CN114378833A - Mechanical arm track planning method based on robust constraint control - Google Patents

Mechanical arm track planning method based on robust constraint control Download PDF

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CN114378833A
CN114378833A CN202210284910.1A CN202210284910A CN114378833A CN 114378833 A CN114378833 A CN 114378833A CN 202210284910 A CN202210284910 A CN 202210284910A CN 114378833 A CN114378833 A CN 114378833A
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mechanical arm
constraint
joint
task
control
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CN114378833B (en
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马建涛
韩峰涛
庹华
张航
何刚
刘凯
韩建欢
张雷
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Luoshi Shandong Robot Group Co ltd
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Rokae Inc
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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Abstract

The invention provides a mechanical arm track planning method based on robust constraint control, which comprises the following steps: step S1, modeling the relevant constraint of the mechanical arm according to the mechanical arm body limitation; step S2, planning the operation track of the mechanical arm; step S3, adjusting the reference estimation of the robot arm; and step S4, adjusting the input quantity of each period to ensure the robustness of the system.

Description

Mechanical arm track planning method based on robust constraint control
Technical Field
The invention relates to the technical field of robots, in particular to a mechanical arm track planning method based on robust constraint control.
Background
With the development of economic society, the mechanical arm is applied in more and more scenes. This makes the working environment that the arm faces more and more complicated, also puts forward higher requirement to the performance of arm simultaneously. A good track planning and control strategy is a guarantee that the mechanical arm can still finish tasks with high quality in a complex environment.
The existing mechanical arm trajectory planning schemes at present are of the following types:
1. the constrained motion plan is not considered. In the method, the performance of the mechanical arm and the constraint of the environment are not considered, an ideal mathematical model is adopted to output a motion instruction, and the performance of the mechanical arm is relied on to guarantee the completion quality of the task. The mechanical arm using the method can only perform the task of a simple scene.
2. And adjusting the motion plan off line. In order to enable the mechanical arm to work in a new scene, the method needs to continuously adjust the track of the mechanical arm, adjust the parameters of the mechanical arm and further arrange the mechanical arm to perform tasks. By using the method, the parameters and the tracks are required to be adjusted repeatedly before the task starts, and a large amount of debugging and programming work is required to be carried out by workers, so that the working efficiency is greatly reduced.
Meanwhile, external interference factors are not considered in a planning control algorithm in the schemes, and when the mechanical arm is subjected to external interference, the mechanical arm is difficult to self-adjust, so that the operation quality is reduced.
Disclosure of Invention
The object of the present invention is to solve at least one of the technical drawbacks mentioned.
Therefore, the invention aims to provide a mechanical arm track planning method based on robust constraint control.
In order to achieve the above object, an embodiment of the present invention provides a method for planning a trajectory of a mechanical arm based on robust constraint control, including the following steps:
step S1, modeling the related constraint of the mechanical arm according to the mechanical arm body limit, wherein the modeling process is as follows:
each joint angle satisfies the constraint:
Figure 681210DEST_PATH_IMAGE002
；
wherein,
Figure 739296DEST_PATH_IMAGE004
respectively representing the joint angle, the upper limit and the lower limit of the joint angle of the ith joint; m represents the total number of joints;
simultaneously, because motor speed and motor moment limit, the arm faces speed and moment restraint respectively in the motion process:
Figure 456716DEST_PATH_IMAGE005
；
wherein,
Figure 524029DEST_PATH_IMAGE006
respectively representing the joint angular velocity of the ith joint, the upper limit and the lower limit of the joint angular velocity; m represents the total number of joints;
Figure 213767DEST_PATH_IMAGE008
wherein,
Figure 973913DEST_PATH_IMAGE010
respectively representing the moment of the ith joint and the upper limit of the moment of the joint; m represents the total number of joints;
step S2, planning the operation track of the mechanical arm;
in step S3, a reference estimate of the robot arm is adjusted, wherein,
the adjusted reference track is
Figure 913050DEST_PATH_IMAGE011
Wherein,
Figure 784054DEST_PATH_IMAGE012
respectively representing the adjusted reference position track and the adjusted reference speed track;
and step S4, adjusting the input quantity of each period to ensure the robustness of the system.
Further, in the step S2,
and representing the tasks of the mechanical arm by adopting a series of target points of a task space, and smoothly connecting the target points to form a task curve of the mechanical arm. Wherein, X represents any point on the task curve, then the relationship between the task curve of the mechanical arm and the joint angle thereof is expressed as:
Figure 853598DEST_PATH_IMAGE014
wherein,
Figure 50224DEST_PATH_IMAGE016
respectively representing the first derivative and the second derivative of the task vector, the Jacobian matrix of the mechanical arm and the first derivative of the Jacobian matrix of the mechanical arm.
In addition note
Figure 7816DEST_PATH_IMAGE017
Wherein, U represents the input of the system, and the above formula represents that the angular acceleration of the mechanical arm is used as the input of the system;
the task needs to be discretized during the motion of the mechanical arm:
Figure 948090DEST_PATH_IMAGE019
wherein,
Figure 409159DEST_PATH_IMAGE020
k represents the kth control period, and Ts represents the manipulator control period;
meanwhile, when the control quantity of the system faces a task, the following constraints need to be met:
Figure 776686DEST_PATH_IMAGE022
wherein,
Figure 424836DEST_PATH_IMAGE024
respectively representing task parameters and task constraints.
Further, in the step S2, each planning procedure is expressed as follows:
s21: inputting parameters
Figure 637643DEST_PATH_IMAGE026
；
S22: calculating mechanical arm hard constraint and kinematic parameters;
s23: solving the expected state of the next step according to the constraint;
s24: solving the feasible range of the system control quantity U according to the constraint;
s25: solving the optimal solution under the following multiple constraints:
(1) and (3) constraint:
Figure 218797DEST_PATH_IMAGE028
(2) optimizing the target:
Figure 491646DEST_PATH_IMAGE029
s26: refresh output quantity:
Figure 158251DEST_PATH_IMAGE031
。
further, in the step S3, when the external force interferes, the mechanical arm reference trajectory is adjusted by using an admittance filter as follows:
Figure 174749DEST_PATH_IMAGE033
wherein,
Figure 610409DEST_PATH_IMAGE034
respectively representing position adjustment quantity, speed adjustment quantity, a robot quality matrix, a robot damping matrix and external interference force;
the adjusted reference track is
Figure 585318DEST_PATH_IMAGE011
Wherein,
Figure 473640DEST_PATH_IMAGE012
respectively representing the adjusted reference position trajectory and the reference velocity trajectory.
Further, in the step S4,
recording:
Figure 559408DEST_PATH_IMAGE035
in the periodic control, there is a relationship as follows:
Figure 849575DEST_PATH_IMAGE037
wherein:
Figure 723947DEST_PATH_IMAGE038
for each step, the angle, angular velocity and angular acceleration need to satisfy the following relationship
Figure 99564DEST_PATH_IMAGE040
Wherein i represents a joint number, and m represents a maximum joint number;
the set that satisfies the above constraints is represented as:
Figure 457865DEST_PATH_IMAGE042
from the foregoing derivation, each step of updating satisfies:
Figure DEST_PATH_IMAGE044
wherein,
Figure DEST_PATH_IMAGE046
the interference amount and the model error are respectively expressed, and the range is used
Figure 477904DEST_PATH_IMAGE048
Represents;
while expressing the constraint of angular acceleration as
Figure 529037DEST_PATH_IMAGE050
The angle and angular acceleration control amount of each step needs to satisfy:
Figure 391951DEST_PATH_IMAGE052
where ≧ indicates the solving of the minkowski sum;
in addition, the angular acceleration needs to satisfy:
Figure DEST_PATH_IMAGE054
simultaneously, the moment needs to be satisfied:
Figure 491625DEST_PATH_IMAGE056
wherein,
Figure 225226DEST_PATH_IMAGE058
representing the coriolis force matrix of the robotic arm.
According to the mechanical arm trajectory planning method based on robust constraint control, the technical points of the mechanical arm trajectory planning method based on robust constraint control, the trajectory and moment planning operator, the robust input adjusting operator and the like are provided. The invention realizes that the mechanical arm automatically adjusts and plans and controls the input quantity according to the external environment, and saves the trouble of manually adjusting the path; the constraints are divided into mechanical arm hard constraints and task constraints, and the tasks are directly related to the instructions.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a flowchart of a robot path planning method based on robust constraint control according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The invention provides a mechanical arm trajectory planning method based on robust constraint control, which realizes the motion planning of a mechanical arm by combining constraint optimization and trajectory planning. In the method, the motion of the mechanical arm is tracked on a continuously updated and corrected reference track, and meanwhile, the reaction control is combined, the input quantity of the whole control system is continuously adjusted, and the mechanical arm can work in high quality even facing a complex environment.
As shown in fig. 1, the method for planning a trajectory of a mechanical arm based on robust constraint control according to the embodiment of the present invention includes the following steps:
and step S1, modeling the relevant constraint of the mechanical arm according to the mechanical arm body limit.
Specifically, according to the mechanical arm body limitation, the relevant constraint is modeled as follows:
first, each joint angle satisfies the constraint:
Figure 181680DEST_PATH_IMAGE059
（1）
wherein,
Figure 531890DEST_PATH_IMAGE060
respectively representing the joint angle, the upper limit and the lower limit of the joint angle of the ith joint; m represents the total number of joints.
Simultaneously, because motor speed and motor moment limit, the arm faces speed and moment restraint respectively in the motion process:
Figure 763151DEST_PATH_IMAGE062
（2）
wherein,
Figure 147996DEST_PATH_IMAGE064
respectively representing the joint angular velocity of the ith joint, the upper limit and the lower limit of the joint angular velocity; m represents the total number of joints.
Figure 105430DEST_PATH_IMAGE065
（3）
Wherein,
Figure 942936DEST_PATH_IMAGE066
respectively representing the moment of the ith joint and the upper limit of the moment of the joint; m represents the total number of joints.
And step S2, planning the operation track of the mechanical arm.
In this step, the task of the robot arm may be represented by a series of target points in the task space, which are smoothly connected to form a task curve. X represents any point on the task curve, the relationship between the task curve of the mechanical arm and its joint angle can be expressed as:
Figure 446730DEST_PATH_IMAGE013
（4）
wherein,
Figure 686082DEST_PATH_IMAGE015
respectively representing the first derivative and the second derivative of the task vector, the Jacobian matrix of the mechanical arm and the first derivative of the Jacobian matrix of the mechanical arm.
In addition note
Figure 249918DEST_PATH_IMAGE017
（5）
Where U represents the input to the system and the above equation represents the angular acceleration of the robotic arm as the input to the system.
The task needs to be discretized during the motion of the mechanical arm:
Figure DEST_PATH_IMAGE067
（6）
wherein,
Figure 981245DEST_PATH_IMAGE020
k denotes the kth control period, and Ts denotes the robot arm control period.
Meanwhile, when the control quantity of the system faces a task, the following constraints need to be met:
Figure DEST_PATH_IMAGE068
（7）
wherein,
Figure DEST_PATH_IMAGE069
representing task parameters and task constraints, respectively
Then each step of the planning process can be represented as follows:
inputting:
Figure DEST_PATH_IMAGE070
(ii) a And (3) outputting:
Figure DEST_PATH_IMAGE072
the method comprises the following specific steps:
s21: inputting parameters
Figure DEST_PATH_IMAGE073
；
S22: calculating mechanical arm hard constraint and kinematic parameters, comprising: jacobian matrix, task vector;
s23: solving the expected state of the next step according to the constraint;
s24: solving the feasible range of the system control quantity U according to the constraint;
s25: solving the optimal solution under the following multiple constraints:
(1) and (3) constraint:
Figure DEST_PATH_IMAGE074
（8）
(2) optimizing the target:
Figure 711566DEST_PATH_IMAGE029
（9）
s26: the output quantity is refreshed.
Figure DEST_PATH_IMAGE075
In step S3, the reference estimate of the robot arm is adjusted.
In a complex environment, the mechanical arm is inevitably disturbed by external force when moving. When the external force is interfered, the motion instruction of the mechanical arm needs to be adjusted, so that the motion of the mechanical arm is kept stable.
When the mechanical arm is interfered by external force, the following admittance filter is adopted to adjust the reference track of the mechanical arm:
Figure DEST_PATH_IMAGE076
（11）
wherein
Figure 149631DEST_PATH_IMAGE034
Respectively representing the position adjustment amount, the speed adjustment amount, the robot quality matrix, the robot damping matrix and the external interference force.
The adjusted reference track is
Figure 612931DEST_PATH_IMAGE011
（12）
Wherein
Figure 893870DEST_PATH_IMAGE012
Respectively representing the adjusted reference position trajectory and the reference velocity trajectory.
And step S4, adjusting the input quantity of each period to ensure the robustness of the system.
First, note:
Figure 942729DEST_PATH_IMAGE035
（13）
in the periodic control, there is a relationship as follows:
Figure DEST_PATH_IMAGE077
（14）
wherein:
Figure DEST_PATH_IMAGE078
（15）
wherein, for each step, the angle, the angular velocity and the angular acceleration need to satisfy the following relationship:
Figure DEST_PATH_IMAGE079
（16）
wherein i represents a joint number, and m represents a maximum joint number
The set that satisfies the above constraints is represented as:
Figure DEST_PATH_IMAGE080
（17）
from the foregoing derivation, each step of updating satisfies:
Figure DEST_PATH_IMAGE081
（18）
wherein,
Figure DEST_PATH_IMAGE082
the interference amount and the model error are respectively expressed, and the range is used
Figure DEST_PATH_IMAGE083
And (4) showing.
While expressing the constraint of angular acceleration as
Figure DEST_PATH_IMAGE084
（19）
The angle and angular acceleration control amount of each step needs to satisfy:
Figure DEST_PATH_IMAGE085
（20）
where ≧ indicates the resolution of the minkowski sum.
In addition, the angular acceleration needs to satisfy:
Figure DEST_PATH_IMAGE086
（21）
simultaneously, the moment needs to be satisfied:
Figure DEST_PATH_IMAGE087
（22）
wherein,
Figure DEST_PATH_IMAGE088
coriolis torque matrix representing a robotic arm
According to the method, the angle, the angular speed and the angular acceleration of each control period are accelerated, and the joint moment is adjusted to ensure the robustness of the system.
According to the mechanical arm trajectory planning method based on robust constraint control, the technical points of the mechanical arm trajectory planning method based on robust constraint control, the trajectory and moment planning operator, the robust input adjusting operator and the like are provided. The invention realizes that the mechanical arm automatically adjusts and plans and controls the input quantity according to the external environment, and saves the trouble of manually adjusting the path; the constraints are divided into mechanical arm hard constraints and task constraints, and the tasks are directly related to the instructions.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1. A mechanical arm track planning method based on robust constraint control is characterized by comprising the following steps:
step S1, modeling the related constraint of the mechanical arm according to the mechanical arm body limit, wherein the modeling process is as follows:
each joint angle satisfies the constraint:
Figure 865718DEST_PATH_IMAGE002
；
wherein,
Figure 624552DEST_PATH_IMAGE004
respectively representing the joint angle, the upper limit and the lower limit of the joint angle of the ith joint; m represents the total number of joints;
simultaneously, because motor speed and motor moment limit, the arm faces speed and moment restraint respectively in the motion process:
Figure 517422DEST_PATH_IMAGE006
；
wherein,
Figure 291343DEST_PATH_IMAGE008
respectively representing the joint angular velocity of the ith joint, the upper limit and the lower limit of the joint angular velocity; m represents the total number of joints;
Figure 218848DEST_PATH_IMAGE010
wherein,
Figure 420022DEST_PATH_IMAGE012
respectively representing the moment of the ith joint and the upper limit of the moment of the joint; m represents the total number of joints;
step S2, planning the operation track of the mechanical arm;
in step S3, a reference estimate of the robot arm is adjusted, wherein,
the adjusted reference track is
Figure 65767DEST_PATH_IMAGE014
Wherein,
Figure 377800DEST_PATH_IMAGE016
respectively representing the adjusted reference position track and the adjusted reference speed track;
and step S4, adjusting the input quantity of each period to ensure the robustness of the system.
2. The method for planning trajectories of mechanical arms based on robust constraint control as claimed in claim 1, wherein in the step S2,
representing the tasks of the mechanical arm by adopting a series of target points of a task space, and smoothly connecting the target points to form a task curve of the mechanical arm; wherein, X represents any point on the task curve, then the relationship between the task curve of the mechanical arm and the joint angle thereof is expressed as:
Figure 425390DEST_PATH_IMAGE018
wherein,
Figure 797465DEST_PATH_IMAGE020
respectively representing a first derivative and a second derivative of the task vector, a Jacobian matrix of the mechanical arm and a first derivative of the Jacobian matrix of the mechanical arm;
in addition note
Figure 930507DEST_PATH_IMAGE022
Wherein, U represents the input of the system, and the above formula represents that the angular acceleration of the mechanical arm is used as the input of the system;
the task needs to be discretized during the motion of the mechanical arm:
Figure 46230DEST_PATH_IMAGE024
wherein,
Figure 682748DEST_PATH_IMAGE025
k represents the kth control period, and Ts represents the manipulator control period;
meanwhile, when the control quantity of the system faces a task, the following constraints need to be met:
Figure 225725DEST_PATH_IMAGE027
wherein,
Figure 314903DEST_PATH_IMAGE029
respectively representing task parameters and task constraints.
3. The method for planning the trajectory of the mechanical arm based on robust constraint control as claimed in claim 2, wherein in the step S2, each step of the planning process is represented as follows:
s21: inputting parameters
Figure 968739DEST_PATH_IMAGE031
；
S22: calculating mechanical arm hard constraint and kinematic parameters;
s23: solving the expected state of the next step according to the constraint;
s24: solving the feasible range of the system control quantity U according to the constraint;
s25: solving the optimal solution under the following multiple constraints:
(1) and (3) constraint:
Figure 725342DEST_PATH_IMAGE033
(2) optimizing the target:
Figure 173641DEST_PATH_IMAGE034
s26: refresh output quantity:
Figure 750116DEST_PATH_IMAGE036
。
4. the method for planning the trajectory of the mechanical arm based on the robust constraint control as recited in claim 1, wherein in the step S3, when the mechanical arm is disturbed by the external force, the mechanical arm reference trajectory is adjusted by using the following admittance filter:
Figure 213501DEST_PATH_IMAGE038
wherein,
Figure 824611DEST_PATH_IMAGE039
respectively representing position adjustment quantity, speed adjustment quantity, a robot quality matrix, a robot damping matrix and external interference force;
the adjusted reference track is
Figure 974970DEST_PATH_IMAGE040
Wherein,
Figure DEST_PATH_IMAGE041
respectively representing the adjusted reference position trajectory and the reference velocity trajectory.
5. The method for planning trajectories of mechanical arms based on robust constraint control as claimed in claim 1, wherein in the step S4,
recording:
Figure 835478DEST_PATH_IMAGE042
in the periodic control, there is a relationship as follows:
Figure 831116DEST_PATH_IMAGE044
wherein:
Figure DEST_PATH_IMAGE045
for each step, the angle, angular velocity and angular acceleration need to satisfy the following relationship
Figure DEST_PATH_IMAGE047
Wherein i represents a joint number, and m represents a maximum joint number;
the set that satisfies the above constraints is represented as:
Figure 421366DEST_PATH_IMAGE049
from the foregoing derivation, each step of updating satisfies:
Figure DEST_PATH_IMAGE051
wherein,
Figure DEST_PATH_IMAGE053
respectively representing the interference magnitude and the modeType error, using its range
Figure DEST_PATH_IMAGE055
Represents;
while expressing the constraint of angular acceleration as
Figure DEST_PATH_IMAGE057
The angle and angular acceleration control amount of each step needs to satisfy:
Figure DEST_PATH_IMAGE059
where ≧ indicates the solving of the minkowski sum;
in addition, the angular acceleration needs to satisfy:
Figure DEST_PATH_IMAGE061
simultaneously, the moment needs to be satisfied:
Figure DEST_PATH_IMAGE063
wherein,
Figure DEST_PATH_IMAGE065
representing the coriolis force matrix of the robotic arm.
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CN111152212A (en) * 2019-12-05 2020-05-15 北京蒂斯科技有限公司 Mechanical arm movement track planning method and device based on optimal power
CN113843791A (en) * 2021-09-11 2021-12-28 杭州锐沃机器人科技有限公司 Mechanical arm multipoint motion trajectory planning method

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