A method, apparatus, equipment and medium for controlling a concentric tube robot

Abstract

This invention relates to the field of robot control technology, and discloses a method, device, equipment, and medium for controlling a concentric tube robot. The method includes acquiring a sequence of joint motion states of the concentric tube robot and inputting it into a preset temporal neural network model, outputting a temporal state feature vector containing physical lag characteristics; using the temporal state feature vector as conditional input, and through a physical information neural network based on Cosserat link theory, under the guidance of physical constraints including torque balance conditions and geometric compatibility conditions, modeling the continuous spatial morphology of the concentric tube robot along the arc length direction, and predicting the robot's end-effector pose; based on a given target trajectory and end-effector pose, constructing an optimization objective function including tracking error, and solving the optimization objective function under the condition of satisfying physical constraints to obtain the optimal joint drive command and control the movement of the concentric tube robot. This invention improves the accuracy of concentric tube robot control.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and more specifically, to a method, apparatus, equipment, and medium for controlling a concentric tube robot. Background Technology

[0002] Concentric tube robots (CTRs) are continuum robots composed of multiple pre-bent, hyperelastic thin tubes nested coaxially. They achieve highly flexible, high-degree-of-freedom manipulation through the relative translational and rotational movements of the tubes. Due to their compact structure and ability to navigate narrow and tortuous paths, CTRs are widely used in minimally invasive surgeries such as neurosurgery, otolaryngology, cardiovascular surgery, and urology, significantly reducing surgical trauma and risks. However, due to the coupling between the multiple tubes, the motion of CTRs exhibits strong nonlinearity and history dependence. This makes accurate modeling of the kinematics and control of the continuum robot a core challenge for its safe and reliable application in complex surgical procedures.

[0003] Existing technologies for modeling and controlling CTR (Continuous Torque Tracing) generally employ Cosserat link theory to construct the physical mapping between joint input and end-effector pose. This involves establishing torque balance equations for the tube, geometric compatibility conditions, and complex differential equation boundary value problems (such as solving for relative torsional angles) to ensure mechanical compatibility during deformation. Alternatively, static neural network structures such as multilayer perceptrons (MLPs) are used to directly learn the instantaneous mapping from joint space to task space. However, existing technologies suffer from the following drawbacks: Cosserat-based theoretical models face limitations such as high computational complexity, reliance on numerical approximations, and difficulty in meeting real-time control requirements when incorporating nonlinear factors like friction, hysteresis, and inter-tube gaps. Furthermore, pure data-driven methods based on static networks are black-box models, lacking physical constraints and interpretability. They can only establish instantaneous mappings and struggle to capture the significant dynamic hysteresis characteristics caused by material compliance, internal friction, and torsional effects, resulting in the inability to achieve high-precision modeling and control. Summary of the Invention

[0004] To overcome the shortcomings of low modeling and control accuracy in existing concentric tube robot technology, this invention proposes the following technical solution:

[0005] In a first aspect, the present invention proposes a control method for a concentric tube robot, comprising:

[0006] Obtain the joint motion state sequence of the concentric tube robot, wherein the joint motion state sequence includes joint motion data at the current moment and within the historical time window;

[0007] The joint motion state sequence is input into a preset temporal neural network model for feature extraction, and the output is a temporal state feature vector containing physical hysteresis characteristics.

[0008] Using the temporal state feature vector as a conditional input, and guided by physical information neural networks based on Cosserat rod theory, the continuous spatial morphology of the concentric tube robot along the arc length direction is modeled through physical constraints including torque balance conditions and geometric compatibility conditions, and the robot end pose is predicted.

[0009] Based on the given target trajectory and the end-effector pose, an optimization objective function including tracking error is constructed. Under the condition of satisfying physical constraints, the optimization objective function is solved to obtain the optimal joint drive command and control the movement of the concentric tube robot.

[0010] As a preferred technical solution, the temporal neural network model includes a temporal convolutional network and a long short-term memory network; the step of inputting the joint motion state sequence into the temporal neural network model for feature extraction includes:

[0011] The joint motion state sequence is preprocessed using an asymmetric zero-padding method, and the processed sequence is then input into the temporal convolutional network. The layer uses dilated convolution to extract feature vectors, and its expression is as follows:

[0012]

[0013] In the formula, Indicates the first Layer at time The output feature vector, This represents the activation function. Indicates the first The convolutional kernel weight tensor of the layer, Indicates the expansion rate One-dimensional convolution operation, Indicates the first Layer bias vector;

[0014] The feature vector output by the temporal convolutional network is input into the first layer of the long short-term memory network to encode the angle changes in the feature vector and generate an intermediate state feature vector. The intermediate state feature vector is then input into the second layer of the long short-term memory network to generate an intermediate state feature vector containing long-term lag characteristics. The intermediate state feature vector containing long-term lag characteristics is then flattened to obtain the temporal state feature vector, the expression of which is as follows:

[0015]

[0016]

[0017]

[0018] in, , This represents the feature sequence output by a temporal convolutional network. and These represent the operational functions of the first and second layers of the Long Short-Term Memory network, respectively. This represents the intermediate state feature vector output by the first layer of the Long Short-Term Memory network. This represents the state feature vector output by the second-layer Long Short-Term Memory network, which includes non-linear coupling behavior. Indicates the flattening operation. This represents the temporal state feature vector.

[0019] As a preferred technical solution, the temporal state feature vector is used as a conditional input. Guided by physical constraints including torque balance and geometric compatibility conditions, a physical information neural network based on Cosserat rod theory models the continuous spatial morphology of the concentric tube robot along the arc length direction, predicting the robot's end-effector pose. This includes:

[0020] The temporal state feature vector is processed through a fully connected layer. The position of the concentric tube robot's centerline in the global coordinate system, the orientation of the corresponding cross section, and the strain vector composed of curvature and torsion, which is mapped to the sampling s along the arc length, are expressed as follows:

[0021]

[0022] Where p(s), R(s), and u(s) are all continuous functions defined over the arc length interval of the robot, describing the spatial trajectory of the centerline, the evolution of the cross-sectional posture, and the strain distribution, respectively. This represents the implicit function expression obtained from network training.

[0023] As a preferred technical solution, a physical information neural network based on Cosserat rod theory is used to model the continuous spatial morphology of the concentric tube robot along the arc length direction, guided by physical constraints including torque balance and geometric compatibility conditions. This includes:

[0024] In the training process of the physical information neural network, the geometric relations, moment balance equations, and constitutive relations of Cosserat theory are used as physical constraints embedded in the loss function. An automatic differentiation mechanism is used to differentiate the network output with respect to the arc length parameter s, and a physical loss function is constructed under the non-shearing assumption. It satisfies the following relationship:

[0025]

[0026]

[0027]

[0028]

[0029] in, and This represents the geometrically consistent positional and rotational errors distributed along the arc length s. Indicates the torque balance error. This represents the residual function, which includes the moment equilibrium equations and the material constitutive equations, constructed based on Cosserat theory. This represents the expectation of the arc length parameter s within the arc length interval of the robot. Represents the axial unit vector in the local coordinate system of the cross section;

[0030] Substituting the total arc length L of the concentric tube robot into the implicit function expression constructed by the physical information neural network... Obtain the end effector pose predicted by the network and calculate the data error function between it and the true end effector pose. :

[0031]

[0032] in, The number of samples in the training data. The actual end-effector pose of the concentric tube robot is output by the electromagnetic tracker. This represents the pose of the output terminal of the physical information neural network;

[0033] Based on the physical characteristics of the fixed base of the concentric tube robot, boundary condition constraints on position and orientation are introduced, and a boundary condition error function is constructed. :

[0034]

[0035] in, and These are the boundary conditions for the base position and attitude, respectively. It is the identity matrix;

[0036] According to the physical loss function Data error function and boundary condition error function Construct the total loss function of the physical information neural network :

[0037]

[0038] in, , and These are the weighting coefficients for physical loss, boundary condition loss, and data loss, respectively.

[0039] As a preferred technical solution, before constructing the optimization objective function that includes tracking error, the method further includes:

[0040] At the current control moment Based on the given target end trajectory Select length as N In the prediction time domain, construct the end pose sequence to be tracked;

[0041] Using pre-built inverse kinematics network models The end-effector pose sequence to be tracked is mapped to a reference joint sequence. Its expression is as follows:

[0042]

[0043] in, Indicates the prediction of the first time domain The target end pose at any given time.

[0044] As a preferred technical solution, the expression for the optimization objective function including tracking error is as follows:

[0045]

[0046] in, Indicates the first The state of joint movement at any given moment. This represents the model error term after correction using sensor feedback at the current moment. The weight matrix represents the end-effector pose tracking error. The weight matrix represents the joint reference trajectory tracking error. The weight matrix representing the rate of change of joint control quantities. and Indicates the adjustment parameter. This indicates the amount of joint control at the previous moment. This is a pre-constructed positive kinematic network.

[0047] As a preferred technical solution, the physical constraints include joint amplitude constraints and joint rate of change constraints, which satisfy the following relationship:

[0048]

[0049]

[0050] in, and These represent the minimum and maximum values ​​of the joint actuation force of the concentric tube robot, respectively. This indicates the maximum permissible variation in joint drive quantity between adjacent control moments.

[0051] Secondly, the present invention also proposes a concentric tube robot control device, applied in the concentric tube robot control method as described in any embodiment of the first aspect, comprising:

[0052] The acquisition module is used to acquire the joint motion state sequence of the concentric tube robot, which includes joint motion data at the current moment and within the historical time window.

[0053] The extraction module is used to input the joint motion state sequence into a preset temporal neural network model for feature extraction and output a temporal state feature vector containing physical lag characteristics.

[0054] The prediction module is used to take the temporal state feature vector as a conditional input, introduce a physical information neural network based on Cosserat rod theory, and model the continuous spatial morphology of the concentric tube robot along the arc length direction under the guidance of physical constraints such as torque balance conditions and geometric compatibility conditions, and directly predict the end pose of the concentric tube robot.

[0055] The control module is used to construct an optimized objective function including tracking error based on the given target trajectory and the end-effector pose, solve the optimized objective function under the condition of satisfying physical constraints, obtain the optimal joint drive command, and control the movement of the concentric tube robot.

[0056] Thirdly, the present invention also proposes an electronic device 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 perform the operations performed by the concentric tube robot control method as described in any of the embodiments of the first aspect.

[0057] In a fourth aspect, the present invention also provides a computer-readable storage medium on which a program is stored, the program being executed by a processor as performed by the concentric tube robot control method described in any of the embodiments of the first aspect.

[0058] The beneficial effects of the present invention include at least the following:

[0059] This invention effectively extracts and characterizes the complex physical hysteresis characteristics of concentric tube robots caused by material compliance, internal friction, and torsional coupling by inputting joint motion state sequences containing historical time window data into a temporal neural network model, thus solving the historical dependency problem in kinematic modeling. Furthermore, by using the mapped and combined with the torque balance and geometric compatibility conditions of link theory, continuous functions describing the spatial trajectory of the centerline, cross-sectional posture evolution, and strain distribution over the arc length interval of the concentric tube robot are calculated. This essentially embeds physical laws as constraints into the forward propagation process of the network. This physically guided approach not only endows the network model with clear physical interpretability and generalization ability, ensuring that the kinematic mapping conforms to real physical laws, but also effectively avoids the high computational overhead caused by complex numerical integration and iterative solutions of differential equations in traditional physical models. Finally, by constructing an optimization objective function that includes tracking errors and solving for the optimal joint drive commands under physical constraints, model prediction errors and external disturbances can be compensated in real time. This significantly improves the accuracy and robustness of concentric tube robot modeling and trajectory tracking control while ensuring the physical consistency of the system. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the concentric tube robot control method provided in an embodiment of the present invention.

[0061] Figure 2 This is a graph showing the change in the reciprocating motion angle of the fourth joint of the robot provided in an embodiment of the present invention.

[0062] Figure 3 This is a schematic diagram illustrating the comparative experimental results of the present invention and the traditional LSTM network model in the forward kinematics prediction task for capturing hysteresis characteristics, as provided in the embodiments of the present invention.

[0063] Figure 4 This is a schematic diagram of the workspace data distribution of a concentric tube robot collected using an NDI electromagnetic sensor and a motor encoder, as provided in an embodiment of the present invention.

[0064] Figure 5 This is an architectural diagram of the concentric tube robot control device provided in an embodiment of the present invention.

[0065] Figure 6 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0066] The embodiments of the present invention will be described below with reference to the accompanying drawings and preferred technical solutions. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred technical solutions are only for illustrating the present invention and not for limiting the scope of protection of the present invention.

[0067] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0068] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0069] Example 1

[0070] This embodiment proposes a control method for a concentric tube robot, such as... Figure 1 As shown, Figure 1 This is a flowchart illustrating a control method for a concentric tube robot provided in this embodiment. The method includes the following steps:

[0071] S1: Obtain the joint motion state sequence of the concentric tube robot, the joint motion state sequence including the joint motion data at the current time and within the historical time window;

[0072] S2: Input the joint motion state sequence into a preset temporal neural network model for feature extraction, and output a temporal state feature vector containing physical lag characteristics;

[0073] S3: Using the temporal state feature vector as a conditional input, and guided by physical information neural networks based on Cosserat rod theory, the continuous spatial morphology of the concentric tube robot along the arc length direction is modeled through physical constraints including torque balance conditions and geometric compatibility conditions, and the robot end pose is predicted.

[0074] S4: Based on the given target trajectory and the end-effector pose, construct an optimization objective function that includes tracking error. Solve the optimization objective function under the condition of satisfying physical constraints to obtain the optimal joint drive command and control the movement of the concentric tube robot.

[0075] Understandably, by inputting the joint motion state sequence containing historical time window data into the temporal neural network model, the complex physical hysteresis characteristics of the concentric tube robot caused by material compliance, internal friction, and torsional coupling can be effectively extracted and characterized, solving the historical dependence problem in kinematic modeling. Furthermore, under the joint guidance of temporal features and physical constraints, the torsional distribution corresponding to the current joint state is implicitly modeled and reconstructed, outputting the whole-body morphology and end-effector pose. In effect, physical laws are embedded as constraints into the loss function. This physical guidance not only gives the network model clear physical interpretability and generalization ability, ensuring that the kinematic mapping conforms to the real physical laws, but also effectively avoids the high computational overhead caused by the complex numerical integration and iterative solution of differential equations in traditional physical models. Finally, by constructing an optimization objective function that includes tracking error and solving for the optimal joint drive command under the condition of satisfying physical constraints, the model prediction error and external disturbances can be compensated in real time. Thus, while ensuring the physical consistency of the system, the accuracy and robustness of the modeling and trajectory tracking control of the concentric tube robot are significantly improved.

[0076] Example 2

[0077] This embodiment is an improvement on the concentric tube robot control method proposed in Embodiment 1.

[0078] In this embodiment, the temporal neural network model includes a temporal convolutional network and a long short-term memory network; the step of inputting the joint motion state sequence into the temporal neural network model for feature extraction includes:

[0079] The joint motion state sequence is preprocessed using an asymmetric zero-padding method, and the processed sequence is then input into the temporal convolutional network. The layer uses dilated convolution to extract feature vectors, and its expression is as follows:

[0080]

[0081] In the formula, Indicates the first Layer at time The output feature vector, This represents the activation function. Indicates the first The convolutional kernel weight tensor of the layer, Indicates the expansion rate One-dimensional convolution operation, Indicates the first The bias vector of the layer.

[0082] It should be noted that, considering the nonlinear hysteresis characteristics of the concentric tube robot caused by material compliance, inter-tube friction, and torsional effects, this embodiment employs a temporal convolutional network (TCN) to model the joint motion state sequence. This network utilizes a one-dimensional dilated causal convolution structure, employing asymmetric zero-padding to ensure that the prediction at time t depends only on current and past input information, avoiding the leakage of future information and thus guaranteeing temporal causality. By introducing an interval-sampling dilated convolution mechanism, TCN can exponentially expand the receptive field without increasing the number of parameters or network depth, thereby efficiently capturing the dynamic correlations and macroscopic patterns of hysteresis loops over long time spans in the joint sequence.

[0083] The feature vector output by the temporal convolutional network is input into the first layer of the long short-term memory network to encode the angle changes in the feature vector and generate an intermediate state feature vector. The intermediate state feature vector is then input into the second layer of the long short-term memory network to generate an intermediate state feature vector containing long-term lag characteristics. The intermediate state feature vector containing long-term lag characteristics is then flattened to obtain the temporal state feature vector, the expression of which is as follows:

[0084]

[0085]

[0086]

[0087] It should be noted that, in order to further explore the micro-dynamic evolution patterns in the features extracted by TCN, this embodiment constructs a two-layer Long Short-Term Memory (LSTM) network. The first layer of LSTM receives the long-range dependent time window feature sequence output by TCN. The first layer focuses on encoding the joint angle changes at each time step in the input sequence to extract short-term dynamic features. The second layer LSTM further learns higher-level temporal dependency features based on this. Finally, through the Flatten operation, the comprehensive dynamic encoding information in the time dimension is transformed into a temporal state feature vector in the spatial dimension. , It contains all the spatiotemporal context information sufficient to determine the equivalent rotation matrix in the subsequent physical model.

[0088] In this embodiment, the concentric tube robot includes a coaxially nested outer tube and an inner tube; using the temporal state feature vector as a conditional input, and guided by a physical information neural network based on Cosserat rod theory, the continuous spatial morphology of the concentric tube robot along the arc length direction is modeled through physical constraints including torque balance conditions and geometric compatibility conditions, and the robot's end-effector pose is predicted, including:

[0089] The temporal state feature vector is processed through a fully connected layer. The position of the concentric tube robot's centerline in the global coordinate system, the orientation of the corresponding cross section, and the strain vector composed of curvature and torsion, which is mapped to the sampling s along the arc length, are expressed as follows:

[0090]

[0091] in, This represents any sampling position of the concentric tube robot within its arc length interval; The parameter is The nonlinear implicit mapping function constructed by the physical information neural network; This indicates the network's prediction in arc length. The centerline position vector at that location; This indicates the network's prediction in arc length. The rotation matrix of the cross section at that location; This indicates the network's prediction in arc length. The strain vector at that point.

[0092] In this embodiment, a physical information neural network based on Cosserat rod theory is used to model the continuous spatial morphology of the concentric tube robot along the arc length direction, guided by physical constraints including torque balance and geometric compatibility conditions. This includes:

[0093] Using a physical information neural network based on Cosserat rod theory, guided by physical constraints including torque balance and geometric compatibility conditions, the continuous spatial morphology of a concentric tube robot along the arc length direction is modeled, including:

[0094] In the training process of the physical information neural network, the geometric relations, moment balance equations, and constitutive relations of Cosserat theory are used as physical constraints embedded in the loss function. An automatic differentiation mechanism is used to differentiate the network output with respect to the arc length parameter s, and a physical loss function is constructed under the non-shearing assumption. It satisfies the following relationship:

[0095]

[0096]

[0097]

[0098]

[0099] in, and This represents the geometrically consistent positional and rotational errors distributed along the arc length s. Indicates the torque balance error. This represents the residual function, which includes the moment equilibrium equations and the material constitutive equations, constructed based on Cosserat theory. This represents the expectation of the arc length parameter s within the arc length interval of the robot. This represents the axial unit vector in the local coordinate system of the cross section.

[0100] It should be noted that this embodiment introduces a physical information neural network, transforming the black-box characteristics of the neural network into parameters with explicit physical meaning, thus achieving a deep integration of data-driven approaches and mechanistic models. During training, the geometric relationships of Cosserat, the moment balance equations, and the constitutive relations are directly embedded into the loss function. An automatic differentiation mechanism is used to differentiate the network output with respect to the arc length parameter s, avoiding the explicit solution of the relative torsion angle differential equation in traditional methods.

[0101] In this embodiment, the total arc length L of the concentric tube robot is substituted into the implicit function expression constructed by the physical information neural network. Obtain the end effector pose predicted by the network and calculate the data error function between it and the true end effector pose. :

[0102]

[0103] in, The number of samples in the training data. This is the CTR end position output by the 5-DOF NDI electromagnetic tracker. This represents the pose of the output terminal of the physical information neural network;

[0104] Based on the physical characteristics of the fixed base of the concentric tube robot, boundary condition constraints on position and orientation are introduced, and a boundary condition error function is constructed. :

[0105]

[0106] in, and These are the boundary conditions for the base position and attitude, respectively. It is the identity matrix;

[0107] According to the physical loss function Data error function and boundary condition error function Construct the total loss function of the physical information neural network :

[0108]

[0109] in, , and These are the weighting coefficients for physical loss, boundary condition loss, and data loss, respectively.

[0110] It should be noted that, through the above approach, the proposed method achieves high-precision prediction of CTR morphology and end-effector pose relying solely on joint angle sequences and end-effector pose observations. This method avoids the high computational overhead of numerical integration and shooting methods in traditional Cosserat models, while achieving a balance between physical consistency and data-driven modeling by utilizing a physical information neural network, significantly improving the model's generalization ability and stability in real-world systems.

[0111] To achieve efficient closed-loop control, an inverse kinematics network model pre-constructed using the aforementioned method is introduced. In each control cycle, the network adjusts the target trajectory accordingly. Quickly generate a set of reference joint sequences that satisfy geometric constraints. This provides a high-quality initial solution (WarmStart) for subsequent Model Predictive Control (MPC), preventing the optimization from getting trapped in local minima.

[0112] In this embodiment, before constructing the optimization objective function that includes tracking error, the method further includes:

[0113] At the current control moment Based on the given target end trajectory Select length as N In the prediction time domain, construct the end pose sequence to be tracked;

[0114] Using pre-built inverse kinematics network models The end-effector pose sequence to be tracked is mapped to a reference joint sequence. Its expression is as follows:

[0115]

[0116] in, Indicates the prediction of the first time domain The target end pose at any given time.

[0117] In this embodiment, the expression for the optimization objective function that includes tracking error is as follows:

[0118]

[0119] in, Indicates the first The amount of joint control at any given moment. This represents the model error term after correction using sensor feedback at the current moment. The weight matrix represents the end-effector pose tracking error. The weight matrix represents the joint reference trajectory tracking error. The weight matrix representing the rate of change of joint control quantities. and Indicates the adjustment parameter. This indicates the amount of joint control at the previous moment. This is a pre-constructed positive kinematic network.

[0120] In this embodiment, the physical constraints include joint amplitude constraints and joint rate of change constraints, which satisfy the following relationship:

[0121]

[0122]

[0123] in, and These represent the minimum and maximum values ​​of the joint actuation force of the concentric tube robot, respectively. This indicates the maximum permissible variation in joint drive quantity between adjacent control moments.

[0124] It should be noted that the optimization objective function in this embodiment consists of three parts: the first term is the end-effector pose tracking error, which includes an error correction term. , and The end-effector pose obtained from the NDI electromagnetic tracker at the actual CTR end-effector and the CTR joint angle obtained from the motor encoder are measured in real time. Real-time feedback from the sensors at the current moment is used to compensate for the model prediction online, eliminating steady-state errors. The second constraint optimization solution does not deviate from the reference trajectory provided by the inverse kinematics network. The first condition ensures the rationality of the understanding; the second condition limits the rate of change of the control variable to ensure smooth motion. Simultaneously, the optimization process strictly adheres to physical constraints, including the maximum change in a single step corresponding to the joint's travel limits and the motor's speed limits. By solving this quadratic programming problem within each control cycle and executing only the first optimal control increment, robust rolling time-domain control is achieved.

[0125] Figure 2This is a graph showing the change in the reciprocating motion angle of the fourth joint of the robot provided in an embodiment of the present invention. Figure 2 It can be observed that due to the material compliance and internal friction of the concentric tube robot, the system exhibits significant hysteresis characteristics, that is, the same joint angle value corresponds to different end poses in different motion paths or historical states (such as different stages of reciprocating motion) (which is manifested as non-overlapping trajectories in the spatial diagram).

[0126] Figure 3 This diagram illustrates the comparative experimental results of the present invention and the traditional LSTM network model in capturing hysteresis characteristics in forward kinematics prediction tasks, as provided in an embodiment of the present invention. Figure 3 The diagram illustrates the end-effector spatial pose trajectory corresponding to the joint motion sequence. The black curve represents the actual end-effector trajectory of the concentric tube robot, the red curve represents the predicted trajectory of this invention, and the orange curve represents the predicted trajectory of the traditional LSTM model. The comparison shows that the orange curve (LSTM) fails to effectively capture the pose difference caused by different paths, deviating significantly from the actual trajectory. In contrast, the red curve (this invention) highly overlaps with the black actual trajectory, accurately reproducing the shape of the hysteresis loop. This demonstrates that, compared to a single LSTM network, this invention can more effectively extract long- and short-term historical features, thereby accurately capturing the nonlinear physical hysteresis phenomenon of the concentric tube robot.

[0127] Figure 4 This is a schematic diagram showing the distribution of workspace data for a concentric tube robot collected using an NDI electromagnetic sensor and a motor encoder in an embodiment of the present invention. Figure 4 As shown in the figure, the dense 3D point cloud set intuitively demonstrates the reachable workspace range of the concentric tube robot's end effector in the Cartesian coordinate system. During the construction of the neural network training dataset, the system drives the concentric tube robot to traverse diverse joint motion paths, uses a high-precision NDI electromagnetic tracker to calibrate and record its end-effector pose in real time, and simultaneously collects the joint angle sequence fed back by the motor encoder, thereby obtaining a large number of experimental samples containing the correspondence between joint state sequences and end-effector poses. These measured data covering a wide working area constitute the basis for training the physical information neural network model of this invention, providing complete data support for the model to learn the complex nonlinear kinematic mapping and hysteresis characteristics of the concentric tube robot.

[0128] Example 3

[0129] like Figure 5 As shown, this embodiment proposes a concentric tube robot control device, which is applied to the concentric tube robot control method described in the above embodiment, including: an acquisition module 100, an extraction module 200, a prediction module 300, and a control module 400.

[0130] The acquisition module 100 is used to acquire the joint motion state sequence of the concentric tube robot, which includes joint motion data within the current time and historical time windows. The extraction module 200 is used to input the joint motion state sequence into a preset temporal neural network model for feature extraction and output a temporal state feature vector containing physical lag characteristics. The prediction module 300 is used to take the temporal state feature vector as a conditional input and, under the guidance of physical constraints including torque balance conditions and geometric coordination conditions, model the continuous spatial shape of the concentric tube robot along the arc length direction through a physical information neural network based on Cosserat rod theory, and predict the robot's end-effector pose. The control module 400 is used to construct an optimization objective function including tracking error based on the given target trajectory and the end-effector pose, solve the optimization objective function under the condition of satisfying physical constraints, obtain the optimal joint drive command, and control the movement of the concentric tube robot.

[0131] It should be noted that the foregoing explanation of the concentric tube robot control method embodiment also applies to the concentric tube robot control device of this embodiment, and will not be repeated here.

[0132] Example 4

[0133] Figure 6 This is a schematic diagram of the structure of the electronic device 500 provided in this embodiment. The electronic device 500 includes: a memory 501, a processor 502, and a computer program stored in the memory 501 and executable on the processor 502.

[0134] When the processor 502 executes the program, it implements the concentric tube robot control method provided in the above embodiments.

[0135] Furthermore, the electronic device 500 also includes a communication interface 503 for communication between the memory 501 and the processor 502.

[0136] The memory 501 may include high-speed RAM (Random Access Memory) and may also include non-volatile memory, such as at least one disk storage device.

[0137] If the memory 501, processor 502, and communication interface 503 are implemented independently, then the communication interface 503, memory 501, and processor 502 can be interconnected via a bus to complete communication between them. The bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus, or an EISA (Extended Industry Standard Architecture) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0138] Optionally, in a specific implementation, if the memory 501, processor 502, and communication interface 503 are integrated on a single chip, then the memory 501, processor 502, and communication interface 503 can communicate with each other through an internal interface.

[0139] Processor 502 may be a CPU (Central Processing Unit), an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement embodiments of the present invention.

[0140] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described concentric tube robot control method.

[0141] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0142] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0143] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more N executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of the invention pertain.

[0144] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any of the following techniques known in the art, or a combination thereof: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (FPGAs), field-programmable gate arrays (FPGAs), etc.

[0145] Those skilled in the art will understand that all or part of the steps of the methods described in the above embodiments can be implemented by a program instructing related hardware, and the program can be stored in a computer-readable storage medium. When executed, the program includes one or a combination of the steps of the method embodiments.

[0146] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A control method for a concentric tube robot, characterized in that, include: Obtain the joint motion state sequence of the concentric tube robot, wherein the joint motion state sequence includes joint motion data at the current moment and within the historical time window; The joint motion state sequence is input into a pre-defined temporal neural network model, including a temporal convolutional network and a long short-term memory network, for feature extraction. The output is a temporal state feature vector containing physical lag characteristics, including: The joint motion state sequence is preprocessed using an asymmetric zero-padding method, and the processed sequence is then input into the temporal convolutional network. The layer uses dilated convolution to extract feature vectors, and its expression is as follows: In the formula, Indicates the first Layer at time The output feature vector, This represents the activation function. Indicates the first The convolutional kernel weight tensor of the layer, Indicates the expansion rate One-dimensional convolution operation, Indicates the first Layer bias vector; The feature vector output by the temporal convolutional network is input into the first layer of the long short-term memory network to encode the angle changes in the feature vector and generate an intermediate state feature vector. The intermediate state feature vector is then input into the second layer of the long short-term memory network to generate an intermediate state feature vector containing long-term lag characteristics. The intermediate state feature vector containing long-term lag characteristics is then flattened to obtain the temporal state feature vector, the expression of which is as follows: in, , This represents the feature sequence output by a temporal convolutional network. and These represent the operational functions of the first and second layers of the Long Short-Term Memory network, respectively. This represents the intermediate state feature vector output by the first layer of the Long Short-Term Memory network. This represents the state feature vector output by the second-layer Long Short-Term Memory network, which includes non-linear coupling behavior. Indicates the flattening operation. This represents the temporal state feature vector; Using the temporal state feature vector as conditional input, and guided by physical information neural networks based on Cosserat rod theory, the continuous spatial morphology of the concentric tube robot along the arc length direction is modeled through physical constraints including torque balance and geometric compatibility conditions, and the robot's end-effector pose is predicted, including: The temporal state feature vector is processed through a fully connected layer. The position of the concentric tube robot's centerline in the global coordinate system, the orientation of the corresponding cross section, and the strain vector composed of curvature and torsion, which is mapped to the sampling s along the arc length, are expressed as follows: in, This represents any sampling position of the concentric tube robot within its arc length interval; The parameter is The nonlinear implicit mapping function constructed by the physical information neural network; This indicates the network's prediction in arc length. The centerline position vector at that location; This indicates the network's prediction in arc length. The rotation matrix of the cross section at that location; This indicates the network's prediction in arc length. The strain vector at the point; Based on the given target trajectory and the end-effector pose, an optimization objective function including tracking error is constructed. Under the condition of satisfying physical constraints, the optimization objective function is solved to obtain the optimal joint drive command and control the movement of the concentric tube robot.

2. The concentric tube robot control method according to claim 1, characterized in that, Using a physical information neural network based on Cosserat rod theory, guided by physical constraints including torque balance and geometric compatibility conditions, the continuous spatial morphology of a concentric tube robot along the arc length direction is modeled, including: In the training process of the physical information neural network, the geometric relations, moment balance equations, and constitutive relations of Cosserat theory are used as physical constraints embedded in the loss function. An automatic differentiation mechanism is used to differentiate the network output with respect to the arc length parameter s, and a physical loss function is constructed under the non-shearing assumption. It satisfies the following relationship: in, and This represents the geometrically consistent positional and rotational errors distributed along the arc length s. Indicates the torque balance error. This represents the residual function, which includes the moment equilibrium equations and the material constitutive equations, constructed based on Cosserat theory. This represents the expectation of the arc length parameter s within the arc length interval of the robot. Represents the axial unit vector in the local coordinate system of the cross section; Substituting the total arc length L of the concentric tube robot into the implicit function expression constructed by the physical information neural network... Obtain the end effector pose predicted by the network and calculate the data error function between it and the true end effector pose. : in, The number of samples in the training data. The actual end-effector pose of the concentric tube robot is output by the electromagnetic tracker. This represents the pose of the output terminal of the physical information neural network; Based on the physical characteristics of the fixed base of the concentric tube robot, boundary condition constraints on position and orientation are introduced, and a boundary condition error function is constructed. : in, and These are the boundary conditions for the base position and attitude, respectively. It is the identity matrix; According to the physical loss function Data error function and boundary condition error function Construct the total loss function of the physical information neural network : in, , and These are the weighting coefficients for physical loss, boundary condition loss, and data loss, respectively.

3. The concentric tube robot control method according to claim 2, characterized in that, Before constructing the optimization objective function that includes tracking error, the method further includes: At the current control moment Based on the given target end trajectory Select length as N In the prediction time domain, construct the end pose sequence to be tracked; Using pre-built inverse kinematics network models The end-effector pose sequence to be tracked is mapped to a reference joint sequence. Its expression is as follows: in, Indicates the prediction of the first time domain The target end pose at any given time.

4. The concentric tube robot control method according to claim 3, characterized in that, The expression for the optimization objective function, which includes tracking error, is as follows: in, Indicates the first The amount of joint control at any given moment. This represents the model error term after correction using sensor feedback at the current moment. The weight matrix represents the end-effector pose tracking error. The weight matrix represents the joint reference trajectory tracking error. The weight matrix representing the rate of change of joint control quantities. and Indicates the adjustment parameter. This indicates the amount of joint control at the previous moment. This is a pre-constructed positive kinematic network.

5. The concentric tube robot control method according to claim 4, characterized in that, The physical constraints include joint amplitude constraints and joint rate of change constraints, which satisfy the following relationship: in, and These represent the minimum and maximum values ​​of the joint actuation force of the concentric tube robot, respectively. This indicates the maximum permissible variation in joint drive quantity between adjacent control moments.

6. A concentric tube robot control device, applied to the concentric tube robot control method as described in any one of claims 1 to 5, characterized in that, include: The acquisition module is used to acquire the joint motion state sequence of the concentric tube robot, which includes joint motion data at the current moment and within the historical time window. The extraction module is used to input the joint motion state sequence into a preset temporal neural network model for feature extraction and output a temporal state feature vector containing physical lag characteristics. The prediction module is used to take the temporal state feature vector as a conditional input, and through a physical information neural network based on Cosserat rod theory, under the guidance of physical constraints including torque balance conditions and geometric compatibility conditions, to model the continuous spatial morphology of the concentric tube robot along the arc length direction and predict the robot's end pose. The control module is used to construct an optimized objective function including tracking error based on the given target trajectory and the end-effector pose, solve the optimized objective function under the condition of satisfying physical constraints, obtain the optimal joint drive command, and control the movement of the concentric tube robot.

7. 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, wherein the processor executes the computer program to perform the operations performed by the concentric tube robot control method as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that is executed by a processor as described in any one of claims 1 to 5, using the concentric tube robot control method.

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