CN-122008263-A - Rope-driven mechanical tracking control method based on TDE and recursion nonsingular terminal sliding mode

CN122008263ACN 122008263 ACN122008263 ACN 122008263ACN-122008263-A

Abstract

The invention discloses a rope-driven mechanical tracking control method based on a TDE and a recursive nonsingular terminal sliding mode, which relates to the technical field of mechanical hand control and comprises the following steps of determining a dynamic standard equation of a mechanical hand through mechanical dynamics analysis, converting the dynamic standard equation into a TDE simplified equation, and defining tracking errors; the method comprises the steps of constructing FNTSM functions containing proportional control parameters, combining recursive integral items to form recursive nonsingular terminal sliding mode variables, designing an interference adaptation law to dynamically adjust the proportional control parameters, analyzing convergence speed and buffeting characteristics of tracking errors to generate a composite approach law, extracting generalized output vectors of a joint controller containing dynamic oscillation parameters based on the composite approach law and an updated TDE simplified equation to form a complete control law, outputting the generalized vectors in real time through the control law, simulating a motion track of a manipulator, and realizing high-precision tracking control.

Inventors

YAN FEI
LI JIANHUA
HAN HUAWEI
FAN HONGYUAN
HAN PENGJU
YANG QINCHEN

Assignees

烟台大学

Dates

Publication Date: 20260512
Application Date: 20260416

Claims (8)

1. A rope-driven mechanical tracking control method based on TDE and recursion nonsingular terminal sliding mode is characterized by comprising the following specific steps: The degree of freedom of the rope driving manipulator to be controlled is analyzed through mechanical dynamics, a dynamic standard equation of the rope driving manipulator to be controlled under the generalized output vector of the joint controller is determined, the dynamic standard equation is converted into a TDE simplified equation through a TDE estimation algorithm, and tracking errors are defined based on the track of the joints of the manipulator; According to the tracking error of the manipulator joint, a FNTSM function containing proportional control parameters is constructed, a recursive integral term is introduced based on the FNTSM function, and a recursive nonsingular terminal sliding mode variable is constructed by integrating the FNTSM function and the recursive integral term; Designing an interference adaptation law based on the recursive nonsingular terminal sliding mode variable, dynamically adjusting the proportional control parameter through the interference adaptation law, and analyzing the convergence speed and buffeting characteristics of the tracking error of the rope driving manipulator to be controlled so as to generate a composite approach law according to the recursive nonsingular terminal sliding mode variable; based on the composite approach law, updating the TDE simplified equation by combining FNTSM functions and recursive nonsingular terminal sliding mode variables, and extracting a generalized output vector of the joint controller containing the turbulence parameters based on the updated TDE simplified equation to form a complete control law; Based on the complete control law, the joint controller is controlled to output a real-time generalized output vector, and the motion track of the rope-driven manipulator to be controlled is simulated, so that actual tracking control is realized.
2. The rope-driven mechanical tracking control method based on the TDE and the recursive nonsingular terminal sliding mode, which is characterized in that the logic based on which the degree of freedom of the rope-driven mechanical arm to be controlled is determined is that the number of joints and the number of joint motion constraints of the rope-driven mechanical arm to be controlled are determined, and the degree of freedom of the rope-driven mechanical arm to be controlled is analyzed based on the number of joints and the number of joint motion constraints of the rope-driven mechanical arm to be controlled; The logic on which the dynamic standard equation of the rope driving manipulator to be controlled is specifically built is that the dynamic standard equation of the rope driving manipulator to be controlled is comprehensively built by combining a mass inertia matrix with a position vector of a joint and introducing a centrifugal force vector, a gravity vector and a viscous friction vector, wherein the dynamic standard equation is specifically expressed as follows: In the formula, Driving the manipulator joint to a position vector for a rope to be controlled A mass-inertia matrix of the material is provided, The position vector of the manipulator joint is driven by the rope to be controlled, Is the second time derivative of the position vector, As the first time derivative of the position vector, Representing the centrifugal force vector of the manipulator joint driven by the rope to be controlled, The gravity vector of the manipulator joint is driven by the rope to be controlled, For the viscous friction vector of the manipulator joint driven by the rope to be controlled, As the external interference vector(s), The mass inertia matrix is specifically a matrix with the same number of rows and columns as the degree of freedom.
3. The rope-driven mechanical tracking control method based on the TDE and the recursive nonsingular terminal sliding mode, which is disclosed by claim 2, is characterized in that the logic based on the specific basis of converting a dynamic standard equation into a TDE simplified equation through a TDE estimation algorithm is that the dynamic standard equation is simplified through the TDE estimation algorithm, and the specific expression of the TDE simplified equation is as follows: In the formula, For a constant value inertial gain matrix, For lumped unknown dynamic terms of rope driven manipulator tracking control, Motion disturbance items for the injected joints; defining a tracking error based on the track of the manipulator joint, wherein the tracking error is specifically expressed as: In the formula, The tracking error of the ith joint of the manipulator, For the expected motion trail position vector of the ith joint of the manipulator, The actual motion track position vector and the expected motion track position of the ith joint of the manipulator are specifically represented by a position function taking time as an independent variable, i is the joint index of the manipulator driven by the rope to be controlled, N is the total number of joints of the rope driving manipulator to be controlled.
4. The rope-driven mechanical tracking control method based on TDE and recursive nonsingular terminal sliding mode according to claim 3, wherein a FNTSM function containing proportional control parameters is constructed according to tracking errors of a manipulator joint, and the FNTSM function is specifically expressed as: In the formula, Is a function value of FNTSM, To track the first derivative vector of the error with respect to the time variable, For the first proportional control parameter, Is a second proportional control parameter, and And Are all larger than 0 and are not smaller than 0, As an index vector of the values of the index, In order to track the error vector, Is a nonlinear control function; The first derivative vector of the tracking error on the time variable is specifically expressed as: In the formula, The first derivative of the tracking error with respect to time variable for the ith joint of the manipulator, Tracking the first derivative of the error to the time variable for the nth joint of the manipulator; the tracking error vector is similarly expressed as: In the formula, Tracking error of the nth joint of the manipulator; The exponent vector The concrete steps are as follows: In the formula, For the index component of the i-th joint of the manipulator, An index component of the nth joint of the manipulator, the index component value meeting ; The nonlinear control function is specifically expressed as: In the formula, The absolute value of the tracking error for the ith joint of the manipulator, As a sign function.
5. The rope-driven mechanical tracking control method based on the TDE and the recursive nonsingular terminal sliding mode according to claim 4 is characterized in that a formula on which the recursive nonsingular terminal sliding mode variable is specifically built is as follows: In the formula, For the recursive non-singular terminal sliding mode variable, In order to recursively integrate the terms, Is a recursive matrix, in particular a positive diagonal matrix, in particular expressed as: In the formula, Representing the function of the construction of the diagonal matrix, Is a recursive matrix main diagonal element; the derivative term of the recursive integral term is specifically expressed as: In the formula, In order to recursively integrate the derivatives of the terms, Is a recursive derivative matrix, which is a positive definite diagonal matrix, specifically expressed as: In the formula, Is the main diagonal element of the recursive derivative matrix.
6. The rope-driven mechanical tracking control method based on TDE and recursive nonsingular terminal sliding mode according to claim 5, wherein the interference adaptation law is specifically expressed as: In the formula, Is the interference adaptation law at the time t, Adjust the coefficients for scaling, an , The self-adaptive variable is at the moment t, wherein t is the time variable of the tracking control process; The specific formula on which the proportion control parameters are dynamically adjusted through the interference adaptation law is as follows: In the formula, And The values of the first and second proportional control parameters at time t are updated respectively, And Nominal values of the first and second proportional control parameters, respectively, and And Are all greater than 0; the specific updating rule of the self-adaptive variable at the time t is as follows: In the formula, To adapt to the proportion coefficient, and Is more than 0 of the total number of the components, The magnitude of the recursive nonsingular terminal sliding mode variable at the moment t is represented, For the upper bound of the adaptive variable, A sliding mode variable threshold value for a recursive non-singular terminal; the size of the t-moment recursion nonsingular terminal sliding mode variable is specifically expressed as follows: In the formula, Is a margin constant, which 。
7. The rope-driven mechanical tracking control method based on the TDE and the recursive nonsingular terminal sliding mode according to claim 6 is characterized in that the formula on which the composite approach law is generated specifically is as follows: In the formula, Is a composite approach law, and is used for the control of the system, For the first composite approach matrix, For the second composite approach matrix, Is a composite proportionality coefficient, and The first and second composite approach matrices are specifically represented as: In the formula, Is a main diagonal element of the composite approach matrix.
8. The rope-driven mechanical tracking control method based on the TDE and the recursive nonsingular terminal sliding mode, which is characterized in that the logic based on which the generalized output vector of the joint controller containing the dynamic oscillation parameter is extracted based on an updated TDE simplified equation is that the lumped unknown dynamic item of the rope-driven mechanical arm tracking control and the motion interference item of the injection joint in the TDE simplified equation are updated so as to update the generalized output vector of the joint controller; The updated motion disturbance term of the injection joint is specifically expressed as: In the formula, A second derivative of the expected motion trail position of the manipulator joint with respect to time; The updated lumped unknown dynamic item of the tracking control of the rope-driven manipulator is specifically expressed as: In the formula, Is that The generalized output vector of the moment-of-time joint controller, As a function of the oscillation parameters, Is that The second derivative of the expected motion trail position of the manipulator joint with respect to time at the moment; And forming a complete control law of the generalized output vector of the joint controller in the rope-driven manipulator to be controlled according to the updated motion disturbance item of the injection joint and the updated lumped unknown dynamic item of the tracking control of the rope-driven manipulator.

Description

Rope-driven mechanical tracking control method based on TDE and recursion nonsingular terminal sliding mode Technical Field The invention relates to the technical field of mechanical arm control, in particular to a rope-driven mechanical tracking control method based on a TDE and a recursion nonsingular terminal sliding mode. Background The conventional underwater mechanical arm is generally based on direct motor drive installed in a sealing joint, and has the problems of large volume, heavy weight, high energy consumption and the like, so that the conventional underwater mechanical arm is not suitable for a compact AUV (Autonomous Underwater Vehicle ) platform with limited energy. Rope driven robots have gained great attention in robotics because of their inherent advantages, including large working space, high load to weight ratios, and low structural inertia, which have led to their successful use in a number of fields of large scale operations, aerial photography, and industrial automation. In recent years, the application of rope drive mechanisms has been expanded to underwater environments, particularly in the development of lightweight manipulators for autonomous underwater vehicle-manipulator systems, in order to ensure that the rope drive mechanism can handle complex nonlinear coupling and time-varying loads, and to simplify the controller design, TDE (TIME DELAY Estimation of time delay) has been generally used in the prior art to design the controller of the rope drive mechanism. However, practical application of steering rope drive systems in the underwater field presents a complex challenge, and dynamics of such systems become a complex mixture of rigid body mechanics, flexible rope dynamics and strong fluid-solid coupling, constituting rigid-flexible-liquid coupling problems. In addition, underwater operations are subject to significant external disturbances such as time-varying hydrodynamic forces, ocean currents, and rope tension variations. Therefore, it is a difficult task to achieve high precision trajectory tracking control of rope driven underwater manipulators, and the control strategy must be robust to inherent model uncertainties resulting from complex coupling dynamics, as well as external environmental disturbances. While advanced control techniques such as sliding mode control provide robustness, their direct application is hampered by the need for accurate dynamic models and the persistent buffeting problem. Therefore, there is an urgent need for a practical high performance control frame to ensure accurate and stable operation of the rope-driven robot in a severe and uncertain environment such as an underwater field. The above information disclosed in the background section is only for enhancement of understanding of the background of the disclosure and therefore it may include information that does not form the prior art that is already known to a person of ordinary skill in the art. Disclosure of Invention The invention aims to provide a rope-driven mechanical tracking control method based on TDE and a recursive nonsingular terminal sliding mode, so as to solve the problems in the background technology. In order to achieve the above purpose, the present invention provides the following technical solutions: a rope-driven mechanical tracking control method based on TDE and recursion nonsingular terminal sliding mode comprises the following specific steps: The degree of freedom of the rope driving manipulator to be controlled is analyzed through mechanical dynamics, a dynamic standard equation of the rope driving manipulator to be controlled under the generalized output vector of the joint controller is determined, the dynamic standard equation is converted into a TDE simplified equation through a TDE estimation algorithm, and tracking errors are defined based on the track of the joints of the manipulator; According to the tracking error of the manipulator joint, a FNTSM function containing proportional control parameters is constructed, a recursive integral term is introduced based on the FNTSM function, and a recursive nonsingular terminal sliding mode variable is constructed by integrating the FNTSM function and the recursive integral term; Designing an interference adaptation law based on the recursive nonsingular terminal sliding mode variable, dynamically adjusting the proportional control parameter through the interference adaptation law, and analyzing the convergence speed and buffeting characteristics of the tracking error of the rope driving manipulator to be controlled so as to generate a composite approach law according to the recursive nonsingular terminal sliding mode variable; Based on the composite approach law, updating the TDE simplified equation by combining FNTSM functions and recursive nonsingular terminal sliding mode variables, extracting a generalized output vector of the joint controller containing the turbulence parameters based on the updated TDE simpli