Shape control method and system of flexible robot

Abstract

The invention relates to a shape control method and system for a flexible robot, and the method comprises the steps: inputting an expected shape of the flexible robot and a current tendon driving amount data set into a shape Jacobian matrix estimation model constructed offline for shape Jacobian matrix estimation, and obtaining a current shape Jacobian matrix and a predicted motion speed; the shape Jacobian matrix estimation model is corrected online by calculating the speed error between the real-time movement speed and the predicted movement speed, and the shape control problem of the flexible robot is constructed into a quadratic programming problem with constraint conditions based on the online corrected shape Jacobian matrix estimation model. And solving the quadratic programming problem by adopting a neurodynamic optimizer to obtain an optimal driving instruction meeting the constraint condition to drive the flexible robot to reach the expected shape. Therefore, the high-precision shape control of the flexible body robot is realized, and meanwhile, the self-adaptability and the real-time calculation efficiency are considered.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer, in particular to a shape control method and system of a flexible robot. BACKGROUND

[0002] The flexible body robot is different from the traditional rigid joint robot, can continuously deform to realize multi-degree of freedom motion, has good environmental adaptability, flexibility and human-computer interaction safety. Therefore, the flexible body robot has important application value in the narrow space operation such as minimally invasive surgery, industrial detection and maintenance. However, the redundant degree of freedom and strong nonlinear characteristics brought by the compliant structure of the flexible body robot make the shape accurate control become a key technical problem, which directly affects the reliability of task execution.

[0003] In the field of shape control of the flexible body robot, the control accuracy mainly depends on the accuracy of the kinematic modeling. The current mainstream modeling methods can be divided into two categories based on physical model and data driven, but they all have significant defects. The modeling method based on physical model, such as constant curvature model, Cosserat model and Euler-Bernoulli beam model, tries to describe the relationship between driving and deformation through geometric or mechanical principles. However, these methods have inherent limitations: the constant curvature model is difficult to accurately represent the deformation characteristics of the flexible body under complex deformation conditions; the Cosserat model is complex to calculate, and it is difficult to meet the real-time control requirements; the Euler-Bernoulli model is difficult to ensure the shape control accuracy under large deformation conditions or complex load environment due to the neglect of shear effect. The data driven modeling method, such as neural network, Gaussian process regression or online least square method, does not need explicit physical modeling, and establishes the input-output mapping through machine learning. But this kind of method is seriously dependent on a large number of offline training data, it is difficult to deal with unexpected sudden conditions, and the model optimization and parameter adjustment process has high computational cost, and the real-time performance and stability of online learning are difficult to guarantee.

[0004] Therefore, there is an urgent need for a flexible body robot shape control scheme that can balance high precision, adaptability and real-time computing efficiency. SUMMARY

[0005] The technical problem to be solved by the present application is that the present application provides a shape control method and system of a flexible robot, which realizes high-precision shape control of the flexible body robot while balancing adaptability and real-time computing efficiency.

[0006] In order to solve the above technical problems, the technical scheme adopted by the present application is: In a first aspect, the present application provides a shape control method of a flexible body robot, comprising: The expected shape and the current tendon driving amount data set of the flexible robot are collected, the expected shape and the current tendon driving amount data set are input into an offline constructed shape Jacobian matrix estimation model for shape Jacobian matrix estimation, and a current shape Jacobian matrix is obtained, and a predicted motion speed is obtained according to the current shape Jacobian matrix; The real-time motion speed of the flexible robot is collected, a speed error of the real-time motion speed and the predicted motion speed is calculated, the shape Jacobian matrix estimation model is corrected online according to the speed error, and an online corrected shape Jacobian matrix estimation model is obtained; The shape control problem of the flexible robot is constructed into a quadratic programming problem with constraint conditions based on the online corrected shape Jacobian matrix estimation model, an optimizer of neural dynamics is used to solve the quadratic programming problem, so that the optimal driving instruction meeting the constraint condition is obtained, and the flexible robot is driven to the expected shape according to the optimal driving instruction.

[0007] The application has the beneficial effects that: through the hierarchical design of offline construction and online correction, the generalization of the shape Jacobian matrix estimation model is improved. The expected shape and the current tendon driving amount data set are input into the pre-constructed shape Jacobian matrix estimation model to obtain the expected motion speed, the shape Jacobian matrix estimation model is corrected online according to the speed error of the real-time motion speed and the expected motion speed, the shape Jacobian matrix estimation model does not need to be retrained by re-construction of training data, the online correction of the shape Jacobian matrix estimation model is realized through the speed error, the real-time performance of online learning of the shape Jacobian matrix estimation model is ensured, and the adaptability and stability of adapting to dynamic complex environment and flexibly facing sudden working conditions are ensured. The shape control problem of the flexible robot is constructed into a quadratic programming problem with constraint conditions, the constraint condition does not need to be iteratively judged, the convergence speed is improved, the neural dynamics optimizer is used for solving, the real-time calculation efficiency is improved, and it is ensured that the optimal driving instruction can respond to the change of the real-time motion speed in real time and stably reach the expected shape.

[0008] Optionally, before the expected shape and the current tendon driving amount data set are input into the offline constructed shape Jacobian matrix estimation model for shape Jacobian matrix estimation, the method further includes: 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 flexible backbone are collected; The offline three-dimensional coordinates of each feature point are converted into offline unit direction vectors according to a unit direction vector formula to obtain an offline unit direction 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 direction vector dataset is combined with a normalized offline tendon driving amount dataset as 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.

[0009] According to the above description, the offline tendon driving amount dataset of the flexible robot is collected in a random driving manner, ensuring that the offline tendon driving amount dataset contains diversified deformation characteristics. The offline three-dimensional coordinates of the K feature points uniformly distributed on the flexible backbone are collected, rather than concentrated in the local or both ends, which can completely capture the overall change rule of the flexible robot, obtain a complete shape representation, improve the fitting accuracy of the shape Jacobian matrix estimation model, convert the offline three-dimensional coordinates into offline unit direction vectors, eliminate the dependence on absolute position, and normalize the offline tendon driving amount dataset to eliminate the numerical range difference of different numerical ranges, so that the shape Jacobian matrix estimation model can adapt to flexible robots of different scenes and lengths, and improve the cross-scene adaptability.

[0010] Optionally, the inputting the input vector into the radial basis neural network for offline training to generate the shape Jacobian matrix estimation model comprises: The real shape Jacobian matrix of the input vector is calculated by using a constant curvature assumption, the real 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 the kernel function center of the Gaussian function in the radial basis neural network, and the kernel function width of the Gaussian function in the radial basis neural network is initialized according to the kernel function center to obtain an initialized Gaussian function. The initialized Gaussian function 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 of the offline shape Jacobian matrix and the real shape Jacobian matrix is calculated, and the initial weight matrix is optimized by using a stochastic gradient descent method with the minimum mean square error as the target, to complete the offline training of the radial basis neural network and generate the shape Jacobian matrix estimation model.

[0011] According to the above description, the real shape Jacobian matrix is calculated by the constant curvature pseudo shape, which realizes the real label acquisition at low cost, avoids the training of the shape Jacobian matrix estimation model due to the lack of real labels, and provides a clear direction for the optimization of the initial weight matrix. The input vectors are clustered by the clustering algorithm to initialize the kernel function center of the Gaussian function in the radial basis neural network, and the kernel function width is initialized according to the kernel function center, so that the kernel function center and the kernel function width are matched, and the fitting precision is improved. The random gradient descent method is used to optimize the initial weight matrix with the minimum mean square error as the target, which reduces the time consumption of offline training, dynamically optimizes the initial weight matrix, and improves the precision of the generated shape Jacobian matrix estimation model.

[0012] Optionally, the obtaining the predicted motion velocity according to the current shape Jacobian matrix comprises: obtaining a current time period, and calculating a current tendon real-time driving velocity according to the current time period and the current tendon driving amount data set; inputting the current tendon real-time driving velocity and the current shape Jacobian matrix into a first motion formula to obtain a predicted motion velocity, the first motion formula being: ; wherein, the predicted motion velocity is represented by v, the current shape Jacobian matrix is represented by J, and the current tendon real-time driving velocity is represented by v real.

[0013] According to the above description, the current tendon real-time driving velocity is calculated according to the current time period and the current tendon driving amount data set, the error of the tendon real-time driving velocity caused by the periodic fluctuation is eliminated, and the accuracy of the predicted motion velocity calculated according to the current tendon real-time driving velocity and the current shape Jacobian matrix is ensured, so as to realize the real-time and accurate coupling of driving and shape.

[0014] Optionally, the modifying the shape Jacobian matrix estimation model according to the velocity 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 velocity error, updating the initial weight matrix according to the differential update equation to obtain a real-time weight matrix, and modifying the shape Jacobian matrix estimation model according to the real-time weight matrix; the differential update equation is: ; ; ; ; ; wherein, represents a real-time weight matrix, represents a first convergence coefficient, represents a kernel function vector of a regularized Gaussian function, represents a transpose matrix of the kernel function vector of the Gaussian function, represents an initial weight matrix, represents a kernel function vector of a Gaussian function, represents that the i-th node of the hidden layer of the radial basis neural network selects a Gaussian function for the input vector, and m represents a number of nodes of the hidden layer of the radial basis neural network, represents m dimensions, represents an input vector, represents a second convergence coefficient, represents a current tendon real-time driving speed after a regularized processing, represents a current tendon real-time driving speed, represents a transpose matrix of the current tendon real-time driving speed, represents a third convergence coefficient, represents an actual motion speed, represents a speed error.

[0015] According to the above description, the online speed error is converted into a stable update of the initial weight matrix, the initial weight matrix is ensured to be updated and converged through a differential update equation and a convergence coefficient, the shape Jacobian matrix estimation model is prevented from losing control due to disturbance, and the shape Jacobian matrix estimation model corrected according to the real-time weight matrix is ensured to always fit the actual situation.

[0016] Optionally, the objective function of the quadratic programming problem is:

[0017] wherein, represents an objective function of a quadratic programming problem, represents an expected motion speed of an expected shape, represents a current shape Jacobian matrix, represents a current tendon real-time driving speed, represents a coefficient of balance shape accuracy, control ability, and motion smoothness; The constraint condition is:

[0018] wherein, represents a lower limit of tendon driving amount, represents an upper limit of tendon driving amount, represents the current tendon real-time driving amount, represents the lower limit of the tendon driving speed, represents the upper limit of the tendon driving speed, represents the current tendon real-time driving speed.

[0019] According to the above description, the objective function of the quadratic programming problem balances the shape accuracy and the control energy in two dimensions, covers the tendon driving amount and the tendon driving speed, and takes into account safety while improving accuracy.

[0020] Optionally, the neural dynamics-based optimizer solving the quadratic programming problem comprises: transforming the quadratic programming problem into a KKT optimality condition group, the KKT optimality condition group comprising a zero gradient equation and a complementary relaxation condition; processing the complementary relaxation condition by using 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 using a neural dynamics-based optimizer.

[0021] Optionally, the zero gradient equation is:

[0022] wherein, represents the transpose matrix of the current shape Jacobian matrix, represents the transpose matrix of the current shape Jacobian matrix, represents the optimal driving instruction, the expected motion speed of the expected shape, represents the coefficient balancing the tracking accuracy and the control energy, represents the Lagrange multiplier, represents the unit matrix; the complementary relaxation condition is:

[0023] wherein, represents the transpose matrix of the Lagrange multiplier, d represents the constraint deviation variable, and C represents the constraint coefficient matrix, represents the optimal driving instruction, represents the lower limit of the tendon driving amount, represents the upper limit of the tendon driving amount, represents the current tendon real-time driving amount, represents the lower limit of the tendon driving speed, represents the upper limit of the tendon driving speed, represents a current tendon real-time driving speed, represents a first transfer boundary, represents a second transfer boundary, represents a third transfer boundary, represents a fourth transfer boundary, represents a first transfer coefficient, represents a second transfer coefficient.

[0024] According to the above description, the quadratic programming problem is converted into a KKT optimality condition group, without complex iterative search logic, simplifying the solving process, and using the FB smoothing function to process the complementary relaxation condition of the KKT optimality condition group, converting the non-continuous condition into a continuous equation, without constraint activation judgment, avoiding the time-consuming of constraint judgment. And the continuous characteristics of the FB smoothing function make the gradient change of the continuous nonlinear equation group gentle, ensuring the stability of the solution.

[0025] In a second aspect, the present application provides a shape control system of a flexible robot, comprising 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 of the flexible robot according to the first aspect.

[0026] The technical effects of the shape control system of the flexible robot according to the second aspect are the same as those of the shape control method of the flexible robot according to the first aspect. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 a flowchart of the shape control method of the flexible robot according to the present embodiment; Figure 2 a schematic diagram of the overall flow of the shape control method of the flexible robot according to the present embodiment; Figure 3 an offline construction process of the shape Jacobian matrix estimation model according to the present embodiment; Figure 4 a structural schematic diagram of the shape control system of the flexible robot according to the present embodiment.

[0028] LEGEND 1. A shape control system of a flexible robot; 2. A processor; 3. A memory. DETAILED DESCRIPTION

[0029] For a better understanding of the above technical solutions, the exemplary embodiments of the present application will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present application are shown in the accompanying drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present application can be more clearly, thoroughly understood and the scope of the present application can be completely conveyed to those skilled in the art.

[0030] Embodiment one Please refer to Figures 1 to 3 The present application provides a shape control method of a flexible robot, comprising the steps of: S1, collecting a desired shape and a current tendon driving amount data set of the 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; In the embodiment, as shown in Figure 2 , the desired shape and the current tendon driving amount data set of the flexible robot are collected, the current tendon driving amount data set refers to the displacement data of each tendon of the flexible robot, the desired shape and the current tendon driving amount data set are input into the offline constructed shape Jacobian matrix estimation model to perform shape Jacobian matrix estimation, the current shape Jacobian matrix is obtained, and the predicted motion speed is obtained according to the current shape Jacobian matrix.

[0031] At this time, before the step S1 of 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, it comprises: S11, 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; S12, converting the offline three-dimensional coordinates of each feature point into an offline unit direction vector according to a unit direction vector formula to obtain an offline unit direction vector data set, and normalizing the offline tendon driving amount data set to a preset normalization range to obtain a normalized offline tendon driving amount data set according to a normalization formula; S13, combining the offline unit direction vector data set and the normalized offline tendon driving amount data set into an input vector, inputting the input vector into a radial basis neural network to perform offline training, and generating a shape Jacobian matrix estimation model.

[0032] In the embodiment, as shown in Figure 3As shown, the flexible robot is driven in a random driving manner to collect 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. The offline tendon driving amount data set can be represented as: ∈ ,n=1,2, N represents the total number of tendons, and each offline three-dimensional coordinate can be represented All offline three-dimensional coordinates of the feature points can be represented as: ∈ , K represents the total number of feature points, represents 3K dimensions. Each offline three-dimensional coordinate of the feature points is converted into an offline unit direction vector according to a unit direction vector formula, where the unit direction vector formula is: ; wherein, represents an offline unit direction vector data set, and K represents the total number of feature points.

[0033] At the same time, the offline tendon driving amount data set is normalized to a preset normalization range according to a normalization formula, where the normalization formula is: ; wherein, represents the i-th normalized offline tendon driving amount, represents the i-th offline tendon driving amount, n represents the number of tendons of the flexible robot, represents the lower limit of the tendon driving amount, represents the upper limit of the tendon driving amount.

[0034] The offline unit direction vector data set and the normalized offline tendon driving amount data set are combined into an input vector to input a radial basis neural network for offline training to generate a shape Jacobian matrix estimation model. It should be noted that when the expected shape and the current tendon driving amount data set are input into the shape Jacobian matrix estimation model for shape Jacobian matrix estimation, the expected shape will also be converted into a unit direction vector according to the unit direction vector formula, and the current tendon driving amount data set will also be normalized according to the normalization formula.

[0035] At this time, the inputting of the input vector into the radial basis neural network for offline training to generate the shape Jacobian matrix estimation model in step S13 includes: S131, calculate the real shape Jacobian matrix of the input vector by using the constant curvature assumption, input the real Jacobian matrix and the input vector into a radial basis neural network for offline training, cluster the input vector by a clustering algorithm to initialize the kernel function center of the Gaussian function in the radial basis neural network, and initialize the kernel function width of the Gaussian function in the radial basis neural network according to the kernel function center to obtain an initialized Gaussian function; S132, combine the initialized Gaussian function and the initial weight matrix of the radial basis neural network to perform nonlinear transformation on the input vector to output an offline shape Jacobian matrix; S133, calculate the mean square error of the offline shape Jacobian matrix and the real shape Jacobian matrix, and optimize the initial weight matrix by using a stochastic gradient descent method with the minimum mean square error as the target to complete offline training of the radial basis neural network and generate a shape Jacobian matrix estimation model.

[0036] In the embodiment, as Figure 3 described, the real shape Jacobian matrix of the input vector is calculated by using the constant curvature assumption, the real shape Jacobian matrix and the input vector are input into a radial basis neural network for offline training, at this time, the real shape Jacobian matrix is taken as the real label of the input vector, the input vector is clustered by a clustering algorithm to initialize the kernel function center of the Gaussian function in the radial basis neural network, and the kernel function width of the Gaussian function in the radial basis neural network is initialized according to the kernel function center, that is, the kernel function center and the kernel function width are matched to obtain an initialized Gaussian function. The initialized Gaussian function and the 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 of the offline shape Jacobian matrix and the real shape Jacobian matrix is calculated, and the initial weight matrix is optimized by using a stochastic gradient descent method with the minimum mean square error as the target to complete offline training of the radial basis neural network and generate a shape Jacobian matrix estimation model.

[0037] At this time, the predicted motion velocity obtained according to the current shape Jacobian matrix in step S1 includes: S14, obtain a current time period, and calculate a current tendon real-time driving speed according to the current time period and the current tendon driving amount data set; S15, input the current tendon real-time driving speed and the current shape Jacobian matrix into a first motion formula to obtain a predicted motion velocity, the first motion formula being: ; wherein, the predicted motion velocity is represented by v, the current tendon real-time driving speed is represented by v real-time, and the current shape Jacobian matrix is represented by J. a current shape Jacobian matrix, a current tendon real-time driving speed.

[0038] In the embodiment, the current tendon real-time driving speed is calculated according to the obtained current time period and the current tendon driving amount data set, the current tendon real-time driving speed is input into the first motion formula together with the current shape Jacobian matrix to calculate a predicted motion speed. Figure 2

[0039] S2, collecting a real-time motion speed of the flexible robot, calculating a speed error of the real-time motion speed and the predicted motion speed, online correcting the shape Jacobian matrix estimation model according to the speed error to obtain an online corrected shape Jacobian matrix estimation model; In the embodiment, the shape Jacobian matrix estimation model is designed in a hierarchical manner by offline construction and online correction, and the shape Jacobian matrix estimation model is corrected by calculating a speed error of the real-time motion speed of the flexible robot and the predicted motion speed to obtain an online corrected shape Jacobian matrix estimation model.

[0040] At this time, the online correction of the shape Jacobian matrix estimation model according to the speed error in step S2 comprises: S21, 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 online correcting the shape Jacobian matrix estimation model according to the real-time weight matrix; The differential update equation is: ; ; ; ; ; wherein, the real-time weight matrix, the first convergence coefficient, the kernel function vector of the regularized Gaussian function, the transpose matrix of the kernel function vector of the Gaussian function, the initial weight matrix, the kernel function vector of the Gaussian function, the i-th node of the hidden layer of the radial basis neural network selects the Gaussian function for the input vector, and m represents the number of nodes of the hidden layer of the radial basis neural network, ​represents m dimensions, represents an input vector, represents a second convergence coefficient, represents a current tendon real-time driving speed after a regularization process, represents a current tendon real-time driving speed, represents a transpose matrix of the current tendon real-time driving speed, represents a third convergence coefficient, represents an actual motion speed, represents a speed error.

[0041] In the embodiment, as shown in Figure 2 , an initial weight matrix of a shape Jacobian matrix estimation model is obtained, a differential update equation of the initial weight matrix is constructed according to the speed error, the initial weight matrix is updated according to the differential update equation to obtain a real-time weight matrix, and the shape Jacobian matrix estimation model is corrected online according to the real-time weight matrix.

[0042] S3, the shape control problem of the flexible robot is constructed as a quadratic programming problem with a constraint condition based on the shape Jacobian matrix estimation model corrected online, an optimizer of neural dynamics is used to solve the quadratic programming problem to obtain an optimal driving instruction meeting the constraint condition, and the flexible robot is driven to the expected shape according to the optimal driving instruction.

[0043] In the embodiment, as shown in Figure 2 , the shape control problem of the flexible robot is constructed as a quadratic programming problem with a constraint condition based on the shape Jacobian matrix estimation model corrected online, an optimizer of neural dynamics is used to solve the quadratic programming problem to obtain an optimal driving instruction meeting the constraint condition, and the flexible robot is driven to the expected shape according to the optimal driving instruction.

[0044] wherein, represents an objective function of the quadratic programming problem, represents an expected motion speed of the expected shape, represents a current shape Jacobian matrix, represents a current tendon real-time driving speed, represents a coefficient balancing shape accuracy, control ability and motion smoothness; The constraint condition is:

[0045] wherein, represents a lower limit of the tendon driving amount, represents an upper limit of the tendon driving amount, represents a current tendon real-time driving amount, 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.

[0046] At this point, the step S3 of using a neurodynamics optimizer to solve the quadratic programming problem includes: S31. Transform the quadratic programming problem into a set of KKT optimality conditions, which includes zero gradient equations and complementary relaxation conditions. In this embodiment, the zero gradient equation is:

[0047] 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; The complementary relaxation condition is:

[0048] 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.

[0049] S32, processing the complementary slackness condition by using the FB smoothing function to obtain a 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 using a neural dynamics optimizer.

[0050] In the embodiment, as shown in Figure 2 the quadratic programming problem is converted into a KKT optimality condition group, the complementary slackness condition in the KKT optimality condition group is processed by using the FB smoothing function to obtain a FB smoothing equation, wherein the FB smoothing function is: ; wherein, represents the FB smoothing function, represents a smoothing parameter, and w and s represent two variables in the complementary slackness condition.

[0051] The complementary slackness condition processed by the FB smoothing function, i.e., the FB smoothing equation, is:

[0052] wherein d represents a constraint deviation variable, and C represents a constraint coefficient matrix.

[0053] The FB smoothing equation and the zero gradient equation in the KKT optimality condition group are integrated into a continuous nonlinear equation group, and the continuous nonlinear equation is: ; ; ; ; ; wherein, represents the corresponding element elimination, and daig represents a diagonal matrix.

[0054] The continuous nonlinear equation group is solved by using a neural dynamics optimizer.

[0055] Embodiment two Please refer to Figure 4 The application provides a shape control system 1 of a flexible robot, which comprises a memory 3, a processor 2, and a computer program stored in the memory 3 and capable of running on the processor 2, and the processor 2 implements the steps in the embodiment one when the computer program is executed.

[0056] The system / device used for implementing the method of the embodiments of the present application described above can be understood by those skilled in the art based on the method of the embodiments of the present application described above, and thus will not be described here again. The system / device used for implementing the method of the embodiments of the present application described above all belong to the scope of the present application.

[0057] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system or a computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program codes.

[0058] The present application is described with reference to flowcharts and / or block diagrams of the method, device (system) and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions.

[0059] It should be noted that in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The application can be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the claims, the word "first", "second", "third" etc. does not limit the number for these elements. These words are only used to distinguish between alternative claims. The word "comprise", "comprising", "contain", "containing" or "including" does not exclude the presence of elements or steps not listed in a claim. The word "one" does not exclude the presence of plural referents or steps, unless otherwise indicated.

[0060] In addition, it should be noted that in the description of the specification, the description of the terms "one embodiment", "some embodiments", "embodiment", "example", "specific example" or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In the specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in the specification and the features of the different embodiments or examples without contradiction.

[0061] While the preferred embodiments of the application have been described, those skilled in the art will recognize that many modifications and variations of this preferred embodiment are possible without departing from the spirit or scope of the present application. Thus, it is intended that the present application encompass all such modifications and variations as fall within the scope of the appended claims and their equivalents.

[0062] Obviously, many modifications and variations of the present application are possible in light of the above teachings. It is, therefore, to be understood that within the scope of the appended claims and their equivalents, the application can be practiced otherwise than as specifically described.

Claims

1. A shape control method for a flexible robot, characterized in that, include: 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; 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. 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.

2. The shape control method for a flexible robot as described in claim 1, characterized in that, Before inputting the expected shape and the current tendon drive quantity dataset into the offline-built shape Jacobian matrix estimation model for shape Jacobian matrix estimation, the following steps are included: 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; 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. 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.

3. The shape control method for a flexible robot as described in claim 2, characterized in that, The input vector is fed into a radial basis neural network for offline training to generate a shape Jacobian matrix estimation model, including: The true shape Jacobian matrix of the input vector is calculated using the constant curvature assumption. The true shape 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. 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. 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.

4. The shape control method for a flexible robot as described in claim 1, characterized in that, The step of obtaining the predicted motion speed based on the current shape Jacobian matrix includes: 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; 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: ； 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.

5. The shape control method for a flexible robot as described in claim 1, characterized in that, The online correction of the shape Jacobian matrix estimation model based on the velocity error includes: 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 perform online correction of the shape Jacobian matrix estimation model based on the real-time weight matrix. The differential update equation is: ； ； ； ； ； 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.

6. The shape control method for a flexible robot as described in claim 1, characterized in that, The objective function of the quadratic programming problem is: in, Let represent the objective function of the quadratic programming problem. This represents the expected velocity of 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; The constraints are as follows: 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.

7. The shape control method for a flexible robot as described in claim 1, characterized in that, The optimization using neurodynamics to solve the quadratic programming problem includes: The quadratic programming problem is transformed into a set of KKT optimality conditions, which includes zero gradient equations and complementary relaxation conditions. 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.

8. The shape control method for a flexible robot as described in claim 7, characterized in that, The zero gradient equation is: in, This represents the transpose of the current shape Jacobian matrix. This represents the current shape Jacobian matrix. Indicates the optimal driving instruction. This represents the expected velocity of the desired shape. A coefficient representing the balance between tracking accuracy and control energy. Represents the Lagrange multipliers. Represents the identity matrix; The complementary relaxation condition is: 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.

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

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