Robot adaptive trajectory control method based on radial basis function neural network
By adopting an adaptive trajectory control method based on radial basis function neural networks, the problems of control accuracy and stability of continuum robots in complex environments are solved, efficient trajectory tracking control is achieved, and the performance of robots in complex environments is improved.
Patent Information
- Application Number
- CN202511559838.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-29
- Publication Date
- 2026-01-27
AI Technical Summary
Existing technologies struggle to effectively address the control accuracy and stability issues of continuum robots in complex environments due to model uncertainties, especially in high-dimensional state spaces and highly nonlinear dynamic characteristics. These technologies are highly dependent on sensors, have a heavy computational burden, and are difficult to meet real-time control requirements.
An adaptive trajectory control method based on radial basis function neural networks is adopted. By constructing a nominal dynamic model and approximating the unknown dynamic components with a radial basis function neural network, a Lyapunov function and a virtual controller are designed to achieve adaptive compensation for Coriolis force, gravity, elastic force and external disturbances, thereby reducing the computational burden and improving control accuracy.
It significantly improves the trajectory tracking control accuracy of continuum robots, reduces computational burden and time cost, and maintains high robustness and fast convergence performance under unknown disturbance environments.
Smart Images
Figure CN121403364A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent equipment control, and more specifically, to a robot adaptive trajectory control method based on radial basis function neural networks. Background Technology
[0002] The exceptional properties of slender, flexible bodies made of elastic materials have made continuum robots a crucial technological solution for navigating curved paths and operating in confined spaces. Their superior deformation capabilities, structural compliance, and safe interaction advantages have made this technology highly favored in surgical interventions and industrial applications. However, in real-world working environments, due to the inherent compliance and deformability of continuum robots, the system exhibits highly coupled nonlinear dynamics and multi-source uncertainties. These uncertainties include structural uncertainties such as centroid shift, inertial parameter variations, and differences in structural compliance, as well as non-structural uncertainties such as system nonlinearity, friction, and unknown external disturbances. These complex factors severely restrict control accuracy and stability, becoming a core bottleneck hindering the technology's transition from laboratory research to widespread engineering applications. Therefore, how to effectively compensate for model uncertainties to improve the control performance of continuum robots has become a critical problem that urgently needs to be solved.
[0003] As a key indicator for evaluating the performance of continuum robot controllers, tracking error accuracy (i.e., the deviation between the actual and expected values of the lateral and longitudinal bending angles of the robot's end effector) is heavily influenced by model uncertainty compensation strategies and control algorithm design. Existing control methods for addressing model uncertainty can be broadly categorized into two types: one based entirely on dynamic optimization models, and the other employing data-driven model-free methods such as neural networks, fuzzy logic, and reinforcement learning. Dynamic model-based control methods aim to comprehensively describe various deformation behaviors, but their complex model structures often come with enormous computational burdens, making it difficult to meet the computational efficiency requirements of real-time control. While data-driven model-free control methods avoid explicit modeling, they heavily rely on high-precision, low-latency sensor feedback, and sensor noise or transmission delays can easily introduce control errors. Furthermore, data-driven methods that rely on training typically require long learning times and large amounts of labeled data. Since continuum robot systems generally possess high-dimensional state spaces and strongly nonlinear dynamic characteristics, acquiring datasets covering all operating conditions is extremely costly, further limiting the practical application of these methods. Summary of the Invention The purpose of this invention is to provide a robot adaptive trajectory control method based on radial basis function neural network, which significantly reduces the huge computational burden of traditional optimization strategies, avoids the resulting time and space costs, and does not rely on the model training learning process before control, thereby effectively improving the trajectory tracking control accuracy of continuum robot.
[0004] This invention is achieved through the following technical solution: An adaptive trajectory control method for robots based on radial basis function neural networks includes the following steps: S1. Construct the nominal dynamic model of the continuum robot using the Lagrange algorithm; S2. Design a radial basis function neural network function for approximation estimation of Coriolis force, gravity, elastic force and external disturbances in subsequent controller design; S3. Subtract the actual output of the system (the lateral and longitudinal bending angles at the end) from the ideal output to form the tracking error z1, and construct the first error variable; S4. Design a Lyapunov candidate function by integrating the first error variable, and design the first virtual controller. S5. Using the difference between the first error variable and the first virtual controller as the second variable, design a second Lyapunov candidate function. Introduce the radial basis function neural network function designed in step S2 to handle unknown system uncertainties (Coriolis force, gravity, elastic force and external disturbances). During the process, the approximation result and the lower bound of the norm of the inertia matrix are simultaneously adaptively processed. Finally, the actual controller of the continuum is designed.
[0005] Furthermore, the nominal dynamic model of the continuum robot in step S1 is as follows: , in , and These are the system's state vectors, representing the generalized angular position, angular velocity, and angular acceleration vectors, respectively. This represents the angle between the initial plane and the curved plane. Let be the curvature angle of the plane in the xz plane. It is the inertia matrix. It is the matrix of Coriolis force and centripetal force. It is a vector of gravity and stiffness. It is an external disturbance variable. It controls the input torque.
[0006] Furthermore, by order , , The nominal dynamic model of the continuum robot described above can be rewritten as follows: , in, , , Suppose there exists an unknown positive number. , making .
[0007] Furthermore, step S2 specifically includes the following steps: 1) The radial basis function (RBF) neural network is constructed as follows: , in, Let be the radial basis input vector, where The dimension of the input space is represented by the weight vector. express, It is the number of neurons in the hidden layer, and the basis function vector is defined as follows: Each basis function All models were modeled using Gaussian kernels: , in, Indicates the first The center position of each basis function, and That is its width parameter; 2) These radial basis function neural networks were used to approximate an unknown smooth nonlinear mapping. ,Right now , in, This represents the approximation error, and its upper bound is restricted: , It is a known constant, an ideal weight vector Defined in the domain The solution that minimizes the worst-case approximation error can be obtained by solving the following optimization problem: .
[0008] Furthermore, the first error variable in step S3 is: in, It is the ideal output position signal.
[0009] Furthermore, step S4 specifically includes the following steps: Design the Lyapunov candidate function as follows: , Taking its derivative, we get: , The virtual controller is derived as follows: , in, , and These are the positive control adjustment parameters designed for this purpose.
[0010] Furthermore, step S5 specifically includes the following steps: 1) State variables The difference between the virtual controller and the virtual controller is used as the second variable, i.e. , Taking the derivative with respect to the virtual controller, we get: , Then to Differentiation yields: , 2) Design the second Lyapunov function as follows: , in, It is a diagonal matrix. right Differentiation yields: , in, , For position functions, Output of the radial basis neural network Approximation, such that for any positive constant... All of them have: , Using Young's inequality, we can obtain: , , , therefore, , in, , , Introduction adaptive parameter estimates and estimation error : , Right now , The actual controller is derived. and adaptive rate for: ,
[0011] in, and , , , , ,and All of these are positive control parameters designed for this purpose.
[0012] Compared with the prior art, the beneficial effects of the present invention are: 1. Based on Lyapunov's stability theorem, the stability of the proposed method is rigorously proven theoretically. Furthermore, on a practical continuum robot platform, the proposed method is compared with the traditional PID method. Experimental results show that the proposed method has better tracking performance and disturbance rejection capability.
[0013] 2. The designed RBF neural network is used to approximate the uncertain dynamic components in the dynamic model, including Coriolis force, gravity, elasticity and external disturbances, and eliminate the influence of the unmodeled dynamic parts on the system control.
[0014] 3. For the inertia matrix, which serves as the system control coefficient in a continuum robot, this scheme also treats it as an unknown quantity. It is assumed that the inertia matrix has an unknown norm lower bound, but this unknown lower bound is not present in the actual controller through adaptive processing, that is, there is no need to define the actual value of this lower bound.
[0015] In summary, the nominal dynamic model of the continuum retains the actual physical meaning while treating all dynamic uncertainties as unknown, thus solving the problem of the impact of dynamic nonlinear uncertainty on the control effect. Attached Figure Description
[0016] Figure 1 This is the tracking effect without external interference in Experiment 1 of the present invention; Figure 2 This is the input torque without external interference in Experiment 1 of the present invention; Figure 3 This refers to the tracking effect in Experiment 2 of the present invention, which involves external interference. Figure 4 The input torque in Experiment 2 of this invention is subject to external interference. Detailed Implementation
[0017] The present invention will now be further described in conjunction with the accompanying drawings.
[0018] An example of an adaptive trajectory control method for a robot based on a radial basis function neural network includes the following steps: S1. Construct the nominal dynamic model of the continuum robot using the Lagrange algorithm; S2. Design a radial basis function neural network function for approximation estimation of Coriolis force, gravity, elastic force and external disturbances in subsequent controller design; S3. Subtract the actual output of the system (the lateral and longitudinal bending angles at the end) from the ideal output to form the tracking error z1, and construct the first error variable; S4. Design a Lyapunov candidate function by integrating the first error variable, and design the first virtual controller. S5. Using the difference between the first error variable and the first virtual controller as the second variable, design a second Lyapunov candidate function. Introduce the radial basis function neural network function designed in step S2 to handle unknown system uncertainties (Coriolis force, gravity, elastic force and external disturbances). During the process, the approximation result and the lower bound of the norm of the inertia matrix are simultaneously adaptively processed. Finally, the actual controller of the continuum is designed.
[0019] The nominal dynamic model of the continuum robot in step S1 is: , in , and These are the system's state vectors, representing the generalized angular position, angular velocity, and angular acceleration vectors, respectively. This represents the angle between the initial plane and the curved plane. Let be the curvature angle of the plane in the xz plane. It is the inertia matrix. It is the matrix of Coriolis force and centripetal force. It is a vector of gravity and stiffness. It is an external disturbance variable. The control input torque is used. In actual motion, since continuum dynamics are uncertain, this application assumes that the dynamic characteristics and external disturbances are also uncertain, i.e. , , , All of these are unknown quantities.
[0020] By order , , The nominal dynamic model of the continuum robot described above can be rewritten as follows: , in, , , Suppose there exists an unknown positive number. , making .
[0021] Step S2 specifically includes the following steps: 1) The radial basis function (RBF) neural network is constructed as follows: , in, Let be the radial basis input vector, where The dimension of the input space is represented by the weight vector. express, It is the number of neurons in the hidden layer, and the basis function vector is defined as follows: Each basis function All models were modeled using Gaussian kernels: , in, Indicates the first The center position of each basis function, and That is its width parameter; 2) These radial basis function neural networks were used to approximate an unknown smooth nonlinear mapping. ,Right now , in, This represents the approximation error, and its upper bound is restricted: , It is a known constant, an ideal weight vector Defined in the domain The solution that minimizes the worst-case approximation error can be obtained by solving the following optimization problem: .
[0022] The first error variable in step S3 is: in, It is the ideal output position signal.
[0023] Step S4 specifically includes the following steps: Design the Lyapunov candidate function as follows: , Taking its derivative, we get: , The virtual controller is derived as follows: , in, , and These are the positive control adjustment parameters designed for this purpose.
[0024] Step S5 specifically includes the following steps: 1) State variables The difference between the virtual controller and the virtual controller is used as the second variable, i.e. , Taking the derivative with respect to the virtual controller, we get: , Then to Differentiation yields: , 2) Design the second Lyapunov function as follows: , in, It is a diagonal matrix. right Differentiation yields: , in, , For position functions, Output of the radial basis neural network Approximation, such that for any positive constant... All of them have: , Using Young's inequality, we can obtain: , , , therefore, , in, , , Introduction adaptive parameter estimates and estimation error : , Right now , The actual controller is derived. and adaptive rate for: ,
[0025] in, and , , , , ,and All of these are positive control parameters designed for this purpose.
[0026] It also includes a stability proof: substituting the actual controller and adaptive rate into the derivative formula for the second Lyapunov function: , Right now: , because ,have ,Right now , We can obtain the following using Young's inequality: , Right now
[0027] in, It is a positive number. In a closed-loop system, all signals are bounded.
[0028] The parameters of the self-built continuum robot hardware platform are shown in Table 1 below.
[0029] Table 1 Parameters of the Continuum Robot
[0030] The robot's end effector reference trajectory is designed as follows:
[0031] The initial position of the continuum robot is set as follows The proposed robot adaptive trajectory control method based on radial basis function neural network (hereinafter referred to as RBFNN-ATC) sets the control parameters as follows: , , , , The parameter configuration for the Radial Basis Function Neural Network (RBFNN) is as follows: center value Width value To ensure the rigor and fairness of the design, the PID control parameters are setpoints from existing literature.
[0032] Experiment 1: The performance of the proposed RBFNN-ATC scheme in a continuous robot system without external disturbances was evaluated and compared with that of the PID method.
[0033] Bending angle and rotation angle The trajectory and its tracking error, such as Figure 1As shown, both methods achieve convergence of tracking error to zero, but RBFNN-ATC exhibits a faster convergence speed. Under the RBFNN-ATC scheme, the angle... The root mean square error (RMSE) for trajectory tracking is 0.0048 rad, while that of the PID method is 0.0075 rad; for angle... The RMSE of RBFNN-ATC is 0.0172 rad, while that of the PID method is 0.0199 rad. The performance advantage of RBFNN-ATC stems from its treatment of Coriolis force, gravity, elastic force, and inertia as all unknowns in the uncertain modeling part of a dynamic adaptive system, whereas PID relies on a fixed model function and lacks real-time adjustment. Furthermore, Figure 2 The changes in driving force under undisturbed conditions are demonstrated, and both methods can produce a smooth and stable force output.
[0034] Experiment 2: To verify the performance of the proposed RBFNN-ATC scheme under unknown perturbations, an external perturbation was applied to the continuum robot. ,in , , The RBFNN-ATC scheme and the PID method were compared and analyzed under the same perturbation conditions.
[0035] Under the influence of external disturbances, the bending angle and rotation angle Trajectory and tracking error such as Figure 3 As shown, both RBFNN-ATC and the PID method can achieve error convergence, but RBFNN-ATC exhibits a faster convergence speed. The root mean square error (RMSE) of trajectory tracking is 0.0063 rad under the RBFNN-ATC scheme and 0.0091 rad under the PID method; angle The RMSE is 0.0201 rad under RBFNN-ATC and 0.0249 rad under the PID method. Compared with the RMSE under undisturbed conditions, external disturbances have a smaller impact on the RBFNN-ATC scheme, while the performance of the PID method significantly decreases. The results indicate that RBFNN-ATC has higher tracking accuracy and stronger robustness under disturbed environments, which stems from the approximation of unknown external disturbances through radial basis neural networks and adaptive compensation. Furthermore, Figure 4 The changes in driving force under undisturbed conditions are demonstrated, and both methods can produce a smooth and stable force output.
[0036] This method effectively compensates for uncertainties in the dynamic model of the system. Based on the nominal dynamic model, it eliminates the need for complex model optimization. Instead, it utilizes a radial basis function (RBF) adaptive algorithm to estimate and compensate for multiple uncertainties, including inertial forces, Coriolis forces, gravity, elastic forces, friction, and unknown external disturbances, online in real time. This significantly reduces the enormous computational burden of traditional optimization strategies, avoiding the resulting time and space costs. Furthermore, it eliminates the need for pre-control model training, thereby effectively improving the trajectory tracking control accuracy of the continuum robot.
Claims
1. A robot adaptive trajectory control method based on radial basis function neural network, characterized in that: Includes the following steps: S1. Construct the nominal dynamic model of the continuum robot using the Lagrange algorithm; S2. Design a radial basis function neural network function for approximation estimation of Coriolis force, gravity, elastic force and external disturbances in subsequent controller design; S3. Subtract the actual output from the ideal output of the system to form the tracking error z1, and construct the first error variable; S4. Design a Lyapunov candidate function by integrating the first error variable, and design the first virtual controller. S5. The difference between the first error variable and the first virtual controller is used as the second variable. A second Lyapunov candidate function is designed for this. The radial basis function designed in step S2 is introduced to handle the unknown system uncertainty. During the process, the approximation result and the lower bound of the norm of the inertia matrix are simultaneously adaptively processed. Finally, the actual controller of the continuum is designed.
2. The robot adaptive trajectory control method based on radial basis function neural network according to claim 1, characterized in that: The nominal dynamic model of the continuum robot in step S1 is: ， in , and These are the system's state vectors, representing the generalized angular position, angular velocity, and angular acceleration vectors, respectively. This represents the angle between the initial plane and the curved plane. Let be the curvature angle of the plane in the xz plane. It is the inertia matrix. It is the matrix of Coriolis force and centripetal force. It is a vector of gravity and stiffness. It is an external disturbance variable. It controls the input torque.
3. The robot adaptive trajectory control method based on radial basis function neural network according to claim 2, characterized in that: By order , , The nominal dynamic model of the continuum robot described above can be rewritten as follows: ， in, , , Suppose there exists an unknown positive number. , making .
4. The robot adaptive trajectory control method based on radial basis function neural network according to claim 1, characterized in that: Step S2 specifically includes the following steps: 1) The radial basis function neural network is constructed as follows: ， in, Let be the radial basis input vector, where The dimension of the input space is represented by the weight vector. express, It is the number of neurons in the hidden layer, and the basis function vector is defined as follows: Each basis function All models were modeled using Gaussian kernels: ， in, Indicates the first The center position of each basis function, and That is its width parameter; 2) These radial basis function neural networks were used to approximate an unknown smooth nonlinear mapping. ,Right now ， in, This represents the approximation error, and its upper bound is restricted: , It is a known constant, an ideal weight vector Defined in the domain The solution that minimizes the worst-case approximation error can be obtained by solving the following optimization problem: 。 5. The robot adaptive trajectory control method based on radial basis function neural network according to claim 1, characterized in that: The first error variable in step S3 is: in, It is the ideal output position signal.
6. The robot adaptive trajectory control method based on radial basis function neural network according to claim 1, characterized in that: Step S4 specifically includes the following steps: Design the Lyapunov candidate function as follows: ， Taking its derivative, we get: ， The virtual controller is derived as follows: ， in, , and These are the positive control adjustment parameters designed for this purpose.
7. The robot adaptive trajectory control method based on radial basis function neural network according to claim 6, characterized in that: Step S5 specifically includes the following steps: 1) State variables The difference between the virtual controller and the virtual controller is used as the second variable, i.e. ， Taking the derivative with respect to the virtual controller, we get: ， Then to Differentiation yields: ， 2) Design the second Lyapunov function as follows: ， in, It is a diagonal matrix. right Differentiation yields: ， in, , For position functions, Output of the radial basis neural network Approximation, such that for any positive constant... All of them have: ， Using Young's inequality, we can obtain: ， ， ， therefore, ， in, , , Introduction adaptive parameter estimates and estimation error : ， Right now ， The actual controller is derived. and adaptive rate for: ， in, and , , , , ,and All of these are positive control parameters designed for this purpose.