Method for position control of a continuum manipulator, computer program product and device
By combining adaptive Jacobian matrix and zero-return neurodynamic model, the control accuracy problem caused by modeling error of continuum manipulator is solved, and fast and smooth position control of continuum manipulator is realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- TONGJI UNIV
- Filing Date
- 2024-01-09
- Publication Date
- 2026-06-26
AI Technical Summary
Errors in the kinematic modeling of continuous manipulators can cause the end effector to deviate from the desired trajectory, making it difficult to achieve precise position control, especially under nonlinear and coupled problems where it is difficult to obtain ideal control performance.
By employing an adaptive Jacobian matrix and an improved zero-return neurodynamic model, and by designing kinematic equations, calculating the position deviation vector function, and the pseudo-inverse of the adaptive Jacobian matrix, model-free position control is achieved, and adaptive learning is performed using sensor feedback information.
It achieves rapid convergence and smooth motion trajectory of the end effector position of the continuous robotic arm, improving the stability and real-time application capability of the control system.
Smart Images
Figure CN117773937B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent medical technology, and more specifically, to a position control method, computer program product, and device for a continuous robotic arm. Background Technology
[0002] After decades of development, continuum robots have become an important branch of robotics. Continuum robots typically use compliant materials to construct their robotic arms and actuators. Due to their compliant structure and superior flexibility, continuum robots are increasingly used in fields such as laparoscopic surgery, attracting widespread attention.
[0003] However, the flexibility and suppleness of continuum robots lead to more challenging modeling and control problems. Currently, there are many kinematic modeling methods for continuum manipulators, with the most widely used being the constant curvature circular arc assumption model. Regardless of the modeling method used, the model is an approximation of the actual system. Due to the inherent errors between theoretical and practical models, the end effector motion of the continuum manipulator often deviates from the expected trajectory. The accuracy of the continuum manipulator model depends on the accuracy of its parameters, and accurate models are generally quite complex. The coupling and nonlinearity between different continuous segments further complicate the modeling and control of the manipulator, making it difficult to achieve ideal control performance. Therefore, it is essential to develop a model-free position control method for continuum manipulators to achieve precise position control. Summary of the Invention
[0004] To address the aforementioned deficiencies in existing technologies, this invention provides a position control method, computer program product, and device for a continuous robotic arm. It utilizes an improved zero-return neurodynamic model for model-free control of the continuous robotic arm, independent of model parameters and structure, and converts internal, implicit, and unmeasurable model information into external, explicit, and measurable input and output information.
[0005] To achieve the above objectives, on the one hand, the present invention provides a position control method for a continuum manipulator, characterized by model-free position control of the continuum manipulator based on an adaptive Jacobian matrix, comprising the following steps:
[0006] Step S101: Design the kinematic equations of the continuous robot arm to generate the driving force at time t, change the length of the driving cable, and adjust the position of the end effector of the continuous robot arm so that the end effector of the continuous robot arm reaches the desired position r. m ;
[0007] Step S102: Differentiating both sides of the kinematic equations of step S101 with respect to time t yields the relationship between the change in the driving force of the continuum manipulator and the velocity vector at the end of the manipulator, and gives the definition of the Jacobian matrix;
[0008] Step S103: Calculate the position deviation vector function between the actual position and the target position. Using the zero-return neurodynamics design formula, make each element in the position deviation vector function converge to zero, thus realizing the position control of the continuum robot arm.
[0009] Step S104: Obtain the explicit expression of the control input signal based on the position deviation vector function and the zero-return neurodynamic design formula, and give the control of the adaptive unknown Jacobian matrix pseudo-inverse through the explicit expression of the control input signal;
[0010] Step S105: Apply the zero-return neurodynamics method again to obtain the Jacobian matrix adaptive equation of the control system; the sensors of the continuous manipulator measure the position, velocity and acceleration of the continuous manipulator in real time and feed them back to the Jacobian matrix for adaptive learning;
[0011] Step S106: Calculate the driving change of the continuum robot arm using the updated Jacobian matrix, thereby controlling the end effector of the robot arm to move to the desired position.
[0012] Furthermore, the position control method is applicable to both non-singular and singular configurations of the continuous robotic arm.
[0013] Furthermore, when the continuum robot arm is in a non-singular configuration, the kinematic equations in step S101 are:
[0014] f(p(t))-r(t),
[0015] In the above formula, This represents the actuation quantity of the continuous robotic arm at time t. This represents the position vector of the end effector of the continuum robot arm. The continuous nonlinear positive kinematic mapping represents the continuous manipulator model with known parameters and structure; the Jacobian matrix in step S102 is defined as follows:
[0016]
[0017] in, It is the Jacobian matrix at the end effector of the robotic arm, defined as
[0018] Furthermore, in step S103, the position deviation vector function can be expressed by the formula z(t) = r m-r(t) is obtained; using the zero-return neural dynamics design formula, each element z in the position deviation vector function is made... i The expression (t)(i=1,2,...,m) converges to zero, as shown in the following formula:
[0019]
[0020] in, The convergence rate of the position deviation vector function is controlled by L(·), which is a nonlinear and monotonically increasing odd function. Further, based on the position deviation vector function and the zero-return neural dynamics design formula, we can obtain:
[0021] Furthermore, in step S104, the expressed formula is as follows:
[0022]
[0023] in, Let J(p(t)) be the pseudo-inverse matrix of the Jacobian matrix. The control of the adaptive unknown Jacobian matrix pseudo-inverse is given by explicitly expressing the control input signal. The simplified formula for the explicit expression is as follows:
[0024]
[0025] in, It is the unknown pseudo-inverse of the Jacobian matrix that needs to be adapted.
[0026] Furthermore, in step S105, in order to obtain the Jacobian matrix adapted to the continuum robot arm, the unknown Jacobian matrix... The vector-valued error function is defined as follows:
[0027]
[0028] in Applying the zero-return neurodynamics method again:
[0029]
[0030] in, The convergence rate of the vector-valued error function is controlled by K(·), which is a nonlinear and monotonically increasing odd function. Meanwhile, the adaptive function for the unknown Jacobian matrix can be obtained as follows:
[0031]
[0032] Furthermore, the adaptive equation of the Jacobian matrix of the control system can be obtained:
[0033]
[0034] The pseudo-inverse calculation of the non-empty driving change is as follows: It is the transpose of the driving variable.
[0035] Furthermore, the continuous robotic arm is in a singular configuration, which is addressed by introducing remedial measures to transform the singular configuration into a non-singular configuration: using approximate An approximate solution for engineering applications, where k > 0 is a sufficiently small constant, and I is the identity matrix.
[0036] On the other hand, the present invention provides a computer program product, characterized in that, when the computer program is executed by a processor, it implements the position control method of the continuous body robotic arm as described above.
[0037] In another aspect, the present invention provides a position control device for a continuous robotic arm, including a sensor data interaction port, a memory, and a processor, characterized in that it stores executable instructions, which, when executed by one or more processors, enable the one or more processors to execute the aforementioned position control method for the continuous robotic arm.
[0038] Compared with the prior art, the present invention has the following technical effects:
[0039] This invention proposes a Jacobian matrix-based adaptive method for position control of a continuum robot. By utilizing an improved zero-return neurodynamic model, model-free control and Jacobian matrix adaptation of the continuum robot are achieved. This results in faster convergence of the error between the actual and desired positions of the end effector, providing a novel control approach for continuum robots. The control method of this invention can be easily implemented in real-time, ensuring the convergence and stability of the control system. Real-time feedback of the end effector motion information adjusts the adaptive Jacobian matrix, improving the smoothness of the continuum robot's trajectory. Attached Figure Description
[0040] Figure 1 This is a flowchart of a position control method for a continuous robotic arm in one embodiment of the present invention;
[0041] Figure 2 This is a system block diagram of the position control system of a continuous robotic arm in one embodiment of the present invention. Detailed Implementation
[0042] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but these are not intended to limit the scope of the invention.
[0043] In the following detailed description, numerous specific details are set forth to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that well-known algorithms are not shown in detail to avoid obscuring the spirit of the invention.
[0044] Furthermore, the execution order of actions, steps, etc. in the apparatus and methods shown in the claims, specification, and drawings can be implemented in any order, unless a specific order is explicitly specified, and as long as the output of the preceding processing is not used in the subsequent processing.
[0045] Example 1
[0046] In this embodiment, the continuous robotic arm is a wire-driven continuous robotic arm, consisting of a hyperelastic carbon fiber rod, a base disk, a spacer disk, and a drive cable. Changes in the length of the drive cable control the movement of the robotic arm, thereby adjusting the position of its end effector. This embodiment provides a model-free position control method for a continuous robotic arm based on Jacobian matrix adaptation, the flowchart of which is shown below. Figure 1 As shown, taking the continuum robot arm in a non-singular configuration as an example, the specific steps are as follows:
[0047] Step S101: Design the kinematic equations of the continuous robot arm to generate the driving force at time t, change the length of the driving cable, and adjust the position of the end effector of the continuous robot arm so that the end effector reaches the desired position r. m More specifically, the kinematic equations for the continuous body robotic arm are designed, as follows:
[0048] f(p(t))=r(t),
[0049] in, This represents the actuation quantity of the continuous robotic arm at time t. This represents the position vector of the end effector of the continuum robot arm. This represents the continuous nonlinear positive kinematic mapping of a continuum manipulator model with known parameters and structure.
[0050] Step S102: Differentiate both sides of the kinematic equations from step S101 with respect to time t to obtain the relationship between the change in the driving force of the continuum manipulator and the velocity vector at the end of the manipulator, and give the definition of the Jacobian matrix:
[0051]
[0052] in, It is the Jacobian matrix at the end effector of the robotic arm, defined as
[0053] Step S103: Calculate the position deviation vector function between the actual position and the target position. Using the zero-return neural dynamics design formula, ensure that each element of the position deviation vector function converges to zero, thus achieving position control of the continuum robot arm. More specifically, the position deviation vector function can be obtained using the following formula:
[0054] z(t) = r m -r(t),
[0055] Using the zero-return neurodynamics design formula, each element z in the position deviation vector function is made possible. i If (t)(i=1,2,...,m) converges to zero, then the position control of the continuous robot arm is achieved;
[0056]
[0057] in, L(·) is a nonlinear and monotonically increasing odd function used to control the convergence rate of the position deviation vector function z(t), accelerating its convergence so that each term in the function converges to zero in a finite time. The left side of the equation represents the rate of change of z(t), and the right side represents the negative feedback mechanism that brings z(t) closer to zero. Based on the position deviation vector function and the zero-return neurodynamic design formula, we can further derive:
[0058]
[0059] Zero-return neurodynamics is a special type of neurodynamics developed from neural networks, which guarantees that the error function converges to zero.
[0060] Step S104: Obtain an explicit expression of the control input signal based on the position deviation vector function and the zero-return neurodynamic design formula. Use this explicit expression of the control input signal to provide control with an adaptive unknown Jacobian matrix pseudo-inverse. More specifically, the formula obtained in step S103 is modified into an explicit expression of the control input signal, as follows:
[0061]
[0062] in, Let J(p(t)) be the pseudo-inverse of the Jacobian matrix. From the above expression, it can be seen that the feedback information is the position information of the end effector of the continuum robot, and the control system is closed-loop. Unlike continuum robot models with known parameters and structure, this invention studies the position control of a model-free continuum robot. It adaptively adapts the Jacobian matrix and provides the control of the pseudo-inverse of the unknown Jacobian matrix through an explicit expression of the control input signal. The simplified formula of the explicit expression is as follows:
[0063]
[0064] in, It is the unknown pseudo-inverse of the Jacobian matrix that needs to be adapted.
[0065] Step S105: To achieve adaptive Jacobian matrix adaptation for the continuum robot arm, the unknown Jacobian matrix... The vector-valued error function is defined as follows:
[0066]
[0067] in Applying the zero-return neurodynamics method again,
[0068]
[0069] in K(·) is used to control the convergence rate of the vector-valued error function. It is a nonlinear and monotonically increasing odd function that accelerates the convergence of the vector-valued error function ε(t), ensuring that each term in the function converges to zero in a finite time. The left side of the equation represents the rate of change of ε(t), and the right side represents the negative feedback mechanism that brings ε(t) closer to zero. Furthermore, the adaptive function for the unknown Jacobian matrix can be derived from the following equation:
[0070]
[0071] Furthermore, the adaptive equation of the Jacobian matrix of the control system can be obtained:
[0072]
[0073] The pseudo-inverse calculation of the non-empty driving change is as follows: It is the transpose of the driving variable.
[0074] This embodiment obtains the adaptive equation of the Jacobian matrix of the control system by using the zero-return neurodynamics method twice. See also Figure 2 Ten points are selected as target points in the free space of the continuous robot arm's workspace. The end effector starts from the initial zero point and initializes the Jacobian matrix with an initial value of J0 based on the initial position and driving force of the continuous robot arm, and initializes the corresponding parameters. The position, velocity, and acceleration of the end effector of the continuous robot arm are measured in real time using high-precision position, velocity, and acceleration sensors, and the unknown Jacobian matrix is adaptively learned using real-time feedback information.
[0075] Step S106: The updated Jacobian matrix can be obtained by using the adaptive Jacobian matrix equation, thereby obtaining the driving change of the continuous robot arm, which is output to the controller to control the end of the robot arm to move to the desired position.
[0076] The above technical solution addresses the scenario where the continuous robot arm is in a non-singular configuration. When the continuous robot arm is in a singular configuration, remedial measures are introduced to transform the singular configuration into a non-singular configuration: using... approximate An approximate solution is found in engineering applications, where k > 0 is a sufficiently small constant, and I is the identity matrix. Therefore, the proposed Jacobian matrix adaptive method remains feasible.
[0077] Example 2
[0078] This embodiment provides a computer program product, which, when executed by a processor, implements the position control method for a continuous robotic arm as described in Embodiment 1.
[0079] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0080] Example 3
[0081] This embodiment provides a position control device for a continuous robotic arm, including a sensor data interaction port, a memory, and a processor. The processor stores executable instructions, which, when executed by one or more processors, enable the one or more processors to perform the position control method for the continuous robotic arm described in Embodiment 1.
[0082] In summary, this invention provides a position control method, computer program product, and device for a continuous robotic arm. The position control method is based on an adaptive Jacobian matrix to achieve model-free position control of the continuous robotic arm, including steps such as constructing the kinematic equations of the continuous robotic arm, obtaining the relationship between the driving change and the end effector velocity, calculating the position deviation vector function, obtaining the control of the pseudo-inverse of the adaptive unknown Jacobian matrix, adaptively learning the Jacobian matrix using feedback information, and achieving the desired position at the end effector of the continuous robotic arm. This invention utilizes an improved zero-return neurodynamic model for model-free control of the continuous robotic arm, independent of the parameters and structure of the model. It can provide real-time feedback of the motion information of the end effector of the continuous robotic arm, adjust the adaptive Jacobian matrix, improve the smoothness of the continuous robotic arm's motion trajectory, and achieve faster convergence of the error between the actual and desired positions of the end effector.
[0083] Those skilled in the art should understand that variations can be implemented by combining existing technology with the above embodiments, which will not be elaborated here. Such variations do not affect the essence of the present invention, and will not be elaborated here either.
[0084] The preferred embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and the devices and structures not described in detail should be understood as being implemented in a conventional manner in the art. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention using the methods and techniques disclosed above, or modify them into equivalent embodiments with equivalent changes, without departing from the scope of the present invention. This does not affect the essential content of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the present invention's technical solutions still fall within the protection scope of the present invention.
[0085] Those skilled in the art will recognize that the units, i.e., algorithm steps, of the various examples described in connection with this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
Claims
1. A position control method for a continuous body robotic arm, characterized in that, Model-free position control of a continuum robot arm based on adaptive Jacobian matrix includes the following steps: Step S101: Design the kinematic equations of the continuous body manipulator to achieve the desired kinematic performance. The system continuously generates driving signals, changes the length of the driving cable, and adjusts the position of the end effector of the continuous robot arm to achieve the desired position. ; Step S102, the kinematic equations of step S101 with respect to time Differentiation yields the relationship between the change in the driving force of the continuum manipulator and the velocity vector at the end of the manipulator, and the definition of the Jacobian matrix is given; Step S103: Calculate the actual position With the target location Positional deviation vector function By using the zero-return neurodynamics design formula, each element in the position deviation vector function converges to zero, thus realizing the position control of the continuum robot arm. Step S104: Obtain the explicit expression of the control input signal based on the position deviation vector function and the zero-return neurodynamic design formula, and give the control of the adaptive unknown Jacobian matrix pseudo-inverse through the explicit expression of the control input signal; Step S105: Apply the zero-return neurodynamics method again to obtain the Jacobian matrix adaptive equation of the control system; the sensors of the continuous manipulator measure the position, velocity and acceleration of the continuous manipulator in real time and feed them back to the Jacobian matrix for adaptive learning; Step S106: Calculate the drive change of the continuum robot arm through the updated Jacobian matrix, thereby controlling the end effector of the robot arm to move to the desired position. The position control method is applicable to situations where the continuous robot arm is in a non-singular or singular configuration. When the continuum robot arm is in a non-singular configuration, the kinematic equations in step S101 are: ， In the above formula, express The driving force of the continuous robotic arm at any given moment. This represents the position vector of the end effector of the continuum robot arm. The continuous nonlinear positive kinematic mapping represents the continuous manipulator model with known parameters and structure; the Jacobian matrix in step S102 is defined as follows: ， in, It is the Jacobian matrix at the end effector of the robotic arm, defined as ; In step S103, the position deviation vector function is obtained through the formula... Obtain; using the zero-return neurodynamics design formula, ensure that each element in the position deviation vector function... It converges to zero, as shown in the following formula: ， in, for Regarding time The first derivative, Used to control the convergence speed of the position deviation vector function. It is a nonlinear and monotonically increasing odd function; further, based on the position deviation vector function and the zero-return neurodynamic design formula, we can obtain: ; In step S104, the explicitly expressed formula is as follows: ， in, Representing the Jacobian matrix The pseudo-inverse matrix is obtained; the control of the adaptive unknown Jacobian matrix pseudo-inverse is given by the explicit expression of the control input signal. The simplified formula of the explicit expression is as follows: ， in, It is the unknown pseudo-inverse of the Jacobian matrix that needs to be adapted; In step S105, in order to obtain the Jacobian matrix adapted to the continuum robot arm, the unknown Jacobian matrix... Vector value error function The definition is as follows: ， in ;Reapplying the zero-return neurodynamics method: ， in, It is the time derivative of the vector-valued error function used for Jacobian matrix estimation. Used to control the convergence speed of the vector-valued error function. It is a nonlinear and monotonically increasing odd function; and the adaptive equation for the unknown Jacobian matrix can be obtained as follows: Furthermore, the adaptive equation of the Jacobian matrix of the control system can be obtained: The pseudo-inverse of the non-empty driving change The calculation is as follows: , It is the transpose of the driving change; The continuous robotic arm is in a singular configuration, which is addressed by introducing remedial measures to transform the singular configuration into a non-singular configuration: using approximate Approximate solutions in engineering applications, where It is a sufficiently small constant. It is the identity matrix. It is an unknown Jacobian matrix The false rebellion, It is an unknown Jacobian matrix The transpose of .
2. A computer program product, characterized in that, When the computer program is executed by the processor, it implements the position control method for the continuous robotic arm as described in claim 1.
3. A position control device for a continuous robotic arm, comprising a sensor data interaction port, a memory, and a processor, characterized in that, It stores executable instructions that, when executed by one or more processors, enable the one or more processors to perform the position control method of the continuous robot arm as described in claim 1.