A method and system for shape control of a flexible robot

Abstract

This invention relates to a shape control method and system for a flexible robot. The method inputs the desired shape of the flexible robot and the current tendon actuation data set into an offline-constructed shape Jacobian matrix estimation model to estimate the shape Jacobian matrix, obtaining the current shape Jacobian matrix and predicted motion velocity. The method then corrects the shape Jacobian matrix estimation model online by calculating the velocity error between the real-time motion velocity and the predicted motion velocity. Based on the online-corrected shape Jacobian matrix estimation model, the shape control problem of the flexible robot is constructed as a constrained quadratic programming problem. A neurodynamics optimizer is used to solve the quadratic programming problem to obtain the optimal driving command that satisfies the constraints, driving the flexible robot to achieve the desired shape. Therefore, this invention achieves high-precision shape control of a flexible robot while also considering adaptability and real-time computational efficiency.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a method and system for shape control of a flexible robot. Background Technology

[0002] Flexible robots, unlike traditional rigid-jointed robots, can achieve multi-degree-of-freedom motion through continuous deformation, exhibiting excellent environmental adaptability, flexibility, and human-robot interaction safety. Therefore, flexible robots have significant application value in confined space operations such as minimally invasive surgery and industrial inspection and maintenance. However, the redundant degrees of freedom and strong nonlinear characteristics brought about by the compliant structure of flexible robots make precise shape control a key technical challenge, directly affecting the reliability of task execution.

[0003] In the field of shape control for flexible robots, control accuracy primarily depends on the accuracy of kinematic modeling. Current mainstream modeling methods can be broadly categorized into two types: physical model-based and data-driven, but both have significant drawbacks. Physical model-based methods, such as constant curvature models, Cosserat models, and Euler-Bernoulli beam models, attempt to describe the relationship between actuation and deformation through geometric or mechanical principles. However, these methods have inherent limitations: constant curvature models struggle to accurately characterize the deformation characteristics of flexible bodies under complex deformation conditions; Cosserat models are computationally complex and difficult to meet real-time control requirements; and Euler-Bernoulli models, by neglecting shear effects, struggle to guarantee shape control accuracy under large deformation conditions or complex load environments. Data-driven modeling methods, such as those based on neural networks, Gaussian process regression, or online least squares, do not require explicit physical modeling and establish input-output mappings through machine learning. However, these methods heavily rely on large amounts of offline training data, making them ill-equipped to handle unforeseen sudden conditions. Furthermore, model optimization and parameter tuning processes are computationally expensive, and the real-time performance and stability of online learning are difficult to guarantee.

[0004] Therefore, there is an urgent need for a shape control scheme for flexible robots that can balance high precision, adaptability, and real-time computing efficiency. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: the present invention provides a shape control method and system for flexible robots, which achieves high-precision shape control of flexible robots while taking into account adaptability and real-time computing efficiency.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] In a first aspect, the present invention provides a shape control method for a flexible robot, comprising:

[0008] Collect the expected shape and current tendon actuation data of the flexible robot, input the expected shape and current tendon actuation data into the offline constructed shape Jacobian matrix estimation model to estimate the shape Jacobian matrix, obtain the current shape Jacobian matrix, and obtain the predicted motion speed based on the current shape Jacobian matrix;

[0009] The real-time motion speed of the flexible robot is collected, the speed error between the real-time motion speed and the predicted motion speed is calculated, and the shape Jacobian matrix estimation model is corrected online based on the speed error to obtain the online corrected shape Jacobian matrix estimation model.

[0010] Based on the online-corrected shape Jacobian matrix estimation model, the shape control problem of the flexible robot is constructed as a quadratic programming problem with constraints. A neural dynamics optimizer is used to solve the quadratic programming problem to obtain the optimal driving command that satisfies the constraints. The flexible robot is then driven to achieve the expected shape according to the optimal driving command.

[0011] The beneficial effects of this invention are as follows: Through a hierarchical design of offline construction and online correction, the generalization ability of the shape Jacobian matrix estimation model is improved. By inputting the expected shape and the current tendon drive quantity dataset into the pre-constructed shape Jacobian matrix estimation model, the expected motion velocity can be obtained. The shape Jacobian matrix estimation model is then corrected online based on the velocity error between the real-time motion velocity and the expected motion velocity. This eliminates the need to re-train the model using reconstructed training data; online correction of the shape Jacobian matrix estimation model can be achieved through velocity error alone, ensuring the real-time online learning of the shape Jacobian matrix estimation model and its adaptability and stability in adapting to dynamic and complex environments and flexibly handling sudden working conditions. The shape control problem of the flexible robot is constructed as a constrained quadratic programming problem, eliminating the need for iterative constraint judgment, thus improving convergence speed. A neurodynamics optimizer is used for solving the problem, improving real-time computational efficiency and ensuring that the optimal drive command can respond in real-time to changes in real-time motion velocity, stably achieving the expected shape.

[0012] Optionally, the step of inputting the expected shape and the current tendon drive quantity dataset into the offline constructed shape Jacobian matrix estimation model for shape Jacobian matrix estimation includes:

[0013] Collect offline tendon drive data of flexible robot under random drive and the offline three-dimensional coordinates of K feature points uniformly distributed on the corresponding flexible skeleton;

[0014] The offline 3D coordinates of each feature point are converted into offline unit direction vectors according to the unit direction vector formula to obtain an offline unit direction vector dataset. At the same time, the offline tendon drive quantity dataset is normalized to a preset normalization range according to the normalization formula to obtain a normalized offline tendon drive quantity dataset.

[0015] The offline unit orientation vector dataset and the normalized offline tendon drive vector dataset are combined into an input vector, which is then input into a radial basis neural network for offline training to generate a shape Jacobian matrix estimation model.

[0016] As described above, collecting offline tendon actuation data of flexible robots in a random driving manner ensures that the offline tendon actuation data contains diverse deformation features. Collecting the offline three-dimensional coordinates of K feature points evenly distributed on the flexible skeleton, rather than concentrating them locally or at both ends, can completely capture the overall change law of the flexible robot, obtain a complete shape representation, and improve the fitting accuracy of the shape Jacobian matrix estimation model. Converting the offline three-dimensional coordinates into offline unit direction vectors eliminates the dependence on absolute position. At the same time, normalizing the offline tendon actuation data set eliminates the difference in numerical range between different ranges, making the shape Jacobian matrix estimation model adaptable to flexible robots of different scenarios and lengths, thus improving cross-scenario adaptability.

[0017] Optionally, the step of inputting the input vector into a radial basis neural network for offline training to generate a shape Jacobian matrix estimation model includes:

[0018] The true shape Jacobian matrix of the input vector is calculated using the constant curvature assumption. The true Jacobian matrix and the input vector are then input into a radial basis function neural network for offline training. The input vector is clustered using a clustering algorithm to initialize the kernel center of the Gaussian function in the radial basis function neural network. At the same time, the kernel width of the Gaussian function in the radial basis function neural network is initialized according to the kernel center to obtain the initialized Gaussian function.

[0019] The initialized Gaussian function is combined with the initial weight matrix of the radial basis neural network to perform a nonlinear transformation on the input vector to output an offline shape Jacobian matrix.

[0020] The mean square error between the offline shape Jacobian matrix and the true shape Jacobian matrix is ​​calculated. The initial weight matrix is ​​optimized using stochastic gradient descent with the goal of minimizing the mean square error, thereby completing the offline training of the radial basis function neural network and generating a shape Jacobian matrix estimation model.

[0021] As described above, calculating the true shape Jacobian matrix using the constant curvature assumption achieves low-cost acquisition of true labels and avoids training the shape Jacobian matrix estimation model without a clear objective due to the lack of true labels, providing a clear direction for optimizing the initial weight matrix. Clustering algorithms are used to cluster the input vectors to initialize the kernel center of the Gaussian function in the radial basis function neural network. The kernel width is then initialized based on the kernel center, ensuring a match between the kernel center and the kernel width, thus improving fitting accuracy. Stochastic gradient descent is employed to optimize the initial weight matrix with the goal of minimizing the mean squared error. This reduces offline training time while dynamically optimizing the initial weight matrix, improving the accuracy of the generated shape Jacobian matrix estimation model.

[0022] Optionally, obtaining the predicted motion velocity based on the current shape Jacobian matrix includes:

[0023] Obtain the current time period, and calculate the current real-time drive velocity of the tendon based on the current time period and the current tendon drive volume dataset;

[0024] The current real-time driving velocity of the tendon and the current shape Jacobian matrix are input into the first motion formula for calculation to obtain the predicted motion velocity. The first motion formula is:

[0025] ;

[0026] in, Indicates the predicted speed of motion. This represents the current shape Jacobian matrix. This indicates the current real-time drive speed of the tendon.

[0027] As described above, the current real-time driving speed of the tendon is calculated based on the current time period and the current tendon driving volume dataset, eliminating the error in the real-time driving speed of the tendon caused by periodic fluctuations. This ensures the accuracy of the predicted motion speed calculated based on the current real-time driving speed of the tendon and the current shape Jacobian matrix, thus achieving real-time and precise coupling between driving and shape.

[0028] Optionally, the step of correcting the shape Jacobian matrix estimation model based on the velocity error includes:

[0029] Obtain the initial weight matrix of the shape Jacobian matrix estimation model, construct the differential update equation of the initial weight matrix based on the velocity error, update the initial weight matrix according to the differential update equation to obtain the real-time weight matrix, and correct the shape Jacobian matrix estimation model according to the real-time weight matrix.

[0030] The differential update equation is:

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] in, Represents the real-time weight matrix. Denotes the first convergence coefficient. This represents the kernel vector of the Gaussian function after regularization. The transpose of the kernel vector of the Gaussian function is given. Represents the initial weight matrix. The kernel vector represents the Gaussian function. Let m represent the Gaussian function chosen by the i-th node of the hidden layer in a radial basis function neural network for the input vector, and m represent the number of hidden layer nodes in the radial basis function neural network. Represents m dimensions, Represents the input vector. Denotes the second convergence coefficient. This represents the current real-time drive velocity of the tendon after regularization. This indicates the current real-time drive velocity of the tendon. The transpose matrix represents the current real-time drive velocity of the tendon. This represents the third convergence coefficient. Indicates the actual speed of motion. This indicates the speed error.

[0037] As described above, the online velocity error is converted into a stable update of the initial weight matrix. The convergence of the initial weight matrix update is guaranteed by the differential update equation and the convergence coefficient, which avoids the shape Jacobian matrix estimation model from getting out of control due to disturbances and ensures that the shape Jacobian matrix estimation model, which is corrected according to the real-time weight matrix, always fits the reality.

[0038] Optionally, the objective function of the quadratic programming problem is:

[0039]

[0040] in, Let represent the objective function of the quadratic programming problem. Indicates the expected velocity of motion for the desired shape. This represents the current shape Jacobian matrix. This indicates the current real-time drive velocity of the tendon. A coefficient representing the balance shape accuracy, control capability, and motion smoothness;

[0041] The constraints are as follows:

[0042]

[0043] in, This indicates the lower limit of tendon drive. This indicates the upper limit of tendon drive. This indicates the current real-time drive of the tendon. This indicates the lower limit of tendon drive velocity. This indicates the upper limit of tendon drive velocity. This indicates the current real-time drive speed of the tendon.

[0044] As described above, the objective function of the quadratic programming problem balances the constraints of shape accuracy and control energy, covering tendon drive quantity and tendon drive velocity, thus improving accuracy while ensuring safety.

[0045] Optionally, the optimization using neurodynamics to solve the quadratic programming problem includes:

[0046] The quadratic programming problem is transformed into a set of KKT optimality conditions, which includes zero gradient equations and complementary relaxation conditions.

[0047] The complementary relaxation conditions are processed using the FB smoothing function to obtain the FB smoothed equation. The FB smoothed equation and the zero gradient equation are integrated into a continuous nonlinear equation system. The continuous nonlinear equation system is solved using a neurodynamic optimizer.

[0048] Optionally, the zero gradient equation is:

[0049]

[0050] in, This represents the transpose of the current shape Jacobian matrix. This represents the transpose of the current shape Jacobian matrix. Indicates the optimal driving instruction. The expected velocity of the expected shape A coefficient representing the balance between tracking accuracy and control energy. Represents the Lagrange multipliers. Represents the identity matrix;

[0051] The complementary relaxation condition is:

[0052]

[0053] in, Let denote the transpose of the Lagrange multipliers, d denote the constraint deviation variables, and C denote the constraint coefficient matrix. Indicates the optimal driving instruction. This indicates the lower limit of tendon drive. This indicates the upper limit of tendon drive. This indicates the current real-time drive of the tendon. This indicates the lower limit of tendon drive velocity. This indicates the upper limit of tendon drive velocity. This indicates the current real-time drive velocity of the tendon. Indicates the first transition boundary. Indicates the second transition boundary. Indicates the third transition boundary. Indicates the fourth transition boundary. Indicates the first transfer coefficient. This represents the second transfer coefficient.

[0054] As described above, transforming the quadratic programming problem into a set of KKT optimality conditions eliminates the need for complex iterative search logic, simplifying the solution process. Furthermore, employing the FB smoothing function to handle the complementary relaxation conditions of the KKT optimality condition set transforms discontinuous conditions into continuous equations, eliminating the need for constraint activation judgments and avoiding the time-consuming constraint checks. Moreover, the continuous nature of the FB smoothing function ensures smooth gradient changes in the continuous nonlinear equation system, guaranteeing the stability of the solution.

[0055] In a second aspect, the present invention provides a shape control system for a flexible robot, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the shape control method for a flexible robot described in the first aspect.

[0056] The technical effects of the shape control system for a flexible robot provided in the second aspect are the same as those of the shape control method for a flexible robot provided in the first aspect. Attached Figure Description

[0057] Figure 1 This is a flowchart of a shape control method for a flexible robot provided in this embodiment;

[0058] Figure 2 This is a schematic diagram of the overall process of a shape control method for a flexible robot provided in this embodiment;

[0059] Figure 3This describes the offline construction process of the shape Jacobian matrix estimation model involved in this embodiment;

[0060] Figure 4 This is a schematic diagram of the shape control system of a flexible robot provided in this embodiment.

[0061] [Explanation of Labels in the Attached Image]

[0062] 1. A shape control system for a flexible robot;

[0063] 2. Processor;

[0064] 3. Memory. Detailed Implementation

[0065] To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and that the scope of the present invention can be fully conveyed to those skilled in the art.

[0066] Example 1

[0067] Please refer to Figures 1 to 3 This invention provides a shape control method for a flexible robot, comprising the following steps:

[0068] S1. Collect the expected shape and current tendon drive amount dataset of the flexible robot, input the expected shape and the current tendon drive amount dataset into the offline constructed shape Jacobian matrix estimation model to estimate the shape Jacobian matrix, obtain the current shape Jacobian matrix, and obtain the predicted motion speed based on the current shape Jacobian matrix.

[0069] In this embodiment, as Figure 2 As shown, the expected shape and current tendon actuation data of the flexible robot are collected. The current tendon actuation data refers to the displacement data of each tendon of the flexible robot. The expected shape and current tendon actuation data are input into the offline constructed shape Jacobian matrix estimation model to estimate the shape Jacobian matrix and obtain the current shape Jacobian matrix. The predicted motion speed is then obtained based on the current shape Jacobian matrix.

[0070] At this point, before step S1 involves inputting the expected shape and the current tendon drive quantity dataset into the offline-constructed shape Jacobian matrix estimation model for shape Jacobian matrix estimation, the following steps are included:

[0071] S11. Collect the offline tendon drive data set generated by the flexible robot under random drive and the offline three-dimensional coordinates of K feature points uniformly distributed on the corresponding flexible skeleton;

[0072] S12. Convert the offline three-dimensional coordinates of each feature point into an offline unit direction vector according to the unit direction vector formula to obtain an offline unit direction vector dataset. At the same time, normalize the offline tendon drive quantity dataset to a preset normalization range according to the normalization formula to obtain a normalized offline tendon drive quantity dataset.

[0073] S13. Combine the offline unit direction vector dataset with the normalized offline tendon drive vector dataset into an input vector, and input the input vector into a radial basis neural network for offline training to generate a shape Jacobian matrix estimation model.

[0074] In this embodiment, as Figure 3 As shown, a flexible robot is driven by random actuation to collect an offline tendon actuation dataset and the offline 3D coordinates of K feature points uniformly distributed on the corresponding flexible skeleton. The offline tendon actuation dataset can be represented as: ∈ n=1,2, N represents the total number of tendons, and each offline 3D coordinate can represent The offline 3D coordinates of all feature points can be represented as: ∈ , K represents the total number of feature points. This represents 3K dimensions. The offline 3D coordinates of each feature point are converted into an offline unit direction vector using the unit direction vector formula:

[0075] ;

[0076] in, This represents the offline unit direction vector dataset, where K represents the total number of feature points.

[0077] Simultaneously, the offline tendon drive data set is normalized to a preset normalization range according to the normalization formula, which is:

[0078] ;

[0079] in, This represents the i-th normalized offline tendon drive quantity. Let represent the offline tendon actuation quantity of the i-th muscle, and n represent the number of tendons in the flexible robot. This indicates the lower limit of tendon drive. This indicates the upper limit of tendon drive.

[0080] The offline unit orientation vector dataset and the normalized offline tendon drive quantity dataset are combined as input vectors and fed into a radial basis function neural network for offline training to generate a shape Jacobian matrix estimation model. It should be noted that when inputting the expected shape and the current tendon drive quantity dataset into the shape Jacobian matrix estimation model for shape Jacobian matrix estimation, the expected shape is also transformed into a unit orientation vector according to the unit orientation vector formula, and the current tendon drive quantity dataset is normalized according to the normalization formula.

[0081] At this point, step S13, which involves inputting the input vector into a radial basis neural network for offline training to generate a shape Jacobian matrix estimation model, includes:

[0082] S131. Calculate the true shape Jacobian matrix of the input vector using the constant curvature assumption. Input the true Jacobian matrix and the input vector into a radial basis function neural network for offline training. Cluster the input vector using a clustering algorithm to initialize the kernel center of the Gaussian function in the radial basis function neural network. Simultaneously, initialize the kernel width of the Gaussian function in the radial basis function neural network based on the kernel center to obtain the initialized Gaussian function.

[0083] S132. The initialized Gaussian function is combined with the initial weight matrix of the radial basis neural network to perform a nonlinear transformation on the input vector to output an offline shape Jacobian matrix.

[0084] S133. Calculate the mean square error between the offline shape Jacobian matrix and the true shape Jacobian matrix. Optimize the initial weight matrix using stochastic gradient descent with the goal of minimizing the mean square error, complete the offline training of the radial basis function neural network, and generate a shape Jacobian matrix estimation model.

[0085] In this embodiment, as Figure 3The method employs the constant curvature assumption to calculate the true shape Jacobian matrix of the input vector. This true shape Jacobian matrix, along with the input vector, is input into a radial basis function neural network (RBN) for offline training. The true shape Jacobian matrix serves as the true label for the input vector. A clustering algorithm is used to cluster the input vector, initializing the kernel center of the Gaussian function in the RBN. Simultaneously, the kernel width of the Gaussian function in the RBN is initialized based on the kernel center, ensuring that the kernel center matches the kernel width, thus obtaining the initialized Gaussian function. The initialized Gaussian function is then combined with the initial weight matrix of the RBN to perform a nonlinear transformation on the input vector, outputting the offline shape Jacobian matrix. The mean square error (MSE) between the offline shape Jacobian matrix and the true shape Jacobian matrix is ​​calculated. Stochastic gradient descent is used to optimize the initial weight matrix with the goal of minimizing the MSE, completing the offline training of the RBN and generating a shape Jacobian matrix estimation model.

[0086] At this point, the step S1 of obtaining the predicted motion velocity based on the current shape Jacobian matrix includes:

[0087] S14. Obtain the current time period, and calculate the current real-time drive speed of the tendon based on the current time period and the current tendon drive volume dataset.

[0088] S15. The current real-time driving speed of the tendon and the current shape Jacobian matrix are input into the first motion formula for calculation to obtain the predicted motion speed. The first motion formula is:

[0089] ;

[0090] in, Indicates the predicted speed of motion. This represents the current shape Jacobian matrix. This indicates the current real-time drive speed of the tendon.

[0091] In this embodiment, as Figure 2 As shown, the current real-time driving speed of the tendon is calculated based on the obtained current time period and current tendon driving volume dataset. The current real-time driving speed of the tendon and the current shape Jacobian matrix are input into the first motion formula for calculation to obtain the predicted motion speed.

[0092] S2. Collect the real-time motion speed of the flexible robot, calculate the speed error between the real-time motion speed and the predicted motion speed, and correct the shape Jacobian matrix estimation model online based on the speed error to obtain the online corrected shape Jacobian matrix estimation model.

[0093] In this embodiment, the shape Jacobian matrix estimation model adopts a hierarchical design of offline construction and online correction. The shape Jacobian matrix estimation model is corrected by calculating the speed error between the real-time motion speed and the predicted motion speed of the flexible robot, thus obtaining the online corrected shape Jacobian matrix estimation model.

[0094] At this point, the online correction of the shape Jacobian matrix estimation model based on the velocity error in step S2 includes:

[0095] S21. Obtain the initial weight matrix of the shape Jacobian matrix estimation model, construct the differential update equation of the initial weight matrix according to the velocity error, update the initial weight matrix according to the differential update equation to obtain the real-time weight matrix, and perform online correction of the shape Jacobian matrix estimation model according to the real-time weight matrix.

[0096] The differential update equation is:

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] in, Represents the real-time weight matrix. Denotes the first convergence coefficient. This represents the kernel vector of the Gaussian function after regularization. The transpose of the kernel vector of the Gaussian function is given. Represents the initial weight matrix. The kernel vector represents the Gaussian function. Let m represent the Gaussian function chosen by the i-th node of the hidden layer in a radial basis function neural network for the input vector, and m represent the number of hidden layer nodes in the radial basis function neural network. Represents m dimensions, Represents the input vector. Denotes the second convergence coefficient. This represents the current real-time drive velocity of the tendon after regularization. This indicates the current real-time drive velocity of the tendon. The transpose matrix represents the current real-time drive velocity of the tendon. This represents the third convergence coefficient. Indicates the actual speed of motion. This indicates the speed error.

[0103] In this embodiment, as Figure 2 As shown, the initial weight matrix of the shape Jacobian matrix estimation model is obtained. A differential update equation for the initial weight matrix is ​​constructed based on the velocity error. The initial weight matrix is ​​then updated according to the differential update equation to obtain the real-time weight matrix. The shape Jacobian matrix estimation model is then corrected online based on the real-time weight matrix.

[0104] S3. Based on the online corrected shape Jacobian matrix estimation model, the shape control problem of the flexible robot is constructed as a quadratic programming problem with constraints. The optimization problem is solved using a neural dynamics optimizer to obtain the optimal driving command that satisfies the constraints. The flexible robot is then driven to achieve the expected shape according to the optimal driving command.

[0105] In this embodiment, as Figure 2 As shown, based on the online-corrected shape Jacobian matrix estimation model, the shape control problem of the flexible robot is constructed as a constrained quadratic programming problem. With the goal of minimizing shape error and control energy, the objective function of the quadratic programming problem is constructed as follows:

[0106]

[0107] in, Let represent the objective function of the quadratic programming problem. Indicates the expected velocity of motion for the desired shape. This represents the current shape Jacobian matrix. This indicates the current real-time drive velocity of the tendon. A coefficient representing the balance shape accuracy, control capability, and motion smoothness;

[0108] The constraints are as follows:

[0109]

[0110] in, This indicates the lower limit of tendon drive. This indicates the upper limit of tendon drive. This indicates the current real-time drive of the tendon. This indicates the lower limit of tendon drive velocity. This indicates the upper limit of tendon drive velocity. This indicates the current real-time drive speed of the tendon.

[0111] At this point, the step S3 of using a neurodynamics optimizer to solve the quadratic programming problem includes:

[0112] S31. Transform the quadratic programming problem into a set of KKT optimality conditions, which includes zero gradient equations and complementary relaxation conditions.

[0113] In this embodiment, the zero gradient equation is:

[0114]

[0115] in, This represents the transpose of the current shape Jacobian matrix. This represents the transpose of the current shape Jacobian matrix. Indicates the optimal driving instruction. The expected velocity of the expected shape A coefficient representing the balance between tracking accuracy and control energy. Represents the Lagrange multipliers. Represents the identity matrix;

[0116] The complementary relaxation condition is:

[0117]

[0118] in, Let denote the transpose of the Lagrange multipliers, d denote the constraint deviation variables, and C denote the constraint coefficient matrix. Indicates the optimal driving instruction. This indicates the lower limit of tendon drive. This indicates the upper limit of tendon drive. This indicates the current real-time drive of the tendon. This indicates the lower limit of tendon drive velocity. This indicates the upper limit of tendon drive velocity. This indicates the current real-time drive velocity of the tendon. Indicates the first transition boundary. Indicates the second transition boundary. Indicates the third transition boundary. Indicates the fourth transition boundary. Indicates the first transfer coefficient. This represents the second transfer coefficient.

[0119] S32. The complementary relaxation conditions are processed using the FB smoothing function to obtain the FB smoothed equation. The FB smoothed equation and the zero gradient equation are integrated into a continuous nonlinear equation system. The continuous nonlinear equation system is solved using a neurodynamic optimizer.

[0120] In this embodiment, as Figure 2As shown, the quadratic programming problem is transformed into a set of KKT optimality conditions. The complementary relaxation conditions in the KKT optimality conditions are handled using the FB smoothing function to obtain the FB smoothed equation, where the FB smoothing function is:

[0121] ;

[0122] in, Represents the FB smoothing function. Let w represent the smoothing parameter, and s represent the two variables in the complementary relaxation condition.

[0123] The complementary relaxation conditions after processing with the FB smoothing function, i.e., the FB smoothing equation, are as follows:

[0124]

[0125] Where d represents the constraint deviation variable and C represents the constraint coefficient matrix.

[0126] The FB smoothing equations and the zero gradient equations in the KKT optimality condition set are integrated into a continuous nonlinear equation set, which is as follows:

[0127] ;

[0128] ;

[0129] ;

[0130] ;

[0131] ;

[0132] in, This indicates the elimination of corresponding elements, and daig represents a diagonal matrix.

[0133] A neurodynamic optimizer is used to solve the continuous nonlinear equation system.

[0134] Example 2

[0135] Please refer to Figure 4 The present invention provides a shape control system 1 for a flexible robot, including a memory 3, a processor 2, and a computer program stored in the memory 3 and executable on the processor 2. When the processor 2 executes the computer program, it implements the steps in Embodiment 1.

[0136] Since the systems / devices described in the above embodiments of the present invention are systems / devices used to implement the methods of the above embodiments of the present invention, those skilled in the art can understand the specific structure and modifications of the systems / devices based on the methods described in the above embodiments of the present invention, and therefore will not be repeated here. All systems / devices used in the methods of the above embodiments of the present invention fall within the scope of protection of the present invention.

[0137] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0138] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions.

[0139] It should be noted that any reference numerals placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In claims that enumerate several means, several of these means may be embodied by the same hardware. The use of the terms first, second, third, etc., is merely for convenience of expression and does not indicate any order. These terms can be understood as part of the component names.

[0140] Furthermore, it should be noted that in the description of this specification, the terms "one embodiment," "some embodiments," "embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0141] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the claims should be interpreted to include both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0142] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, then this invention should also include these modifications and variations.

Claims

1. A shape control method of a flexible robot, characterized by, The method comprises the following steps: Collecting a desired shape and a current tendon driving amount data set of a flexible robot, inputting the desired shape and the current tendon driving amount data set into an offline constructed shape Jacobian matrix estimation model to perform shape Jacobian matrix estimation, obtaining a current shape Jacobian matrix, and obtaining a predicted motion speed according to the current shape Jacobian matrix; Collecting a real-time motion speed of the flexible robot, calculating a speed error between the real-time motion speed and the predicted motion speed, and performing online correction on the shape Jacobian matrix estimation model according to the speed error to obtain an online corrected shape Jacobian matrix estimation model; Based on the online corrected shape Jacobian matrix estimation model, the shape control problem of the flexible robot is constructed as a quadratic programming problem with constraints, an optimizer of neural dynamics is used to solve the quadratic programming problem to obtain optimal driving instructions that satisfy the constraints, and the flexible robot is driven to the desired shape according to the optimal driving instructions.

2. The shape control method of a flexible robot according to claim 1, wherein Before inputting the desired shape and the current tendon driving amount data set into the offline constructed shape Jacobian matrix estimation model to perform shape Jacobian matrix estimation, the method comprises the following steps: Collecting an offline tendon driving amount data set generated by the flexible robot under random driving and offline three-dimensional coordinates of K feature points uniformly distributed on the corresponding flexible backbone; According to a unit directional vector formula, the offline three-dimensional coordinates of each feature point are converted into offline unit directional vectors to obtain an offline unit directional vector data set, and the offline tendon driving amount data set is normalized to a preset normalization range according to a normalization formula to obtain a normalized offline tendon driving amount data set; The offline unit directional vector data set and the normalized offline tendon driving amount data set are combined into an input vector, and the input vector is input into a radial basis neural network for offline training to generate a shape Jacobian matrix estimation model.

3. The shape control method of a flexible robot according to claim 2, wherein The input vector is input into the radial basis neural network for offline training to generate the shape Jacobian matrix estimation model, which comprises the following steps: A constant curvature assumption is used to calculate a true shape Jacobian matrix of the input vector, the true shape Jacobian matrix and the input vector are input into the radial basis neural network for offline training, the input vector is clustered by a clustering algorithm to initialize kernel function centers of Gaussian functions in the radial basis neural network, and kernel function widths of the Gaussian functions in the radial basis neural network are initialized according to the kernel function centers to obtain initialized Gaussian functions; The initialized Gaussian functions and an initial weight matrix of the radial basis neural network are combined to perform nonlinear transformation on the input vector to output an offline shape Jacobian matrix; The mean square error between the offline shape Jacobian matrix and the true shape Jacobian matrix is calculated, and the initial weight matrix is optimized by a stochastic gradient descent method with the minimum mean square error as the target to complete offline training of the radial basis neural network to generate the shape Jacobian matrix estimation model.

4. The shape control method of a flexible robot according to claim 1, wherein The predicted motion speed is obtained according to the current shape Jacobian matrix, which comprises the following steps: obtaining a current time period, calculating a current tendon real-time driving speed according to the current time period and the current tendon driving amount data set; calculating the current tendon real-time driving speed and the current shape Jacobian matrix input first motion formula to obtain a predicted motion speed, the first motion formula being: ； wherein, denotes the predicted motion velocity, denotes the current shape Jacobian matrix, denotes the current tendon real-time driving velocity.

5. The shape control method of a flexible robot according to claim 1, wherein the online correction of the shape Jacobian matrix estimation model according to the speed error comprises: obtaining an initial weight matrix of the shape Jacobian matrix estimation model, constructing a differential update equation of the initial weight matrix according to the speed error, updating the initial weight matrix according to the differential update equation to obtain a real-time weight matrix, and correcting the shape Jacobian matrix estimation model according to the real-time weight matrix; the differential update equation is: ； ； ； ； ； wherein, denotes a real-time weight matrix, denotes a first convergence coefficient, denotes a kernel function vector of a Gaussian function after regularization processing, denotes a transpose matrix of the kernel function vector of the Gaussian function, denotes an initial weight matrix, denotes a kernel function vector of a Gaussian function, denotes a Gaussian function selected by an i-th node of a hidden layer of a radial basis neural network for an input vector, and m denotes a number of nodes of the hidden layer of the radial basis neural network, denotes m dimensions, denotes an input vector, denotes a second convergence coefficient, denotes a current tendon real-time driving speed after regularization processing, denotes a current tendon real-time driving speed, denotes a transpose matrix of the current tendon real-time driving speed, denotes a third convergence coefficient, denotes an actual movement speed, denotes a speed error.

6. The shape control method of a flexible robot according to claim 1, wherein the objective function of the quadratic programming problem is: wherein, represents an objective function of a quadratic programming problem, represents a desired motion velocity of the expected shape, represents a current shape Jacobian matrix, represents a current tendon real-time driving velocity, represents a coefficient of balance shape accuracy, control ability, and motion smoothness; the constraint condition is: wherein, represents a lower limit of the tendon drive amount, represents an upper limit of the tendon drive amount, represents a current tendon real-time drive amount, represents a lower limit of the tendon drive speed, represents an upper limit of the tendon drive speed, represents a current tendon real-time drive speed.

7. The shape control method of a flexible robot according to claim 1, wherein the solving of the quadratic programming problem by the neural dynamics optimizer comprises: transforming the quadratic programming problem into a KKT optimality condition group, the KKT optimality condition group including a zero gradient equation and a complementary relaxation condition; processing the complementary relaxation condition by an FB smoothing function to obtain an FB smoothing equation, integrating the FB smoothing equation and the zero gradient equation into a continuous nonlinear equation group, and solving the continuous nonlinear equation group by a neural dynamics optimizer.

8. The shape control method of a flexible robot according to claim 7, wherein the zero gradient equation is: wherein denotes the transpose of the current shape Jacobian matrix, denotes the current shape Jacobian matrix, denotes the optimal driving command, denotes the desired motion velocity of the expected shape, denotes a coefficient balancing tracking accuracy and control energy, denotes the Lagrange multiplier, denotes the identity matrix; the complementary relaxation condition is: wherein, denotes a transpose matrix of a Lagrange multiplier, D denotes a constraint bias variable, and C denotes a constraint coefficient matrix, denotes an optimal drive command, denotes a lower limit of a tendon drive amount, denotes an upper limit of a tendon drive amount, denotes a current tendon real-time drive amount, denotes a lower limit of a tendon drive speed, denotes an upper limit of a tendon drive speed, denotes a current tendon real-time drive speed, denotes a first transfer boundary, denotes a second transfer boundary, denotes a third transfer boundary, denotes a fourth transfer boundary, denotes a first transfer coefficient, denotes a second transfer coefficient.

9. A shape control system of a flexible robot comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, the processor executes the computer program to implement the method in any one of claims 1 to 8.

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