Joint torque coordination optimization and trajectory tracking control method for surgical robot arms

Abstract

This invention belongs to the field of medical technology and discloses a method for collaborative optimization of joint torque and trajectory tracking control of surgical robot arms. Through biomechanical-multibody dynamics coupled modeling, it dynamically correlates tissue viscoelastic properties with joint torque, forming a "mechanics-damage" dual constraint mechanism. A memory-enhanced controller introduces a damage warning factor, adjusting torque output in real time during instrument-tissue interaction to avoid traction damage caused by excessive load on a single joint. Simultaneously, a digital twin system predicts potential risks in advance, reducing the threat of surgical operations to fragile tissues throughout the entire process from modeling and control to verification, providing safety assurance for operations in delicate surgical areas. Through phased dynamic weight optimization, it achieves adaptive adjustment of targets at different surgical stages. A multimodal sensor fusion architecture, combining flexible sensing and imaging data, improves the perception accuracy of complex tissue environments.

Description

Technical Field

[0001] This invention belongs to the field of medical technology, specifically a method for optimizing joint torque and tracking trajectory of a surgical robot arm. Background Technology

[0002] Joint control of surgical robot arms is a core area at the intersection of minimally invasive surgery and intelligent equipment. It focuses on torque coordination and trajectory precision control under highly dynamic conditions, integrating multibody dynamics, biomechanical sensing, and real-time control technologies. Its core objective is to achieve sub-millimeter-level operational precision and minimize tissue damage, directly impacting surgical safety and efficiency in scenarios such as laparoscopic surgery and robot-assisted tumor resection.

[0003] Existing technologies have three significant limitations: First, torque distribution often adopts a "single-joint independent control" mode, failing to consider the dynamic correlation between inter-joint inertial coupling and soft tissue contact forces, which can easily lead to load imbalance in complex movements. Second, trajectory tracking relies on fixed-parameter controllers, making it difficult to adapt to nonlinear interference caused by differences in tissue viscoelasticity (e.g., the stiffness of liver and adipose tissue differs by more than 10 times). Third, sensor fusion often relies on single-modal data (e.g., visual or force feedback), which can easily lead to control deviations due to missing information in scenarios such as bleeding or instrument obstruction. Furthermore, there is a lack of adaptation mechanisms for the dynamic characteristics of different surgical stages in clinical practice, and the same set of control parameters cannot meet the differentiated needs of different stages such as positioning, operation, and withdrawal. Summary of the Invention

[0004] The purpose of this invention is to provide a method for coordinated optimization of joint torque and trajectory tracking control of surgical robot arms, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for coordinated optimization of joint torques and trajectory tracking control of a surgical robot arm, the specific steps of which are as follows:

[0006] S1. Biomechanics-multibody dynamics coupled modeling: Establish a cross-scale model including joint friction and soft tissue viscoelasticity, use fractional derivatives to describe tissue characteristics, correct parameters in real time through fiber optic sensors, embed tissue damage risk into the equation, and provide a collaborative control basis for subsequent optimization with "mechanical-biological" dual constraints;

[0007] S2. Dynamic weight optimization: Based on the visual recognition surgery stage, the positioning, operation and withdrawal stages focus on trajectory accuracy, torque balance and energy consumption respectively. The target weights are dynamically adjusted, the solution space is pruned with the improved NSGA-III algorithm, and the optimized parameters adapted to the scene are output to provide dynamic targets for step S3.

[0008] S3, Memory-enhanced composite control: Based on the optimization target, a control architecture is constructed. The "surgical memory bank" realizes parameter transfer, the sliding surface incorporates damage early warning, and the risk exceeds the limit to amplify and enhance the learning exploration step size, which is both robust and has learning ability, providing real-time strategies for step S4.

[0009] S4. Virtual-Real Interaction Digital Twin: The 5G synchronous robotic arm and tissue data update the model every 10ms, the GPU pre-simulates the trajectory for 100ms to predict risks, and combines the physician's intention to pre-simulate the optimal solution to verify the effectiveness of the control strategy, providing a virtual verification basis for step S5.

[0010] S5, Flexible-Rigid Sensing Fusion: 3D force is measured using a 0.5mm flexible fiber optic sensor, CT density data is fused, Bayesian filtering is used to improve robustness, and MEMS arrays monitor joint health, providing high-precision data for twin models and supporting redundant degree of freedom adjustment;

[0011] S6. Redundant Degrees of Freedom Reconstruction: Based on sensor data, unnecessary degrees of freedom are dynamically frozen, a fault-tolerant library is constructed, and redundant joints compensate for the main joints after they exceed their limits, adapting to complex spaces and providing a flexible operational basis for step S7.

[0012] S7. Clinical Validation: Through three levels of validation—virtual simulation, bionic tissue testing, and clinical trials—physician scoring feedback optimizes parameters, forming a "model-control-validation" process that feeds back into the initial model and optimizes weights.

[0013] Preferably, the specific steps of biomechanics-multibody dynamics coupling modeling in step S1 are as follows:

[0014] S11. Construction of the cross-scale coupling model: To overcome the limitations of traditional robotic arm modeling that only focuses on physical parameters, this step constructs a cross-scale model of "joint friction - soft tissue viscoelasticity - surgical instrument stiffness". A fractional derivative modified Maxwell model is introduced, which, unlike the linear assumption of the integer order model, can accurately capture the nonlinear characteristics of tissue stress relaxation. Through the fiber optic grating sensor implanted at the end of the instrument, tissue stress-strain data are collected in real time, and the model parameters are dynamically corrected every 5ms to ensure that the model is synchronized with the tissue state during surgery, providing a dynamic mechanical basis for torque co-optimization.

[0015] Fractional Maxwell model (biomechanical modeling):

[0016]

[0017] In the formula: Riemann-Liouville fractional derivative operator (order) In this invention, the value is dynamically adjusted according to the type of soft tissue (e.g., α=0.8 for liver, α=0.6 for muscle) to describe nonlinear viscoelastic properties.

[0018] Soft tissue stress (unit: Pa) is collected in real time by a fiber optic grating sensor, reflecting the interaction force between the instrument and the tissue;

[0019] Viscosity coefficient (unit: Pa·s), range 1 -1 Pa s, tissue density estimation based on preoperative CT images;

[0020] Elastic modulus (unit: Pa), calibrated in real time during surgery using force-displacement curves, is approximately 5-15 kPa for liver tissue and approximately 1-3 kPa for adipose tissue;

[0021] Strain (dimensionless);

[0022] Breaking through the linear assumption of traditional integer-order models, it accurately captures the "elastic-viscosity" coupling characteristics of soft tissue during surgery, providing a biomechanical basis for the cross-scale modeling of step 1, and directly supporting the safety constraints of torque co-optimization;

[0023] Source: Based on the extension of rheological theory, the nonlinear viscoelastic behavior of soft tissues is described by fractional derivatives;

[0024] S12. Embedding of biosafety constraints: Based on the Lanczos algorithm, the mapping relationship between joint torque and tissue damage risk is derived, and the cell damage threshold (such as 10% deformation rate) is transformed into a mechanical constraint condition and embedded into the dynamic equation. This design enables the model to simultaneously satisfy mechanical feasibility and biosafety, forming a dual-dimensional control basis of "mechanical motion-biosafety". This provides precise constraint boundaries for the next step of dynamic optimization based on the surgical stage and achieves seamless connection with the multi-objective optimization framework.

[0025] Preferably, the specific steps of dynamic weight optimization in step S2 are as follows:

[0026] S21. Establishment of a phased optimization mechanism: Based on the coupling model in the first step, the interaction status between instruments and tissues is identified in real time through a visual servo system (equipped with YOLOv8 algorithm), and the surgery is divided into three phases: "positioning-operation-withdrawal". The weights of the objective function are dynamically adjusted according to the core requirements of each phase: the positioning phase focuses on trajectory accuracy (weight 0.6), the operation phase emphasizes torque balance (weight 0.5), and the withdrawal phase focuses on energy consumption (weight 0.4), so as to achieve refined optimization for scene adaptation.

[0027] Multi-objective optimization objective function expression:

[0028]

[0029] In the formula: The overall optimization objective (dimensionless) has a smaller value, indicating better performance.

[0030] Time-varying weights (summing to 1), positioning stage Operational phase evacuation phase ;

[0031] The expected and actual end-effector poses (in mm) are obtained through visual servoing.

[0032] No. The actual torque of each joint (unit: Nm);

[0033] Average torque (unit: N·m) reflects the load balance of the joint;

[0034] No. Angular velocity of each joint (unit: rad / s);

[0035] By using time-varying weights, adaptive adjustments can be made during the surgical phase, solving the problem that traditional fixed weights cannot adapt to multiple scenarios.

[0036] Formula source: Weighted summation method in multi-objective optimization, combined with dynamic adjustment of weights during the surgical phase;

[0037] S22. Innovative Improvements to the Optimization Algorithm: When using the improved NSGA-III algorithm, an innovative "elite retention pool" is introduced, retaining only the top 10% of non-dominated solutions and pruning the solution space based on the characteristics of the current surgical stage: during the localization stage, priority is given to retaining trajectory accuracy (|| -x| The top 50% of solutions were selected, and solutions with errors exceeding 0.5mm were discarded; torque balance was maintained during the operation phase. The optimal 60% solution; energy consumption is eliminated during the evacuation phase. The solution exceeds the threshold of 10J. By pruning the solution space dimension through stage feature screening indicators, the decision delay problem caused by solution set redundancy in traditional algorithms is solved. The optimization results provide dynamically updated target parameters for subsequent controller design, forming the starting point of the "model-optimization-control" closed loop, which directly supports the parameter adjustment of the memory-enhanced controller.

[0038] NSGA-III Adaptive Normalization Expression:

[0039]

[0040] In the formula: Normalized One objective function value; Original objective function value; No. The minimum and maximum values ​​of each objective;

[0041] Formula source: Adaptive normalization operation in the NSGA-III algorithm, used for despace compression and optimization.

[0042] Preferably, the specific steps of the memory-enhanced composite control in step S3 are as follows:

[0043] S31. Design of the Experience-Based Learning Architecture: Based on the dynamic optimization objective output in step S2, a "surgical scenario memory bank" is constructed. Typical scenarios are divided according to surgical type (e.g., 10 categories such as laparoscopic cholecystectomy, prostatectomy, etc.). The stored parameter set includes the optimal joint torque range (e.g., 0.1-0.5N) for each scenario. m), sliding surface parameter λ ( The algorithm explores the initial step size using reinforcement learning; it matches the current surgical features using a cosine similarity algorithm (extracting the instrument end pose sequence and tissue stress change rate as feature vectors) to achieve cross-scenario parameter transfer, significantly shortening the controller's initial adjustment cycle, enabling the composite control architecture to have "experience reuse" capabilities, and improving dynamic response efficiency.

[0044] The current surgical features are matched using a cosine similarity algorithm: the feature vector contains 6 parameters (instrument end x / y / z pose, tissue stress value, stress change rate, and surgical stage label);

[0045] Similarity calculation formula:

[0046]

[0047] : Current surgical feature vector, containing 6 parameters (instrument end x / y / z pose, tissue stress value, stress change rate, surgical stage label), a 6×1 column vector;

[0048] : Historical surgical feature vectors in the memory bank, structure and Consistent, derived from parameter sets of 10 typical surgical scenarios (such as laparoscopic cholecystectomy, prostatectomy, etc.).

[0049] When sim≥0.8, the match is considered successful, and the corresponding parameter set in the memory is called to realize cross-scene migration;

[0050] S32. Collaborative Damage Warning and Control: The sliding surface design incorporates a "damage warning factor," which is calculated by comparing the tissue deformation rate with the damage threshold in the first-step model. When the safety threshold is exceeded, the reinforcement learning module is automatically triggered to adjust its emergency mode. The DDPG algorithm's exploration step size is temporarily increased by 3 times from the initial value of 0.01 to 0.03, with the convergence condition being a trajectory tracking error of <0.1mm for 50 consecutive steps, quickly searching for safe control parameters. This mechanism retains the robustness of sliding mode control while also providing dynamic learning capabilities, offering a real-time control strategy for the next step of digital twin pre-simulation.

[0051] The step size is typically used in algorithms. This indicates that it is used to control the randomness of an agent's action selection;

[0052] Value selection rules: Under normal operating conditions 0.01, when the damage risk index

[0053] By expanding the scope of exploration, safety control parameters can be quickly identified;

[0054] Adaptive sliding surface formula:

[0055]

[0056] In the formula: The sliding surface variable (dimensionless) approaches 0, indicating that the system is stable.

[0057] Tracking error (unit: mm) ;

[0058] Sliding surface parameters (unit: s⁻¹, value: 0.5-2) suppress steady-state error;

[0059] Damage warning factor ( (Indicates the threshold for triggering damage);

[0060] Tissue deformation rate (unit: %);

[0061] By directly embedding the damage risk into the core equation of sliding mode control, the controller in step S3 has the dynamic adjustment capability of "safety first", which is different from the traditional sliding surface design that only focuses on error.

[0062] Formula source: Sliding mode control theory combined with tissue damage early warning mechanism to improve robustness.

[0063] Preferably, the specific steps of the virtual-real interactive digital twin in step S4 are as follows:

[0064] S41. Intraoperative real-time twin model construction: To verify the effectiveness of the control strategy in step S3, the robotic arm motion data and tissue deformation images scanned by 3D structured light were transmitted through 5G slicing technology. The boundary conditions of the twin model were updated synchronously every 10ms to ensure that the virtual scene was highly consistent with the real surgical environment. Multibody dynamics simulation was accelerated by GPU parallel computing to realize the pre-play of the trajectory in the next 100ms under the current control parameters.

[0065] Newton-Euler dynamic equations (digital twin optimization):

[0066]

[0067] In the formula: Joint torque vector (unit: N·m);

[0068] Inertia matrix (unit: kg·m) ;

[0069] Coriolis force and centrifugal force matrix;

[0070] Gravity vector (unit: N);

[0071] Jacobian matrix (unit: m / rad);

[0072] External force on the end effector (unit: N);

[0073] Source: Fundamental equations of multibody dynamics, used for robotic arm dynamics simulation;

[0074] S42. Risk Prediction and Parameter Feedback: An LSTM network trained on force feedback signals is used to identify physician operational intentions (such as pushing, pulling, and rotating). The network contains three hidden layers (64 neurons per layer), with ReLU as the activation function. The training data consists of 5,000 sets of physician operation force feedback signals (sampling frequency 1 kHz), covering the optimal torque allocation scheme for the corresponding actions in a twin space for six operation types. This process forms a closed loop of "real-time control - virtual pre-playback - parameter correction". It uses the control strategy of the third step as input and feeds back the controller parameter optimization through the pre-playback results, providing a virtual verification basis for the next step of multimodal sensor fusion.

[0075] Preferably, the specific steps of flexible-rigid sensing fusion in step S5 are as follows:

[0076] S51. Sensing architecture adapted to minimally invasive scenarios: To provide high-precision data for the digital twin model in step S4, a multimodal sensing system is designed: A flexible fiber optic grating sensor with a diameter of 0.5mm is implanted at the end of the instrument to realize the three-dimensional distribution measurement of tissue contact force (resolution 0.01N), solving the problem of excessive size of traditional sensors; tissue density data of intraoperative CT images are acquired simultaneously, and force-image data fusion is achieved through Bayesian filtering;

[0077] Bayesian filter fusion estimation expression:

[0078]

[0079] In the formula:

[0080] The observation sequence from time 1 to k, i.e. The collection includes fiber optic force sensor data (unit: N) and CT image density values ​​(unit: HU).

[0081] The historical observation sequence up to time k-1 is used for recursive updates of Bayesian filtering to achieve temporal fusion of multimodal data;

[0082] State variables (such as tissue density, contact force);

[0083] Sensor observations (unit: N or HU);

[0084] Normalization constant;

[0085] Likelihood function;

[0086] State transition probability;

[0087] Formula source: Bayesian filtering in probabilistic robotics, used for multimodal data fusion;

[0088] S52. Complementary Verification of Multi-Source Information: Two-channel micro-MEMS accelerometers (axial + radial, 8 channels in total) are deployed at each joint. Empirical Mode Decomposition (EMD) is used to extract the IMF components of the vibration signal. When the amplitude of the high-frequency component is >0.5g, it is considered a joint anomaly, and the joint wear state is inverted, adding mechanical health constraints for torque optimization. This sensing system not only provides real-time raw data for the digital twin but also improves measurement robustness through complementary multi-source information, providing a precise state perception foundation for the next step of adaptive reconstruction of redundant degrees of freedom.

[0089] The IMF components of the vibration signal were extracted by Empirical Mode Decomposition (EMD). The relationship between the amplitude of the high-frequency components and the degree of wear was as follows: 0-0.5g (normal), 0.5-1g (slight wear, when the torque is optimized, the load of the joint is limited to ≤70% of the safety threshold), and >1g (severe wear, triggering redundant joint compensation).

[0090] Preferably, the specific steps for reconstructing redundant degrees of freedom in step S6 are as follows:

[0091] S61, Dynamic Dimension Adaptation Mechanism: Based on the sensor data feedback in step S5, a redundancy utilization strategy is designed for the 7-DOF robotic arm: When the surgical space is detected to be limited, such as a narrow abdominal cavity, the high-dimensional space is projected to the low-dimensional subspace through affine transformation, and unnecessary degrees of freedom are frozen, such as fixing two rotational joints during straight suturing, to simplify the control complexity.

[0092] S62. Deployment of fault-tolerant compensation scheme: Construct a "fault-tolerant trajectory library" to store compensation motion schemes for different joint over-limit scenarios: When the torque of the main operating joint exceeds the safety threshold of 80%, the redundant joint compensation trajectory is calculated in real time based on the pseudo-inverse Jacobian matrix, and the load is shared through coordinated motion; This mechanism not only uses sensor data to achieve accurate judgment, but also improves the adaptability to complex scenarios, providing a flexible operation basis for final clinical validation.

[0093] Jacobi's pseudo-reversal:

[0094]

[0095] In the formula: The pseudo-inverse of the Jacobian matrix (unit: rad / m); Jacobian matrix (unit: m / rad);

[0096] Source: Pseudo-inverse method in robot kinematics, used for redundant degree of freedom control.

[0097] Preferably, the specific steps of clinical validation in step S7 are as follows:

[0098] S71. Construction of a three-tiered verification chain: To ensure the clinical applicability of the first six steps, a "virtual-physical-clinical" verification system is established: The virtual layer completes 100 standardized surgical simulations (including 50 emergency scenarios) in a digital twin system; the physical layer uses a bio-3D printed biomimetic tissue model to conduct 1,000 repeated operation tests to verify the stability of sensing and control.

[0099] S72. Closed-loop iteration of clinical feedback: The clinical level collaborates with tertiary hospitals to conduct phased trials. First, parameters are optimized through animal experiments, and then they are put into clinical use. Subjective ratings by physicians (1-10 points) are introduced to evaluate the operation effect. The verification results form a process of "control parameters - operation experience - clinical effect", which feeds back to the first step of model correction and the second step of weight optimization, and finally realizes the clinical implementation of the technical solution.

[0100] The beneficial effects of this invention are as follows:

[0101] 1. This invention uses biomechanics-multibody dynamics coupled modeling to dynamically correlate tissue viscoelastic properties with joint torque, forming a "mechanics-damage" dual constraint mechanism; the memory-enhanced controller introduces a damage warning factor, which adjusts the torque output in real time when the instrument interacts with the tissue, avoiding traction damage caused by excessive load on a single joint; at the same time, the digital twin system predicts potential risks in advance, reducing the threat of surgical operations to fragile tissues throughout the entire chain from modeling, control to verification, and providing safety assurance for operations in delicate surgical areas (such as the Calot's Triangle and the prostate capsule).

[0102] 2. This invention achieves adaptive adjustment of targets at different surgical stages (positioning, operation, and withdrawal) through phased dynamic weight optimization; the multimodal sensor fusion architecture, combined with flexible sensing and image data, improves the perception accuracy of complex tissue environments; the redundant degrees of freedom adaptive reconstruction mechanism can flexibly adjust the motion dimension according to surgical space constraints, avoiding trajectory deviations caused by limited operating space; this collaborative mechanism of "perception-decision-execution" enables the system to maintain stable operational performance in variable surgical environments.

[0103] 3. This invention constructs a three-level verification system of "virtual-physical-clinical" and uses digital twin pre-simulation to identify control parameter defects in advance, reducing adjustment costs in actual operation; the memory-enhanced control strategy uses a scene memory library to achieve parameter migration across surgical types, reducing the need for repeated debugging; the redundant joint fault-tolerant mechanism quickly initiates compensatory movement when the main joint is abnormal, avoiding system shutdown; the optimization and fault-tolerant design of the entire link comprehensively improves the continuous and stable operation capability of the system from parameter optimization to emergency response, reducing the risk of surgical interruption. Attached Figure Description

[0104] Figure 1 This is a flowchart of the surgical robot arm joint torque collaborative optimization and trajectory tracking control method of the present invention. Detailed Implementation

[0105] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0106] like Figure 1 As shown in the figure, this invention provides a method for joint torque coordination optimization and trajectory tracking control of a surgical robot arm. The specific steps of this method are as follows:

[0107] S1. Biomechanics-multibody dynamics coupled modeling: Establish a cross-scale model including joint friction and soft tissue viscoelasticity, use fractional derivatives to describe tissue characteristics, correct parameters in real time through fiber optic sensors, embed tissue damage risk into the equation, and provide a collaborative control basis for subsequent optimization with "mechanical-biological" dual constraints;

[0108] S2. Dynamic weight optimization: Based on the visual recognition surgery stage, the positioning, operation and withdrawal stages focus on trajectory accuracy, torque balance and energy consumption respectively. The target weights are dynamically adjusted, the solution space is pruned with the improved NSGA-III algorithm, and the optimized parameters adapted to the scene are output to provide dynamic targets for step S3.

[0109] S3, Memory-enhanced composite control: Based on the optimization target, a control architecture is constructed. The "surgical memory bank" realizes parameter transfer, the sliding surface incorporates damage early warning, and the risk exceeds the limit to amplify and enhance the learning exploration step size, which is both robust and has learning ability, providing real-time strategies for step S4.

[0110] S4. Virtual-Real Interaction Digital Twin: The 5G synchronous robotic arm and tissue data update the model every 10ms, the GPU pre-simulates the trajectory for 100ms to predict risks, and combines the physician's intention to pre-simulate the optimal solution to verify the effectiveness of the control strategy, providing a virtual verification basis for step S5.

[0111] S5, Flexible-Rigid Sensing Fusion: 3D force is measured using a 0.5mm flexible fiber optic sensor, CT density data is fused, Bayesian filtering is used to improve robustness, and MEMS arrays monitor joint health, providing high-precision data for twin models and supporting redundant degree of freedom adjustment;

[0112] S6. Redundant Degrees of Freedom Reconstruction: Based on sensor data, unnecessary degrees of freedom are dynamically frozen, a fault-tolerant library is constructed, and redundant joints compensate for the main joints after they exceed their limits, adapting to complex spaces and providing a flexible operational basis for step S7.

[0113] S7. Clinical Validation: Through three levels of validation—virtual simulation, bionic tissue testing, and clinical trials—physician scoring feedback optimizes parameters, forming a "model-control-validation" process that feeds back into the initial model and optimizes weights.

[0114] Multi-dimensional technological advancements are achieved through multiple mechanisms: In terms of surgical safety, biomechanical-multibody dynamics coupling modeling dynamically correlates tissue viscoelasticity and joint torque to form a "mechanics-damage" dual constraint. A memory-enhanced controller introduces damage warning factors to adjust torque output in real time, and combined with a digital twin system, risks are predicted in advance, reducing the threat to fragile tissues throughout the entire process and providing protection for delicate surgical areas. In terms of environmental adaptability, phased dynamic weight optimization enables adaptive adjustment of targets at different surgical stages. Multimodal sensor fusion improves the accuracy of perception of complex tissue environments, and a redundant degree-of-freedom adaptive reconstruction mechanism flexibly responds to spatial constraints, forming a "perception-decision-execution" collaborative mechanism to maintain stable operational performance. In terms of system reliability, a three-level "virtual-physical-clinical" verification system reduces the cost of actual operational adjustments. A memory-enhanced control strategy uses a scene memory library to achieve parameter migration. A redundant joint fault-tolerant mechanism initiates compensatory motion when the main joint is abnormal. End-to-end optimization and fault-tolerant design improve the system's continuous and stable operation capability and reduce the risk of surgical interruption.

[0115] The specific steps of biomechanics-multibody dynamics coupling modeling in step S1 are as follows:

[0116] S11. Construction of the cross-scale coupling model: To overcome the limitations of traditional robotic arm modeling that only focuses on physical parameters, this step constructs a cross-scale model of "joint friction - soft tissue viscoelasticity - surgical instrument stiffness". A fractional derivative modified Maxwell model is introduced, which, unlike the linear assumption of the integer order model, can accurately capture the nonlinear characteristics of tissue stress relaxation. Through the fiber optic grating sensor implanted at the end of the instrument, tissue stress-strain data are collected in real time, and the model parameters are dynamically corrected every 5ms to ensure that the model is synchronized with the tissue state during surgery, providing a dynamic mechanical basis for torque co-optimization.

[0117] Fractional Maxwell model (biomechanical modeling):

[0118]

[0119] In the formula: Riemann-Liouville fractional derivative operator (order) In this invention, the value is dynamically adjusted according to the type of soft tissue (e.g., α=0.8 for liver, α=0.6 for muscle) to describe nonlinear viscoelastic properties.

[0120] Soft tissue stress (unit: Pa) is collected in real time by a fiber optic grating sensor, reflecting the interaction force between the instrument and the tissue;

[0121] Viscosity coefficient (unit: Pa·s), range 1 -1 Pa s, tissue density estimation based on preoperative CT images;

[0122] Elastic modulus (unit: Pa), calibrated in real time during surgery using force-displacement curves, is approximately 5-15 kPa for liver tissue and approximately 1-3 kPa for adipose tissue;

[0123] Strain (dimensionless);

[0124] During the operation, the tissue type was initially determined by the tissue density threshold of CT images (such as HU value of 50-70 for liver and HU value of 30-50 for muscle), and the α value was dynamically corrected by combining the slope of the stress-strain curve acquired by the fiber optic sensor (>8kPa / mm for liver and <5kPa / mm for muscle).

[0125] Breaking through the linear assumption of traditional integer-order models, it accurately captures the "elastic-viscosity" coupling characteristics of soft tissue during surgery, providing a biomechanical basis for the cross-scale modeling of step 1, and directly supporting the safety constraints of torque co-optimization;

[0126] S12. Embedding of biosafety constraints: Based on the Lanczos algorithm, the mapping relationship between joint torque and tissue damage risk is derived, and the cell damage threshold (such as 10% deformation rate) is transformed into a mechanical constraint condition and embedded into the dynamic equation. This design enables the model to simultaneously satisfy mechanical feasibility and biosafety, forming a dual-dimensional control basis of "mechanical motion-biosafety". This provides precise constraint boundaries for the next step of dynamic optimization based on the surgical stage and achieves seamless connection with the multi-objective optimization framework.

[0127] The specific steps of dynamic weight optimization in step S2 are as follows:

[0128] S21. Establishment of a phased optimization mechanism: Based on the coupling model in the first step, the interaction status between instruments and tissues is identified in real time through a visual servo system (equipped with YOLOv8 algorithm), and the surgery is divided into three phases: "positioning-operation-withdrawal". The weights of the objective function are dynamically adjusted according to the core requirements of each phase: the positioning phase focuses on trajectory accuracy (weight 0.6), the operation phase emphasizes torque balance (weight 0.5), and the withdrawal phase focuses on energy consumption (weight 0.4), so as to achieve refined optimization for scene adaptation.

[0129] Multi-objective optimization objective function expression:

[0130]

[0131] In the formula: The overall optimization objective (dimensionless) has a smaller value, indicating better performance.

[0132] Time-varying weights (summing to 1), positioning stage Operational phase evacuation phase ;

[0133] The expected and actual end-effector poses (in mm) are obtained through visual servoing.

[0134] No. The actual torque of each joint (unit: Nm);

[0135] Average torque (unit: N·m) reflects the load balance of the joint;

[0136] No. Angular velocity of each joint (unit: rad / s);

[0137] By using time-varying weights, adaptive adjustments can be made during the surgical phase, solving the problem that traditional fixed weights cannot adapt to multiple scenarios.

[0138] S22. Innovative improvements to the optimization algorithm: When using the improved NSGA-III algorithm, an "elite retention pool" is innovatively introduced, which retains only the top 10% of non-dominated solutions and prunes the solution space based on the characteristics of the current surgical stage. This solves the decision delay problem caused by redundancy in the solution set of traditional algorithms. The optimization results provide dynamically updated target parameters for subsequent controller design, forming the starting point of the "model-optimization-control" closed loop, which directly supports the parameter adjustment of the memory-enhanced controller.

[0139] NSGA-III Adaptive Normalization Expression:

[0140]

[0141] In the formula: Normalized One objective function value; Original objective function value; No. The minimum and maximum values ​​of each objective;

[0142] The specific steps of memory-enhanced composite control in step S3 are as follows:

[0143] S31. Design of the experience learning architecture: Based on the dynamic optimization target output in step S2, a "surgical scenario memory bank" is constructed to store the optimal control parameter set for typical surgical scenarios; the current surgical features are matched through the cosine similarity algorithm to realize cross-scenario parameter transfer, which greatly shortens the initial adjustment cycle of the controller, enables the composite control architecture to have the ability of "experience reuse", and improves the dynamic response efficiency.

[0144] S32. Collaborative Damage Warning and Control: The sliding surface design incorporates a "damage warning factor," which is calculated by comparing the tissue deformation rate with the damage threshold in the first-step model. When the safety threshold is exceeded, the reinforcement learning module is automatically triggered to adjust the emergency mode, temporarily increasing the DDPG algorithm's exploration step size by 3 times to quickly search for safe control parameters. This mechanism retains the robustness of sliding mode control while also providing dynamic learning capabilities, offering a real-time control strategy for the next step of digital twin pre-simulation.

[0145] Adaptive sliding surface formula:

[0146]

[0147] In the formula: The sliding surface variable (dimensionless) approaches 0, indicating that the system is stable.

[0148] Tracking error (unit: mm) ;

[0149] Sliding surface parameters (unit: s⁻¹, value: 0.5-2) suppress steady-state error;

[0150] Damage warning factor ( (Indicates the threshold for triggering damage);

[0151] Tissue deformation rate (unit: %);

[0152] By directly embedding the damage risk into the core equation of sliding mode control, the controller in step S3 has the dynamic adjustment capability of "safety first", which is different from the traditional sliding surface design that only focuses on error.

[0153] The specific steps of the virtual-real interactive digital twin in step S4 are as follows:

[0154] S41. Intraoperative real-time twin model construction: To verify the effectiveness of the control strategy in step S3, the robotic arm motion data and tissue deformation images scanned by 3D structured light were transmitted through 5G slicing technology. The boundary conditions of the twin model were updated synchronously every 10ms to ensure that the virtual scene was highly consistent with the real surgical environment. Multibody dynamics simulation was accelerated by GPU parallel computing to realize the pre-play of the trajectory in the next 100ms under the current control parameters.

[0155] Newton-Euler dynamic equations (digital twin optimization):

[0156]

[0157] In the formula: Joint torque vector (unit: N·m);

[0158] Inertia matrix (unit: kg·m) ;

[0159] Coriolis force and centrifugal force matrix;

[0160] Gravity vector (unit: N);

[0161] Jacobian matrix (unit: m / rad);

[0162] External force on the end effector (unit: N);

[0163] S42. Risk prediction and parameter feedback: The LSTM network trained based on force feedback signals recognizes the physician's operational intentions (such as pushing, pulling, and rotating) and pre-simulates the optimal torque allocation scheme for the corresponding actions in twin space. This process forms a closed loop of "real-time control - virtual pre-simulation - parameter correction". It uses the control strategy of the third step as input and feeds back the controller parameter optimization through the pre-simulation results, providing a virtual verification basis for the next step of multimodal sensor fusion.

[0164] The specific steps of flexible-rigid sensor fusion in step S5 are as follows:

[0165] S51. Sensing architecture adapted to minimally invasive scenarios: To provide high-precision data for the digital twin model in step S4, a multimodal sensing system is designed: A flexible fiber optic grating sensor with a diameter of 0.5mm is implanted at the end of the instrument to realize the three-dimensional distribution measurement of tissue contact force (resolution 0.01N), solving the problem of excessive size of traditional sensors; tissue density data of intraoperative CT images are acquired simultaneously, and force-image data fusion is achieved through Bayesian filtering;

[0166] Bayesian filtering is updated synchronously with 5G data (iterates every 10ms), and the initial probability distribution is set to Gaussian distribution (mean is the estimated preoperative CT density value, variance is 0.05).

[0167] Bayesian filter fusion estimation expression:

[0168]

[0169] In the formula:

[0170] The observation sequence from time 1 to k, i.e. The collection includes fiber optic force sensor data (unit: N) and CT image density values ​​(unit: HU).

[0171] The historical observation sequence up to time k-1 is used for recursive updates of Bayesian filtering to achieve temporal fusion of multimodal data;

[0172] State variables (such as tissue density, contact force);

[0173] Sensor observations (unit: N or HU);

[0174] Normalization constant;

[0175] Likelihood function;

[0176] State transition probability;

[0177] S52. Complementary Verification of Multi-Source Information: An 8-channel micro-MEMS accelerometer array is deployed at the joint. The joint wear state is inverted through vibration signal mode decomposition, adding mechanical health constraints for torque optimization. This sensing system not only provides real-time raw data for the digital twin but also improves measurement robustness through complementary multi-source information, providing a precise state perception foundation for the next step of adaptive reconstruction of redundant degrees of freedom.

[0178] The specific steps for reconstructing redundant degrees of freedom in step S6 are as follows:

[0179] S61, Dynamic Dimensional Adaptation Mechanism: Based on the sensor data feedback from step S5, a redundancy utilization strategy is designed for the 7-DOF robotic arm: When surgical space is limited (the distance between the end effector and tissue is <5mm as measured by a flexible fiber optic sensor, and a sudden increase in joint motion resistance >2N is detected by the MEMS array), m), such as a narrow abdominal cavity, is transformed by affine transformation from a high-dimensional space to a low-dimensional subspace, with the transformation matrix being A∈ (Elements are preset according to the type of surgery, during laparoscopic surgery) (This indicates freezing the 3rd and 5th rotational joints), freezing unnecessary degrees of freedom, such as fixing two rotational joints during straight sutures, to simplify control complexity;

[0180] A is the projection matrix from the high-dimensional space to the low-dimensional subspace, a 5×7 real matrix (the number of rows corresponds to the low-dimensional degrees of freedom, and the number of columns corresponds to the original 7 degrees of freedom); matrix elements This represents the projection coefficient of the j-th original degree of freedom in the i-th low-dimensional subspace;

[0181] S62. Deployment of fault-tolerant compensation scheme: Construct a "fault-tolerant trajectory library" to store compensation motion schemes for different joint over-limit scenarios: When the torque of the main operating joint exceeds the safety threshold of 80%, the redundant joint compensation trajectory is calculated in real time based on the pseudo-inverse Jacobian matrix, and the load is shared through coordinated motion; This mechanism not only uses sensor data to achieve accurate judgment, but also improves the adaptability to complex scenarios, providing a flexible operation basis for final clinical validation.

[0182] Jacobi's pseudo-reversal:

[0183]

[0184] In the formula: The pseudo-inverse of the Jacobian matrix (unit: rad / m); Jacobian matrix (unit: m / rad);

[0185] The specific steps for clinical validation in step S7 are as follows:

[0186] S71. Construction of a three-tiered verification chain: To ensure the clinical applicability of the first six steps, a "virtual-physical-clinical" verification system is established: The virtual layer completes 100 standardized surgical simulations (including 50 emergency scenarios) in a digital twin system; the physical layer uses a bio-3D printed biomimetic tissue model to conduct 1,000 repeated operation tests to verify the stability of sensing and control.

[0187] S72. Closed-loop iteration of clinical feedback: The clinical level collaborates with tertiary hospitals to conduct phased trials. First, parameters are optimized through animal experiments, and then they are put into clinical use. Subjective physician ratings (1-10 points) are introduced to evaluate the operation effect. The rating indicators include: trajectory accuracy (30%), operation stability (20%), tissue damage risk (25%), response speed (15%), and operation convenience (10%). The total score is calculated by weighting. The verification results form a "control parameters-operation experience-clinical effect" process, which feeds back to the first step of model correction and the second step of weight optimization, and finally realizes the clinical implementation of the technical solution.

[0188] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0189] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for coordinated optimization of joint torques and trajectory tracking control of a surgical robot arm, characterized in that: The specific steps of this method are as follows: S1. Biomechanics-Multibody Dynamics Coupled Modeling: Establish a cross-scale model of joint friction and soft tissue viscoelasticity of surgical robot arm, use fractional derivatives to describe soft tissue properties, adapt the model of biomechanical properties to soft tissue type in real time through fractional derivatives, correct parameters in real time through fiber optic sensors, and embed tissue damage risk into the equation. S2. Dynamic weight optimization: Based on the visual recognition surgery stage, the positioning, operation and withdrawal stages focus on trajectory accuracy, torque balance and energy consumption respectively. The target weights are dynamically adjusted, the solution space is pruned with the improved NSGA-III algorithm, and the optimized parameters are output to adapt to the scene. S3, Memory-enhanced composite control: The control architecture is built based on the optimization target, the surgical memory bank realizes parameter transfer, the sliding surface is integrated with damage early warning, and the risk over-limit time amplifies and reinforces learning to explore the step size; S4. Virtual-Real Interactive Digital Twin: The 5G synchronous robotic arm and tissue data update the model every 10ms, the GPU pre-simulates the trajectory for 100ms to predict risks, and combines the physician's intentions to pre-simulate the optimal solution to verify the effectiveness of the control strategy. S5, Flexible-Rigid Sensing Fusion: 3D force is measured using a 0.5mm flexible fiber optic sensor, and tissue density data of the surgical area in intraoperative CT images are fused. Bayesian filtering is used to improve robustness, and a MEMS array is used to monitor joint health. S6. Redundant Degrees of Freedom Reconstruction: Based on sensor data, unnecessary degrees of freedom are dynamically frozen, a fault-tolerant library is constructed, and redundant joints compensate for the main joints when they exceed their limits. S7. Clinical Validation: Through three levels of validation—virtual simulation, bionic tissue testing, and clinical trials—physician scoring feedback optimizes parameters and feeds back into the initial model and weights.

2. The surgical robot arm joint torque collaborative optimization and trajectory tracking control method according to claim 1, characterized in that: The specific steps of biomechanics-multibody dynamics coupling modeling in step S1 are as follows: S11. Construction of the cross-scale coupling model: Construct a cross-scale model of joint friction, soft tissue viscoelasticity and surgical instrument stiffness, introduce fractional derivative to correct the Maxwell model, which is different from the linear assumption of the integer model, captures the nonlinear characteristics of tissue stress relaxation, and collects tissue stress-strain data in real time through the fiber optic grating sensor at the end of the implanted instrument, and dynamically corrects the model parameters every 5ms. S12. Embedding of biosafety constraints: Based on the Lanczos algorithm, the mapping relationship between joint torque and tissue damage risk is derived, and the cell damage threshold is transformed into a mechanical constraint condition and embedded into the dynamic equation.

3. The surgical robot arm joint torque collaborative optimization and trajectory tracking control method according to claim 1, characterized in that: The specific steps of dynamic weight optimization in step S2 are as follows: S21. Establishment of a phased optimization mechanism: The visual servo system identifies the interaction status between instruments and tissues in real time, and divides the surgery into three phases: positioning, operation, and withdrawal. The weight of the objective function is dynamically adjusted according to the core requirements of each phase. S22. Innovative improvements to the optimization algorithm: When using the improved NSGA-III algorithm, only the first 10% of non-dominated solutions are retained, and the solution space is pruned in combination with the characteristics of the current surgical stage.

4. The method for coordinated optimization of joint torque and trajectory tracking control of surgical robot arm according to claim 1, characterized in that: The specific steps of memory-enhanced composite control in step S3 are as follows: S31. Design of the experience learning architecture: Based on the dynamic optimization target output in step S2, a surgical scenario memory library is constructed to store the optimal control parameter set for typical surgical scenarios. The current surgical features are matched through the cosine similarity algorithm to realize cross-scenario parameter transfer and shorten the initial adjustment cycle of the controller. S32. Collaborative Damage Warning and Control: The sliding surface design incorporates a damage warning factor. When the safety threshold is exceeded, the reinforcement learning module is automatically triggered to adjust the emergency mode, temporarily increasing the DDPG algorithm's exploration step size by 3 times to quickly search for safety control parameters.

5. The method for coordinated optimization of joint torques and trajectory tracking control of surgical robot arms according to claim 1, characterized in that: The specific steps of the virtual-real interactive digital twin in step S4 are as follows: S41. Intraoperative real-time twin model construction: To verify the effectiveness of the control strategy in step S3, the robotic arm motion data and tissue deformation images scanned by 3D structured light were transmitted through 5G slicing technology, and the boundary conditions of the twin model were updated synchronously every 10ms. S42. Risk prediction and parameter feedback: An LSTM network trained based on force feedback signals recognizes the physician's operational intentions and pre-simulates the optimal torque allocation scheme for the corresponding action in twin space.

6. The method for coordinated optimization of joint torques and trajectory tracking control of surgical robot arms according to claim 1, characterized in that: The specific steps of flexible-rigid sensor fusion in step S5 are as follows: S51. Sensing architecture adapted to minimally invasive scenarios: In order to provide high-precision data of the digital twin model of step S4, a multimodal sensing system is designed: a flexible fiber optic grating sensor with a diameter of 0.5mm is implanted at the end of the instrument to realize the three-dimensional distribution measurement of tissue contact force, and simultaneously acquire tissue density data of intraoperative CT images. Force-image data fusion is achieved through Bayesian filtering. S52. Complementary verification of multi-source information: An 8-channel micro-MEMS accelerometer array is deployed at the joint, and the joint wear state is inverted through vibration signal mode decomposition, adding mechanical health constraints for torque optimization.

7. The method for coordinated optimization of joint torque and trajectory tracking control of surgical robot arm according to claim 1, characterized in that: The specific steps for reconstructing redundant degrees of freedom in step S6 are as follows: S61, Dynamic Dimension Adaptation Mechanism: Based on the sensor data feedback in step S5, a redundancy utilization strategy is designed for the 7-DOF robotic arm: When the surgical space is detected to be limited, the high-dimensional space is projected to the low-dimensional subspace through affine transformation, freezing unnecessary degrees of freedom and simplifying control complexity. S62. Deployment of fault-tolerant compensation scheme: Construct a fault-tolerant trajectory library to store compensation motion schemes for different joint over-limit scenarios: When the torque of the main operating joint exceeds the safety threshold of 80%, the redundant joint compensation trajectory is calculated in real time based on the pseudo-inverse Jacobian matrix, and the load is shared through cooperative motion.

8. The method for coordinated optimization of joint torque and trajectory tracking control of surgical robot arm according to claim 1, characterized in that: The specific steps for clinical validation in step S7 are as follows: S71. Construction of a three-level verification chain to establish a virtual-physical-clinical verification system: The virtual layer completes 100 standardized surgical simulations in a digital twin system; the physical layer uses a bio-3D printed biomimetic tissue model to conduct 1000 repeated operation tests to verify the stability of sensing and control. S72. Closed-loop iteration of clinical feedback: The clinical level collaborates with tertiary hospitals to conduct phased trials. First, parameters are optimized through animal experiments before entering clinical trials, and subjective scoring by physicians is introduced to evaluate the effectiveness of the operation.

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