CN115741679A - Dynamic capture algorithm based on high-order smooth planning and speed superposition - Google Patents
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Abstract
The invention relates to the technical field of robot grabbing, and discloses a dynamic grabbing algorithm based on high-order smooth planning and speed superposition r (x r ,y r ,z r ) And velocity V r And the position P of the gripping point of the object on the conveyor belt 0 (x 0 ,y 0 ,z 0 ) And an operating speed V C0 And an acceleration A C0 (ii) a Position P of a gripping point of an object on a conveyor belt 0 (x 0 ,y 0 ,z 0 ) And determining the offset height h by the grabbing strategy 2 Thereby determining a point of approach P 0 ' position of the first step, then planning a course P according to the high-order smooth speed planning algorithm r (x r ,y r ,z r ) Point to approach point P 0 ' can be calculated to obtain h 1 Total running time T required for shifting of segment and S segment 01 (ii) a And performing speed smooth planning by adopting five sections of S-shaped curves, and simultaneously performing superposition in a position value mode. The invention avoids the problem of conveying beltThe position prediction is inaccurate due to speed fluctuation or variable acceleration, and the positioning precision and the tracking speed are large in error. On the premise of not increasing hardware cost, the tracking error of the conveyor belt is reduced, and the tracking and grabbing precision is ensured.
Description
Technical Field
The invention relates to the technical field of robot grabbing, in particular to a dynamic grabbing algorithm based on high-order smooth planning and speed superposition.
Background
The mechanical arm is used for dynamically grabbing the object moving along with the conveying belt, the grabbing action of the mechanical arm is designed to be coordinated with the moving speed of the object, namely the mechanical arm is used for tracking and predicting the position of the material moving along with the conveying belt, and the mechanical arm is used for dynamically grabbing the object when the position and the speed are consistent. Currently, the commonly used tracking function of the conveyor belt generally adopts a dynamic tracking method based on PID and an interception method based on position prediction.
When the speed of a conveyor belt is relatively high, the traditional PID-based tracking method is easy to cause large curvature of a tracking track and deteriorate the tracking effect. The traditional PID form tracking algorithm essentially adjusts the position and the direction of the tail end of the robot in real time through high-frequency target position refreshing, so that the motion direction of the tail end of the robot always points to the current position of a target object until the motion directions and the speeds of the tail end of the robot and the target object are consistent after tracking is finished, and then the tail end of the robot moves along with the target object.
The interception type grabbing is to calculate the position of the robot at any future time according to the position, the speed and the acceleration of the current object, and then plan the action of the tail end of the robot so that the robot can meet the target object in the shortest time.
The position where the tail end of the robot meets the target object is obtained in advance through calculation, so that the robot is controlled to directly move to the position, the movement distance of the tail end of the robot can be shortened, the grabbing time is shortened, and the grabbing efficiency is improved.
The existing intercepting type grabbing easily causes large errors of positioning precision and tracking speed under the condition of variable accelerated motion and does not meet the places with high precision requirements for uniform motion with certain speed or uniform accelerated motion with certain accelerated speed. Therefore, a dynamic grab algorithm based on high-order smooth planning and velocity superposition is needed.
Disclosure of Invention
The invention aims to provide a dynamic grabbing algorithm based on high-order smooth programming and speed superposition, and the dynamic grabbing algorithm inherits the characteristics of short time consumption and high grabbing efficiency of intercepting type grabbing. Meanwhile, by means of a sectional planning mode, the defect that the errors of positioning accuracy and tracking speed are large due to inaccurate position prediction caused by the speed fluctuation of the conveying belt or under the condition of variable acceleration is avoided. Therefore, on the premise of not needing additional sensors and improving hardware cost, the tracking error of the conveyor belt is reduced, and the tracking and grabbing precision is ensured. Errors in the pursuit process can be compensated, and the tracking and dynamic grabbing precision is improved;
the invention is realized in the following way:
the invention provides a dynamic capture algorithm based on high-order smooth planning and velocity superposition, which is specifically executed according to the following steps:
S 1 : obtaining the position P of the current robot r (x r ,y r ,z r ) And velocity V r And the position P of the object's gripping point on the conveyor belt 0 (x 0 ,y 0 ,z 0 ) And a running speed V C0 And an acceleration A C0 ；
S 2 : position P of object grabbing point on conveyer belt 0 (x 0 ,y 0 ,z 0 ) And determining the offset height h by a grabbing strategy 2 Thereby determining a point of approach P 0 ' position of the first step, then planning a course P according to the high-order smooth speed planning algorithm r (x r ,y r ,z r ) Point to approach point P 0 ' can be calculated to obtain h 1 Total time T of operation required for the displacement of segments and S segments 01 (ii) a The high-order smooth speed planning algorithm comprises but is not limited to a trapezoidal speed planning algorithm, a five-segment S-shaped speed planning algorithm, a seven-segment S-shaped speed planning algorithm or other high-order polynomial speed planning algorithms, and the position P of the object on the conveyor belt 0 Over point h 2 Near point P of 0 ' Point is the intersection of the standard portal trajectory, the approach point P 0 The' point may also be the starting point of a transition arc of a gate-type trajectory based on a rounded corner transition.
S 3 : the speed smooth planning is carried out by adopting five sections of S-shaped curves, meanwhile, the five sections of S-shaped curves are overlapped in a position value mode, and the position, speed and acceleration expressions under the speed planning condition of the five sections of S-shaped curves are as formulas (1) to (3);
where S (t) represents an S-shaped curve, v (t) represents velocity, and a (t) represents acceleration.
S 4 : according to total time T of movement 01 And the measured running speed V of the conveyor belt C And acceleration A C Calculating to obtain T 01 Distance L of belt travel in time C And velocity V of the robot r1 (ii) a Specifically formula (4) -formula (5);
L C ＝V C0 *T 01 +0.5*A C0 *T 01 2 formula (4)
Vc 1 ＝V r *T 01 +0.5*A C0 *T 01 Formula (5)
The arrangement direction of the conveyor belt is parallel to the Y-axis direction of the coordinate axis of the robot, and the speed direction of the conveyor belt is along the positive direction of the Y-axis of the robot to obtain T 01 Position P of the object on the conveyor after time 1 (x 1 ,y 1 ,z 1 ) (ii) a Wherein, the formula is (6);
P 1 .x 1 ＝P 0 .x 0
P 1 .y 1 ＝P 0 .y 0 +L C formula (6)
P 1 .z 1 ＝P 0 .z 0
S 5 : during the error update and compensation synchronization phase, due to h 1 The time required for the segments and the S segment is long and the speed and the acceleration of the conveyor belt are inevitably fluctuated during the movement, resulting in T 01 Tracking position P of time robot 1 (x 1 ,y 1 ,z 1 ) And the actual position P of the object on the conveyor belt 1 ’(x 10 ,y 10 ,z 10 ) A position deviation Delta L and a speed deviation Delta V exist between the two parts; the positional deviation Δ L is (x) 10 -x 1 ,y 10 -y 1 ,z 10 -z 1 ) Indicates the tracking position P 1 And the actual position P 1 ' deviations in the X, Y and Z axes, respectively; wherein the positional deviation Δ L is represented by the formula (7);
ΔL.x＝x 10 -x 1 ＝0
ΔL.y＝y 10 -y 1
ΔL.z＝z 10 -z 1 =0 type (7)
Where Δ L represents a positional deviation;
S 6 : calculating and updating step S 5 And planning h according to a high-order smooth speed planning algorithm 2 Time T of the segment 02 According to the actual position P of the object on the current conveyor belt 1 ', running speed V C1 ', acceleration A C1 ' and time of exercise T 02 ；
S 7 : calculating to obtain T 02 After the moment, the theoretical position P of the object on the conveyor belt in the direction of the conveyor belt 2 And a compensated feed speed V in the direction of the conveyor belt C2 (ii) a Specifically formula (8);
P 2 .x＝P 0 .x 0
P 2 .y＝P 0 .y 0 +L C +ΔL.y+V C1 ’*T 02 +0.5*A C1 ’*T 02 2 formula (8)
P 2 .z＝P 0 .z 0
V C2 ＝V C1 ’+A C1 ’*T 02
S 8 : the time h when the robot descends along the Z direction is obtained 2 The motion speed and trajectory curve of the segment;
specifically, the planning input conditions at this time are as follows: starting point position P 1 Starting point speed V r1 Target point position P 2 And target point velocity V C2 (ii) a H is mentioned 1 And h 2 Can be different when h 1 And h 2 When the heights of the robot are different, the current point and the grabbing point of the robot are positioned on different planes;
S 9 : in the grabbing speed superposition stage, the robot superposes the calculated compensation feeding speed along the direction of the conveyor belt and the movement speed descending along the Z direction, the speed smooth planning is carried out by adopting a fifth-order polynomial, and the superposition is carried out in a position value mode, wherein the position, the speed and the acceleration expression under the condition of the fifth-order polynomial speed planning are as shown in the formula (9);
p(t)＝C 0 +C 1 t+C 2 t 2 +C 3 t 3 +C 4 t 4 +C 5 t 5
v(t)＝C 1 +2C 2 t+3C 3 t 2 +4C 4 t 3 +5C 5 t 4 formula (9)
a(t)＝2C 2 +6C 3 t+12C 4 t 2 +20C 5 t 3
S 10 : the speed superposition can be replaced by a position superposition mode in the automation equipment of the discrete system, and the position value at the superposition moment is the integral of the two speeds to be superposed in the control period; the robot can compensate the original displacement error in the descending and grabbing process by comparing the displacement curve with the speed curve, so that the robot is kept synchronous with objects on a conveyor belt when descending to the lowest point, the speed after superposition can be ensured not to damage the smooth acceleration and speed curve obtained by the original planning, and the robot can move smoothly without shaking in the whole moving process.
Further, in step S 1 The position and velocity mentioned in (a) are both expressed in the same reference coordinate system, which may be chosen from, but not limited to, the world coordinate system or the robot coordinate system. According to automation industry practice or related standards, the conveyor belt arrangement direction is parallel to the Y axis direction of the robot coordinate axis, and the conveyor belt speed direction is forward along the Y axis of the robot.
Compared with the prior art, the invention has the beneficial effects that:
1. solving key grabbing points of the interception type grabbing and planning the speed of the robot in the whole motion process. Compared with the prior art that the pursuit time and the position are optimized and solved by converting the grabbing point calculation into the pursuit problem, the method is used for calculating each period of time in the track based on the high-order smooth speed planning algorithm, further calculating the theoretical pursuit position, and is small in calculation amount and capable of being realized on hardware with lower cost.
2. The idea provided by the invention is suitable for various high-order smooth velocity planning algorithms, and can be expanded and applied to different application places.
3. The dynamic grabbing process realized by the invention is divided into 2 stages, and the error in the pursuit process can be compensated, so that the tracking and dynamic grabbing precision is improved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
FIG. 1 is a schematic diagram of algorithm staging according to the present invention;
FIG. 2 is a flow chart of a method of the present invention;
FIG. 3 is a schematic diagram of a standard gate-type trajectory capture strategy of the present invention;
FIG. 4 is a schematic diagram of a rounded transition trajectory capture strategy of the present invention;
FIG. 5 is a graph of the position overlay of the present invention;
fig. 6 is a velocity overlay curve of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without inventive efforts based on the embodiments of the present invention, are within the scope of protection of the present invention. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Referring to fig. 1-6, a dynamic capture algorithm based on high-order smooth programming and velocity stacking is specifically executed according to the following steps:
S 1 : obtaining a current robot position P r (x r ,y r ,z r ) And velocity V r And the position P of the object's gripping point on the conveyor belt 0 (x 0 ,y 0 ,z 0 ) And an operating speed V C0 And acceleration A C0 (ii) a Both position and velocity are expressed under the same reference coordinate system, which may be selected from, but not limited to, the world coordinate system or the robot coordinate system. According to the convention or relevant standard of the automation industry, the arrangement direction of the conveyor belt is parallel to the Y-axis direction of the coordinate axis of the robot, and the speed direction of the conveyor belt is along the positive direction of the Y-axis of the robot.
S 2 : position P of a gripping point of an object on a conveyor belt 0 (x 0 ,y 0 ,z 0 ) And determining the offset height h by the grabbing strategy 2 Thereby determining an approach point P 0 ' position of the first step, then planning a course P according to the high-order smooth speed planning algorithm r (x r ,y r ,z r ) Point to approach point P 0 ' can be calculated to obtain h 1 Total time T of operation required for the displacement of segments and S segments 01 (ii) a The high-order smooth speed planning algorithm comprises but is not limited to a trapezoidal speed planning algorithm, a five-segment S-shaped speed planning algorithm, a seven-segment S-shaped speed planning algorithm or other high-order polynomial speed planning algorithms, and the position P of the object on the conveyor belt 0 Over point h 2 Near point P of 0 ' Point is the intersection of the standard portal trajectory, the approach point P 0 The' point may also be the starting point of a transition arc of a gate-type trajectory based on a rounded transition.
S 3 : the speed smooth planning is carried out by adopting five sections of S-shaped curves, meanwhile, the five sections of S-shaped curves are overlapped in a position value mode, and the position, speed and acceleration expressions under the speed planning condition of the five sections of S-shaped curves are as formulas (1) to (3);
wherein S (t) represents an S-shaped curve, v (t) represents a velocity, and a (t) represents an acceleration.
S 4 : according to total time T of movement 01 And the measured running speed V of the conveyor belt C And acceleration A C Calculating to obtain T 01 Distance L of belt travel in time C And velocity V of the robot r1 (ii) a Specifically formula (4) -formula (5);
L C ＝V C0 *T 01 +0.5*A C0 *T 01 2 formula (4)
Vc 1 ＝V r *T 01 +0.5*A C0 *T 01 Formula (5)
The arrangement direction of the conveyor belt is parallel to the Y-axis direction of the coordinate axis of the robot, and the speed direction of the conveyor belt is positive along the Y-axis of the robot to obtain T 01 Position P of the object on the conveyor after time 1 (x 1 ,y 1 ,z 1 ) (ii) a Wherein, the formula is (6);
P 1 .x 1 ＝P 0 .x 0
P 1 .y 1 ＝P 0 .y 0 +L C formula (6)
P 1 .z 1 ＝P 0 .z 0
S 5 : during the error update and compensation synchronization phase, due to h 1 The time required for the segments and the S segment is long and the speed and the acceleration of the conveyor belt are inevitably fluctuated during the movement, resulting in T 01 Tracking position P of time robot 1 (x 1 ,y 1 ,z 1 ) And the actual position P of the object on the conveyor belt 1 ’(x 10 ,y 10 ,z 10 ) A position deviation Delta L and a speed deviation Delta V exist between the two parts; the positional deviation Δ L is (x) 10 -x 1 ,y 10 -y 1 ,z 10 -z 1 ) Indicates the tracking position P 1 And the actual position P 1 ' deviations in the X, Y and Z axes, respectively; wherein the positional deviation Δ L is represented by the formula (7);
ΔL.x＝x 10 -x 1 ＝0
ΔL.y＝y 10 -y 1
ΔL.z＝z 10 -z 1 =0 type (7)
Where Δ L represents a positional deviation;
S 6 : calculating and updating step S 5 And planning h according to a high-order smooth speed planning algorithm 2 Time T of the segment 02 According to the actual position P of the object on the current conveyor belt 1 ', running speed V C1 ', acceleration A C1 ' and time of exercise T 02 ；
S 7 : calculating to obtain T 02 After the moment, the theoretical position P of the object on the conveyor belt in the direction of the conveyor belt 2 And a compensated feed speed V in the direction of the conveyor belt C2 (ii) a In particular formula (8);
P 2 .x＝P 0 .x 0
P 2 .y＝P 0 .y 0 +L C +ΔL.y+V C1 ’*T 02 +0.5*A C1 ’*T 02 2 formula (8)
P 2 .z＝P 0 .z 0
V C2 ＝V C1 ’+A C1 ’*T 02
S 8 : the time h when the robot descends along the Z direction is obtained 2 The motion speed and trajectory curve of the segment;
specifically, the planning input conditions at this time are as follows: starting point position P 1 Starting point velocity V r1 Target point position P 2 And target point velocity V C2 (ii) a H is 1 And h 2 Can be different when h 1 And h 2 When the heights of the robot are different, the current point and the grabbing point of the robot are positioned on different planes;
S 9 : in a grabbing speed superposition stage, the robot superposes the calculated compensation feeding speed in the direction of the conveying belt and the movement speed descending in the Z direction, a fifth-order polynomial is adopted for speed smooth planning, and simultaneously, superposition is carried out in a position value mode, and the position, the speed and the acceleration expression under the fifth-order polynomial speed planning condition are as shown in a formula (9); the superimposed position curve is shown in fig. 3 and the velocity curve is shown in fig. 4.
p(t)＝C 0 +C 1 t+C 2 t 2 +C 3 t 3 +C 4 t 4 +C 5 t 5
v(t)＝C 1 +2C 2 t+3C 3 t 2 +4C 4 t 3 +5C 5 t 4 Formula (9)
a(t)＝2C 2 +6C 3 t+12C 4 t 2 +20C 5 t 3
In this embodiment, the velocity superposition in the automation device of the discrete system may be replaced by a position superposition manner, and the position value at the moment of superposition is the integral of the two velocities to be superposed in the control period; the robot can compensate the original displacement error in the descending and grabbing process by comparing the displacement curve with the speed curve, so that the robot is kept synchronous with objects on a conveyor belt when descending to the lowest point, the speed after superposition can be ensured not to damage the smooth acceleration and speed curve obtained by the original planning, and the robot can move smoothly without shaking in the whole moving process.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A dynamic capture algorithm based on high-order smooth programming and velocity superposition is characterized by being specifically executed according to the following steps:
S 1 : obtaining a current robot position P r (x r ,y r ,z r ) And velocity V r And the position P of the gripping point of the object on the conveyor belt 0 (x 0 ,y 0 ,z 0 ) And an operating speed V C0 And acceleration A C0 ；
S 2 : position P of a gripping point of an object on a conveyor belt 0 (x 0 ,y 0 ,z 0 ) And determining the offset height h by a grabbing strategy 2 Thereby determining an approach point P 0 ' position of the first step, then planning a course P according to the high-order smooth speed planning algorithm r (x r ,y r ,z r ) Point to point of approach P 0 ' can be calculated to obtain h 1 Total running time T required for shifting of segment and S segment 01 ；
S 3 : performing speed smooth planning by adopting a five-section S-shaped curve, and simultaneously stacking in a position value mode, wherein the position, speed and acceleration expressions under the speed planning condition of the five-section S-shaped curve are as shown in the formulas (1) to (3);
wherein S (t) represents an S-shaped curve, v (t) represents a speed, and a (t) represents an acceleration;
S 4 : according to total time T of movement 01 And the measured running speed V of the conveyor belt C And acceleration A C Calculating to obtain T 01 Distance L of belt travel in time C And the velocity V of the robot r1 (ii) a Specifically formula (4) -formula (5);
L C ＝V C0 *T 01 +0.5*A C0 *T 01 2 formula (4)
Vc 1 ＝V r *T 01 +0.5*A C0 *T 01 Formula (5)
The arrangement direction of the conveyor belt is parallel to the Y-axis direction of the coordinate axis of the robot, and the speed direction of the conveyor belt is along the positive direction of the Y-axis of the robot to obtain T 01 Position P of the object on the conveyor after time 1 (x 1 ,y 1 ,z 1 ) (ii) a Wherein, the formula is (6);
S 5 : in the error update and compensation synchronization phase, T 01 Tracking position P of time robot 1 (x 1 ,y 1 ,z 1 ) And the actual position P of the object on the conveyor belt 1 ’(x 10 ,y 10 ,z 10 ) A position deviation Delta L and a speed deviation Delta V exist between the two parts; the positional deviation Δ L is (x) 10 -x 1 ,y 10 -y 1 ,z 10 -z 1 ) Indicates the tracking position P 1 With fruitInterpositional position P 1 ' deviations in the X, Y and Z axes, respectively; wherein the positional deviation Δ L is represented by the formula (7);
ΔL.x＝x 10 -x 1 ＝0
ΔL.y＝y 10 -y 1
ΔL.z＝z 10 -z 1 =0 type (7)
Wherein Δ L represents a positional deviation;
S 6 : calculating and updating step S 5 Deviation error in (d), and planning h according to high-order smooth velocity planning algorithm 2 Time T of the segment 02 According to the actual position P of the object on the current conveyor belt 1 ', running speed V C1 ', acceleration A C1 ' and time of exercise T 02 ；
S 7 : calculating to obtain T 02 After the moment, the theoretical position P of the object on the conveyor belt in the direction of the conveyor belt 2 And a compensated feed speed V in the direction of the conveyor belt C2 (ii) a In particular formula (8);
V C2 ＝V C1 ’+A C1 ’*T 02
S 8 : the time h when the robot descends along the Z direction is obtained 2 The motion speed and trajectory curve of the segment;
S 9 : in a grabbing speed superposition stage, the robot superposes the calculated compensation feeding speed in the direction of the conveying belt and the movement speed descending in the Z direction, a fifth-order polynomial is adopted for speed smooth planning, and simultaneously, superposition is carried out in a position value mode, and the position, the speed and the acceleration expression under the fifth-order polynomial speed planning condition are as shown in a formula (9);
S 10 : by comparing the displacement curve with the speed curve, the robot is ensured to compensate the original displacement error in the descending and grabbing process, so that the robot is kept synchronous with objects on a conveyor belt when descending to the lowest point, and the superposed speed is ensured not to damage the smooth acceleration curve and the speed curve obtained by the original planning, so that the robot moves smoothly without shaking in the whole moving process.
2. The dynamic grabbing algorithm based on high-order smooth programming and velocity superposition as claimed in claim 1, wherein in step S 1 The position and velocity mentioned in (a) are both expressed in the same reference coordinate system, which may be chosen from, but not limited to, the world coordinate system or the robot coordinate system. According to the convention or relevant standard of the automation industry, the arrangement direction of the conveyor belt is parallel to the Y-axis direction of the coordinate axis of the robot, and the speed direction of the conveyor belt is along the positive direction of the Y-axis of the robot.
3. The dynamic grab algorithm based on high-order smooth programming and velocity stack as claimed in claim 1, wherein: in step S 2 The high-order smooth velocity planning algorithm includes, but is not limited to, a trapezoidal velocity planning algorithm, a five-segment S-shaped velocity planning algorithm, a seven-segment S-shaped velocity planning algorithm or other high-order polynomial velocity planning algorithm, and the position P of the object on the conveyor belt 0 Over point h 2 Near point P of 0 ' Point is the intersection of the standard portal trajectory, the approach point P 0 The' point may also be the starting point of a transition arc of a gate-type trajectory based on a rounded corner transition.
4. The dynamic grabbing algorithm based on high-order smooth programming and velocity superposition as claimed in claim 1, wherein in step S 8 Specifically, the planning input conditions at this time are: starting point position P 1 Starting point velocity V r1 Target point position P 2 And target point velocity V C2 。
5. A method according to claim 4 based on higher order smoothingDynamic grab algorithm for planning and velocity stack, characterized in that h is 1 And h 2 When there is an error in the height value of (a), i.e. when h is inconsistent 1 And h 2 When the height of the robot is different, the current point and the grabbing point of the robot are located on different planes.
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