A continuum robot control method based on steady-state constraint cupterman model

Abstract

The application discloses a continuum robot control method based on a steady-state constraint Kupman model, and relates to the technical field of robot control.The method comprises the following steps: acquiring a dynamic data set and a steady-state data set of a continuum robot; based on the dynamic data set and the steady-state data set, a fixed reference model is solved by taking the weighted sum of a dynamic prediction error and a steady-state balance residual error as the target; acquiring measured state data of the continuum robot, and generating a residual increment matrix according to a nominal prediction deviation of the measured state data relative to the fixed reference model; fusing the fixed reference model and the residual increment matrix to obtain a current prediction model; based on the current prediction model, an optimal control sequence that satisfies a preset constraint condition is optimized and solved in a prediction time domain, and a control instruction at a current time is obtained, which is used to control the continuum robot to perform movement. The application improves the control accuracy of the continuum robot under the condition that the fixed offline model has a steady-state relationship mismatch.

Description

Technical Field

[0001] This application relates to the field of robot control technology, and in particular to a control method for a continuum robot based on a steady-state constrained Koopman model. Background Technology

[0002] Continuum robots, constructed from flexible materials, can achieve continuous deformations such as bending and stretching through pneumatic cavities or flexible drive segments, making them suitable for confined space operations and human-robot collaboration. However, the inherent nonlinearity, hysteresis, and time-varying nature of flexible materials make robot motion susceptible to material aging, load variations, and unmodeled dynamics, making it difficult for fixed-parameter models to maintain accuracy over long periods. Traditional geometric models are insufficient to fully describe dynamic effects such as inertia, damping, and drive coupling, while high-fidelity dynamic models suffer from complex modeling and high computational costs for online solutions.

[0003] Traditional Koopman modeling methods primarily rely on dynamic transient data to identify the model. When the excitation of each driving channel is unbalanced, the control input matrix identification is insufficient, leading to a deviation between the steady-state input-output relationship and the actual equilibrium relationship. The proportion of steady-state samples in dynamic trajectory data is low, making it difficult to effectively constrain the direction of the control input matrix near the equilibrium point. Even if the model's short-term prediction error is small, it may still produce persistent deviations near the target position. Furthermore, fixed offline models cannot compensate for model mismatches caused by changes in load, contact, and material properties; while repeatedly updating all Koopman matrices online not only increases the computational burden but may also disrupt the established steady-state structure of the offline model, making it difficult to simultaneously meet the requirements of control accuracy and real-time performance.

[0004] Therefore, improving the control accuracy of continuum robots under the condition of steady-state relationship mismatch in the fixed offline Koopman model is an urgent problem to be solved. Summary of the Invention

[0005] The main objective of this application is to provide a control method for continuum robots based on a steady-state constrained Koopman model, aiming to solve the technical problem of how to improve the control accuracy of continuum robots under the condition of steady-state relationship mismatch in the fixed offline Koopman model.

[0006] To achieve the above objectives, this application proposes a continuum robot control method based on a steady-state constrained Koopman model, the method comprising: Obtain dynamic and steady-state datasets for the continuum robot; Based on the dynamic dataset and the steady-state dataset, a fixed benchmark model is obtained by minimizing the weighted sum of dynamic prediction error and steady-state equilibrium residual. Acquire measured state data of the continuum robot, and generate a residual increment matrix based on the nominal prediction deviation of the measured state data relative to the fixed reference model; The fixed benchmark model and the residual increment matrix are fused to obtain the current prediction model; Based on the current prediction model, the optimal control sequence that satisfies the preset constraints is optimized and solved in the prediction time domain to obtain the control command at the current moment. The control command is used to control the continuous robot to perform motion.

[0007] In one embodiment, the step of acquiring the dynamic dataset and steady-state dataset of the continuum robot includes: Apply time-varying input to each drive channel within a preset input range, collect state information and drive input information at adjacent sampling times, and obtain a set of dynamic snapshot pairs; Apply constant drive input to each drive channel. When the state change at adjacent sampling times meets the preset steady-state determination condition, record the current steady-state state information and the corresponding constant drive input information to obtain a set of steady-state snapshot pairs. The state information and driving input information in the dynamic snapshot pair set and the steady-state snapshot pair set are time-aligned, outlier-removed, and normalized to obtain the dynamic dataset and the steady-state dataset.

[0008] In one embodiment, the step of solving for a fixed baseline model based on the dynamic dataset and the steady-state dataset, with the objective of minimizing the weighted sum of dynamic prediction error and steady-state equilibrium residual, includes: Based on the dimension-upgrading function, the dynamic dataset and the steady-state dataset are mapped to the dimension-upgrading space respectively, and a dynamic augmented regression matrix, a dynamic successor output matrix, a steady-state augmented regression matrix, and a steady-state output matrix are constructed. Construct an objective function, which is a weighted sum of a dynamic prediction error term and a steady-state constraint term; wherein, the dynamic prediction error term is the squared Frobenius norm of the dynamic prediction error between the dynamic augmented regression matrix and the dynamic successor output matrix; and the steady-state constraint term is the squared Frobenius norm of the steady-state equilibrium residual between the steady-state augmented regression matrix and the steady-state output matrix. The objective function is minimized to obtain a fixed baseline model, which includes a nominal state transition matrix and a nominal control input matrix.

[0009] In one embodiment, the step of mapping the dynamic dataset and the steady-state dataset to an increased-dimensional space according to the increased-dimensional function, and constructing a dynamic augmented regression matrix, a dynamic successor output matrix, a steady-state augmented regression matrix, and a steady-state output matrix, includes: A predetermined number of basis functions are selected to form an up-dimensional function, and the first few components of the up-dimensional function are the same as the original state components of the continuum robot. Based on the dimensionality-upgrading function, each current state in the dynamic dataset is mapped to the current dimensionality-upgrading state, and each next state is mapped to the next dimensionality-upgrading state. The current dimensionality-upgrading state is vertically concatenated with the dynamic driving input in the dynamic dataset to obtain a dynamic augmented regression matrix. The next dimensionality-upgrading state is arranged in columns to obtain a dynamic successor output matrix. Based on the dimensionality-upgrading function, each steady-state state in the steady-state dataset is mapped to a steady-state dimensionality-upgrading state. The steady-state dimensionality-upgrading state is then vertically concatenated with the steady-state driving input in the steady-state dataset to obtain a steady-state augmented regression matrix. Finally, the steady-state dimensionality-upgrading states are arranged in columns to obtain a steady-state output matrix.

[0010] In one embodiment, the step of acquiring measured state data of a continuum robot and generating a residual increment matrix based on the nominal prediction deviation of the measured state data relative to a fixed reference model includes: Obtain the measured state data at the current sampling time, and map the measured state data to the upgraded space based on the upgraded function to obtain the current measured upgraded state; Based on the fixed benchmark model and the driving input at the previous sampling time, the nominal prediction upscaling state at the current sampling time is calculated, and the difference between the current measured upscaling state and the nominal prediction upscaling state at the current sampling time is taken as the current nominal prediction residual. Store the current nominal prediction residual into a sliding window, and determine whether the amount of data in the sliding window has reached a preset window length threshold. If the amount of data within the sliding window does not reach the preset window length threshold, the residual increment matrix is ​​set to zero. If the amount of data in the sliding window has reached the preset window length threshold, then based on the nominal prediction residual, the measured dimensionality increase state and the driving input at each historical sampling time in the sliding window, a residual data matrix and a residual regression matrix are constructed. Using the residual increment matrix as the optimization variable, a residual update objective function is constructed, which is a weighted sum of the residual fitting term and the regularization term; The residual update objective function is minimized to obtain the residual increment matrix.

[0011] In one embodiment, the step of fusing the fixed baseline model and the residual increment matrix to obtain the current prediction model includes: Obtain the nominal state transition matrix and nominal control input matrix in the fixed baseline model, and obtain the state increment sub-block and input increment sub-block in the residual increment matrix; The nominal state transition matrix is ​​added to the state increment sub-block to obtain the current state transition matrix; The nominal control input matrix is ​​added to the input increment sub-block to obtain the current control input matrix; Based on the current state transition matrix, the current control input matrix, and the preset output matrix, a current prediction model is constructed. The current prediction model is used to describe the recursive relationship of the state along the prediction time domain in the upgraded space.

[0012] In one embodiment, the step of optimizing and solving the optimal control sequence that satisfies preset constraints in the prediction time domain based on the current prediction model to obtain the control command at the current time includes: Obtain the measured state data at the current sampling time, and map the measured state data to the increased dimension space based on the increased dimension function, as the initial increased dimension state for prediction in the time domain; Freeze the current prediction model in the prediction time domain, and recursively predict the dimensionality increase state of each prediction step based on the current prediction model and the initial dimensionality increase state in the prediction time domain. The reference state of the reference trajectory at each prediction step is obtained, and the reference state is mapped to the dimension-upper space based on the dimension-upper function to obtain the reference dimension-upper state of each prediction step. The stage cost is determined based on the tracking deviation between the predicted up-dimensional state and the corresponding reference up-dimensional state at each prediction step. The terminal cost is determined based on the tracking deviation between the predicted up-dimensional state of the terminal in the predicted time domain and the corresponding reference up-dimensional state. A cost function is constructed based on the sum of the stage costs and the sum of the terminal costs of each prediction step. Under preset allowable state constraints, allowable drive input constraints, and terminal constraints, the cost function is minimized to obtain the optimal control sequence. The first control variable is extracted from the optimal control sequence and used as the control command at the current moment.

[0013] Furthermore, to achieve the above objectives, this application also proposes a continuum robot control device based on a steady-state constrained Koopman model, wherein the continuum robot control device based on the steady-state constrained Koopman model includes: The data acquisition module is used to acquire the dynamic and steady-state datasets of the continuum robot. The model solving module is used to solve for a fixed benchmark model based on the dynamic dataset and the steady-state dataset, with the objective of minimizing the weighted sum of dynamic prediction error and steady-state equilibrium residual. The residual generation module is used to acquire the measured state data of the continuum robot and generate a residual increment matrix based on the nominal prediction deviation of the measured state data relative to the fixed reference model. The matrix fusion module is used to fuse the fixed benchmark model and the residual increment matrix to obtain the current prediction model; The instruction generation module is used to optimize and solve the optimal control sequence that satisfies preset constraints in the prediction time domain based on the current prediction model, and obtain the control instruction at the current moment. The control instruction is used to control the continuous robot to perform motion.

[0014] In addition, to achieve the above objectives, this application also proposes an electronic device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the continuum robot control method based on the steady-state constrained Koopman model as described above.

[0015] In addition, to achieve the above objectives, this application also proposes a non-transitory storage medium on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the continuum robot control method based on the steady-state constrained Koopman model as described above.

[0016] One or more technical solutions proposed in this application have at least the following technical effects: (1) Obtain the dynamic and steady-state datasets of the continuum robot; based on the dynamic and steady-state datasets, the fixed baseline model is obtained by minimizing the weighted sum of dynamic prediction error and steady-state equilibrium residual. The technique of jointly using dynamic and steady-state datasets for model identification is adopted, which solves the problems of insufficient identification of control input matrix and deviation of steady-state gain from actual equilibrium relationship, and realizes accurate constraint of input-output relationship of model near equilibrium point. Since the technique of minimizing the weighted sum of dynamic prediction error and steady-state equilibrium residual is adopted to solve the fixed baseline model, the problem of unreliable steady-state structure of fixed offline model is solved.

[0017] (2) Obtain the measured state data of the continuum robot, and generate a residual increment matrix based on the nominal prediction deviation of the measured state data relative to the fixed reference model; fuse the fixed reference model and the residual increment matrix to obtain the current prediction model; optimize the optimal control sequence that satisfies the preset constraints in the prediction time domain based on the current prediction model to obtain the control command at the current moment, which is used to control the continuum robot to perform motion. Generating the residual increment matrix based on the nominal prediction deviation of the measured state data relative to the fixed reference model solves the problem of local time-varying model mismatch caused by load changes, contact effects and material property changes, and realizes targeted compensation for unmodeled dynamics. Embedding the fused current prediction model into model predictive control and optimizing the optimal control sequence under preset constraints solves the problem of heavy online solution burden of nonlinear predictive control and improves the control accuracy and motion stability of the continuum robot. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the control system structure of the continuum robot in this application; Figure 2 This is a flowchart illustrating the first embodiment of the continuum robot control method based on the steady-state constrained Koopman model of this application. Figure 3 This is a flowchart illustrating the online adaptive predictive control strategy for the steady-state constrained Koopman model in this application. Figure 4 This is a comparison of the root mean square errors of the planar star, rose, and Lissajous curve trajectories in this application. Figure 5 The image shows a comparison of the root mean square errors of the spatial circle, spatial figure-eight, and spiral trajectories in this application. Figure 6 A comparison of the root mean square error of star-shaped and figure-eight-shaped trajectories when a 25 g external load is applied to this application; Figure 7 This is a comparison of the root mean square error of star-shaped and figure-eight-shaped trajectories in space when subjected to external contact disturbances.

[0021] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0022] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0023] This application provides a control method for a continuum robot based on a steady-state constrained Koopman model. It should be noted that the continuum robot includes soft pneumatic continuum robots and rigid wire-driven continuum robots. The soft pneumatic continuum robot's body is integrally molded or segmented from flexible materials such as silicone or elastomers, and has multiple independent pneumatic cavities distributed circumferentially inside. Uneven expansion is generated by adjusting the inflation pressure of each cavity, thereby driving the robot to achieve continuous deformation movements such as bending, extension, and torsion. The rigid wire-driven continuum robot consists of multiple series-connected rigid or quasi-rigid segments. Tension differences are applied by ropes or tendons arranged circumferentially around the segments, and the geometric mapping relationship between rope displacement and joint rotation angles is used to drive the robot to achieve continuous bending motion. The embodiments and implementation methods of this application do not limit the specific type of continuum robot.

[0024] The continuum robot control method based on the steady-state constrained Koopman model provided in this application can be applied to continuum robot control systems, such as... Figure 1 The continuum robot control system includes the robot body, a pneumatic drive unit, a state measurement unit, and a controller. The robot body is a three-segment independently controlled bellows-type pneumatic soft robotic arm; the pneumatic drive unit includes an air pump, solenoid valves, and a MOS switch board; the state measurement unit includes an Intel RealSense D435i depth camera and image processing software; and the controller includes a computer and an Arduino Mega 2560 microcontroller. Specifically, refer to... Figure 2 , Figure 2 This is a flowchart illustrating the first embodiment of the continuum robot control method based on the steady-state constrained Koopman model of this application. In this embodiment, the continuum robot control method based on the steady-state constrained Koopman model includes steps S10 to S50:

[0025] Step S10: Obtain the dynamic dataset and steady-state dataset of the continuum robot.

[0026] It should be noted that a continuum robot is constructed of flexible materials, has no discrete joints, and generates continuous bending and stretching deformation through pneumatic cavities or flexible drive segments. It can include soft pneumatic continuum robots and rigid linearly driven continuum robots. A dynamic dataset refers to the set of state sequences and corresponding input sequences collected from the transition process data of a robot changing from one state to another under different drive inputs. A steady-state dataset refers to the set of state quantities and corresponding constant input quantities collected after the robot's drive inputs remain constant and the state no longer changes over time.

[0027] Step S20: Based on the dynamic dataset and the steady-state dataset, the fixed benchmark model is obtained by minimizing the weighted sum of the dynamic prediction error and the steady-state equilibrium residual.

[0028] It should be noted that the dynamic prediction error is the deviation between the one-step prediction of the state at the next time step in the dynamic dataset by the fixed reference model and the actual measured value. At the equilibrium point corresponding to the steady-state dataset, the deviation between the predicted state change and zero given by the state evolution equation of the fixed reference model after substituting constant inputs is the steady-state equilibrium residual. The dynamic prediction error and the steady-state equilibrium residual are assigned weights and then added together. The overall magnitude of this sum is used as the optimization objective, and its minimization is achieved. The Koopman state transition matrix, obtained offline and remaining unchanged in subsequent control processes, together with the Koopman control input matrix, constitute the fixed reference model.

[0029] Step 30: Obtain the measured state data of the continuum robot, and generate the residual increment matrix based on the nominal prediction deviation of the measured state data relative to the fixed reference model.

[0030] It should be noted that the measured state data refers to the actual state of the robot at the current moment, collected in real time by sensors during the control process. The nominal prediction bias can be understood as the difference between the predicted state output by the model after substituting the measured state data into the fixed reference model and the actual measured state of the robot at the next moment. The residual increment matrix is ​​used to describe the identification and correction matrix of the local prediction error of the fixed reference model at the current moment.

[0031] Step S40: The fixed baseline model and the residual increment matrix are fused to obtain the current prediction model.

[0032] It should be noted that the current prediction model is an updated prediction model obtained by fusing the matrices of the fixed baseline model with the residual increment matrix, and is used to reflect the robot's current actual dynamic characteristics.

[0033] Step S50: Based on the current prediction model, optimize and solve the optimal control sequence that satisfies the preset constraints in the prediction time domain to obtain the control command at the current time.

[0034] It should be noted that the prediction time domain refers to the length of the number of state steps simulated forward by the model predictive controller during rolling optimization. The preset constraints are the pre-defined allowable ranges of values ​​for the robot's state variables and the drive input variables. The optimal control sequence refers to the set of control input vectors arranged in chronological order that satisfy the preset constraints within the prediction time domain and minimize the combined cost of tracking error and control quantity changes. The control command at the current moment is the first control input taken from the optimal control sequence and applied to the robot; this control command is used to control the continuous robot to perform motion.

[0035] In this embodiment, a technique combining dynamic and steady-state datasets for model identification is employed, addressing the issues of insufficient control input matrix identification and steady-state gain deviation from the actual equilibrium relationship. This achieves accurate constraints on the input-output relationship of the model near the equilibrium point. By using a technique that minimizes the weighted sum of dynamic prediction error and steady-state equilibrium residuals to solve the fixed baseline model, the unreliable steady-state structure of the fixed offline model is addressed. Furthermore, the technique of generating a residual increment matrix based on the nominal prediction deviation of measured state data relative to the fixed baseline model resolves the local time-varying model mismatch caused by load changes, contact interactions, and material property variations, enabling targeted compensation for unmodeled dynamics. Embedding the fused current prediction model into model predictive control and optimizing the optimal control sequence under preset constraints solves the problem of heavy online solution burden in nonlinear predictive control, improving the control accuracy and motion stability of the continuum robot.

[0036] In one embodiment, step S10 includes: Step S101: Apply time-varying input to each driving channel within a preset input range, collect state information and driving input information at adjacent sampling times, and obtain a set of dynamic snapshot pairs.

[0037] For example, the sampling time is recorded as The discrete-time dynamics of the robot are expressed as: in, The state vector must include at least the position of the robot's end effector. To drive the input vector; and These are the allowed state set and the allowed input set, respectively; This is an unknown nonlinear state transition mapping.

[0038] Within the allowed input range, time-varying inputs are applied to each drive channel, and the states and inputs at adjacent time points are collected to form a dynamic dataset, represented as follows: in, For dynamic datasets; The number of dynamic snapshot pairs; Indicates by the first The first to the second A dynamic snapshot pair consisting of the state, input, and state at each sampling time.

[0039] Step S102: Apply constant drive input to each drive channel. When the state change at adjacent sampling times meets the preset steady-state determination condition, record the current steady-state information and the corresponding constant drive input information to obtain a set of steady-state snapshot pairs.

[0040] For example, a constant input is applied to the driving channel, and when the change between adjacent states is less than the steady-state threshold, the steady-state state and input are recorded to form a steady-state dataset, represented as follows: in, For steady-state datasets; For steady-state sample indexing; For the first A steady-state vector; In order to be with the first The constant driving input vector corresponding to each steady state; The number of steady-state snapshot pairs; The steady-state determination threshold; Let L2 be the norm of the state difference between two adjacent sampling times. When this L2 is not greater than... At that time, it was determined that the robot had entered a steady state.

[0041] Step S103: Perform time alignment, outlier removal, and normalization on the state information and driving input information in the dynamic snapshot pair set and the steady-state snapshot pair set to obtain the dynamic dataset and the steady-state dataset.

[0042] For example, dynamic and steady-state data are time-aligned according to a uniform sampling period before entering the model for identification, and outlier removal and low-pass filtering are performed on state measurements. State variables and input variables are normalized according to a preset scale to avoid deterioration of the regression matrix numerical conditions caused by differences in the order of magnitude of different physical quantities. The data used for identification covers the robot's predetermined working area and the allowed input range; for end-effector position control tasks, the dynamic trajectory includes at least individual and combined motions in each coordinate direction, and the steady-state data covers at least multiple constant input levels for each drive channel. After identification is completed, the controller saves the normalized parameters and uses the same scale transformation during online measurement and control output.

[0043] In this embodiment, time-varying inputs are applied to each drive channel within a preset input range, and state information and drive input information at adjacent sampling times are collected to obtain a dynamic snapshot pair set, achieving high-quality dynamic data acquisition of the robot's dynamic characteristics. By applying constant drive inputs to each drive channel and recording steady-state state information and constant drive input information when the state change at adjacent sampling times meets preset steady-state determination conditions to obtain a steady-state snapshot pair set, a reliable data foundation is provided for subsequent model steady-state constraints. Time alignment, outlier removal, and normalization processing are performed on the state information and drive input information in the dynamic and steady-state snapshot pair sets to ensure the numerical stability and accuracy of the model identification.

[0044] In one implementation, step S20 includes: Step S201: Map the dynamic dataset and the steady-state dataset to the increased-dimensional space according to the increased-dimensional function, and construct the dynamic augmented regression matrix, the dynamic successor output matrix, the steady-state augmented regression matrix, and the steady-state output matrix.

[0045] Specifically, step S201 includes: selecting a preset number of basis functions to form an upscaling function, wherein the first few components of the upscaling function are the same as the original state components of the continuum robot; mapping each current state in the dynamic dataset to the current upscaling state based on the upscaling function, mapping each next state to the next upscaling state, vertically concatenating the current upscaling state with the dynamic driving input in the dynamic dataset to obtain a dynamic augmented regression matrix, and arranging the next upscaling states by column to obtain a dynamic successor output matrix; mapping each steady-state state in the steady-state dataset to a steady-state upscaling state based on the upscaling function, vertically concatenating the steady-state upscaling state with the steady-state driving input in the steady-state dataset to obtain a steady-state augmented regression matrix, and arranging the steady-state upscaling states by column to obtain a steady-state output matrix.

[0046] For example, one can select The basis functions constitute the increasing-dimensional function, expressed as: in, A dimension-upgrading function that maps the original state to a dimension-upgrading space; For the first One ascending-dimensional basis function ; Let be the number of basis functions for the increased dimension, and let be the dimension of the increased dimension state.

[0047] Define the dimensional upgrade state The robot dynamics are approximated by the following formula, which is: in, For the up-dimensional state transition matrix, For the control input matrix of the dimension increase, This is the state output matrix. When the first... When each component is in its original state, take .

[0048] It should be noted that the increased-dimensionality basis functions are determined based on the robot's state dimension and the predetermined control period. Too few basis functions make it difficult to describe the nonlinear deformation of flexible structures; too many basis functions increase the computational load for matrix identification and online prediction. This embodiment employs a polynomial increased-dimensionality function that includes the original state, first-order cross terms, quadratic terms, and constant terms. This allows the original state to be directly obtained from a fixed output matrix and maintains a linear state update form suitable for quadratic programming solutions.

[0049] Furthermore, construct a matrix based on the dynamic dataset: in, This is a matrix of upgraded state data formed by arranging the upgraded states at each current moment in the dynamic dataset in columns; This is a data matrix of subsequent upgraded states formed by arranging the upgraded states corresponding to the next upgraded time step in columns; It is an input data matrix formed by arranging the driving inputs corresponding to each dynamic snapshot in columns.

[0050] The dynamic augmented regression matrix and the nominal parameter matrix are expressed as follows: in, This is a dynamic augmented regression matrix; This is the nominal Koopman parameter matrix; The nominal up-dimensional state transition matrix obtained from offline identification; The nominal up-dimensional control input matrix is ​​obtained from offline identification.

[0051] Mapping the steady-state to an increased-dimensional space, we construct the steady-state matrix, which is represented as: in, This is the steady-state-upgraded-dimensionality matrix formed by arranging each steady-state-upgraded-dimensionality state in columns; The steady-state input matrix is ​​formed by arranging each steady-state constant input in columns; This is the steady-state augmented regression matrix.

[0052] It should be noted that the steady-state upscaling state corresponding to constant input should satisfy: Step S202: Construct the objective function, which is the weighted sum of the dynamic prediction error term and the steady-state constraint term.

[0053] The dynamic prediction error term is the squared Frobenius norm of the dynamic prediction error between the dynamic augmented regression matrix and the dynamic successor output matrix; the steady-state constraint term is the squared Frobenius norm of the steady-state equilibrium residual between the steady-state augmented regression matrix and the steady-state output matrix.

[0054] Step S203: Minimize the objective function to obtain the fixed benchmark model.

[0055] It should be noted that the fixed baseline model includes a nominal state transition matrix and a nominal control input matrix. Considering the viscoelasticity of soft materials, measurement noise, and modeling errors, this embodiment does not set the steady-state equilibrium relationship as a strict equality. Instead, the steady-state equilibrium residuals are used as physical regularization terms, which, together with the dynamic prediction residuals, identify the same nominal Koopman parameter matrix. For example, the objective function is expressed as:

[0056] in, Represented by the nominal parameter matrix Minimize the variables to be identified; Denotes the Frobenius norm; The first term represents the one-step prediction error of the dynamic data, and the second term represents the physical equilibrium residual of the steady-state data. When... At that time, the identification process only uses dynamic data; increase At that time, the role of steady-state data in parameter solving is enhanced. The selection is based on the fitting error of the validation set, in order to balance dynamic prediction accuracy and steady-state consistency.

[0057] The weighted augmented matrix is ​​represented as: in, For weighted augmented regression matrix; For weighted augmented output matrix; It is the arithmetic square root of the steady-state constraint weights.

[0058] The closed-form solution to the nominal Koopman parameter matrix is: in, for Moore-Penrose pseudo-reverse.

[0059] Furthermore, the information matrix corresponding to the weighted augmented matrix is: Among them, the sub-blocks in the steady-state information term that are directly related to the control input matrix are: when At this point, the steady-state input can cover all driving input directions, thereby improving the numerical conditions of the input-related regression subspace and increasing the nominal control input matrix. The identifiability. If the rank condition is not met, then supplementary steady-state samples corresponding to the missing drive channels are collected, instead of simply increasing the number of samples. .

[0060] In this embodiment, a technique is employed to map the dynamic and steady-state datasets to an increased-dimensional space using an increased-dimensional function, constructing a dynamic augmented regression matrix, a dynamic successor output matrix, a steady-state augmented regression matrix, and a steady-state output matrix. This addresses the difficulty of jointly identifying the same parameter matrix for dynamic and steady-state data in a high-dimensional space, achieving a unified mapping of nonlinear dynamic transition information and steady-state equilibrium information to a high-dimensional linear space. The objective function is constructed as a weighted sum of dynamic prediction error terms and steady-state constraint terms, resolving the inconsistency between the model's steady-state relationship and the actual equilibrium relationship, effectively improving the identifiability of the control input matrix near the equilibrium point. Minimizing the objective function provides a reliable fixed benchmark for updating only the residual increment matrix in the online phase, thereby improving the control accuracy of the continuum robot while meeting online real-time requirements.

[0061] Based on the above implementation methods, in one embodiment, the steady-state data fusion and nominal model can be verified, specifically including: applying an up-dimensional function to the dynamic state transition pairs. Perform mapping to construct a dynamic data matrix. , , and augmented matrix Apply constant input to each input channel respectively, when Record steady-state state - input pair, construct , and Using the same nominal parameter matrix Jointly minimize dynamic prediction error and steady-state equilibrium error: ;structure , The above objective is transformed into an augmented least squares problem; in candidate The models are identified separately, and the fitting error on the validation set is used to determine the model. Exemplary exist 50 candidate values ​​are selected evenly within the range, and the selection is verified. ;examine If the steady-state data does not cover all input directions, then supplement the steady-state data of the corresponding channels, instead of simply increasing the range. ;use Seek , and combined with the output matrix Construct the nominal Koopman model; , and Fixed as a nominal benchmark; only utilized in the online phase , The current model is formed without recursively accumulating the residual increments to the nominal matrix.

[0062] Furthermore, the offline prediction model is obtained from the nominal matrix, and is expressed as: in, and These represent the next-time upgraded state and the original state predicted by the nominal model, respectively.

[0063] In this embodiment, the steady-state data is not used to train a static model separately, nor is it simply spliced ​​together as ordinary dynamic samples. Instead, it is used to identify the same nominal parameter matrix together with the dynamic prediction residual in the form of physical equilibrium residual, and directly supplements the identification direction related to the control input matrix.

[0064] In one implementation, step S30 includes: Step S301: Obtain the measured state data at the current sampling time, and map the measured state data to the upgraded space based on the upgraded function to obtain the current measured upgraded state.

[0065] For example, maintaining online control and Without changing the model, only the increment relative to the nominal model is estimated, and the corresponding formula is: in, and The first The current up-dimensional state transition matrix and the current up-dimensional control input matrix actually used for predictive control at each control moment; and Relative to the nominal matrix and The state transition increment matrix and the control input increment matrix; This is the current residual increment parameter matrix.

[0066] Step S302: Based on the fixed benchmark model and the driving input at the previous sampling time, calculate the nominal predicted dimensionality upgrade state at the current sampling time, and use the difference between the current measured dimensionality upgrade state and the nominal predicted dimensionality upgrade state at the current sampling time as the current nominal prediction residual.

[0067] For example, the actual upgraded state is calculated based on the state measurement value, and the difference between it and the nominal prediction value is defined as the prediction residual, with the corresponding formula as follows: in, For the first The nominal prediction residual at each sampling time point; The actual upgraded state is calculated based on the actual measurement state; For the nominal model to the first The predicted value of the upgraded state at each sampling time.

[0068] Step S303: Store the current nominal prediction residual into the sliding window and determine whether the amount of data in the sliding window has reached the preset window length threshold; if the amount of data in the sliding window has not reached the preset window length threshold, set the residual increment matrix to zero matrix; if the amount of data in the sliding window has reached the preset window length threshold, construct the residual data matrix and residual regression matrix based on the nominal prediction residual, measured dimensionality upgrade state and driving input at each historical sampling time in the sliding window.

[0069] For example, in a length of Within the sliding window, the model mismatch is approximated as a locally slowly changing increment matrix, expressed as: in, For the data index within the sliding window; The length of the sliding window; For the first The regression vector formed by vertically concatenating the upgraded state at each sampling moment and the driving input; For the first The nominal prediction residual at each sampling time point.

[0070] The residual data matrix and regression matrix are constructed using the following formulas: in, The residual data matrix is ​​formed by arranging the predicted residuals within the sliding window in columns; It is the residual regression matrix formed by arranging the regression vectors in the sliding window column by column.

[0071] Step S304: Construct a residual update objective function using the residual increment matrix as the optimization variable; perform a minimization solution on the residual update objective function to obtain the residual increment matrix.

[0072] It should be noted that the residual update objective function is a weighted sum of the residual fitting term and the regularization term. For example, the residual increment matrix can be obtained by solving a least-squares problem with Tikhonov regularization, and the residual update objective function is expressed as:

[0073] in, The closed-form solution for updating regularized weights to residuals is expressed as: in, for An identity matrix of order 1.

[0074] When online snapshots are less than When the sliding window is full, the incremental matrix is ​​set to zero and the nominal model is used. Once the sliding window is full, the incremental matrix is ​​updated according to the formulas corresponding to steps S302 to S303. This update method uses a fixed nominal matrix as a benchmark, and the online part only compensates for local model mismatches reflected by recent data.

[0075] Sliding window length The range of data used for online updates is determined. Shorter windows reflect local changes more quickly but are more susceptible to measurement noise and transient disturbances; longer windows reduce matrix fluctuations but slow down the response to rapid model changes. Regularization weights. This is used to ensure the invertibility of the regression information matrix and limit the magnitude of the increment matrix. When recent data stimulus is weak, the regularization term can suppress excessive numerical updates, but the online residual model is still only used to describe local corrections in the direction of recent data coverage. The controller does not replace the nominal model with the residual matrix, nor does it recursively accumulate the fixed nominal matrix, thereby avoiding the continuous accumulation of initial identification errors and subsequent local errors in the entire model.

[0076] In this embodiment, the measured state is mapped to an upgraded space and the nominal prediction residual is calculated in conjunction with a fixed baseline model, solving the problem of unquantifiable prediction bias and enabling accurate detection of local model mismatch. The residual is stored in a sliding window, and the residual increment matrix is ​​set to zero when data is insufficient, addressing the issue of numerical instability or the introduction of incorrect corrections due to insufficient data. By constructing the residual matrix based on historical data when window data is sufficient and solving the residual update objective function with a regularization term, the problem of overfitting with direct least squares is solved. Local model mismatch compensation is obtained online with low computational cost, providing a basis for correction when fusing the current prediction model, thereby improving the control accuracy of the continuum robot while maintaining the steady-state structure of the offline model.

[0077] In one implementation, step S40 includes: obtaining the nominal state transition matrix and the nominal control input matrix in the fixed baseline model, and obtaining the state increment sub-block and the input increment sub-block in the residual increment matrix; adding the nominal state transition matrix and the state increment sub-block to obtain the current state transition matrix; adding the nominal control input matrix and the input increment sub-block to obtain the current control input matrix; and constructing the current prediction model based on the current state transition matrix, the current control input matrix, and the preset output matrix.

[0078] It should be noted that the current prediction model is used to describe the recursive relationship of states in the increased-dimensional space along the prediction time domain. For example, a fixed nominal matrix with steady-state constraints is used. , Using the predicted residuals within the sliding window as a baseline, the incremental matrix is ​​estimated. , This forms the current matrix, which is represented as:

[0079] Unlike methods that directly use a fixed Koopman model or rewrite all Koopman matrices online recursively, this implementation keeps the nominal matrix unchanged to preserve steady-state consistency. It compensates for local model mismatches caused by recent material changes, load, and contact disturbances only through residual increments. The control strategy is as follows: Figure 3 As shown.

[0080] Specifically, in the first At each control moment, the current matrix will be... and In the prediction time domain Internal freezing, constructing the current prediction model, represented as: in, To predict the length of the time domain; For the prediction step index; , and They were respectively in the second The first control time prediction Step-up state, initial state, and control input; This is the state output matrix.

[0081] In this embodiment, the technique of adding the nominal state transition matrix to the state increment sub-block and adding the nominal control input matrix to the input increment sub-block solves the problem of high computational cost and potential disruption of offline steady-state structure during full-model online updates. This achieves model correction with low computational cost through addition operations, preserving the steady-state consistency of the nominal model while incorporating recent mismatch compensation. Constructing the current prediction model based on the current state transition matrix, the current control input matrix, and the preset output matrix solves the problem that high-maintenance correction models cannot be directly mapped back to the original state space for constraint checks and cost calculations.

[0082] Based on the above implementation methods, in one implementation method, step S50 includes: acquiring the measured state data at the current sampling time, mapping the measured state data to the increased dimension space based on the increased dimension function, and using it as the initial increased dimension state in the prediction time domain; freezing the current prediction model in the prediction time domain, and recursively predicting the increased dimension state of each prediction step based on the current prediction model and the initial increased dimension state in the prediction time domain; acquiring the reference state of the reference trajectory in each prediction step, and mapping the reference state to the increased dimension space based on the increased dimension function to obtain the reference increased dimension state of each prediction step; determining the stage cost based on the tracking deviation between the predicted increased dimension state of each prediction step and the corresponding reference increased dimension state; determining the terminal cost based on the tracking deviation between the predicted increased dimension state of the terminal in the prediction time domain and the corresponding reference increased dimension state; constructing a cost function based on the sum of the stage costs of each prediction step and the sum of the terminal costs, and performing a minimization solution on the cost function under preset allowable state constraints, allowable drive input constraints, and terminal constraints to obtain the optimal control sequence; and extracting the first control quantity from the optimal control sequence as the control command at the current time.

[0083] For example, the reference trajectory is mapped to an upgraded space, and the stage cost and terminal cost are defined based on the predicted state generated by the current matrix, as follows: in, and These are the original reference state and the upgraded reference state, respectively. As a stage cost; For the cost of the terminal; , and These are the positive definite weight matrices for dimensionality tracking, control input, and terminal dimensionality tracking, respectively. The other weighted norms have the same meaning.

[0084] The model predictive control objective is expressed as: in, For the first The predictive control input sequence to be optimized at each control time; Based on the current matrix , The overall objective function is constructed. The optimization process satisfies the following formula:

[0085] in, and These are the allowed state set and the allowed input set, respectively; This represents the set of terminal up-dimensional states. Online residual increments are only used for the current prediction and are not recursively changed. Terminal cost; the terminal upgrade state set and terminal cost are calculated according to a fixed nominal matrix. , Configuration.

[0086] For any Set the local terminal control law, the corresponding formula is: And make it satisfy the following formula: in, This is the local terminal feedback matrix; This refers to the subsequent upgraded state of the fixed nominal model under terminal control and combined disturbances. To meet Bounded composite perturbation; This serves as the upper bound for the composite perturbation. The above conditions ensure that the terminal input satisfies the constraints, the subsequent state remains within the terminal's upgraded state set, and the terminal cost decreases.

[0087] Since the current matrix is ​​frozen in the prediction time domain, when the cost function is quadratic and the constraints are linear inequalities or box sets, the control problem is transformed into quadratic programming. For pneumatically driven robots, the first optimal control input can be limited and its dimensions restored, then converted into a pulse-width modulated signal or pressure command and applied to the pneumatic drive unit. At the next sampling time, the state is remeasured, the residual matrix is ​​updated, and the solution is solved in a rolling manner. The residual increment is always estimated relative to the fixed nominal matrix and is not accumulated to the nominal matrix, thus avoiding long-term drift of the steady-state structure and terminal conditions.

[0088] Relative to the fixed nominal model, the composite perturbation is expressed as: in, For the first Composite perturbation at each sampling time; For external disturbances and unmodeled effects; the first two terms represent the difference between the current adaptive model and the fixed nominal model. The composite disturbance is defined when the up-dimensional state, input, residual matrix, and external disturbance are bounded within the compact working region. Bounded.

[0089] Under the aforementioned terminal conditions and local feasibility, the MPC problem corresponding to the fixed nominal model is recursively feasible, and the nominal closed-loop tracking error subjected to bounded composite perturbations exhibits state stability. It should be noted that this conclusion is not equivalent to an unconditional robust guarantee for the actual adaptive closed loop under arbitrary perturbations; for more stringent perturbation constraint guarantees, state constraint tightening or tubular MPC can be adopted based on the upper bound of the perturbation.

[0090] In this implementation, mapping the current measured state to the initial upgraded state in the prediction time domain solves the problem of inconsistency between the prediction starting point and the actual state. Freezing the current prediction model within the prediction time domain and recursively predicting each upgraded state solves the problem of high computational cost and disruption of steady-state structure caused by recursively rewriting all Koopman matrices online, transforming the control problem into quadratic programming and meeting online real-time requirements. Mapping the reference trajectory to the reference upgraded state enables unified calculation of tracking deviation in the upgraded space. The technique of determining stage cost and terminal cost based on tracking deviation solves the problems of lack of stability in the optimization objective and guarantee of terminal convergence. Extracting the first control variable from the optimal control sequence as the current control command and executing it in a rolling manner solves the problem of heavy online solution burden for nonlinear model predictive control, enabling real-time generation of constraint-satisfied drive commands with lower computational cost, thus improving the control accuracy and motion stability of the continuum robot.

[0091] To illustrate the technical effects of this application, in one embodiment, PCC-NMPC, standard K-MPC, SSCK-MPC with only steady-state constraints, full-model adaptive AK-MPC, and the SSCAK-MPC of this application are compared experimentally. The experimental comparison results are shown in the figure below. Figure 5Current control methods that rely solely on dynamic data to identify the Koopman model are prone to problems such as poor identification conditions of the control input matrix, discrepancies between the model's steady-state relationship and the robot's actual equilibrium relationship, and insufficient adaptability of the model to changes in operating conditions, making it difficult to meet the requirements of real-time control for complex flexible robots. In contrast, this application incorporates dynamic data and steady-state equilibrium data into a unified identification framework, using the same dimensionality-increasing function and parameter matrix. This allows dynamic prediction errors and steady-state equilibrium errors to participate in the nominal model solution, thereby improving the identification conditions of the control input matrix and enhancing the accuracy of steady-state modeling. During online operation, this application maintains the nominal matrix with steady-state constraints unchanged, updating only the residual increment matrix with a regularized least-squares closed-form solution using recent measurement data. While preserving the baseline structure of the nominal model, it effectively compensates for local model mismatches, eliminating the need to retrain the complete dimensionality-increasing model in each control cycle. This application further combines a real-time updated Koopman model with a quadratic cost function to construct a quadratic programming problem with constraints on motion range and drive input range. It employs a rolling time-domain approach, executing only the first input in the optimal control sequence, and re-predicting and optimizing at the next sampling time based on new state measurements and recent model errors. This method does not rely on a pre-established high-fidelity analytical dynamic model and is suitable for continuum robots with complex flexible deformation and drive coupling characteristics. While meeting terminal conditions and local feasibility requirements, it also ensures the recursive feasibility of the fixed nominal model predictive control problem and keeps the tracking error under combined disturbances within a bounded range related to the upper bound of the disturbance. This application demonstrates significant advantages in multiple dimensions, including identification accuracy, online computational efficiency, control performance, and robust reliability. It can better meet the high-precision real-time control needs of continuum robots under complex working conditions and possesses good engineering application value and promotion potential.

[0092] Based on the same inventive concept, this application also provides a continuum robot control device based on a steady-state constrained Koopman model. The continuum robot control device based on the steady-state constrained Koopman model includes: The data acquisition module is used to acquire the dynamic and steady-state datasets of the continuum robot. The model solving module is used to solve for a fixed benchmark model based on the dynamic dataset and the steady-state dataset, with the objective of minimizing the weighted sum of dynamic prediction error and steady-state equilibrium residual. The residual generation module is used to acquire the measured state data of the continuum robot and generate a residual increment matrix based on the nominal prediction deviation of the measured state data relative to the fixed reference model. The matrix fusion module is used to fuse the fixed benchmark model and the residual increment matrix to obtain the current prediction model; The instruction generation module is used to optimize and solve the optimal control sequence that satisfies preset constraints in the prediction time domain based on the current prediction model, and obtain the control instruction at the current moment. The control instruction is used to control the continuous robot to perform motion.

[0093] It should be noted that the continuum robot control device based on the steady-state constrained Koopman model provided in this application embodiment and the continuum robot control method based on the steady-state constrained Koopman model provided in this application embodiment are based on the same application concept. Therefore, the specific implementation of this embodiment can refer to the implementation of the aforementioned continuum robot control method based on the steady-state constrained Koopman model, and the repeated parts will not be described again.

[0094] In some embodiments, an electronic device provided in this application includes: a memory, a processor, and a computer program stored in the memory and executable on the processor. The computer program is configured to implement the above-described continuous robot control method based on a steady-state constrained Koopman model.

[0095] Specifically, the processor may include, for example, a general-purpose microprocessor, an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor may also include onboard memory for caching purposes. The processor may be a single processing unit or multiple processing units for performing different actions of the method flow according to embodiments of this application.

[0096] Memory can be any medium capable of containing, storing, transmitting, propagating, or transmitting instructions. For example, memory can include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, instruments, or propagation media. Specific examples of memory include: magnetic storage devices such as magnetic tape or hard disk drives (HDDs); optical storage devices such as optical discs (CD-ROMs); and also random access memory (RAM) or flash memory; and / or wired / wireless communication links.

[0097] This application also provides a non-transitory storage medium storing a computer program. When executed by a processor, this program implements the aforementioned continuous robot control method based on a steady-state constrained Koopman model. This storage medium may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The aforementioned non-transitory storage medium carries one or more programs, which, when executed, implement the method as described in the embodiments or implementations of this application.

[0098] According to embodiments of this application, a non-transitory storage medium can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. A computer-readable signal medium can also be any storage medium other than a computer-readable storage medium that can transmit, propagate, or transfer a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the storage medium can be transmitted using any suitable medium, including but not limited to: wireless, wired, optical fiber, radio frequency signals, etc., or any suitable combination thereof.

[0099] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0100] Those skilled in the art will understand that the features described in the various embodiments of this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, the features described in the various embodiments of this application can be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application. Therefore, the scope of this application should not be limited to the above embodiments. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A control method for a continuum robot based on a steady-state constrained Koopman model, characterized in that, The method includes: Obtain dynamic and steady-state datasets for the continuum robot; Based on the dynamic dataset and the steady-state dataset, a fixed benchmark model is obtained by minimizing the weighted sum of dynamic prediction error and steady-state equilibrium residual. Acquire measured state data of the continuum robot, and generate a residual increment matrix based on the nominal prediction deviation of the measured state data relative to the fixed reference model; The fixed benchmark model and the residual increment matrix are fused to obtain the current prediction model; Based on the current prediction model, the optimal control sequence that satisfies the preset constraints is optimized and solved in the prediction time domain to obtain the control command at the current moment. The control command is used to control the continuous robot to perform motion.

2. The method as described in claim 1, characterized in that, The steps for obtaining the dynamic and steady-state datasets of the continuum robot include: Apply time-varying input to each drive channel within a preset input range, collect state information and drive input information at adjacent sampling times, and obtain a set of dynamic snapshot pairs; Apply constant drive input to each drive channel. When the state change at adjacent sampling times meets the preset steady-state determination condition, record the current steady-state state information and the corresponding constant drive input information to obtain a set of steady-state snapshot pairs. The state information and driving input information in the dynamic snapshot pair set and the steady-state snapshot pair set are time-aligned, outlier-removed, and normalized to obtain the dynamic dataset and the steady-state dataset.

3. The method as described in claim 1, characterized in that, The step of solving for a fixed baseline model based on the dynamic dataset and the steady-state dataset, with the objective of minimizing the weighted sum of dynamic prediction error and steady-state equilibrium residual, includes: Based on the dimension-upgrading function, the dynamic dataset and the steady-state dataset are mapped to the dimension-upgrading space respectively, and a dynamic augmented regression matrix, a dynamic successor output matrix, a steady-state augmented regression matrix, and a steady-state output matrix are constructed. Construct an objective function, which is a weighted sum of a dynamic prediction error term and a steady-state constraint term; wherein, the dynamic prediction error term is the squared Frobenius norm of the dynamic prediction error between the dynamic augmented regression matrix and the dynamic successor output matrix; and the steady-state constraint term is the squared Frobenius norm of the steady-state equilibrium residual between the steady-state augmented regression matrix and the steady-state output matrix. The objective function is minimized to obtain a fixed baseline model, which includes a nominal state transition matrix and a nominal control input matrix.

4. The method as described in claim 3, characterized in that, The step of mapping the dynamic dataset and the steady-state dataset to the increased-dimensional space according to the increased-dimensional function, and constructing the dynamic augmented regression matrix, the dynamic successor output matrix, the steady-state augmented regression matrix, and the steady-state output matrix, includes: A predetermined number of basis functions are selected to form an up-dimensional function, and the first few components of the up-dimensional function are the same as the original state components of the continuum robot. Based on the dimensionality-upgrading function, each current state in the dynamic dataset is mapped to the current dimensionality-upgrading state, and each next state is mapped to the next dimensionality-upgrading state. The current dimensionality-upgrading state is vertically concatenated with the dynamic driving input in the dynamic dataset to obtain a dynamic augmented regression matrix. The next dimensionality-upgrading state is arranged in columns to obtain a dynamic successor output matrix. Based on the dimensionality-upgrading function, each steady-state state in the steady-state dataset is mapped to a steady-state dimensionality-upgrading state. The steady-state dimensionality-upgrading state is then vertically concatenated with the steady-state driving input in the steady-state dataset to obtain a steady-state augmented regression matrix. Finally, the steady-state dimensionality-upgrading states are arranged in columns to obtain a steady-state output matrix.

5. The method as described in claim 1, characterized in that, The step of acquiring the measured state data of the continuum robot and generating a residual increment matrix based on the nominal prediction deviation of the measured state data relative to a fixed reference model includes: Obtain the measured state data at the current sampling time, and map the measured state data to the upgraded space based on the upgraded function to obtain the current measured upgraded state; Based on the fixed benchmark model and the driving input at the previous sampling time, the nominal prediction upscaling state at the current sampling time is calculated, and the difference between the current measured upscaling state and the nominal prediction upscaling state at the current sampling time is taken as the current nominal prediction residual. Store the current nominal prediction residual into a sliding window, and determine whether the amount of data in the sliding window has reached a preset window length threshold. If the amount of data within the sliding window does not reach the preset window length threshold, the residual increment matrix is ​​set to zero. If the amount of data in the sliding window has reached the preset window length threshold, then based on the nominal prediction residual, the measured dimensionality increase state and the driving input at each historical sampling time in the sliding window, a residual data matrix and a residual regression matrix are constructed. Using the residual increment matrix as the optimization variable, a residual update objective function is constructed, which is a weighted sum of the residual fitting term and the regularization term; The residual update objective function is minimized to obtain the residual increment matrix.

6. The method as described in claim 1, characterized in that, The step of fusing the fixed baseline model and the residual increment matrix to obtain the current prediction model includes: Obtain the nominal state transition matrix and nominal control input matrix in the fixed baseline model, and obtain the state increment sub-block and input increment sub-block in the residual increment matrix; The nominal state transition matrix is ​​added to the state increment sub-block to obtain the current state transition matrix; The nominal control input matrix is ​​added to the input increment sub-block to obtain the current control input matrix; Based on the current state transition matrix, the current control input matrix, and the preset output matrix, a current prediction model is constructed. The current prediction model is used to describe the recursive relationship of the state along the prediction time domain in the upgraded space.

7. The method as described in claim 1, characterized in that, The step of optimizing and solving the optimal control sequence that satisfies preset constraints in the prediction time domain based on the current prediction model to obtain the control command at the current time includes: Obtain the measured state data at the current sampling time, and map the measured state data to the increased dimension space based on the increased dimension function, as the initial increased dimension state for prediction in the time domain; Freeze the current prediction model in the prediction time domain, and recursively predict the dimensionality increase state of each prediction step based on the current prediction model and the initial dimensionality increase state in the prediction time domain. The reference state of the reference trajectory at each prediction step is obtained, and the reference state is mapped to the dimension-upper space based on the dimension-upper function to obtain the reference dimension-upper state of each prediction step. The stage cost is determined based on the tracking deviation between the predicted up-dimensional state and the corresponding reference up-dimensional state at each prediction step. The terminal cost is determined based on the tracking deviation between the predicted up-dimensional state of the terminal in the predicted time domain and the corresponding reference up-dimensional state. A cost function is constructed based on the sum of the stage costs and the sum of the terminal costs of each prediction step. Under preset allowable state constraints, allowable drive input constraints, and terminal constraints, the cost function is minimized to obtain the optimal control sequence. The first control variable is extracted from the optimal control sequence and used as the control command at the current moment.

8. A control device for a continuum robot based on a steady-state constrained Koopman model, characterized in that, The continuum robot control device based on the steady-state constrained Koopman model includes: The data acquisition module is used to acquire the dynamic and steady-state datasets of the continuum robot. The model solving module is used to solve for a fixed benchmark model based on the dynamic dataset and the steady-state dataset, with the objective of minimizing the weighted sum of dynamic prediction error and steady-state equilibrium residual. The residual generation module is used to acquire the measured state data of the continuum robot and generate a residual increment matrix based on the nominal prediction deviation of the measured state data relative to the fixed reference model. The matrix fusion module is used to fuse the fixed benchmark model and the residual increment matrix to obtain the current prediction model; The instruction generation module is used to optimize and solve the optimal control sequence that satisfies preset constraints in the prediction time domain based on the current prediction model, and obtain the control instruction at the current moment. The control instruction is used to control the continuous robot to perform motion.

9. An electronic device, characterized in that, The electronic device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the continuum robot control method based on the steady-state constrained Koopman model as described in any one of claims 1 to 7.

10. A non-transitory storage medium, characterized in that, The non-transient storage medium stores a computer program, which, when executed by a processor, implements the steps of the continuum robot control method based on the steady-state constrained Koopman model as described in any one of claims 1 to 7.

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