 Path CDE, L representing straight line segment of horizontal motion 5 Paths EF, L representing curved segments of horizontal to downward motion 6 A path FG representing a straight line segment moving downward.
3. The trajectory planning method for different pick-and-place heights of parallel Delta robot according to claim 2, wherein the intersection point of the vertical tangent and the horizontal tangent of the path BC is H, the intersection point of the vertical tangent and the horizontal tangent of the path EF is I, and the intersection point of the horizontal straight line passing through the point B of the path AB and the pick-and-place operation path ABCDEFG of the parallel Delta robot is L;
let the distance | AB | of the path AB be denoted as j 1 Let the distance | FG | of the path FG be denoted as j 2 The distance | HB | of HB is denoted as m 1 Let the distance of HC | be denoted as k 1 The distance of IF is denoted as m 2 Let the distance of IE | be denoted as k 2 Let the distance | CD | of the CD be denoted as w k1 The distance of DE | is denoted as w k2 The distance | AH | of AH is denoted by h 1 Let the distance | GI | of GI be h 2 The linear distance | AG | of AG is denoted as w.
4. The method of trajectory planning for different pick-and-place heights of parallel Delta robots of claim 3, wherein the curve segment L of the up-to-horizontal motion 2 And said horizontal to downward motion curve segment L 5 All are PH curves, with lengths:
wherein l BC Representing a curved segment L of upward to horizontal movement 2 Length of (l) EF Representing a curve segment L of horizontal to downward motion 5 Length of (d).
5. The method of trajectory planning for different pick-and-place heights of parallel Delta robots of claim 4, wherein the cubic polynomial law of motion is expressed as:
v i (Φ i )＝v 0i +v 1i Φ i +v 2i (Φ i ) 2 +v 3i (Φ i ) 3
wherein phi i ＝t i /T i And phi i ∈[0，1]，i＝L 1 ，L 3 ，L 4 ，L 6 L respectively corresponding to pick-and-place operation paths of parallel Delta robots 1 、L 3 、L 4 And L 6 Segment, T i For the total time of execution of the i-th segment, t i Current time, v, of execution for segment i i (Φ i ) Is the speed, v, of the i-th section 0i ，v 1i ，v 2i ，v 3i Respectively, to be solved parameters of a cubic polynomial motion law.
6. The method for planning trajectories of different pick-and-place heights of parallel Delta robots according to claim 5, wherein the fourth degree polynomial law of motion is expressed as:
v j (Φ j )＝v 0j +v 1j Φ j +v 2j (Φ j ) 2 +v 3j (Φ j ) 3 +v 4j (Φ j ) 4
wherein phi j ＝t j /T j And phi j ∈[0,1]，j＝L 2 ，L 5 L respectively corresponding to pick-and-place operation paths of parallel Delta robots 2 And L 5 Segment, T j For the total time of execution of the j-th segment, t j Current time, v, of execution for the jth segment j (Φ j ) Is the speed of the j-th section, v 0j ，v 1j ，v 2j ，v 3j ，v 4j Respectively are parameters to be solved of the fourth-order polynomial motion law.
7. The method of trajectory planning for different pick-and-place heights of parallel Delta robots of claim 6, wherein the total execution time function of the pick-and-place operation of the parallel Delta robot is expressed as:
wherein, T all Total execution time, V, for parallel Delta robot pick-and-place operations B For the speeds, V, of the parallel Delta robot end effectors at points B and C of the operational path ABCDEFG F For the speeds, V, of the parallel Delta robot end effector at points E and F of the operational path ABCDEFG mid1 Positioning a parallel Delta robot end effector at a curved segment L of an up-to-horizontal motion of an operational path ABCDEFG 2 Speed of the midpoint of (1), l BC Is a curve segment L 2 Length of (V) mid2 For a parallel Delta robot end effector at a curve segment L of the horizontal to downward motion of the operational path ABCDEFG 5 Speed of the midpoint of (1), l EF Is a curved line segment L 5 Length of (V) max The velocity of the parallel Delta robot end effector at point D of the operational path ABCDEFG.
8. The trajectory planning method for different pick-and-place heights of parallel Delta robots according to claim 7, wherein the energy consumption and total execution time of the parallel Delta robot are the optimization objective function of the optimization index, which is expressed as:
f is an optimization objective function between the energy consumption and the total execution time of the parallel Delta robot, m represents the mth of 3 total joints of the parallel Delta robot, and n represents one pick-and-place operation period of the current parallel Delta robot jointNth of middle joint angle number N, theta mn Value, θ, representing the nth joint angle of the mth joint of the parallel Delta robot mn+1 Value, ω, representing the n +1 joint angle of the mth joint of the parallel Delta robot 1 Weight, omega, corresponding to total execution time optimization index of parallel Delta robots 2 And optimizing the weight corresponding to the index for the total energy consumption of the parallel Delta robot.
9. The method for planning the trajectories of different pick-and-place heights of parallel Delta robots according to claim 8, wherein if the pick-and-place operation path of the parallel Delta robot does not comprise the straight line segment L of horizontal motion 3 And L 4 Then L is 1 And L 6 Segment constraint parallel Delta robot end effector speed, L, through first law of motion 2 And L 5 And the speed of the end effector of the parallel Delta robot is constrained by the second motion law.
10. A trajectory planning system for parallel Delta robots at different pick-and-place heights, the trajectory planning system comprising:
a path dividing module configured to obtain a parallel Delta robot pick-and-place operation path, divide the operation path, and obtain a straight line segment L moving upwards 1 Up to horizontal movement curve segment L 2 Straight line segment L of horizontal motion 3 And L 4 Horizontal to downward motion curve segment L 5 And a downward moving straight line segment L 6 ；
A speed constraint module configured as L 1 、L 3 、L 4 And L 6 The speed, L, of the end effector of the parallel Delta robot is constrained by the motion law of a cubic polynomial 2 And L 5 Constraining the speed of the end effector of the parallel Delta robot through a fourth-order polynomial motion law;
the execution time calculation module is configured to obtain a total execution time function of the pick-and-place operation of the parallel Delta robot based on the distances of different segments and the speed of the parallel Delta robot end effector;
and the picking and placing track acquisition module is configured to construct an optimization objective function with the energy consumption and the total execution time of the parallel Delta robot as optimization indexes, and solve the optimization objective function to obtain the picking and placing track of the parallel Delta robot.
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