CN112706165A - Tracking control method and system for wheel type mobile mechanical arm - Google Patents

Tracking control method and system for wheel type mobile mechanical arm Download PDF

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CN112706165A
CN112706165A CN202011525772.9A CN202011525772A CN112706165A CN 112706165 A CN112706165 A CN 112706165A CN 202011525772 A CN202011525772 A CN 202011525772A CN 112706165 A CN112706165 A CN 112706165A
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谭宁
余鹏
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Sun Yat Sen University
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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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • 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 discloses a tracking control method and a system for a wheel type mobile mechanical arm, wherein the method comprises the following steps: s1, giving initial value information and inputting predefined target track information; s2, solving an inverse kinematics problem based on the first zero neural network according to the initial value information, the predefined target track information and the actual information to obtain a driving signal; s3, controlling the motion of the wheel type mobile mechanical arm according to the driving signal and feeding back actual information; s4, estimating the Jacobian matrix based on the second zeroing neural network and the actual information and returning to the step S2 to recalculate the driving signals. The system comprises: the device comprises an initialization module, a driving signal module, a control module and a Jacobian matrix module. The invention can realize the tracking control of the robot under the condition of not knowing the model parameters of the wheel type mobile operation mechanical arm. The tracking control method and system for the wheel type mobile mechanical arm can be widely applied to the field of mechanical arm control.

Description

Tracking control method and system for wheel type mobile mechanical arm
Technical Field
The invention belongs to the field of mechanical arm control, and particularly relates to a tracking control method and system for a wheel type mobile mechanical arm.
Background
In order to realize control tracking, an accurate kinematics model needs to be established for the wheel type mobile operation mechanical arm before solving the inverse kinematics problem of the mechanical arm. This solution has the following drawbacks: firstly, the process of establishing a kinematic model is relatively complicated and has large computation load; secondly, when a control algorithm needs to be applied to different wheel type mobile operation mechanical arms, a kinematics model needs to be established for the different wheel type mobile operation mechanical arms each time, so that the transportability of the control scheme on different robots is poor; finally, when there is a certain difference between the recorded robot model parameters and the real model parameters, the accuracy of the kinematic modeling is greatly affected, thereby affecting the effectiveness of the control algorithm.
Disclosure of Invention
In order to solve the above-mentioned problems, an object of the present invention is to provide a tracking control method and system for a wheeled mobile robot arm, which can solve the inverse kinematics problem of the wheeled mobile robot arm without knowing model parameters (i.e., kinematics model is unknown) of the wheeled mobile robot arm, thereby realizing tracking control of the robot.
The first technical scheme adopted by the invention is a tracking control method facing to a wheel type mobile mechanical arm, which comprises the following steps:
s1, giving initial value information and inputting predefined target track information;
s2, solving an inverse kinematics problem based on the first zero neural network according to the initial value information, the predefined target track information and the actual information to obtain a driving signal;
s3, controlling the motion of the wheel type mobile mechanical arm according to the driving signal and feeding back actual information;
s4, estimating the Jacobian matrix based on the second zeroing neural network and the actual information and returning to the step S2 to recalculate the driving signals.
Further, the initial value information includes a wheel rotation angle initial value, a mechanical arm joint angle initial value and a jacobian array initial value, and the actual information includes position information of an end effector of the mechanical arm, speed information of the end effector of the mechanical arm, acceleration information of the end effector of the mechanical arm, speed information of a base of the mechanical arm and acceleration information of the base of the mechanical arm.
Further, the step of solving an inverse kinematics problem based on the first nulling neural network according to the initial value information, the predefined target trajectory information, and the actual information to obtain the driving signal specifically includes:
constructing a first error function according to predefined target track information and position information of an end effector of the mechanical arm;
constructing a first zero-ization neural network and substituting a first error function into the first zero-functionalization neural network to obtain a first differential equation;
transforming the first differential equation to obtain a differential equation of the driving signal;
according to the initial value of the wheel rotation angle
Figure BDA0002850549210000021
Initial mechanical arm joint angle initial value theta (0) and predefined target track information rd(t) position information r of the end effector of the robot arma(t), the jacobian matrix j (t) and a differential equation of the drive signal to obtain the drive signal q (t).
Further, the first differential equation expression is as follows:
Figure BDA0002850549210000022
in the above formula, the first and second carbon atoms are,
Figure BDA0002850549210000023
is rdThe time derivative of (t) is,
Figure BDA0002850549210000024
representing robot base velocity information, J (t) representing an estimated Jacobian matrix,
Figure BDA0002850549210000025
representing the driving information, a constant γ ═ 1 is a design parameter of the zero-ized neural network model, rd(t) represents predefined target trajectory information, ra(t) indicates positional information of the robot arm end effector.
Further, the differential equation expression of the driving signal is as follows:
Figure BDA0002850549210000026
in the above formula, the first and second carbon atoms are,
Figure BDA0002850549210000027
representing the pseudo-inverse of the jacobian matrix.
Further, the step of controlling the motion of the wheel-type mobile robot arm according to the driving signal and feeding back the actual information specifically includes:
controlling the motion of the wheel type mobile operation mechanical arm according to the driving signal q (t) so that the end effector of the wheel type mobile operation mechanical arm tracks a predefined track in a task space;
real-time measurement of position information r of mechanical arm end effector based on sensor equipmenta(t) velocity information of the end-effector of the robot arm
Figure BDA0002850549210000028
Acceleration information for end effector of mechanical arm
Figure BDA0002850549210000029
Robot arm base speed information
Figure BDA00028505492100000210
And robot arm base acceleration information
Figure BDA00028505492100000211
Further, the step of estimating the jacobian matrix based on the second zeroing neural network and the actual information and returning to the step S2 to recalculate the driving signal specifically includes:
defining a second error function and inputting the second error function into a second zero neural network to obtain a second differential equation;
transforming the second differential equation to obtain a differential equation related to the Jacobian matrix;
obtaining an estimated Jacobian matrix according to the initial value of the Jacobian matrix, the real-time feedback information, the differential equation of the driving signal and the differential equation related to the Jacobian matrix;
the process returns to step S2 to recalculate the drive signal.
Further, the expression of the second differential equation is as follows:
Figure BDA0002850549210000031
in the above formula, the first and second carbon atoms are,
Figure BDA0002850549210000032
representing the time derivative of the jacobian matrix j (t),
Figure BDA0002850549210000033
representing drive information
Figure BDA0002850549210000034
The constant μ ═ 1 represents the design parameters of the nulling neural network model.
Further, the expression of the differential equation with respect to the jacobian matrix is as follows:
Figure BDA0002850549210000035
in the above formula, the first and second carbon atoms are,
Figure BDA0002850549210000036
representing a vector
Figure BDA0002850549210000037
The pseudo-inverse of (1).
The second technical scheme adopted by the invention is as follows: a tracking control system facing a wheel type mobile mechanical arm comprises the following modules:
the initialization module is used for giving initial value information and inputting predefined target track information;
the driving signal module is used for solving an inverse kinematics problem based on the first zero neural network according to the initial value information, the predefined target track information and the actual information to obtain a driving signal;
the control module is used for controlling the motion of the wheel type mobile mechanical arm according to the driving signal and feeding back actual information;
and the Jacobian matrix module is used for estimating a Jacobian matrix based on the second zeroing neural network and the actual information and returning to recalculate the driving signal.
The method and the system have the beneficial effects that: in addition, the control scheme provided by the invention does not need to establish a kinematics model of the robot, so that the control scheme can be easily applied to wheel type mobile operation mechanical arms with different types and structures, and the uncertainty of the robot model parameters does not influence the effectiveness of the control scheme provided by the invention.
Drawings
Fig. 1 is a flowchart illustrating steps of a tracking control method for a wheeled mobile robot according to an embodiment of the present invention;
fig. 2 is a block diagram of a tracking control system for a wheeled mobile robot according to an embodiment of the present invention;
FIG. 3 is a pre-defined target trajectory and an actual trajectory of an end effector in a task space in accordance with an embodiment of the present invention;
FIG. 4 is a data processing diagram of a control system according to an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments. The step numbers in the following embodiments are provided only for convenience of illustration, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.
Referring to fig. 1 and 4, the present invention provides a tracking control method for a wheeled mobile robot arm, including the steps of:
s1, giving initial value information and inputting predefined target track information;
s2, solving an inverse kinematics problem based on the first zero neural network according to the initial value information, the predefined target track information and the actual information to obtain a driving signal;
s3, controlling the motion of the wheel type mobile mechanical arm according to the driving signal and feeding back actual information;
s4, estimating the Jacobian matrix based on the second zeroing neural network and the actual information and returning to the step S2 to recalculate the driving signals.
Further as a preferred embodiment of the method, the initial value information includes an initial value of a wheel rotation angle, an initial value of a joint angle of the mechanical arm, and an initial value of a jacobian, and the actual information includes position information of the end effector of the mechanical arm, velocity information of the end effector of the mechanical arm, acceleration information of the end effector of the mechanical arm, velocity information of the base of the mechanical arm, and acceleration information of the base of the mechanical arm.
Specifically, an initial value of the wheel rotation angle is given
Figure BDA0002850549210000041
The initial value theta (0) of the joint angle of the mechanical arm is [ 0; -pi/4; 0; 0; 0; 0]And an initial value of the robot jacobian matrix:
Figure BDA0002850549210000042
the predefined target trajectory information is expressed as follows:
Figure BDA0002850549210000043
wherein iota-0.2 meter represents the radius of the target track, TdThe period of the tracking task is represented by 20 seconds, and the target track rd(t) schematic representation in the task space as shown in FIG. 3, using this information as input information to the control system.
Further, as a preferred embodiment of the method, the step of solving the inverse kinematics problem based on the first nulling neural network according to the initial value information, the predefined target trajectory information, and the actual information to obtain the driving signal specifically includes:
specifically, first, the kinematic equation of the wheel-type mobile operation robot arm can be expressed by the following formula:
Figure BDA0002850549210000044
wherein the n-dimensional column vector
Figure BDA0002850549210000045
Angle and column vector of n joints of mechanical arm at t moment
Figure BDA0002850549210000046
Figure BDA0002850549210000047
Indicating the angle that the left and right wheels have turned at time t,
Figure BDA0002850549210000048
the position coordinates of the base of the mechanical arm in a three-dimensional task space are represented, and a nonlinear mapping function h (-) represents a kinematic model of the mechanical arm operated by wheel type movement;
the simultaneous derivation of time t on both sides of equation (3) can be obtained:
Figure BDA0002850549210000049
wherein, the matrix
Figure BDA0002850549210000051
Is the jacobian matrix of the robot at time t,
Figure BDA0002850549210000052
representing the actual velocity of the end effector in the task space,
Figure BDA0002850549210000053
indicating the angular velocity of the arm joint rotation and the velocity of the wheel rotation at time t.
Constructing a first error function according to predefined target track information and position information of an end effector of the mechanical arm;
specifically, the target trajectory r is determined according to the time td(t) and the actual trajectory r of the end-effectora(t) defining a vector error function: e (t) ═ rd(t)-ra(t)。
Constructing a first zero-ization neural network and substituting a first error function into the first zero-functionalization neural network to obtain a first differential equation;
specifically, the first nulling neural network is:
Figure BDA0002850549210000054
substituting the first error function into the first zeroizing neural network model can obtain a first differential equation.
Transforming the first differential equation to obtain a differential equation of the driving signal;
according to the initial wheel rotation angle
Figure BDA0002850549210000055
Initial mechanical arm joint angle theta (0) and predefined target track information rd(t) position information r of the end effector of the robot arma(t), the jacobian matrix j (t) and a differential equation of the drive signal to obtain the drive signal q (t).
Further as a preferred embodiment of the present invention, the first differential equation expression is as follows:
Figure BDA0002850549210000056
in the above formula, the first and second carbon atoms are,
Figure BDA0002850549210000057
is rdThe time derivative of (t) is,
Figure BDA0002850549210000058
representing robot base velocity information, J (t) representing an estimated Jacobian matrix,
Figure BDA0002850549210000059
representing the driving information, a constant γ ═ 1 is a design parameter of the zero-ized neural network model, rd(t) represents predefined target trajectory information, ra(t) indicates positional information of the robot arm end effector.
Further as a preferred embodiment of the present invention, the differential equation expression of the driving signal is as follows:
Figure BDA00028505492100000510
in the above formula, the first and second carbon atoms are,
Figure BDA00028505492100000511
representing the pseudo-inverse of the jacobian matrix.
Further, as a preferred embodiment of the present invention, the step of controlling the motion of the wheeled mobile robot arm according to the driving signal and feeding back the actual information specifically includes:
controlling the motion of the wheel type mobile operation mechanical arm according to the driving signal q (t) so that the end effector of the wheel type mobile operation mechanical arm tracks a predefined track in a task space;
real-time measurement of position information r of mechanical arm end effector based on sensor equipmenta(t) velocity information of the end-effector of the robot arm
Figure BDA00028505492100000512
Acceleration information for end effector of mechanical arm
Figure BDA00028505492100000513
Robot arm base speed information
Figure BDA00028505492100000514
And robot arm base acceleration information
Figure BDA0002850549210000061
Further as a preferred embodiment of the method, the step of estimating the jacobian matrix based on the second nulling neural network and the actual information and returning to the step S2 to recalculate the driving signal specifically includes:
defining a second error function and inputting the second error function into a second zero neural network to obtain a second differential equation;
in particular, a second error function is defined:
Figure BDA0002850549210000062
the second zeroizing neural network:
Figure BDA0002850549210000063
wherein
Figure BDA0002850549210000064
The time derivative of ∈ (t) is expressed, and the constant μ ═ 1 represents the design parameter of the nulling neural network.
Transforming the second differential equation to obtain a differential equation related to the Jacobian matrix;
obtaining an estimated Jacobian matrix according to the initial value of the Jacobian matrix, the real-time feedback information, the differential equation of the driving signal and the differential equation related to the Jacobian matrix;
the process returns to step S2 to recalculate the drive signal.
Further as a preferred embodiment of the method, the expression of the second differential equation is as follows:
Figure BDA0002850549210000065
in the above formula, the first and second carbon atoms are,
Figure BDA0002850549210000066
representing the time derivative of the jacobian matrix j (t),
Figure BDA0002850549210000067
representing drive information
Figure BDA0002850549210000068
The time derivative of (a).
Further as a preferred embodiment of the method, the expression of the differential equation with respect to the jacobian matrix is as follows:
Figure BDA0002850549210000069
in the above formula, the first and second carbon atoms are,
Figure BDA00028505492100000610
representing a vector
Figure BDA00028505492100000611
The pseudo-inverse of (1).
As shown in fig. 2, a tracking control system facing a wheeled mobile robot arm includes the following modules:
the initialization module is used for giving initial value information and inputting predefined target track information;
the driving signal module is used for solving an inverse kinematics problem based on the first zero neural network according to the initial value information, the predefined target track information and the actual information to obtain a driving signal;
the control module is used for controlling the motion of the wheel type mobile mechanical arm according to the driving signal and feeding back actual information;
and the Jacobian matrix module is used for estimating a Jacobian matrix based on the second zeroing neural network and the actual information and returning to recalculate the driving signal.
The contents in the system embodiments are all applicable to the method embodiments, the functions specifically realized by the method embodiments are the same as the system embodiments, and the beneficial effects achieved by the method embodiments are also the same as the beneficial effects achieved by the system embodiments.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A tracking control method facing to a wheel type mobile mechanical arm is characterized by comprising the following steps:
s1, giving initial value information and inputting predefined target track information;
s2, solving an inverse kinematics problem based on the first zero neural network according to the initial value information, the predefined target track information and the actual information to obtain a driving signal;
s3, controlling the motion of the wheel type mobile mechanical arm according to the driving signal and feeding back actual information;
s4, estimating the Jacobian matrix based on the second zeroing neural network and the actual information and returning to the step S2 to recalculate the driving signals.
2. The tracking control method for a wheeled mobile robot according to claim 1, wherein the initial value information includes initial values of wheel rotation angles, joint angles of the robot, and jacobian initial values, and the actual information includes position information of the robot end effector, velocity information of the robot end effector, acceleration information of the robot end effector, robot base velocity information, and robot base acceleration information.
3. The tracking control method for the wheeled mobile mechanical arm according to claim 2, wherein the step of solving the inverse kinematics problem based on the first nulling neural network according to the initial value information, the predefined target trajectory information and the actual information to obtain the driving signal specifically comprises:
constructing a first error function according to predefined target track information and position information of an end effector of the mechanical arm;
constructing a first zero-ization neural network and substituting a first error function into the first zero-functionalization neural network to obtain a first differential equation;
transforming the first differential equation to obtain a differential equation of the driving signal;
according to the initial wheel rotation angle
Figure FDA0002850549200000011
Initial mechanical arm joint angle theta (0) and predefined target track information rd(t) position information r of the end effector of the robot arma(t), the jacobian matrix j (t) and a differential equation of the drive signal to obtain the drive signal q (t).
4. The tracking control method for the wheeled mobile mechanical arm according to claim 3, wherein the first differential equation expression is as follows:
Figure FDA0002850549200000012
in the above formula, the first and second carbon atoms are,
Figure FDA0002850549200000013
is rdThe time derivative of (t) is,
Figure FDA0002850549200000014
representing robot base velocity information, J (t) representing an estimated Jacobian matrix,
Figure FDA0002850549200000015
representing the driving information, a constant γ ═ 1 is a design parameter of the zero-ized neural network model, rd(t) represents predefined target trajectory information,ra(t) indicates positional information of the robot arm end effector.
5. The tracking control method for the wheeled mobile mechanical arm according to claim 4, wherein the differential equation expression of the driving signal is as follows:
Figure FDA0002850549200000021
in the above formula, the first and second carbon atoms are,
Figure FDA0002850549200000022
representing the pseudo-inverse of the jacobian matrix.
6. The tracking control method for the wheeled mobile robot arm according to claim 5, wherein the step of controlling the motion of the wheeled mobile robot arm according to the driving signal and feeding back the actual information specifically comprises:
controlling the motion of the wheel type mobile operation mechanical arm according to the driving signal q (t) so that the end effector of the wheel type mobile operation mechanical arm tracks a predefined track in a task space;
real-time measurement of position information r of mechanical arm end effector based on sensor equipmenta(t) velocity information of the end-effector of the robot arm
Figure FDA00028505492000000212
Acceleration information for end effector of mechanical arm
Figure FDA00028505492000000210
Robot arm base speed information
Figure FDA00028505492000000213
And robot arm base acceleration information
Figure FDA00028505492000000211
7. The tracking control method for the wheeled mobile robot arm as claimed in claim 6, wherein the step of estimating the jacobian matrix based on the second zeroizing neural network and the actual information and returning to step S2 to recalculate the driving signal specifically comprises:
defining a second error function and inputting the second error function into a second zero neural network to obtain a second differential equation;
transforming the second differential equation to obtain a differential equation related to the Jacobian matrix;
obtaining an estimated Jacobian matrix according to the initial value of the Jacobian matrix, the real-time feedback information, the differential equation of the driving signal and the differential equation related to the Jacobian matrix;
the process returns to step S2 to recalculate the drive signal.
8. The tracking control method for the wheeled mobile mechanical arm according to claim 7, wherein the expression of the second differential equation is as follows:
Figure FDA0002850549200000023
in the above formula, the first and second carbon atoms are,
Figure FDA0002850549200000024
representing the time derivative of the jacobian matrix j (t),
Figure FDA0002850549200000025
representing drive information
Figure FDA0002850549200000026
The constant μ ═ 1 represents the design parameters of the nulling neural network model.
9. The tracking control method for the wheeled mobile robot arm according to claim 8, wherein the expression of the differential equation of the jacobian matrix is as follows:
Figure FDA0002850549200000027
in the above formula, the first and second carbon atoms are,
Figure FDA0002850549200000028
representing a vector
Figure FDA0002850549200000029
The pseudo-inverse of (1).
10. A tracking control system facing to a wheel type mobile mechanical arm is characterized by comprising the following modules:
the initialization module is used for giving initial value information and inputting predefined target track information;
the driving signal module is used for solving an inverse kinematics problem based on the first zero neural network according to the initial value information, the predefined target track information and the actual information to obtain a driving signal;
the control module is used for controlling the motion of the wheel type mobile mechanical arm according to the driving signal and feeding back actual information;
and the Jacobian matrix module is used for estimating a Jacobian matrix based on the second zeroing neural network and the actual information and returning to recalculate the driving signal.
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CN113650014B (en) * 2021-08-18 2022-05-17 中山大学 Redundant mechanical arm tracking control method based on echo state network
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Application publication date: 20210427