CN-121973190-A - Super-exponential convergence zero-change neural network method for redundant mechanical arm position tracking

CN121973190ACN 121973190 ACN121973190 ACN 121973190ACN-121973190-A

Abstract

The invention discloses a super-exponential convergence zero-change neural network method for redundant mechanical arm position tracking, and belongs to the technical field of robot motion control and intelligent calculation. A zero-change neural network which fuses a time-varying dynamic attenuation coefficient and a power-sigmoid nonlinear activation function is constructed, and the state of the network is driven to be quickly converged to a true value of a time-varying pseudo-inverse in a super-exponential form by designing an error evolution dynamics equation based on a jacobian matrix Moore-Penrose pseudo-inverse. The output of the network is used as an on-line estimation value of pseudo inverse, and joint speed instructions can be generated in real time by combining end position tracking error feedback, so that the high-precision, rapid and stable tracking of the redundant mechanical arm end to the expected track is realized. The method only depends on a kinematic model, does not need complex dynamics modeling or offline training, has the advantages of simple structure, small calculated amount and strong real-time performance, and is suitable for tracking control scenes of different structural parameters and various complex tracks.

Inventors

WANG ZHIWEI
CHAI BIN
SHEN SHIKAI
HE JUN
YANG BIN
DENG FEI
FANG GANG
SHE YUMEI
WANG WU

Assignees

昆明学院

Dates

Publication Date: 20260505
Application Date: 20260119

Claims (10)

1. A super-exponential convergence zeroing neural network method for redundant mechanical arm position tracking is characterized by comprising the following steps: Establishing a speed mapping relation between the terminal position change and the joint movement of the redundant mechanical arm, namely a differential kinematics model according to the geometric structure of the redundant mechanical arm; calculating a position tracking error according to the expected end reference track and the actual end position, and constructing an expected end speed command based on the error; Constructing and operating a super-exponential convergence nulling neural network for estimating the generalized inverse of the time-varying jacobian matrix in the differential kinematics model on line; taking the output of the hyper-exponential converging and nulling neural network as an online estimation value of generalized inverse, and combining with a desired terminal speed instruction, and calculating to obtain a joint angular speed control instruction; and driving the mechanical arm to move according to the joint angular speed control instruction to form closed-loop control, so that the tail end position tracks the reference track.
2. The method for super-exponential converging nulling neural network for redundant manipulator position tracking of claim 1, wherein said differential kinematics model is specifically expressed as: , Wherein, the Is the end position vector Is used for the rate of change of (a), As a vector of the angular velocity of the joint, As the angular vector of the joint, Representing a time-varying jacobian matrix determined by the structural parameters of the mechanical arm and joint angles.
3. The method for super-exponential converging nulling neural network for redundant mechanical arm position tracking according to claim 1, wherein said calculating a position tracking error comprises: Setting the tracking error of the tail end position as Wherein As a reference trajectory for the reference trajectory, Is a position vector; the desired tip speed command is constructed based on the error as: , wherein, For the rate of change of the reference trajectory, Is the error feedback gain.
4. The method for constructing and running a super-exponential-convergence-nulling neural network for redundant arm position tracking as claimed in claim 1, wherein said constructing and running a super-exponential-convergence-nulling neural network comprises: for solving time-varying jacobian matrix on line The right Moore-Penrose pseudo-inverse of (a), the time-varying error matrix of the network is set as: , wherein, For the nulling of the neural network state matrix, For time-varying jacobian matrices Right Moore-Penrose pseudo-inverse of (c); designing an evolution dynamic equation for driving matrix convergence as follows , wherein, Is a time-varying dynamic decay factor that, A power-sigmoid nonlinear activation function acting on the error matrix; substituting the error matrix into an evolution dynamics equation to obtain a state update law of the zero-change neural network: 。
5. the method of claim 4, wherein the time-varying dynamic attenuation coefficients are based on a super-exponential converging nulling neural network Designed to increase exponentially with time: , wherein, The initial amplitude of the attenuation coefficient is used for adjusting the convergence strength of the initial stage of the error system; Is an exponential growth rate parameter for controlling the rate of increase of the decay factor over time.
6. The method of claim 4, wherein the power-sigmoid nonlinear activation function is a super-exponential convergence nulling neural network Each element of the matrix is subjected to independent nonlinear mapping, and the formula is as follows: , Wherein the activation function For error matrix Acts one by one; is an odd-order power exponent and The nonlinear inhibition capability of the region with larger error is enhanced; the gain coefficient is a hyperbolic sine term gain coefficient and is used for improving the convergence driving force of a large error area; Parameters are adjusted for the hyperbolic tangent function to improve smoothness and steady-state accuracy when the error approaches zero.
7. The method for super-exponential converging nulling neural network for redundant manipulator position tracking according to claim 4, wherein said calculating said joint angular velocity control command comprises: Real-time state matrix of neural network to be zeroed As an estimated value of the pseudo-inverse of the jacobian matrix, a joint angular velocity control instruction is calculated as follows: 。
8. The method of super-exponential converging nulling neural network for redundant arm position tracking as recited in claim 7, wherein said obtaining said joint angular velocity control command comprises Then, in order to ensure that the joint speed meets the physical execution constraint of the mechanical arm, the joint speed can be solved And (3) carrying out saturation treatment on the minimum norm solution on the basis of the minimum norm solution so as to meet the following conditions: , wherein, And Representing minima and maxima, respectively, of the joint velocity.
9. The method of claim 5, wherein the initial magnitude of the attenuation coefficient is based on a super-exponential converging nulling neural network Exponential growth rate Upper limit of saturation value 。
10. The method for super-exponential converging nulling neural network of redundant arm position tracking as recited in claim 6, wherein said power-sigmoid type nonlinear activation function is preferably set with parameters of polynomial order Hyperbolic sine term gain Hyperbolic tangent function adjustment parameters 。

Description

Super-exponential convergence zero-change neural network method for redundant mechanical arm position tracking Technical Field The invention relates to the technical field of robot motion control and intelligent computation, in particular to a redundant mechanical arm tail end position tracking control method based on a zero-change neural network, and particularly relates to a super-exponential convergence zero-change neural network control method integrating a time-varying dynamic attenuation coefficient and a nonlinear activation function. Background The redundant mechanical arm has high flexibility and adaptability in complex tasks by virtue of the multi-degree-of-freedom structure. However, due to the redundancy of degrees of freedom, the inverse kinematics solution is not unique, which is prone to cause joint angle drift problems, resulting in deviation of the end position from the intended trajectory, increasing the risk of self-collision and affecting the control stability. Therefore, high-precision, fast converging tip position tracking control becomes a key challenge in redundant robotic arm control. At the differential kinematics level, tip position tracking requires mapping the desired tip velocity to joint velocity by solving the Moore-Penrose pseudo-inverse of the jacobian matrix. The jacobian matrix has nonlinear time-varying characteristics, and the pseudo-inverse of the jacobian matrix needs to be solved online in real time. The traditional numerical method (such as singular value decomposition) has heavy calculation load under time-varying parameters and is difficult to meet the real-time requirement, so that an efficient and stable online solving strategy is needed. The zero-change neural network is widely applied to time-varying matrix online solving because of the advantages of strong parallel computing capability, simple structure and the like. The existing method mostly adopts a constant attenuation coefficient and an activation function in a fixed form, so that the convergence speed and the steady-state precision are difficult to be compatible under a strong nonlinear and high-frequency time-varying scene, and the parameters are sensitive to the change of working conditions, so that the actual application of the method in redundant mechanical arm control is restricted. Therefore, it is necessary to cooperatively improve the attenuation coefficient and the activation function in the zero-ized neural network, and design a control method capable of self-adaptive adjustment and having super-exponential convergence characteristics so as to realize quick, stable and high-precision online solving of the pseudo-inverse of the time-varying jacobian matrix, thereby improving the real-time performance, convergence speed and robustness of the tail end position tracking of the redundant mechanical arm. Disclosure of Invention Aiming at the problems existing at present, the invention provides a super-exponential convergence zero-change neural network method for redundant mechanical arm position tracking, which is used for constructing a time-varying error matrix based on a jacobian matrix Moore-Penrose pseudo-inverse and designing an error evolution dynamic equation by constructing a zero-change neural network for fusing a time-varying dynamic attenuation coefficient and a power-sigmoid nonlinear activation function, so that system errors are rapidly attenuated in a super-exponential form in a network evolution process, and the time-varying jacobian matrix Moore-Penrose pseudo-inverse is efficiently and stably solved on line. The technical scheme of the invention is as follows: a super-exponential convergence zeroing neural network method for redundant mechanical arm position tracking comprises the following steps: Establishing a speed mapping relation between the terminal position change and the joint movement of the redundant mechanical arm, namely a differential kinematics model according to the geometric structure of the redundant mechanical arm; calculating a position tracking error according to the expected end reference track and the actual end position, and constructing an expected end speed command based on the error; Constructing and operating a super-exponential convergence nulling neural network for estimating the generalized inverse of the time-varying jacobian matrix in the differential kinematics model on line; taking the output of the hyper-exponential converging and nulling neural network as an online estimation value of generalized inverse, and combining with a desired terminal speed instruction, and calculating to obtain a joint angular speed control instruction; and driving the mechanical arm to move according to the joint angular speed control instruction to form closed-loop control, so that the tail end position tracks the reference track. Further, the differential kinematic model is specifically expressed as: , Wherein, the Is the end position vectorIs used for the rate of c