CN111975771A - Mechanical arm motion planning method based on deviation redefinition neural network - Google Patents

Mechanical arm motion planning method based on deviation redefinition neural network Download PDF

Info

Publication number
CN111975771A
CN111975771A CN202010754873.7A CN202010754873A CN111975771A CN 111975771 A CN111975771 A CN 111975771A CN 202010754873 A CN202010754873 A CN 202010754873A CN 111975771 A CN111975771 A CN 111975771A
Authority
CN
China
Prior art keywords
equation
time
mechanical arm
function
redundant
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202010754873.7A
Other languages
Chinese (zh)
Inventor
张智军
郑陆楠
苏铄淼
李泽扬
崔耀威
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
South China University of Technology SCUT
Original Assignee
South China University of Technology SCUT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by South China University of Technology SCUT filed Critical South China University of Technology SCUT
Priority to CN202010754873.7A priority Critical patent/CN111975771A/en
Publication of CN111975771A publication Critical patent/CN111975771A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • 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

Landscapes

  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
  • Physics & Mathematics (AREA)
  • Artificial Intelligence (AREA)
  • Evolutionary Computation (AREA)
  • Fuzzy Systems (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Numerical Control (AREA)
  • Manipulator (AREA)

Abstract

The invention discloses a mechanical arm motion planning method based on a bias redefinition neural network, which comprises the following steps: establishing a kinematic equation of the redundant manipulator according to the model and the parameters of the actual manipulator; converting a redundant manipulator kinematic equation into a speed layer kinematic equation, and describing the speed layer kinematic equation into a smooth time-varying linear equation; acquiring joint angle and tail end track information of a mechanical arm, constructing a time-varying parameter matrix according to parameters of the mechanical arm, the joint angle of the mechanical arm and the tail end track information, and acquiring a corresponding time derivative; designing a deviation function according to a smooth time-varying linear equation; redefining a recurrent neural network by adopting a deviation function, and designing a time-varying linear equation solver aiming at the redundant robot arm by combining a time-varying parameter matrix and a time derivative thereof; and solving a time-varying linear equation solver to obtain the expected motion trail. The invention can stably and accurately plan the motion of the redundant manipulator by adopting the deviation redefinition neural network solver.

Description

Mechanical arm motion planning method based on deviation redefinition neural network
Technical Field
The invention relates to the field of redundant manipulator motion planning, in particular to a manipulator motion planning method based on a deviation redefinition neural network.
Background
The redundant manipulator is a manipulator with redundant joints, and compared with a non-redundant manipulator, the redundant manipulator has more degrees of freedom, so that the problems of single task joint angle and poor practicability generated by the non-redundant manipulator can be solved, and more joint angle combination selections are provided for manipulator motion planning. When the redundant manipulator completes the main tasks of the end effector, additional tasks such as obstacle avoidance, shutdown limit position, manipulator singular state and the like can be completed. In automated industrial production, the mechanical arm is usually required to perform batch production activities, and path planning is often required to be performed on the mechanical arm according to a target, so that production efficiency can be improved if the path planning of the mechanical arm can be completed quickly. Therefore, the method is significant for researching the path planning of the redundant manipulator.
The artificial neural network is a parallel distributed signal processing mathematical model method for simulating the animal nervous system. As an important network form in the artificial neural network, the recurrent neural network method has been widely used in many fields, such as speech recognition, non-convex optimization, algebraic problems, time-varying problems, unmanned aerial vehicles, robots, etc., through many years of development. In the aspect of robots, the mechanical arm motion planning problem can be constructed into a time-varying quadratic planning solving problem, and can be finally converted into a time-varying equation solving problem through a Lagrange multiplier method. In recent years, many researchers pay attention to how to solve the corresponding time-varying equation problem by adopting a recurrent neural network method. Among them, researchers have proposed a zeroth order neural network method with an integral term to solve the time-varying problem with strong anti-interference ability. But the corresponding method can bring problems of excessive operation and the like.
In order to solve the time-varying problem and solve the computation overshoot, and to implement a faster and stronger recurrent neural network design, a recurrent neural network method with stronger performance needs to be provided.
Disclosure of Invention
The invention aims to provide a mechanical arm motion planning method based on a bias redefinition neural network aiming at the defects of the prior art, designs a novel bias redefinition recurrent neural network, and can realize a fast convergence, strong anti-interference and overshoot-free solving result.
The object of the present invention can be achieved by at least one of the following means.
A mechanical arm motion planning method based on a deviation redefinition neural network comprises the following steps:
establishing a kinematic equation of the redundant manipulator according to the model and the parameters of the actual redundant manipulator;
converting the redundant manipulator kinematic equation into a speed layer kinematic equation, and describing the speed layer kinematic equation into a smooth time-varying linear equation;
acquiring joint angle and tail end track information of a mechanical arm through an airborne sensor on the redundant mechanical arm, constructing a time-varying parameter matrix according to parameters of the mechanical arm, the joint angle of the mechanical arm and the tail end track information, and acquiring a corresponding time derivative;
designing a deviation function for completing a motion planning task according to the smooth time-varying linear equation;
redefining a recurrent neural network by adopting the deviation function, and designing a time-varying linear equation solver for the redundant robot arm by combining the time-varying parameter matrix and the time derivative thereof;
and solving the network state solution obtained by the time-varying linear equation solver to obtain an optimal solution of the redundant robot system for completing the motion planning task, wherein the optimal solution is the expected motion track of the redundant robot system.
Further, the redundant manipulator kinematics equation is expressed as:
r(t)＝f(θ(t)) (1)
where θ (t) is the joint angle vector of the redundant manipulator, r (t) is the desired end trajectory vector of the redundant manipulator, and f (·) is a nonlinear mapping function defining the joint angle of the redundant manipulator in a Cartesian coordinate system to the coordinates of the end trajectory.
Further, two sides of the redundant manipulator kinematic equation (1) are derived with respect to time to obtain a redundant manipulator kinematic equation in a velocity layer:
Figure BDA0002611188910000021
wherein J (theta (t)). epsilon.Rm×nIs an m x n dimensional matrix in the real number domain,
Figure BDA0002611188910000022
is a Jacobian matrix of the redundant manipulator, n represents the degree of freedom of the manipulator, m represents the space dimension of the tail end track of the manipulator,
Figure BDA0002611188910000023
and
Figure BDA0002611188910000024
the derivative of the redundant manipulator joint angle and the tip trajectory with respect to time, respectively.
The kinematic equation of the angular derivative of the redundant manipulator joint, namely the following formula (3), can be obtained according to the equation (2), and the planning of the redundant manipulator joint angle is realized through the kinematic equation of the redundant manipulator joint angular derivative,
Figure BDA0002611188910000025
wherein, J-1(θ(t))∈Rn×mIs the inverse matrix of J (theta (t)) in the real number domain. To solve J-1(θ (t)), the redundant manipulator kinematics in the velocity layer equation (2) is described as a smooth time-varying linear equation:
Figure BDA0002611188910000026
t represents a time variable, a (t) J (θ (t)) JT(θ(t))，C＝-JT(θ (t)), at this time, JT(θ (t)) represents the transpose of J (θ), A (t) ε Rm×mAnd C (t) e Rm×nIs a time-varying parameter matrix such that a unique solution X of equation (4) holds*(t) is J to be solved in equation (3)-1(θ (t)), namely X*(t)＝J-1(θ(t))。
Further, the time-varying parameter matrixes A (t) and C (t) in the smooth time-varying linear equation are formed by combining mechanical arm model parameter information, joint angle signals acquired by an actual redundant mechanical arm airborne sensor and system expected operation target signals.
Further, according to the smooth time-varying linear equation, a deviation function is designed as follows:
E(t)＝A(t)X(t)+C(t) (5)
when the deviation function E (t) is equal to zero or converges to zero, then a time-varying unique solution X of the smooth time-varying linear equation (4) can be obtained*(t), X (t) is a solution obtained by an algorithm, and X (t) is converged to X*(t), the optimal solution of equation (4) can be found.
Further, the redefining of the recurrent neural network by using the deviation function, in combination with the time-varying parameter matrix and the time derivative thereof, designs a time-varying linear equation solver for the redundant robot arm, specifically:
the design redefined error function is:
Figure BDA0002611188910000031
wherein the content of the first and second substances,
Figure BDA0002611188910000032
for activating the function, a monotone increasing odd function can be selected, and sigma and rho are positive scalar value parameters for measuring the convergence speed of the recurrent neural network; e (τ) is the deviation function of equation (5) and refers to the initial value of equation (6), i.e.
Figure BDA0002611188910000033
Substituting the error function (6) into the neurodynamics design formula
Figure BDA0002611188910000034
Can obtain
Figure BDA0002611188910000035
Wherein the content of the first and second substances,
Figure BDA0002611188910000036
for the activation function applicable to the zeroing neural network, γ ∈ Rm×mTo measure the positive definite matrix of the convergence rate of the solution process,
Figure BDA0002611188910000037
according to equation (7), the arrangement can be:
Figure BDA0002611188910000038
vectorization conversion is performed on the above equation to obtain the time-varying linear equation solver:
Figure BDA0002611188910000039
wherein the content of the first and second substances,
Figure BDA00026111889100000310
Inthe unit matrix is represented by a matrix of units,
Figure BDA00026111889100000311
derivative denoted as M (t), R (t) ═ M-1(t)，M-1(t) denotes the inverse of M (t),
Figure BDA00026111889100000312
the derivative of the vectorized representation of c (t),
Figure BDA00026111889100000313
is an error function of the vectorization and,
Figure BDA00026111889100000314
is an error function of the vectorization and,
Figure BDA00026111889100000315
is the derivative of the solution of the vectorized time-varying equation,
Figure BDA00026111889100000316
is the vectorized residual.
Further, equation (9) is discretized by the expression
Figure BDA00026111889100000317
Wherein, Delta is discrete step length, k is iteration number,
Figure BDA00026111889100000318
is an approximate solution of the equation from the k-th iteration,
Figure BDA00026111889100000319
is an error function of the k-th order, RkIs the r (t) function of the kth iteration,
Figure BDA00026111889100000320
is the derivative of m (t) for the kth iteration,
Figure BDA00026111889100000321
is the k-th iteration
Figure BDA00026111889100000322
The derivative of (a) of (b),
Figure BDA00026111889100000323
is the error function of the ith vectorization,
Figure BDA00026111889100000324
is the vectorized activation function of the k-th iteration,
Figure BDA00026111889100000325
is an error function of vectorization.
By discretizing equation (10), the solution x (t) J of equation (4) can be obtained iteratively-1(θ (t)) can be obtained
Figure BDA0002611188910000041
And further integrating to obtain a joint angle theta (t) of the redundant manipulator completing the tail end track target task, namely the optimal solution of the redundant robot system completing the motion planning task.
Further, the monotonically increasing odd function is, for example, any one of a linear activation function, a hyperbolic S-type activation function, and a power function type activation function.
Compared with the prior art, the invention has the following beneficial effects:
the method uses a time-varying parameter matrix deviation redefinition recurrent neural network method, has stability, quick convergence and strong robustness in solving a smooth time-varying linear equation problem, adopts a redundant manipulator kinematics equation for description, and models an actual system into a time-varying problem using a neural network method with strong anti-interference capability. The method has the capability of planning and predicting the tail end track of the mechanical arm, can quickly, accurately and real-timely approach the problem and correct solution, solves the problem of overshoot in the prior art, and can better realize the motion planning of the mechanical arm.
Drawings
FIG. 1 is a flow chart of a redundant manipulator motion planning method of the present invention based on bias redefinition of a recurrent neural network.
Fig. 2 is an implementation framework of an actual system solver according to an embodiment of the present invention.
FIG. 3 is a schematic view of a redundant robotic arm according to an embodiment of the present invention moving along a planned path.
FIG. 4 is a schematic illustration of a path of motion of a redundant robotic arm in accordance with an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Examples
The embodiment provides a mechanical arm motion planning method based on a bias redefinition neural network, a flowchart of the method is shown in fig. 1, and the method comprises the following steps:
(1) establishing a kinematic equation of the redundant manipulator according to the parameter relationship between the redundant manipulator tail end track of the redundant manipulator model and the manipulator joint angle in the actual system;
(2) converting the redundant manipulator kinematic equation into a speed layer kinematic equation, and describing the speed layer kinematic equation into a smooth time-varying linear equation;
(3) the method comprises the steps of obtaining joint angle and tail end track information of a mechanical arm through an airborne sensor on the redundant mechanical arm, constructing a time-varying parameter matrix according to parameters of the mechanical arm, the joint angle of the mechanical arm and the tail end track information, and obtaining a corresponding time derivative.
(4) And designing a deviation function of the system for completing a motion planning task according to the smooth time-varying linear equation.
(5) Redefining a recurrent neural network by adopting the deviation function, and designing a time-varying linear equation solver for the redundant robot arm by combining the time-varying parameter matrix and the time derivative thereof;
(6) and solving the network state solution obtained by the time-varying linear equation solver to obtain the optimal solution for completing the motion planning task by the redundant robot system.
The kinematic equation of the redundant manipulator in the step (1) is expressed as follows:
r(t)＝f(θ(t)) (1)
where θ (t) is the joint angle vector of the redundant manipulator, r (t) is the desired end trajectory vector of the redundant manipulator, and f (·) is a nonlinear mapping function defining the joint angle of the redundant manipulator in a Cartesian coordinate system to the coordinates of the end trajectory.
And (3) obtaining a kinematic equation of the redundant manipulator in a speed layer by derivation of time on two sides of the kinematic equation (1) of the redundant manipulator:
Figure BDA0002611188910000051
wherein J (theta (t)). epsilon.Rm×nIs an m x n dimensional matrix in the real number domain,
Figure BDA0002611188910000052
is a Jacobian matrix of the redundant manipulator, n represents the degree of freedom of the manipulator, m represents the space dimension of the tail end track of the manipulator,
Figure BDA0002611188910000053
and
Figure BDA0002611188910000054
respectively the derivative of the joint angle and the tail end track of the redundant manipulator with respect to time t;
the kinematic equation of the angular derivative of the redundant manipulator joint, namely the following formula (3), can be obtained according to the equation (2), and the planning of the redundant manipulator joint angle is realized through the kinematic equation of the redundant manipulator joint angular derivative,
Figure BDA0002611188910000055
where r (t) is the end trajectory, which can be known according to the specification of the task requirements, i.e. can be obtained
Figure BDA0002611188910000056
For example, r (t) may be a sin (t) function, then
Figure BDA0002611188910000057
Is cos (t), J-1(θ(t))∈Rn×mIs an inverse matrix of J (theta (t)) in the real number domain, in order to solve for J-1(θ (t)), the redundant manipulator kinematics in the velocity layer equation (2) is described as a smooth time-varying linear equation:
Figure BDA0002611188910000058
t represents a time variable, a (t) J (θ (t)) JT(θ(t))，C＝-JT(θ (t)), at this time, JT(θ (t)) represents the transpose of J (θ), A (t) ε Rm×mAnd C (t) e Rm×nIs a time-varying parameter matrix; if a unique solution X of linear equation (4) can be found*(t) such that equation (4) holds, and at this time, the solution of equation (4) is x (t) J-1(θ (t)) is J to be solved in equation (3)-1(θ(t))。
The time-varying parameter matrixes A (t) and C (t) in the smooth time-varying linear equation are formed by combining mechanical arm model parameter information, joint angle signals acquired by an actual redundant mechanical arm airborne sensor and system expected operation target signals, and the time derivative matrixes
Figure BDA0002611188910000059
And
Figure BDA00026111889100000510
is known or can be accurately estimated. The time derivative can be accurately estimated by the longstotta method in numerical dispersion.
In the step (4), according to the smooth time-varying linear equation, a deviation function of the system for completing a motion planning task is designed, and the method specifically comprises the following steps:
according to the smooth time-varying linear equation (4), the deviation function is designed as follows:
E(t)＝A(t)X(t)+C(t) (5)
when the deviation function E (t) is equal to zero or converges to zero, then a time-varying unique solution X of the smooth time-varying linear equation (4) can be obtained*(t), X (t) is a solution obtained by an algorithm, and X (t) is converged to X*(t), the optimal solution of equation (4) can be found.
In the step (5), redefining a recurrent neural network by using the deviation function, and designing a time-varying linear equation solver for the redundant robot arm by combining the time-varying parameter matrix and the time derivative thereof, wherein the redefinition is as follows:
the redefined error function is designed to be,
Figure BDA0002611188910000061
wherein the content of the first and second substances,
Figure BDA0002611188910000062
for the activation function, a monotonically increasing odd function may be selected, the monotonically increasing odd function being one of a linear activation function, a hyperbolic sigmoid activation function, and a power function type activation function, σ and ρ are positive scalar value parameters for measuring the convergence speed of the recurrent neural network, and E (τ) is a deviation function of formula (5), which refers to an initial value of formula (6), that is, an initial value of formula (6)
Figure BDA0002611188910000063
Substituting the error function (6) into the neurodynamics design formula
Figure BDA0002611188910000064
Can obtain
Figure BDA0002611188910000065
Wherein the content of the first and second substances,
Figure BDA0002611188910000066
for the activation function applicable to the zeroing neural network, γ ∈ Rm×mTo measure the positive definite matrix of the convergence rate of the solution process,
Figure BDA0002611188910000067
according to equation (7), the arrangement can be:
Figure BDA0002611188910000068
vectorization conversion is carried out on the above formula, and a time-varying linear equation solver can be obtained:
Figure BDA0002611188910000069
wherein the content of the first and second substances,
Figure BDA00026111889100000610
Inthe unit matrix is represented by a matrix of units,
Figure BDA00026111889100000611
derivative denoted as M (t), R (t) ═ M-1(t)，M-1(t) denotes the inverse of M (t),
Figure BDA00026111889100000612
is a vectorized representation of C (t),
Figure BDA00026111889100000613
is an error function of the vectorization and,
Figure BDA00026111889100000614
is an activation function that is vectorized,
Figure BDA00026111889100000615
is the derivative of the solution of the vectorized time-varying equation,
Figure BDA00026111889100000616
is the vectorized residual.
Solving a time-varying linear equation solver in the step (6) to obtain a network state solution, wherein the concrete solving process is as follows:
equation (9) discretizing the expression as
Figure BDA00026111889100000617
Wherein, Delta is discrete step length, k is iteration number,
Figure BDA00026111889100000618
is an approximate solution of the equation from the k-th iteration,
Figure BDA00026111889100000619
is an error function of the k-th order, RkIs the r (t) function of the kth iteration,
Figure BDA0002611188910000071
is the derivative of m (t) for the kth iteration,
Figure BDA0002611188910000072
is the k-th iteration
Figure BDA0002611188910000073
The derivative of (a) of (b),
Figure BDA0002611188910000074
is the error function of the ith vectorization,
Figure BDA0002611188910000075
is the vectorized activation function of the k-th iteration,
Figure BDA0002611188910000076
is an error function of vectorization.
Through the discretization formula (10), the solution X of the equation (4) can be obtained through iteration*(t)＝J-1(θ (t)) can be obtained
Figure BDA0002611188910000077
Further integrating to obtain a joint angle theta (t) of the redundant manipulator completing the tail end track target task, namely the optimal solution of the redundant robot system completing the motion planning taskAnd finishing the motion planning of the mechanical arm.
Fig. 2 is a frame of implementing the robot arm motion planning method based on the bias redefinition neural network according to the embodiment, which includes the following modules:
1) the data acquisition part comprises data obtained by an external sensor, and expected terminal track and mechanical arm state data, and the two parts are basic contents forming a time-varying parameter matrix;
2) the input interface circuit is an interface channel between external set data and a processor and is realized by different interface circuits and protocols according to different sensors;
3) the processor part comprises a time-varying parameter matrix and a time-varying smooth linear equation solver based on a deviation redefinition neural network method, wherein the time-varying parameter matrix part completes matrixing or vectorization on external input data, and the linear equation solver is a system core part; the linear equation solver is formed by modeling, formulating, analyzing and designing a system in advance, and comprises a system model obtained by mathematical modeling, a deviation equation designed, a neural network solver constructed by a deviation redefinition neural network method and the like;
4) the output interface is an interface of a solver solution data and a system optimal theoretical solution request end, and the interface can be a circuit interface or a return value of a program and is different according to different design systems;
5) and the redundant manipulator motion control port receives path planning information planned by a time-varying linear equation solver of a bias redefinition recurrent neural network-based method and controls the redundant manipulator motion path in the actual system.
Fig. 4 is a diagram illustrating motion simulation of the redundant manipulator based on the bias redefinition recurrent neural network according to the embodiment, where a thick line is a motion trajectory of the end of the redundant manipulator, and a thin line is a change process of the posture of each joint of the redundant manipulator when the joint moves, and shows the motion process and the posture change of each joint of the manipulator.
Fig. 3 is a schematic diagram of a redundant manipulator for redefining a recurrent neural network based on deviation, according to an embodiment, moving along a planned path, wherein a dotted line represents a desired tip trajectory of the motion of the tip of the manipulator, and a dotted line represents an actual tip trajectory. As can be seen from the figure, the expected end trajectory and the actual end trajectory coincide, that is, the motion planning method provided by the embodiment can realize rapid convergence, can eliminate the deviation between the expected end trajectory and the actual end trajectory, and effectively improves the accuracy of motion planning of the motion manipulator.
The above description is only for the preferred embodiments of the present invention, but the protection scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution of the present invention and the inventive concept within the scope of the present invention, which is disclosed by the present invention, and the equivalent or change thereof belongs to the protection scope of the present invention.

Claims (8)

1. A mechanical arm motion planning method based on a deviation redefinition neural network is characterized by comprising the following steps:
establishing a kinematic equation of the redundant manipulator according to the model and the parameters of the actual redundant manipulator;
converting the redundant manipulator kinematic equation into a speed layer kinematic equation, and describing the speed layer kinematic equation into a smooth time-varying linear equation;
acquiring joint angle and tail end track information of a mechanical arm through an airborne sensor on the redundant mechanical arm, constructing a time-varying parameter matrix according to parameters of the mechanical arm, the joint angle of the mechanical arm and the tail end track information, and acquiring a corresponding time derivative;
designing a deviation function for completing a motion planning task according to the smooth time-varying linear equation;
redefining a recurrent neural network by adopting the deviation function, and designing a time-varying linear equation solver for the redundant robot arm by combining the time-varying parameter matrix and the time derivative thereof;
and solving the network state solution obtained by the time-varying linear equation solver to obtain an optimal solution of the redundant robot system for completing the motion planning task, wherein the optimal solution is the expected motion track of the redundant robot system.
2. The method for planning the motion of the mechanical arm based on the deviation redefinition neural network as claimed in claim 1, wherein: the redundant manipulator kinematics equation is expressed as:
r(t)＝f(θ(t)) (1)
where θ (t) is the joint angle vector of the redundant manipulator, r (t) is the desired end trajectory vector of the redundant manipulator, and f (·) is a nonlinear mapping function defining the joint angle of the redundant manipulator in a Cartesian coordinate system to the coordinates of the end trajectory.
3. The method according to claim 2, wherein the redundant manipulator kinematics equation is converted into a velocity layer kinematics equation, specifically, two sides of the redundant manipulator kinematics equation are derived from time to obtain a velocity layer kinematics equation of the redundant manipulator:
Figure FDA0002611188900000011
wherein J (theta (t)). epsilon.Rm×nIs an m multiplied by n dimensional matrix on a real number domain, n represents the degree of freedom of the mechanical arm, m represents the space dimension of the tail end track of the mechanical arm,
Figure FDA0002611188900000012
is a Jacobian matrix of the redundant manipulator,
Figure FDA0002611188900000013
and
Figure FDA0002611188900000014
respectively the derivative of the joint angle and the tail end track of the redundant manipulator with respect to time t;
the kinematic equation of the angular derivative of the redundant manipulator joint, namely the following formula (3), can be obtained according to the equation (2), and the planning of the redundant manipulator joint angle is realized through the kinematic equation of the redundant manipulator joint angular derivative,
Figure FDA0002611188900000015
wherein, J-1(θ(t))∈Rn×mIs an inverse matrix of J (theta (t)) in the real number domain, in order to solve for J-1(θ (t)), describing the redundant manipulator in velocity layer kinematics equation (2) as the smooth time-varying linear equation:
Figure FDA0002611188900000016
t represents a time variable, a (t) J (θ (t)) JT(θ(t))，C＝-JT(θ (t)), at this time, JT(θ (t)) represents the transpose of J (θ), A (t) ε Rm×mAnd C (t) e Rm×nIs a time-varying parameter matrix such that a unique solution X of equation (4) holds*(t) is J to be solved in equation (3)-1(θ (t)), namely X*(t)＝J-1(θ(t))。
4. The method for planning the motion of the mechanical arm based on the deviation redefinition neural network as claimed in claim 3, wherein: and time-varying parameter matrixes A (t) and C (t) in the smooth time-varying linear equation are formed by combining mechanical arm model parameter information, joint angle signals acquired by an actual redundant mechanical arm airborne sensor and system expected operation target signals.
5. The method for planning the motion of the mechanical arm based on the deviation redefinition neural network as claimed in claim 3, wherein: according to the smooth time-varying linear equation, designing a deviation function as follows:
E(t)＝A(t)X(t)+C(t) (5)
when the deviation function E (t) is equal to zero or converges to zero, then a time-varying unique solution X of the smooth time-varying linear equation (4) can be obtained*(t), X (t) is a solution obtained by an algorithm, and X (t) is converged to X*(t), the optimal solution of equation (4) can be found.
6. The method for planning the motion of the mechanical arm based on the bias redefinition neural network as claimed in claim 5, wherein the bias function redefinition recurrent neural network is adopted, and a time-varying linear equation solver for the redundant robot arm is designed by combining the time-varying parameter matrix and the time derivative thereof, and specifically comprises:
the design redefined error function is:
Figure FDA0002611188900000021
wherein the content of the first and second substances,
Figure FDA0002611188900000022
for activating the function, a monotone increasing odd function can be selected, and sigma and rho are positive scalar value parameters for measuring the convergence speed of the recurrent neural network; e (τ) is the deviation function of equation (5) and refers to the initial value of equation (6), i.e.
Figure FDA0002611188900000023
Substituting the error function (6) into the neurodynamics design formula
Figure FDA0002611188900000024
Can obtain
Figure FDA0002611188900000025
Wherein the content of the first and second substances,
Figure FDA0002611188900000026
for the activation function applicable to the zeroing neural network, γ ∈ Rm×mTo measure the positive definite matrix of the convergence rate of the solution process,
Figure FDA0002611188900000027
according to equation (7), the arrangement can be:
Figure FDA0002611188900000028
vectorization conversion is performed on the equation to obtain the time-varying linear equation solver:
Figure FDA0002611188900000029
wherein the content of the first and second substances,
Figure FDA00026111889000000210
Inthe unit matrix is represented by a matrix of units,
Figure FDA00026111889000000211
derivative denoted as M (t), R (t) ═ M-1(t)，M-1(t) denotes the inverse of M (t),
Figure FDA0002611188900000031
the derivative of the vectorized representation of c (t),
Figure FDA0002611188900000032
is an error function of the vectorization and,
Figure FDA00026111889000000315
is an error function of the vectorization and,
Figure FDA0002611188900000033
is the derivative of the solution of the vectorized time-varying equation,
Figure FDA0002611188900000034
is the vectorized residual.
7. The method of claim 6, wherein the method comprises: equation (9) discretizing the expression as
Figure FDA0002611188900000035
Wherein, Delta is discrete step length, k is iteration number,
Figure FDA0002611188900000036
is an approximate solution of the equation from the k-th iteration,
Figure FDA0002611188900000037
is an error function of the k-th order, RkIs the r (t) function of the kth iteration,
Figure FDA0002611188900000038
is the derivative of m (t) for the kth iteration,
Figure FDA0002611188900000039
is the k-th iteration
Figure FDA00026111889000000310
The derivative of (a) of (b),
Figure FDA00026111889000000311
is the error function of the ith vectorization,
Figure FDA00026111889000000312
is the vectorized activation function of the k-th iteration,
Figure FDA00026111889000000313
is an error function of vectorization.
By discretizing equation (10), the solution x (t) J of equation (4) can be obtained iteratively-1(θ (t)) can be obtained
Figure FDA00026111889000000314
And further integrating to obtain a joint angle theta (t) of the redundant manipulator completing the tail end track target task, namely the optimal solution of the redundant robot system completing the motion planning task.
8. The method of claim 6, wherein the method comprises: the monotone increasing odd function is any one of a linear activation function, a hyperbolic S-type activation function and a power function type activation function.
CN202010754873.7A 2020-07-30 2020-07-30 Mechanical arm motion planning method based on deviation redefinition neural network Pending CN111975771A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010754873.7A CN111975771A (en) 2020-07-30 2020-07-30 Mechanical arm motion planning method based on deviation redefinition neural network

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010754873.7A CN111975771A (en) 2020-07-30 2020-07-30 Mechanical arm motion planning method based on deviation redefinition neural network

Publications (1)

Publication Number Publication Date
CN111975771A true CN111975771A (en) 2020-11-24

Family

ID=73444822

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010754873.7A Pending CN111975771A (en) 2020-07-30 2020-07-30 Mechanical arm motion planning method based on deviation redefinition neural network

Country Status (1)

Country Link
CN (1) CN111975771A (en)

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112706163A (en) * 2020-12-10 2021-04-27 中山大学 Mechanical arm motion control method, device, equipment and medium
CN113220023A (en) * 2021-04-28 2021-08-06 中国科学院重庆绿色智能技术研究院 High-precision real-time path planning method for unmanned aerial vehicle
CN113843793A (en) * 2021-09-21 2021-12-28 兰州大学 Mobile redundant mechanical arm model prediction control method with obstacle avoidance function
CN114102606A (en) * 2021-12-22 2022-03-01 北京航空航天大学杭州创新研究院 Robot motion information planning method and related device
CN114193452A (en) * 2021-12-29 2022-03-18 佛山智异科技开发有限公司 Multi-joint material distribution arm support tail end track control method and system and storage medium
CN114211500A (en) * 2021-12-31 2022-03-22 华南理工大学 Self-adaptive fuzzy neural network planning method
CN114394113A (en) * 2022-01-19 2022-04-26 广州小鹏自动驾驶科技有限公司 Vehicle track re-planning method and device, electronic equipment and storage medium
CN114800532A (en) * 2022-06-27 2022-07-29 西南交通大学 Mechanical arm control parameter determination method, device, equipment, medium and robot
CN116383574A (en) * 2023-03-23 2023-07-04 哈尔滨工业大学 Humanoid upper limb robot inverse kinematics solving method based on high-order differentiator

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107984472A (en) * 2017-11-13 2018-05-04 华南理工大学 A kind of neural solver design method of change ginseng for redundant manipulator motion planning
CN109033021A (en) * 2018-07-20 2018-12-18 华南理工大学 A kind of linear equation solver design method for joining convergence neural network based on change
US20190184561A1 (en) * 2017-12-15 2019-06-20 The Regents Of The University Of California Machine Learning based Fixed-Time Optimal Path Generation
CN110695994A (en) * 2019-10-08 2020-01-17 浙江科技学院 Finite time planning method for cooperative repetitive motion of double-arm manipulator

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107984472A (en) * 2017-11-13 2018-05-04 华南理工大学 A kind of neural solver design method of change ginseng for redundant manipulator motion planning
US20190184561A1 (en) * 2017-12-15 2019-06-20 The Regents Of The University Of California Machine Learning based Fixed-Time Optimal Path Generation
CN109033021A (en) * 2018-07-20 2018-12-18 华南理工大学 A kind of linear equation solver design method for joining convergence neural network based on change
CN110695994A (en) * 2019-10-08 2020-01-17 浙江科技学院 Finite time planning method for cooperative repetitive motion of double-arm manipulator

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
ZHIJUN ZHANG,LUNAN ZHENG,HUI YANG,XILONG QU: "Design and Analysis of a Novel Integral Recurrent", 《TEEE TRANSCATIONS ON SYBERNETICS》 *

Cited By (17)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112706163B (en) * 2020-12-10 2022-03-04 中山大学 Mechanical arm motion control method, device, equipment and medium
CN112706163A (en) * 2020-12-10 2021-04-27 中山大学 Mechanical arm motion control method, device, equipment and medium
CN113220023B (en) * 2021-04-28 2022-10-14 中国科学院重庆绿色智能技术研究院 High-precision real-time path planning method for unmanned aerial vehicle
CN113220023A (en) * 2021-04-28 2021-08-06 中国科学院重庆绿色智能技术研究院 High-precision real-time path planning method for unmanned aerial vehicle
CN113843793A (en) * 2021-09-21 2021-12-28 兰州大学 Mobile redundant mechanical arm model prediction control method with obstacle avoidance function
CN114102606A (en) * 2021-12-22 2022-03-01 北京航空航天大学杭州创新研究院 Robot motion information planning method and related device
CN114102606B (en) * 2021-12-22 2022-12-23 北京航空航天大学杭州创新研究院 Robot motion information planning method and related device
CN114193452A (en) * 2021-12-29 2022-03-18 佛山智异科技开发有限公司 Multi-joint material distribution arm support tail end track control method and system and storage medium
CN114193452B (en) * 2021-12-29 2024-04-26 佛山智异科技开发有限公司 Multi-joint cloth arm support tail end track control method, system and storage medium
CN114211500B (en) * 2021-12-31 2023-05-30 华南理工大学 Planning method of self-adaptive fuzzy neural network
CN114211500A (en) * 2021-12-31 2022-03-22 华南理工大学 Self-adaptive fuzzy neural network planning method
CN114394113A (en) * 2022-01-19 2022-04-26 广州小鹏自动驾驶科技有限公司 Vehicle track re-planning method and device, electronic equipment and storage medium
CN114394113B (en) * 2022-01-19 2023-08-25 广州小鹏自动驾驶科技有限公司 Vehicle track re-planning method and device, electronic equipment and storage medium
CN114800532B (en) * 2022-06-27 2022-09-16 西南交通大学 Mechanical arm control parameter determination method, device, equipment, medium and robot
CN114800532A (en) * 2022-06-27 2022-07-29 西南交通大学 Mechanical arm control parameter determination method, device, equipment, medium and robot
CN116383574A (en) * 2023-03-23 2023-07-04 哈尔滨工业大学 Humanoid upper limb robot inverse kinematics solving method based on high-order differentiator
CN116383574B (en) * 2023-03-23 2024-06-11 哈尔滨工业大学 Humanoid upper limb robot inverse kinematics solving method based on high-order differentiator

Similar Documents

Publication Publication Date Title
CN111975771A (en) Mechanical arm motion planning method based on deviation redefinition neural network
CN108015763B (en) Anti-noise-interference redundant manipulator path planning method
Zhao et al. System identification of the nonlinear residual errors of an industrial robot using massive measurements
CN109848983B (en) Method for guiding robot to cooperatively work by high-compliance person
CN107984472B (en) Design method of variable parameter neural solver for redundant manipulator motion planning
CN108908327B (en) Robot positioning error grading compensation method
Wilson et al. Relative end-effector control using cartesian position based visual servoing
WO2018107851A1 (en) Method and device for controlling redundant robot arm
Zou et al. Virtual manipulator-based binocular stereo vision positioning system and errors modelling
Wang et al. Nonparametric statistical learning control of robot manipulators for trajectory or contour tracking
CN112605996B (en) Model-free collision avoidance control method for redundant mechanical arm
CN110154024B (en) Assembly control method based on long-term and short-term memory neural network incremental model
CN113910218B (en) Robot calibration method and device based on kinematic and deep neural network fusion
Du et al. A cognitive joint angle compensation system based on self-feedback fuzzy neural network with incremental learning
Landgraf et al. A hybrid neural network approach for increasing the absolute accuracy of industrial robots
Hu et al. Robot positioning error compensation method based on deep neural network
CN111515928B (en) Mechanical arm motion control system
CN114986498A (en) Mobile operation arm cooperative control method
Burlacu et al. Predictive control architecture for real-time image moments based servoing of robot manipulators
Tan et al. Toward unified adaptive teleoperation based on damping ZNN for robot manipulators with unknown kinematics
Tan et al. Uncalibrated and unmodeled image-based visual servoing of robot manipulators using zeroing neural networks
Qi et al. An optimal visual servo trajectory planning method for manipulators based on system nondeterministic model
Li et al. A novel semi-autonomous teleoperation method for the tiangong-2 manipulator system
Laflaquiere et al. Learning an internal representation of the end-effector configuration space
Liu et al. Trajectory prediction and visual localization of snake robot based on BiLSTM neural network

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20201124