CN113967916B - Multi-robot cooperative carrying control method based on centralized predictive control - Google Patents

Multi-robot cooperative carrying control method based on centralized predictive control Download PDF

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CN113967916B
CN113967916B CN202111390059.2A CN202111390059A CN113967916B CN 113967916 B CN113967916 B CN 113967916B CN 202111390059 A CN202111390059 A CN 202111390059A CN 113967916 B CN113967916 B CN 113967916B
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arm
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刘安东
周时钎
朱华中
徐建明
张文安
倪洪杰
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Zhejiang University of Technology ZJUT
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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
    • 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
    • B25J9/1628—Programme controls characterised by the control loop

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Abstract

The invention discloses a centralized predictive control-based multi-robot cooperative handling control method, which comprises the following steps: establishing a dynamic model of the mass centers of each mechanical arm and the grasped object of the multi-robot based on an impedance control strategy; establishing a cooperative transportation closed-chain model; a centralized model predictive controller is designed. The invention mainly aims at the cooperation problem in the multi-robot carrying process, provides a centralized prediction control method, and can realize the cooperation carrying work of the multi-robot to a common object by solving the system optimization problem on line.

Description

Multi-robot cooperative carrying control method based on centralized predictive control
Technical Field
The invention relates to the technical field of multi-robot cooperative control, in particular to a multi-robot cooperative carrying control method based on centralized predictive control.
Background
With the development of science and technology, robots are widely used, and the figure of the robot can be seen in service industry, manufacturing industry or agriculture. The mechanical arm is used as a main actuating mechanism of the robot, and the application performance of the mechanical arm determines the performance of the robot to a great extent. In the complex industry, a single robot suffers from the problem of operation limitation. Therefore, the cooperation of multiple robots occurs at the same time, and for the operation of multiple robots, the complex operation can be completed only by the mutual cooperation of information among the robots.
Model Predictive Control (MPC) is a multivariable control strategy, generally comprising three parts of prediction model, rolling optimization and feedback correction, and is implemented by establishing a state space model for a current system, collecting state quantities of the current time system, and performing the next action by solving an optimal control problem, namely solving an optimal problem.
The problem of multi-robot cooperative transportation is different from the problem of multi-robot formation motion, when a mechanical arm is in contact with a transported object, internal force can be generated between the object and the mechanical arm, meanwhile, the force can be transmitted to other mechanical arms through the object, the stress problem of the mechanical arm and the object needs to be considered during solving, an impedance control strategy is adopted in a commonly adopted method, and dynamic modeling is carried out on a mechanical arm system through stress analysis.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a design method of a centralized predictive controller for multi-robot cooperative transportation, which realizes the work of grabbing and transporting an object together by a double-arm robot and effectively optimizes the motion speed of the system at the same time;
in order to effectively solve the problems, the technical scheme adopted by the invention for solving the technical problems is as follows:
a multi-robot cooperation carrying control method based on centralized predictive control comprises the following steps:
1) Establishing a dynamic model of the end effector of each robot arm of the multi-robot and the body center of the object to be transported based on an impedance control strategy; the impedance control model is expressed in the form:
Figure BDA0003368269490000021
wherein ξ i Is the current coordinates of the end effector of the robot arm i,
Figure BDA0003368269490000022
is the current velocity of the end effector of the robotic arm i,
Figure BDA0003368269490000023
is the current acceleration, ξ, of the end effector of the mechanical arm i i,d To be the desired coordinates of the end effector of the robot arm i,
Figure BDA0003368269490000024
for a desired speed of the end effector of the robot arm i,
Figure BDA0003368269490000025
for the desired acceleration of the end effector of the robot arm i, M i Is the inertia coefficient of the end effector of the mechanical arm i, D i Is the damping coefficient, K, of the mechanical arm i end effector i Is the stiffness coefficient, f, of the end effector of the mechanical arm i i Is the current force of the robot arm i end effector on the object, f i,d A desired force of an end effector on an object for a robotic arm i;
2) Establishing a cooperative transportation closed-chain model; through the stress analysis of the mechanical arm i end effector, the internal force f in the formula (1) i Mainly due to the difference between the desired position and the current position and the influence of other mechanical arms generating internal forces:
Figure BDA0003368269490000026
wherein L is the total number of mechanical arms in the robot cooperative handling system,
Figure BDA0003368269490000027
is a transformation matrix from the object coordinate system to the world coordinate system,
Figure BDA0003368269490000028
is a transformation matrix from a world coordinate system to an object coordinate system,
Figure BDA0003368269490000029
pseudo-inverse of the grabbing matrix for the robot arm i, G j For the grabbing matrix of arm j, K j Is the stiffness coefficient, ξ, of the mechanical arm j end effector j,d Is the desired coordinate, ξ, of the mechanical arm j end effector j Is the current coordinate of the end effector of the mechanical arm j;
substituting the formula (2) into the formula (1) to obtain a collaborative carrying dynamics model of each robot:
Figure BDA00033682694900000210
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00033682694900000211
for robotic i-end executionThe current three-dimensional coordinates of the machine,
Figure BDA00033682694900000212
the current three-dimensional coordinate of the end effector of the mechanical arm j;
obtaining an ith robot state space model according to the robot cooperative transportation dynamic model obtained in the formula (3):
Figure BDA0003368269490000031
wherein the content of the first and second substances,
Figure BDA0003368269490000032
A ii is a mechanical arm i system matrix, B ii Control input matrix for robot arm i, A ij A physical coupling matrix from the mechanical arm j to the mechanical arm i;
and (3) augmenting the model (4) to obtain a closed chain model for multi-robot cooperation carrying:
Figure BDA0003368269490000033
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003368269490000034
A＝[A ij ]，B＝diag(B 11 ,...,B LL )；
3) Designing a model prediction measuring and controlling device; obtaining a discretization state space model by taking T as a discretization period through the collaborative transportation closed-chain model described by the formula (4):
x(k+1)＝G(T)x(k)+H(T)u(k) (6)
wherein, G (T) = e AT ，
Figure BDA0003368269490000035
The predictive control objective function is given by:
Figure BDA0003368269490000036
wherein Q is the weight of the state quantity, R is the weight of the control quantity, and N is the window length;
expanding the discrete state space model of the formula (6) to obtain an N-order form:
Figure BDA0003368269490000037
according to the state space model nth order form, the objective function (7) can be written as:
Figure BDA0003368269490000038
wherein the content of the first and second substances,
Figure BDA0003368269490000039
the optimal solution obtained by respectively deriving U (k) at both sides of the formula (8) is:
Figure BDA0003368269490000041
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003368269490000042
in the rolling optimization strategy, only the first item, namely u (k) is used as the optimal control input, and u (k) is acted on the system to exert the control action on the system.
In the embodiment of the invention, the cooperative carrying work of multiple robots on a common object can be realized, the dynamic model is established through the impedance control strategy, and the error function of the current attitude and the expected attitude of the robot end effector is finally converted into the optimization problem of solving the optimal solution.
Drawings
FIG. 1 is a schematic view of multi-robot cooperative handling in an example of the present invention;
wherein, T i A space coordinate system T with the end effector of the mechanical arm i as an original point O A space coordinate system with the center of gravity of the object as the origin, T W Is a world coordinate system, ξ i The three-dimensional coordinate of the end effector of the mechanical arm i in a world coordinate system;
fig. 2 is a schematic diagram of a multi-robot cooperative handling process in an embodiment of the invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
A multi-robot cooperative handling control method based on centralized predictive control comprises the following steps:
1) Establishing a dynamic model of the end effector of each robot arm of the multi-robot and the body center of the object to be transported based on an impedance control strategy; the impedance control model is expressed in the form:
Figure BDA0003368269490000051
wherein xi is i Is the current coordinates of the end effector of the robot arm i,
Figure BDA0003368269490000052
is the current speed of the end effector of the robot arm i,
Figure BDA0003368269490000053
is the current acceleration, ξ, of the end effector of the mechanical arm i i,d To be the desired coordinates of the end effector of the robot arm i,
Figure BDA0003368269490000054
for a desired speed of the end effector of the robot arm i,
Figure BDA0003368269490000055
is made into a machineDesired acceleration of arm i end effector, M i Is the inertia coefficient of the end effector of the mechanical arm i, D i Is the damping coefficient, K, of the mechanical arm i end effector i Is the stiffness coefficient, f, of the end effector of the mechanical arm i i Is the current force of the robot arm i end effector on the object, f i,d A desired force of an end effector on an object for a robotic arm i;
2) Establishing a cooperative transportation closed-chain model; the cooperative transportation model is shown in figure 1, and the internal force f in the formula (1) is analyzed through the force analysis of the mechanical arm end effector i Mainly due to the difference between the desired position and the current position and the influence of the internal forces generated by other mechanical arms:
Figure BDA0003368269490000056
wherein L is the total number of mechanical arms in the robot cooperative handling system,
Figure BDA0003368269490000057
is a transformation matrix from the object coordinate system to the world coordinate system,
Figure BDA0003368269490000058
is a transformation matrix from the world coordinate system to the object coordinate system,
Figure BDA0003368269490000059
pseudo-inverse of the grabbing matrix for the robot arm i, G j For the grabbing matrix of the robot arm j, K j Is the stiffness coefficient, ξ, of the mechanical arm j end effector j,d Is the desired coordinate, ξ, of the mechanical arm j end effector j Is the current coordinate of the end effector of the mechanical arm j;
substituting the formula (2) into the formula (1) to obtain a collaborative carrying dynamics model of each robot:
Figure BDA00033682694900000510
wherein the content of the first and second substances,
Figure BDA00033682694900000511
is the current three-dimensional coordinates of the end effector of the robotic arm i,
Figure BDA00033682694900000512
the current three-dimensional coordinate of the end effector of the mechanical arm j;
obtaining an ith robot state space model according to the robot cooperative transportation dynamic model obtained in the formula (3):
Figure BDA00033682694900000513
wherein the content of the first and second substances,
Figure BDA0003368269490000061
A ii is a mechanical arm i system matrix, B ii Control input matrix for robot arm i, A ij A physical coupling matrix from the mechanical arm j to the mechanical arm i;
and (3) augmenting the model (4) to obtain a closed chain model for multi-robot cooperation carrying:
Figure BDA0003368269490000062
wherein the content of the first and second substances,
Figure BDA0003368269490000063
A＝[A ij ]，B＝diag(B 11 ,...,B LL )；
3) Designing a model prediction measuring and controlling device; the model prediction measuring and controlling device design method is as shown in fig. 2, and a discretization state space model is obtained by taking T as a discretization period of the cooperative transportation closed chain model described in the formula (4)
x(k+1)＝G(T)x(k)+H(T)u(k) (6)
Wherein G (T) = e AT ，
Figure BDA0003368269490000064
Sampling a system quantity x (k) at a current k moment;
the predictive control objective function is given by:
Figure BDA0003368269490000065
wherein Q is the weight of the state quantity, R is the weight of the control quantity, and N is the window length;
expanding the discrete state space model of the formula (6) to obtain an N-order form
Figure BDA0003368269490000066
According to the state space model nth order form, the objective function (7) can be written as:
Figure BDA0003368269490000067
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003368269490000068
the two sides of the formula (8) respectively conduct on U (k), and the optimal solution can be obtained as
Figure BDA0003368269490000071
Wherein the content of the first and second substances,
Figure BDA0003368269490000072
in the rolling optimization strategy, only the first term, i.e. u (k) is used as the optimal control input, and u (k) is applied to the system, so as to implement the control action on the system, and make k = k +1, and enter the next sampling period.

Claims (1)

1. A multi-robot cooperation carrying control method based on centralized prediction control is characterized by comprising the following steps:
1) Establishing a dynamic model of the end effector of each robot arm of the multiple robots and the physical center of the object to be conveyed based on an impedance control strategy; the impedance control model is expressed in the form:
Figure FDA0003956227150000011
wherein ξ i Is the current coordinates of the end effector of the robot arm i,
Figure FDA0003956227150000012
is the current speed of the end effector of the robot arm i,
Figure FDA0003956227150000013
is the current acceleration, ξ, of the robotic arm i end effector i,d To the desired coordinates of the end effector of the robot arm i,
Figure FDA0003956227150000014
for a desired speed of the end effector of the robot arm i,
Figure FDA0003956227150000015
desired acceleration, M, of the end effector of the robotic arm i i Is the inertia coefficient of the end effector of the mechanical arm i, D i Is the damping coefficient, K, of the mechanical arm i end effector i Is the stiffness coefficient, f, of the end effector of the mechanical arm i i Is the current force of the robot arm i end effector on the object, f i,d A desired force of an end effector on an object for a robotic arm i;
2) Establishing a cooperative transportation closed-chain model; through the stress analysis of the mechanical arm i end effector, the internal force f in the formula (1) i Mainly due to the difference between the desired position and the current position and the influence of other mechanical arms generating internal forces:
Figure FDA0003956227150000016
wherein L is the total number of mechanical arms in the robot cooperative handling system,
Figure FDA0003956227150000017
is a transformation matrix from the object coordinate system to the world coordinate system,
Figure FDA0003956227150000018
is a transformation matrix from the world coordinate system to the object coordinate system,
Figure FDA0003956227150000019
pseudo-inverse of the grabbing matrix for the robot arm i, G j For the grabbing matrix of the robot arm j, K j Is the stiffness coefficient, ξ, of the mechanical arm j end effector j,d Is the desired coordinate, ξ, of the mechanical arm j end effector j The current coordinate of the end effector of the mechanical arm j;
substituting the formula (2) into the formula (1) to obtain a collaborative carrying dynamics model of each robot:
Figure FDA00039562271500000110
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00039562271500000111
is the current three-dimensional coordinates of the end effector of the robotic arm i,
Figure FDA00039562271500000112
is the current three-dimensional coordinate of the end effector of the mechanical arm j;
obtaining an ith robot state space model according to the robot cooperative transportation dynamic model obtained in the formula (3):
Figure FDA0003956227150000021
wherein the content of the first and second substances,
Figure FDA0003956227150000022
A ii is a mechanical arm i system matrix, B ii Control input matrix for robot arm i, A ij A physical coupling matrix from the mechanical arm j to the mechanical arm i;
and (3) augmenting the model (4) to obtain a closed chain model for multi-robot cooperation carrying:
Figure FDA0003956227150000023
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003956227150000024
A＝[A ij ]，B＝diag(B 11 ,...,B LL )；
3) Designing a model prediction measuring and controlling device; obtaining a discretization state space model by taking T as a discretization period through the collaborative transportation closed-chain model described by the formula (5):
x(k+1)＝G(T)x(k)+H(T)u(k) (6)
wherein G (T) = e AT ，
Figure FDA0003956227150000025
The predictive control objective function is given by:
Figure FDA0003956227150000026
wherein Q is the weight of the state quantity, R is the weight of the control quantity, and N is the window length;
and (3) expanding the discretization state space model of the formula (6) to obtain an N-order form:
Figure FDA0003956227150000027
according to the discretized state space model N-th order form, the objective function (7) can be written as:
Figure FDA0003956227150000028
wherein the content of the first and second substances,
Figure FDA0003956227150000031
the optimal solution obtained by respectively deriving U (k) at both sides of the formula (8) is:
Figure FDA0003956227150000032
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003956227150000033
in the rolling optimization strategy, only the first item, namely u (k) is used as the optimal control input, and u (k) is acted on the system to exert the control action on the system.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002018752A (en) * 2000-07-10 2002-01-22 Japan Science & Technology Corp Method for cooperative control of robot
CN111687827A (en) * 2020-06-22 2020-09-22 南京航空航天大学 Control method and control system for coordinating and operating weak rigid member by two robots
CN111941421A (en) * 2020-06-22 2020-11-17 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) Self-adaptive fuzzy force tracking control method based on multi-robot cooperative operation
CN113146615A (en) * 2021-01-29 2021-07-23 佛山树客智能机器人科技有限公司 Multi-robot cooperative transport control method and device

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002018752A (en) * 2000-07-10 2002-01-22 Japan Science & Technology Corp Method for cooperative control of robot
CN111687827A (en) * 2020-06-22 2020-09-22 南京航空航天大学 Control method and control system for coordinating and operating weak rigid member by two robots
CN111941421A (en) * 2020-06-22 2020-11-17 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) Self-adaptive fuzzy force tracking control method based on multi-robot cooperative operation
CN113146615A (en) * 2021-01-29 2021-07-23 佛山树客智能机器人科技有限公司 Multi-robot cooperative transport control method and device

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