CN112428273A - Control method and system considering mechanical arm physical constraint and model unknown - Google Patents

Control method and system considering mechanical arm physical constraint and model unknown Download PDF

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CN112428273A
CN112428273A CN202011278491.8A CN202011278491A CN112428273A CN 112428273 A CN112428273 A CN 112428273A CN 202011278491 A CN202011278491 A CN 202011278491A CN 112428273 A CN112428273 A CN 112428273A
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mechanical arm
joint
parameters
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谭宁
廖申
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
    • B25J9/1656—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
    • 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
    • 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
    • B25J9/1694—Programme controls characterised by use of sensors other than normal servo-feedback from position, speed or acceleration sensors, perception control, multi-sensor controlled systems, sensor fusion

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
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Abstract

The invention discloses a control method and a control system considering mechanical arm physical constraint and model unknown, wherein the method comprises the following steps: presetting an initial posture and expected parameters of the mechanical arm; reading current joint parameters and end effector information of the mechanical arm according to the sensor; constructing an expected position equation set based on a Jacobian matrix estimation method and a quadratic programming method by taking expected parameters and an initial attitude as constraints; obtaining joint angle motion data according to the expected position equation set, the initial posture, the expected parameters, the current joint parameters and the end effector information; and sending the joint angle motion data to a mechanical arm controller to control the mechanical arm to move. The system comprises: the system comprises a parameter presetting module, an information reading module, an equation set constructing module, a solving module and a control module. By using the invention, the mechanical arm can be controlled to complete the tracking control task, and meanwhile, the invention also has the function of avoiding the joint limit. The control method and the control system which consider the physical constraint of the mechanical arm and the unknown model can be widely applied to the field of mechanical control.

Description

Control method and system considering mechanical arm physical constraint and model unknown
Technical Field
The invention belongs to the field of mechanical control, and particularly relates to a control method and a control system considering mechanical arm physical constraint and model unknown.
Background
The existing mechanical arm control method is based on a forward kinematics model, a jacobian matrix is determined by solving the data of each moment of the mechanical arm and controls the movement of the mechanical arm according to the data of each moment of the mechanical arm, however, even though the mechanical arms are in the same batch and type, the jacobian matrix may be different due to the assembly difference of the mechanical arms, so that errors are generated when the algorithm is applied, the accuracy of the solution is influenced, secondly, the types of the mechanical arms are various, and the forward kinematics models of some mechanical arms are difficult to measure and calculate, so that the method is not strong in transportability.
Disclosure of Invention
In order to solve the above technical problems, an object of the present invention is to provide a control method and system considering the physical constraints and unknown model of a robot arm, so that an end effector of the robot arm can move according to a preset path, and the robot arm can avoid joint angles and speed limits of the robot arm during the movement process, thereby completing tasks well.
The first technical scheme adopted by the invention is as follows: a control method that considers mechanical arm physical constraints and model unknowns, comprising the steps of:
presetting an initial posture and expected parameters of the mechanical arm;
reading current joint parameters and end effector information of the mechanical arm according to the sensor;
constructing an expected position equation set based on a Jacobian matrix estimation method and a quadratic programming method by taking expected parameters and an initial attitude as constraints;
obtaining joint angle motion data according to the expected position equation set, the initial posture, the expected parameters, the current joint parameters and the end effector information;
and sending the joint angle motion data to a mechanical arm controller to control the mechanical arm to move.
Further, the expected parameters include an expected track, joint speed limits and angle limits, the current joint parameters include a mechanical arm joint angle, a mechanical arm joint speed and a mechanical arm joint acceleration, and the end effector information includes an actual acceleration of the end of the mechanical arm and an actual speed of the end of the mechanical arm.
Further, the step of constructing the expected position equation set based on the jacobian matrix estimation method and quadratic programming with the expected parameters and the initial attitude as constraints specifically includes:
obtaining a reverse motion equation of the mechanical arm based on a quadratic programming method;
processing the reverse motion equation of the mechanical arm through a primal-dual neural network to obtain a differential equation;
obtaining a position equation based on a Jacobian matrix estimation method;
and obtaining a desired position equation set according to the differential equation and the position equation.
Further, the differential equation is as follows:
Figure RE-GDA0002882108960000021
in the above formula, u (t) is a variable to be solved, m is a dimension of a task space at the end of the manipulator, n is a degree of freedom of the manipulator, γ is a convergence rate parameter of the orthodual neural network, P (·) is a projection function, m (t) is a matrix, and q (t) is a vector.
Further, the position equation is as follows:
Figure RE-GDA0002882108960000022
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002882108960000023
is the variable to be solved for and is,
Figure RE-GDA0002882108960000024
representing the actual acceleration of the tip of the robotic arm,
Figure RE-GDA0002882108960000025
the acceleration of each joint of the mechanical arm is shown,
Figure RE-GDA0002882108960000026
representing the actual velocity of the tip of the robotic arm,
Figure RE-GDA0002882108960000027
the velocity of each joint of the mechanical arm is shown,
Figure RE-GDA0002882108960000028
to represent
Figure RE-GDA0002882108960000029
Mu is a convergence rate parameter.
Further, the obtaining of the joint angle movement data further comprises verifying whether the joint angle movement data is within a limit range according to the joint speed limit and the angle limit.
Further, the joint angle movement data includes angle information and joint velocity information at which the joint should be located at a certain time.
The second technical scheme adopted by the invention is as follows: a control system that accounts for mechanical arm physical constraints and model unknowns, comprising the following modules:
the parameter presetting module is used for presetting an initial posture and expected parameters of the mechanical arm;
the information reading module is used for reading the current joint parameters and the information of the end effector of the mechanical arm according to the sensor;
the system comprises an equation set building module, a position estimation module and a position estimation module, wherein the equation set building module is used for building an expected position equation set based on a Jacobian matrix estimation method and a quadratic programming method by taking expected parameters and an initial attitude as constraints;
the solving module is used for obtaining joint angle motion data according to the expected position equation set, the initial attitude, the expected parameters, the current joint parameters and the end effector information;
and the control module is used for sending the joint angle motion data to the mechanical arm controller and controlling the mechanical arm to move.
The method and the system have the beneficial effects that: under the condition of not using a prior forward kinematics model of the mechanical arm, the mechanical arm can be controlled to complete a tracking control task, and meanwhile, the method also has a joint limit avoiding function, so that the solution accuracy is improved, and the method has strong transportability.
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FIG. 1 is a flow chart of the steps of a control method of the present invention that takes into account physical constraints of the robotic arm and model unknowns;
FIG. 2 is a block diagram of a control system of the present invention that takes into account the physical constraints and model unknowns of the robotic arm;
FIG. 3 is a state diagram of the robotic arm after the initial pose has been entered in accordance with 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.
As shown in fig. 1, the present invention provides a control method considering the physical constraints and model unknowns of a robot arm, the method comprising the steps of:
s1, presetting an initial posture and expected parameters of the mechanical arm;
specifically, the initial posture of the mechanical arm is set as follows: [ -1.596; 4.612, respectively; 1.474; -2.498; 2.011; 0.792], each value representing, in turn from left to right, the angle of each joint of the robot arm from the base to the end, in rad, the joint angle being sent to the controller of the robot arm, which will move to this position, when the state of the robot arm is as in figure 3.
In addition, a desired trajectory of the robot arm tip in three-dimensional space is defined:
x＝x0+r·sin(2πt/T)
Figure RE-GDA0002882108960000031
z＝z0
where r is 0.06m, T represents the current time, T represents the total duration of the trajectory tracking task, and T is 10. x is the number of0、y0And z0Respectively showing the mechanical armsThe initial position of the tip.
S2, reading current joint parameters and end effector information of the mechanical arm according to the sensor;
s3, constructing an expected position equation set based on a Jacobian matrix estimation method and a quadratic programming method by taking the expected parameters and the initial attitude as constraints;
specifically, the system of equations is:
Figure RE-GDA0002882108960000032
Figure RE-GDA0002882108960000033
s4, obtaining joint angle motion data according to the expected position equation set, the initial posture, the expected parameters, the current joint parameters and the end effector information;
and S5, sending the joint angle motion data to the mechanical arm controller to control the mechanical arm to move.
Specifically, the value of u (t) is sent to the mechanical arm by the SendJointAngle method, so that the mechanical arm can move according to the solved expected joint angle at the time t.
Further as a preferred embodiment of the method, the desired parameters include a desired trajectory, joint speed limits, and angle limits, the current joint parameters include a robot joint angle, a robot joint speed, and a robot joint acceleration, and the end effector information includes a robot end actual acceleration and a robot end actual speed.
Further, as a preferred embodiment of the method, the step of constructing the desired position equation set based on the jacobian matrix estimation method and quadratic programming with the desired parameters and the initial pose as constraints specifically includes:
obtaining a reverse motion equation of the mechanical arm based on a quadratic programming method;
specifically, a quadratic programming method is first used to solve the inverse kinematics problem of the manipulator:
Figure RE-GDA0002882108960000041
the constraint conditions are as follows:
J(t)x(t)＝b(t)
ξ-≤x(t)≤ξ+
where x (t) is the decision variable to be solved in real time.
Figure RE-GDA0002882108960000042
Is the angular velocity of the joint of the robot arm, and n is the degree of freedom of the robot arm. The coefficient matrix W is an identity matrix having n rows and n columns. Coefficient vector c ═ l (θ (t) - θm) Wherein thetamIs the intermediate position of the movable angle of each joint, θ (t) is the joint angle at the current time t, and l is a parameter for adjusting the movable range of the joint, and the default is 1. b (t) is the desired trajectory of the end effector of the robotic arm in task space, is a vector, and is a function of time.
ξ-And xi+Are n-dimensional vectors representing the physical limits of the joints of the robotic arm, respectively. Assume that the joints of the robotic arm have speed and angle limits:
θ-≤θ≤θ+
Figure RE-GDA0002882108960000043
the two constraints can be unified into one double-ended constraint through joint limit transitions:
Figure RE-GDA0002882108960000044
alpha is a parameter for adjusting the size of the feasible region after the joint limit transition. Here double-ended constraint after conversion
Figure RE-GDA0002882108960000045
Should be within a range higher than the original speed limit range
Figure RE-GDA0002882108960000046
Slightly larger. Xi-And xi+The specific definition of (A) is as follows:
Figure RE-GDA0002882108960000047
Figure RE-GDA0002882108960000048
processing the reverse motion equation of the mechanical arm through a primal-dual neural network to obtain a differential equation;
obtaining a position equation based on a Jacobian matrix estimation method;
and obtaining a desired position equation set according to the differential equation and the position equation.
Further as a preferred embodiment of the method, the differential equation is as follows:
Figure RE-GDA0002882108960000051
in the above formula, u (t) is a variable to be solved, m is a dimension of a task space at the end of the manipulator, n is a degree of freedom of the manipulator, γ is a convergence rate parameter of the orthodual neural network, P (·) is a projection function, m (t) is a matrix, and q (t) is a vector.
In addition, the projection function P (·), the matrix m (t), and the vector q (t) are defined as follows:
Figure RE-GDA0002882108960000052
Figure RE-GDA0002882108960000053
Figure RE-GDA0002882108960000054
Figure RE-GDA0002882108960000055
is the derivative of the desired position of the end of the robot arm in task space over time, at time t, i.e. the desired velocity in task space. In the present example of the process, the first,
Figure RE-GDA0002882108960000056
the following equation is obtained:
Figure RE-GDA0002882108960000057
Figure RE-GDA0002882108960000058
Figure RE-GDA0002882108960000059
the parameter of the projection function P (-) is a vector, and the projection function is applied to the input vector vi×1Each element of (1) is subjected to upper and lower limit constraints, and the specific values of the upper and lower limits of the ith element are respectively determined by
Figure RE-GDA00028821089600000510
And
Figure RE-GDA00028821089600000511
and (4) specifying.
Figure RE-GDA00028821089600000512
And
Figure RE-GDA00028821089600000513
the following method was used. Suppose thatThe joints of the mechanical arm have speed and angle limits:
θ-≤θ≤θ+
Figure RE-GDA00028821089600000514
the two constraints can be unified into one double-ended constraint through joint limit transitions:
Figure RE-GDA00028821089600000515
alpha is a parameter for adjusting the size of the feasible region after the joint limit transition. Here double-ended constraint after conversion
Figure RE-GDA00028821089600000516
Should be within a range higher than the original speed limit range
Figure RE-GDA00028821089600000517
Slightly larger. Xi-And xi+The specific definition of (A) is as follows:
Figure RE-GDA0002882108960000061
Figure RE-GDA0002882108960000062
Figure RE-GDA0002882108960000063
and
Figure RE-GDA0002882108960000064
is just the above-mentioned joint limit xi-And xi+The respective ith element.
Further as a preferred embodiment of the method, the position equation is as follows:
Figure RE-GDA0002882108960000065
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002882108960000066
is the variable to be solved for and is,
Figure RE-GDA0002882108960000067
representing the actual acceleration of the tip of the robotic arm,
Figure RE-GDA0002882108960000068
the acceleration of each joint of the mechanical arm is shown,
Figure RE-GDA0002882108960000069
representing the actual velocity of the tip of the robotic arm,
Figure RE-GDA00028821089600000610
the velocity of each joint of the mechanical arm is shown,
Figure RE-GDA00028821089600000611
to represent
Figure RE-GDA00028821089600000612
Mu is a convergence rate parameter.
In particular, the amount of the solvent to be used,
Figure RE-GDA00028821089600000613
to represent
Figure RE-GDA00028821089600000614
The derivative with respect to time is that of,
Figure RE-GDA00028821089600000615
and
Figure RE-GDA00028821089600000616
all from a robotic armA specific value is read in the sensor.
Further as a preferred embodiment of the method, the obtaining of the joint angle movement data further comprises verifying whether the joint angle movement data is within a limit range according to the joint speed limit and the angle limit.
In particular, to verify the validity of the proposed method, the joint speed limit (in rad/s) of the robot arm is set to:
[∞；∞；∞；0.2；∞；∞]
the joint angle limit (in rad) for the robot arm is set to:
[2π；2π；1.6；2π；2π；2π]
the maximum velocity of the joint 4 is set to 0.1rad/s and the maximum angle of the joint 3 is set to 1.6 rad.
Further as a preferred embodiment of the method, the joint angular movement data comprises angular information and joint velocity information at which the joint should be located at a certain time.
Specifically, by setting α to 1 and solving the position equation system using the method of ode15s in Matlab, a numerical solution of the time-varying vector function u (t) can be obtained. The input of the function is time t, and the output is a vector u with dimension n + m. The first n items of the vector u are the angles of the n joints of the mechanical arm at the time t, and the mechanical arm can be controlled to complete the track tracking task according to the information.
As shown in fig. 2, a control system that considers mechanical arm physical constraints and model unknowns includes the following modules:
the parameter presetting module is used for presetting an initial posture and expected parameters of the mechanical arm;
the information reading module is used for reading the current joint parameters and the information of the end effector of the mechanical arm according to the sensor;
the system comprises an equation set building module, a position estimation module and a position estimation module, wherein the equation set building module is used for building an expected position equation set based on a Jacobian matrix estimation method and a quadratic programming method by taking expected parameters and an initial attitude as constraints;
the solving module is used for obtaining joint angle motion data according to the expected position equation set, the initial attitude, the expected parameters, the current joint parameters and the end effector information;
and the control module is used for sending the joint angle motion data to the mechanical arm controller and controlling the mechanical arm to move.
The contents in the above method embodiments are all applicable to the present system embodiment, the functions specifically implemented by the present system embodiment are the same as those in the above method embodiment, and the beneficial effects achieved by the present system embodiment are also the same as those achieved by the above method embodiment.
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 (8)

1. A control method considering mechanical arm physical constraints and model unknowns is characterized by comprising the following steps:
presetting an initial posture and expected parameters of the mechanical arm;
reading current joint parameters and end effector information of the mechanical arm according to the sensor;
constructing an expected position equation set based on a Jacobian matrix estimation method and a quadratic programming method by taking expected parameters and an initial attitude as constraints;
obtaining joint angle motion data according to the expected position equation set, the initial posture, the expected parameters, the current joint parameters and the end effector information;
and sending the joint angle motion data to a mechanical arm controller to control the mechanical arm to move.
2. The control method of claim 1, wherein the desired parameters comprise a desired trajectory, joint velocity limits, and angle limits, wherein the current joint parameters comprise a robot joint angle, a robot joint velocity, and a robot joint acceleration, and wherein the end effector information comprises a robot end actual acceleration and a robot end actual velocity.
3. The control method taking physical constraints and unknown models of mechanical arms into consideration as claimed in claim 2, wherein the step of constructing the desired position equation system based on a jacobian matrix estimation method and quadratic programming with the desired parameters and the initial attitude as constraints specifically comprises:
obtaining a reverse motion equation of the mechanical arm based on a quadratic programming method;
processing the reverse motion equation of the mechanical arm through a primal-dual neural network to obtain a differential equation;
obtaining a position equation based on a Jacobian matrix estimation method;
and obtaining a desired position equation set according to the differential equation and the position equation.
4. A control method taking into account the physical constraints and model unknowns of the mechanical arm according to claim 3, wherein the differential equation is as follows:
Figure FDA0002779940250000011
in the above formula, u (t) is a variable to be solved, m is a dimension of a task space at the end of the manipulator, n is a degree of freedom of the manipulator, γ is a convergence rate parameter of the primal-dual neural network, I is a unit matrix with m + n rows and columns, P (·) is a projection function, m (t) is a matrix, and q (t) is a vector.
5. The control method considering the physical constraints and model unknowns of the mechanical arm according to claim 4, wherein the position equation is as follows:
Figure FDA0002779940250000012
in the above formula, the first and second carbon atoms are,
Figure FDA0002779940250000013
is the variable to be solved for and is,
Figure FDA0002779940250000014
representing the actual acceleration of the end of the robot arm,
Figure FDA0002779940250000015
the velocity of each joint of the mechanical arm is shown,
Figure FDA0002779940250000021
representing the actual speed of the end of the robot arm,
Figure FDA0002779940250000022
the speed of each joint of the mechanical arm is shown,
Figure FDA0002779940250000023
to represent
Figure FDA0002779940250000024
Mu is a convergence rate parameter.
6. The control method of claim 5, wherein the obtaining joint angle motion data further comprises verifying whether the joint angle motion data is within a limit based on the joint speed limit and the angle limit.
7. The control method considering the physical constraints and the unknown model of the mechanical arm as claimed in claim 6, wherein the joint angle motion data comprises angle information and joint speed information of the joint at a certain moment.
8. A control system that accounts for mechanical arm physical constraints and model unknowns, comprising the following modules:
the parameter presetting module is used for presetting an initial posture and expected parameters of the mechanical arm;
the information reading module is used for reading the current joint parameters and the information of the end effector of the mechanical arm according to the sensor;
the system comprises an equation set building module, a position estimation module and a position estimation module, wherein the equation set building module is used for building an expected position equation set based on a Jacobian matrix estimation method and a quadratic programming method by taking expected parameters and an initial attitude as constraints;
the solving module is used for obtaining joint angle motion data according to the expected position equation set, the initial attitude, the expected parameters, the current joint parameters and the end effector information;
and the control module is used for sending the joint angle motion data to the mechanical arm controller and controlling the mechanical arm to move.
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