Tandem operation mechanical arm control method and device meeting RCM constraint

Abstract

The invention discloses a series operation mechanical arm control method and device meeting the RCM (remote center of motion) constraint, and relates to the technical field of operation robot control. The control method comprises the following steps that trajectory tracking constraint, remote center of motion constraint and physical limit constraint of a series operation mechanical arm are modeled into a nonlinear time-varying equation system, and the nonlinear time-varying equation system is established; and setting a pseudo-inverse-free enhanced zeroing neural network model based on pseudo-inverse-free real-time solution of the enhanced zeroing neural network. By adopting the pseudo-inverse-free enhanced zero neural network model, the dependence of an existing method on a high-complexity pseudo-inverse operation or a complex optimization process is eliminated, the calculation complexity of motion control is greatly reduced, the effect of high-frequency real-time control is achieved, the strict real-time requirement of minimally invasive surgery on mechanical arm control can be fully met, and the mechanical arm control method is suitable for industrial production. Motion response of the surgical mechanical arm is more timely, and operation lag caused by calculation delay is avoided.

Description

Technical Field

[0001] This invention relates to the field of surgical robot control technology, specifically to a method and apparatus for controlling a serial surgical robotic arm that satisfies RCM constraints. Background Technology

[0002] Robot-assisted surgery is an advanced medical technology that uses robotic systems to assist surgeons in performing surgical procedures. The core of this technology lies in using a robotic platform to provide surgeons with enhanced vision and maneuverability, thereby achieving more precise and safer surgical results. Robot-assisted surgery typically consists of several key components: a main control platform composed of multiple robotic arms, a surgical instrument platform equipped with a high-definition camera, and a control console for the surgeon to operate. The surgeon sits in front of the control console and controls the surgical instruments on the robotic arms by manipulating handles, while simultaneously observing the surgical area through real-time 3D images provided by the system. This design allows surgeons to operate with dexterity that surpasses that of human hands.

[0003] The mainstream methods for constrained control of existing surgical robots' remote motion centers (RCM), whether based on Jacobi pseudoinverses or conventional neural networks, have failed to overcome the core bottleneck of high computational complexity. The former requires highly complex pseudoinverse calculations, while the latter, even with parallel computing capabilities, still relies on complex optimizations or pseudoinverse calculations. These methods are difficult to meet the stringent requirements of high-frequency real-time control in minimally invasive surgery, and inevitably produce lag errors during dynamic trajectory tracking. Ultimately, this results in untimely motion response and insufficient operational precision of the surgical robotic arm, failing to fully guarantee the safety and reliability of minimally invasive surgery, thus becoming a problem restricting the development of robot-assisted minimally invasive surgery. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method and apparatus for controlling a tandem surgical robotic arm that satisfies RCM constraints, thus solving the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a control method and apparatus for a tandem surgical robotic arm satisfying RCM constraints, wherein the control method includes the following steps:

[0006] S1. The trajectory tracking constraints, remote motion center constraints, and physical limit constraints of the serial surgical robotic arm are modeled as a nonlinear time-varying equation system;

[0007] S2. Set up an enhanced null neural network model without pseudo-inverses to process the nonlinear time-varying equation system established in step S1 to obtain the continuous motion trend;

[0008] S3. The continuous motion trend obtained in step S2 is converted into discrete instructions executed by the hardware of the serial surgical robot arm, and the serial surgical robot arm iteratively executes the discrete instructions in a high-frequency control loop.

[0009] Preferably, the constraint mathematical modeling process for the trajectory tracking constraint, the remote center of motion constraint, and the physical limit constraint in step S1 includes:

[0010] The inequality constraints corresponding to the physical limit are transformed into equality constraints by using the ramp function. These are then combined with the equality error terms corresponding to the trajectory tracking constraints and the remote motion center constraints to form a unified set of equality constraints.

[0011] Preferably, the modeling process for the remote center of motion constraint in step S1 is as follows:

[0012] The position of the cannula of the tandem surgical robotic arm is set as a fixed point. The RCM point of the tandem surgical robotic arm is the point where the instrument is aligned with the fixed point. The instrument axis of the tandem surgical robotic arm is limited to sliding along the axial direction and rotating around the RCM point, and lateral displacement is prohibited.

[0013] Preferably, the modeling process for the trajectory tracking constraints in step S1 is as follows:

[0014] Based on the target path of the surgery, the movement trajectory of the surgical instrument tip is aligned with the target path.

[0015] Preferably, the physical limit constraints in step S1 include: joint position constraints, joint velocity constraints, and length constraints of the surgical instruments of the serial surgical robotic arms.

[0016] Preferably, the solution process for the enhanced null neural network in step S2 includes:

[0017] The error function is constructed using the L2 norm, and a time-varying decay factor is introduced to enhance its robustness to noise. The error convergence is obtained through an evolution formula.

[0018] Preferably, the dynamic evolution formula employs a saturated exponential sign double power activation function. This function, through the synergistic effect of the sign double power term and the nonlinear exponential term, ensures that the error converges in a finite time and avoids overshoot of the control signal.

[0019] Preferably, a numerical protection is set during the processing of the evolution formula. The numerical protection is a lower bound set for the denominator of the error function. The numerical protection avoids the error from approaching zero, which would lead to processing singularity.

[0020] Preferably, the generation and execution of the discretization control instructions in step S3 includes:

[0021] System sampling: At the beginning of each control cycle, the sensor data of the tandem surgical robotic arm is read, and the joint state of the tandem surgical robotic arm is obtained;

[0022] Solving for the motion rate: Based on the joint state, process the state vector and substitute it into the enhanced null neural network model to process the state change rate;

[0023] Instruction generation: The target joint state for the next control cycle is processed through numerical integration using the Euler method;

[0024] Command execution: The speed or position command corresponding to the target joint state is transmitted to the underlying controller of the serial surgical robot via the communication bus for execution.

[0025] Preferably, during the iterative execution of step S3, a preset error tolerance value is used as the termination condition. When the decision error is less than the tolerance value, the control convergence is determined and the iterative loop is terminated.

[0026] An apparatus for controlling a tandem surgical robotic arm that satisfies RCM constraints, the apparatus comprising:

[0027] Constraint modeling module, neural network processing module, and discrete control module;

[0028] The constraint modeling module is used to model the trajectory tracking constraints, remote center of motion constraints, and physical limit constraints of the serial surgical robotic arm into a nonlinear time-varying equation system.

[0029] The neural network processing module is an enhanced null neural network module without pseudo-inverses, used to process the nonlinear time-varying equation system output by the constraint modeling module to obtain the continuous motion trend;

[0030] The discrete control module is used to convert the continuous motion trend output by the neural network processing module into discrete instructions for the serial surgical robotic arm hardware, and control the serial surgical robotic arm to execute iteratively in a high-frequency control loop.

[0031] This invention provides a method and apparatus for controlling a tandem surgical robotic arm that satisfies RCM constraints. It offers the following advantages:

[0032] (1) The present invention adopts the Enhanced Zero Neural Network (EZNN) model without pseudo-inverse, which gets rid of the dependence of existing methods on high-complexity pseudo-inverse operation or complex optimization process, greatly reduces the computational complexity of motion control, achieves the effect of high-frequency real-time control, can fully meet the stringent real-time requirements of minimally invasive surgery for robotic arm control, make the motion response of the surgical robotic arm more timely, avoid operation delay caused by computation delay, and meet the stringent requirements of surgical scenarios.

[0033] (2) The core solution logic is designed based on the null neural network and paired with the saturated exponential sign double power activation function to eliminate the lag error in the dynamic trajectory tracking process. At the same time, the error is quickly converged, achieving the effect of high-precision trajectory tracking. This effectively improves the operation accuracy of the surgical robotic arm, ensures that the end of the instrument can accurately follow the surgical target path, avoids additional trauma to the patient due to tracking deviation, and significantly optimizes the operation effect of minimally invasive surgery.

[0034] (3) By introducing a time-varying decay factor into the solution of the model equation and taking advantage of the characteristics of the saturated activation function, the jitter caused by external interference such as sensor noise to the movement of the robotic arm is effectively suppressed, making the movement of the control system smooth and stable, significantly enhancing the robustness and anti-interference ability of the surgical robotic arm control, allowing the robotic arm to maintain stable operation in complex surgical environments, avoiding sudden abnormal movements, and fully ensuring the safety and reliability of minimally invasive surgery. Attached Figure Description

[0035] Figure 1 The flowchart shows the control method and device for a serial surgical robotic arm that satisfies RCM constraints according to the present invention.

[0036] Figure 2 This is a kinematic diagram of the surgical robot constrained by the RCM constraint of the serial surgical robot control method and device satisfying the RCM constraint of the present invention.

[0037] Figure 3 This is a schematic diagram of the RCM constraint of the serial surgical robotic arm control method and device that satisfies the RCM constraint of the present invention.

[0038] Figure 4 This is a comparison diagram of the activation function (SE-SBP-AF) used in the serial surgical robotic arm control method and device that satisfies RCM constraints of the present invention with other activation functions;

[0039] Figure 5 This is a comparison diagram of the trajectory tracking performance of the serial surgical robotic arm control method and device of the present invention that satisfies RCM constraints with the prior art;

[0040] Wherein: (a)-(c) and (j)-(l) are methods based on Jacobi pseudoinverse, (d)-(f) and (m)-(o) are methods based on recurrent neural networks; (g)-(i) and (p)-(r) are the EZNN method of this invention;

[0041] Figure 6 This is a comparison chart of the trajectory tracking performance of the serial surgical robotic arm control method and device of the present invention that satisfies RCM constraints with the prior art. Detailed Implementation

[0042] 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. Example 1

[0043] This invention provides a control method and apparatus for a tandem surgical robotic arm that satisfies RCM constraints. To achieve the above objectives, this invention utilizes the following technical solution: The control method includes the following steps:

[0044] S1. The trajectory tracking constraints, remote motion center constraints, and physical limit constraints of the serial surgical robotic arm are modeled as a nonlinear time-varying equation system. The serial surgical robotic arm is a mechanical structure composed of multiple joints connected in series, which can perform minimally invasive surgical operations. Its movement is controlled by the position / velocity of each joint. The end of the arm carries surgical instruments and needs to be inserted into the patient's body through a small incision on the body surface to complete the operation.

[0045] Trajectory tracking constraint is one of the core constraints of robotic arm motion control. It limits the actual movement trajectory of the surgical instrument's end effector to completely coincide with the target path required for the surgery (such as the path for circumferentially resecting the edge of a tumor), ensuring the precision of the surgical operation. Remote center of motion constraint is one of the core constraints of minimally invasive surgery. It means that when the surgical instrument enters the patient's body through the trocar, the position of the trocar is set as a fixed point (RCM point). The instrument axis is only allowed to slide axially and rotate around the RCM point, and no lateral displacement is allowed to avoid damage to the patient's incision and surrounding tissues. Physical limit constraint is the motion boundary constraint determined by the hardware and instruments of the robotic arm itself. It is used to avoid mechanical damage or surgical risks caused by the robotic arm exceeding its travel, speed, or instrument length exceeding its limit.

[0046] S2. Set up an enhanced nullable neural network model without pseudo-inverses to process the nonlinear time-varying equation system established in step S1 to obtain the continuous motion trend. The nonlinear time-varying equation system is a unified mathematical model formed by integrating multiple heterogeneous constraints (trajectory tracking, RCM, physical limit). Its equation form has nonlinear characteristics, and the parameters change dynamically with time. The model is a dynamic solution without pseudo-inverses. Based on the improvement of the nullable neural network (ZNN), by optimizing the error function, activation function and introducing a time-varying decay factor, the efficient and real-time solution of the nonlinear time-varying equation system is achieved. The real-time solution without pseudo-inverses is a solution method that does not require calculating the pseudo-inverse of the Jacobian matrix (the core step of the traditional method, which has high computational complexity). It can obtain the solution required for the motion control of the robotic arm in real time only through basic operations such as vector-matrix multiplication.

[0047] S3. The continuous motion trend obtained in step S2 is transformed into discrete instructions executed by the hardware of the serial surgical robot. The serial surgical robot iteratively executes the discrete instructions in a high-frequency control loop. The discrete instructions are the continuous motion state change trend obtained by EZNN solution, which is transformed into discrete position / velocity instructions that can be recognized and executed by the robot hardware (lower-level controller) through numerical integration.

[0048] The mathematical modeling process for the trajectory tracking constraint, remote center of motion constraint, and physical limit constraint in step S1 includes:

[0049] The ramp function transforms the inequality constraints corresponding to the physical limits into equality constraints. These equality constraints are then combined with the error terms corresponding to the trajectory tracking constraints and remote motion center constraints to form a unified set of equations. The ramp function is a piecewise function used to transform inequality constraints into equality constraints. Its core function is to transform the inequality constraints of the physical limits (such as the upper and lower limits of joint position / velocity) into equality constraints so that they can be integrated with trajectory tracking and RCM constraints into a unified nonlinear time-varying equation system.

[0050] The modeling process for the remote center of motion constraint in step S1 is as follows:

[0051] The position of the cannula of the tandem surgical robotic arm is set as the fixed point. The RCM point of the tandem surgical robotic arm is the point where the instrument is aligned with the fixed point. The instrument axis of the tandem surgical robotic arm is limited to sliding along the axial direction and rotating around the RCM point, and lateral displacement is prohibited.

[0052] The modeling process for trajectory tracking constraints in step S1 is as follows:

[0053] Based on the target path of the surgery, the movement trajectory of the surgical instrument tip is aligned with the target path.

[0054] The physical limit constraints in step S1 include: joint position constraints, joint velocity constraints, and length constraints of the surgical instruments of the serial surgical robotic arms.

[0055] The solution process for the enhanced null neural network in step S2 includes:

[0056] The error function is constructed using the L2 norm, and a time-varying decay factor is introduced to enhance the robustness to noise. The error convergence is obtained through the evolution formula. The time-varying decay factor is an adjustment factor that dynamically changes with the decision error ε and time t, and its value range is [1,2], which is used to enhance the robustness of the model to noise.

[0057] Preferably, the dynamic evolution formula uses a saturated exponential sign double power activation function. This function ensures finite-time convergence of the error and avoids control signal overshoot through the synergistic effect of the sign double power term and the nonlinear exponential term. Through the synergistic effect of the sign double power term and the nonlinear exponential term, it not only ensures finite-time convergence of the error, but also prevents control signal overshoot when the error is too large, thus maintaining system stability.

[0058] Preferably, numerical protection is set during the processing of the evolution formula. Numerical protection is a lower bound set for the denominator of the error function. Numerical protection avoids the error from approaching zero, which leads to processing singularity. Singularity is a problem in mathematical solution where the error approaches zero, causing the calculation denominator to approach zero, which in turn leads to calculation failure or divergence of results.

[0059] Step S3, the generation and execution of discretized control instructions, includes:

[0060] System sampling: At the beginning of each control cycle, the sensor data of the serial surgical robotic arm is read and the joint status of the serial surgical robotic arm is obtained;

[0061] Solving for motion rate: Process the state vector based on the joint state, and substitute it into the enhanced null neural network model to process the rate of change of state;

[0062] Instruction generation: The target joint state for the next control cycle is processed through numerical integration using the Euler method;

[0063] Command execution: The speed or position command corresponding to the target joint state is transmitted to the underlying controller of the serial surgical robot via the communication bus for execution.

[0064] During the iterative execution of step S3, a preset error tolerance value is used as the termination condition. The error tolerance value is a preset control convergence judgment threshold used to determine whether the movement of the robotic arm meets the constraint requirements. When the decision error is less than the tolerance value, control convergence is determined and the iterative loop is terminated. Example

[0065] Reference Figure 1-6 A method and apparatus for controlling a tandem surgical robotic arm that satisfies RCM constraints, comprising the following steps:

[0066] Step 1: Unified mathematical modeling of multi-constraint tasks;

[0067] The physical motion constraints of the m-degree-of-freedom (modeling expandable) serial surgical robot are transformed into a unified set of mathematical equations, as follows:

[0068] Remote Motion Center (RCM) Constraint Modeling: During surgery, surgical instruments are inserted into the patient's body through a cannula, the position of which is set as follows: , Let be the position dimension of Cartesian space, and let the instrument be at any given moment relative to... The aligned point is denoted as That is, the actual RCM constraint of the robotic arm.

[0069] exist At the RCM point, the instrument axis can slide axially and rotate around the RCM point, but cannot undergo lateral displacement. During the procedure, due to the patient's breathing... Displacement may occur, which will be discussed in this application. Simplifying to a fixed point, i.e., assuming it remains constant over time, the constraint problem of the RCM point is expressed by the following equation:

[0070]

[0071] The known flange point of the robotic arm is and the endpoints are Its mathematical expression is:

[0072]

[0073] in, , This is a proportionality coefficient, used to represent... exist and The position between;

[0074] Taking the derivative of the above equation with respect to time, we get:

[0075]

[0076] in, For corresponding flange points Jacobian matrix, These correspond to the position and velocity of the joint, respectively.

[0077] After reorganization, the result is:

[0078]

[0079] in, , , This indicates the axial sliding speed of the surgical instrument rod along the RCM point, and... The corresponding Jacobian matrix The expression is:

[0080]

[0081] And with The corresponding Jacobian matrix This refers to the velocity component of the Jacobian matrix at the end of the flange of the serial robotic arm.

[0082] Trajectory tracking constraints: The trajectory tracking constraint problem of the surgical instrument tip can be expressed by the following equation:

[0083]

[0084] in This indicates the target path during surgery (e.g., circumferentially cutting the edge of a tumor). Taking the derivative with respect to time, we get:

[0085]

[0086] Physical limits and constraints: Serial robotic arms are inevitably subject to limitations on the position and speed of the robotic arm joints and the length of the surgical instruments, as expressed by the following formula:

[0087]

[0088]

[0089] The superscript signs here indicate the upper and lower limits of the corresponding constraints, respectively. .

[0090] Constructing a unified system of equations: Based on the above formulas, the following system of inequalities can be derived:

[0091]

[0092] in:

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] Introduce a ramp function to transform the system of inequalities:

[0098]

[0099] Using the ramp function, all inequality constraints are transformed into equality constraints. Then, all equality error terms of the three types of constraints—trajectory tracking, RCM, and physical limits—are combined to obtain the following equation.

[0100]

[0101] To simplify subsequent calculations, we define the observation vector:

[0102]

[0103] Define the state vector:

[0104]

[0105] We can obtain the Jacobian matrix corresponding to the above equation:

[0106]

[0107] in:

[0108] ;

[0109] ;

[0110] and , It is a diagonal matrix;

[0111]

[0112] Based on the above calculation formula, a unified mathematical model for multi-constraint tasks can be achieved.

[0113] Step 2 is based on real-time solution without pseudo-inverses using Enhanced Zero-Neural Network (EZNN);

[0114] Error function definition: Error function design different from traditional recurrent neural networks (ZNNs) The design is implemented using the L2 norm, as detailed below:

[0115]

[0116] Taking the time derivative of the error function, we get:

[0117]

[0118] ZNN Evolution Formula Design: Based on the design philosophy of ZNN, an evolution formula with a time-varying term is proposed:

[0119]

[0120] in, This is a user-defined convergence factor used to adjust the convergence strength of the algorithm.

[0121]

[0122] To enhance robustness to noise, a time-varying attenuation factor is introduced. This flexible design allows the model to achieve higher noise tolerance without excessively affecting efficiency, effectively suppressing noise-induced jitter in the system under steady-state conditions;

[0123] Decision error is defined as ,in yes A selected subset is used to control the convergence error of a specific objective;

[0124] In surgical robot scenarios, select ,when When, it is considered as controlled convergence, where It is an adjustable, user-defined threshold;

[0125] and In the design of ZNN, the activation function exists as a nonlinear odd function, which provides nonlinear capability for iterative solution, and also involves the need to prove the stability of Lyapunov in the subsequent process.

[0126] In the EZNN algorithm, in order to improve the solution performance, a novel saturated exponential sign double power activation function (SE-SBP-AF) is defined and designed.

[0127]

[0128] in, The saturation coefficient is... To activate the power exponent;

[0129] This SE-SBP-AF collaboration improves convergence speed and stability by multiplying a sign double power term with a nonlinear exponential term. The former ensures finite-time convergence, while the second term acts as a saturation gain, accelerating convergence as the error increases and preventing control signal overshoot when the error is very large, thereby maintaining system stability.

[0130] Based on the above formula, we can obtain

[0131]

[0132] Based on the theorem: the left pseudoinverse of a row vector is the product of vectors divided by an integer without involving SVD decomposition, and Given a row vector, its left pseudoinverse is as follows:

[0133]

[0134] Through a simple transformation, the following solution formula can be obtained:

[0135]

[0136] This formula completely avoids computationally intensive pseudo-inverse operations, and only includes basic operations such as vector-matrix multiplication, with a computational complexity of only O(mn), ensuring the extremely high real-time performance of the control algorithm.

[0137] Note that when When the denominator of the above expression approaches zero, this can lead to singularities and computational failures. To prevent this in practical implementation, we replace the denominator with... To set a lower bound for it;

[0138] in, It is a function that takes the maximum of two values. It is a small positive number, and this numerical protection measure produces a regularized solution formula:

[0139]

[0140] Step 3: Generation and execution of discretized control instructions;

[0141] The continuous "motion trend" calculated in the previous step is converted into discrete instructions executable by the robot hardware, and then iteratively executed in a high-frequency control loop:

[0142] System sampling: At the beginning of each control cycle, the robot's sensors are read to obtain the current actual joint state;

[0143] To calculate the motion rate: Calculate the state vector based on the current state and substitute it into the EZNN solution formula in step two to calculate the ideal rate of change of state.

[0144] Command generation: The target joint state for the next cycle is calculated through numerical integration (Euler method);

[0145] Command execution: The calculated target joint velocity or position command is sent to the robot's underlying controller via the communication bus for execution, and then the next control cycle begins.

[0146] Its specific execution control process is as follows:

[0147] Algorithm: Discretized EZNN control flow;

[0148] Input: Task Jacobian matrix Rate of change of task error over time Control system step size Iteration counter Error tolerance value ;

[0149] Output: Robot state solution ;

[0150] initialization: ;

[0151] While do

[0152] ;

[0153] sampling: ;

[0154] renew: ;

[0155] Used: EZNN update ;

[0156] renew: ;

[0157] ;

[0158] Through the above steps, precise control of the tandem surgical robotic arm during resection surgery is achieved: end-effector tracking error (TMCE) < 3 × 10⁻⁶. −4 m, RCM point position error (RMCE) < 3 × 10 −4 The single-step calculation time is <0.016ms, which fully meets the requirements of minimally invasive surgery for real-time performance, accuracy and safety. Moreover, the robotic arm movement has no obvious jitter, which verifies the effectiveness of the method of the present invention.

[0159] This invention employs an Enhanced Zero Neural Network (EZNN) model without pseudo-inverses, which avoids the high-complexity Jacobian pseudo-inverse operation in existing technologies. It reduces the computational complexity to the O(mn) level, which only relies on vector-matrix multiplication. The single-step calculation time is extremely short and stable. Combined with a 1kHz high-frequency control loop (1ms step size), the robotic arm can quickly respond to the needs of surgical operations, avoid the lag in instrument movements caused by computation delays, and accurately match the stringent requirements for real-time instrument tracking in resection surgery, ensuring that the doctor's operation instructions can be instantly converted into robotic arm movements.

[0160] Based on the idea of ​​zero-negation neural network, the error convergence mechanism is designed and combined with the saturated exponential sign double power activation function to fundamentally eliminate the lag error of dynamic trajectory tracking. In the surgical cutting path tracking, the actual trajectory of the robotic arm end is highly coincident with the target path, and the remote center of motion (RCM) point is always stably aligned with the fixed position of the cannula needle without lateral displacement deviation. This effectively avoids the risks of tumor residue, vascular damage and other risks caused by trajectory deviation, and provides key guarantee for the accuracy of surgical operation.

[0161] The time-varying decay factor introduced in this model can dynamically adjust the convergence characteristics according to the decision error, effectively suppressing the robotic arm jitter caused by sensor noise (such as joint encoder interference and force sensor fluctuation) during surgery. The numerical protection measures avoid the computational singularity problem when the error approaches zero, ensuring that the control process is stable and without abnormalities. During implementation, the robotic arm joints move smoothly and the instrument slides at a uniform speed without sudden acceleration, which significantly reduces the risk of traction and friction damage to the patient's body tissues and improves the safety of the surgery.

[0162] By using ramp functions to model physical limit constraints such as joint position, velocity, and instrument length, along with RCM constraints and trajectory tracking constraints, into a nonlinear time-varying equation system, the framework is clear and easy to adjust. While adapting to the needs of robotic arms and resection surgery, only the constraint parameters (such as cannula position, target path, and physical limit range) need to be adjusted to migrate to different minimally invasive surgeries and robotic arms with different configurations in series, thus having wide application adaptability. Example 2

[0163] An apparatus for controlling a tandem surgical robotic arm that satisfies RCM constraints, the apparatus comprising:

[0164] Constraint modeling module, neural network processing module, and discrete control module;

[0165] The constraint modeling module is used to model the trajectory tracking constraints, remote center of motion constraints, and physical limit constraints of the serial surgical robotic arm into a nonlinear time-varying equation system;

[0166] The neural network processing module is an enhanced null neural network module without pseudo-inverses, used to process the nonlinear time-varying equation system output by the constraint modeling module to obtain the continuous motion trend;

[0167] The discrete control module is used to convert the continuous motion trend output by the neural network processing module into discrete instructions for the serial surgical robot hardware, and control the serial surgical robot to execute iteratively in a high-frequency control loop.

[0168] In this embodiment, the constraint modeling module specifically transforms the inequality constraints corresponding to the physical limits into equality constraints through the ramp function, and then combines them with the equality error terms corresponding to the trajectory tracking constraints and remote center of motion constraints to form a unified set of equations. In the remote center of motion constraint modeling, the cannula position is set as a fixed point, limiting the instrument axis to slide only along the axial direction and rotate around the RCM point, and prohibiting lateral displacement. In the trajectory tracking constraint modeling, the surgical target path is used as a reference to limit the trajectory of the instrument end to be consistent with it. The physical limit constraints include joint position constraints, joint velocity constraints, and surgical instrument length constraints.

[0169] The neural network processing module uses the L2 norm to construct the error function, introduces a time-varying decay factor to enhance noise robustness, and achieves error convergence through a dynamic evolution formula. The dynamic evolution formula uses a saturated exponential sign double power activation function, and sets a lower bound for the denominator of the error function during the processing to achieve numerical protection and avoid processing singularities caused by the error approaching zero.

[0170] The discrete control module includes a sampling unit, a motion rate solving unit, an instruction generation unit, and an execution unit. The sampling unit is used to read sensor data from the robotic arm and obtain the joint state at the beginning of each control cycle. The motion rate solving unit is used to process the state vector based on the joint state and substitute it into the enhanced null neural network model to process the state change rate. The instruction generation unit is used to process the target joint state of the next control cycle through Euler numerical integration. The execution unit is used to transmit the velocity or position instruction corresponding to the target joint state to the robotic arm's underlying controller for execution via the communication bus.

[0171] The discrete control module is also configured with a preset error tolerance value, which is used as the iteration termination condition. When the decision error is less than the tolerance value, the control is determined to be converged and the iteration loop is terminated.

[0172] 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.

Claims

1. A control method for a serial surgical robotic arm satisfying RCM constraints, characterized in that: The control method includes the following steps: S1. The trajectory tracking constraints, remote motion center constraints, and physical limit constraints of the serial surgical robotic arm are modeled as a nonlinear time-varying equation system; S2. Set up an enhanced null neural network model without pseudo-inverses to process the nonlinear time-varying equation system established in step S1 to obtain the continuous motion trend; S3. The continuous motion trend obtained in step S2 is converted into discrete instructions executed by the hardware of the serial surgical robot arm, and the serial surgical robot arm iteratively executes the discrete instructions in a high-frequency control loop.

2. The control method for a serial surgical robotic arm satisfying RCM constraints according to claim 1, characterized in that: The mathematical modeling process for the trajectory tracking constraint, the remote center of motion constraint, and the physical limit constraint in step S1 includes: The inequality constraints corresponding to the physical limit are transformed into equality constraints by using the ramp function. These are then combined with the equality error terms corresponding to the trajectory tracking constraints and the remote motion center constraints to form a unified set of equality constraints.

3. The control method for a serial surgical robotic arm satisfying RCM constraints according to claim 1, characterized in that: The modeling process for the remote center of motion constraint described in step S1 is as follows: The position of the cannula of the tandem surgical robotic arm is set as a fixed point. The RCM point of the tandem surgical robotic arm is the point where the instrument is aligned with the fixed point. The instrument axis of the tandem surgical robotic arm is limited to sliding along the axial direction and rotating around the RCM point, and lateral displacement is prohibited.

4. The control method for a serial surgical robotic arm satisfying RCM constraints according to claim 1, characterized in that: The modeling process for the trajectory tracking constraints described in step S1 is as follows: Based on the target path of the surgery, the movement trajectory of the surgical instrument tip is aligned with the target path; The physical limit constraints in step S1 include: joint position constraints, joint velocity constraints, and length constraints of the surgical instruments of the serial surgical robotic arms.

5. The control method and apparatus for a tandem surgical robotic arm satisfying RCM constraints according to claim 1, characterized in that: The solution process for the enhanced null neural network described in step S2 includes: The error function is constructed using the L2 norm, and a time-varying decay factor is introduced to enhance its robustness to noise. The error convergence is obtained through an evolution formula.

6. The control method for a serial surgical robotic arm satisfying RCM constraints according to claim 5, characterized in that: The dynamic evolution formula employs a saturated exponential sign double power activation function. This function, through the synergistic effect of the sign double power term and the nonlinear exponential term, ensures that the error converges in finite time and avoids overshoot of the control signal.

7. The control method for a serial surgical robotic arm satisfying RCM constraints according to claim 5, characterized in that: Numerical protection is set during the processing of the evolution formula. The numerical protection is a lower bound set for the denominator of the error function. The numerical protection avoids the error from approaching zero, which would lead to processing singularities.

8. The control method for a serial surgical robotic arm satisfying RCM constraints according to claim 1, characterized in that: The generation and execution of the discretized control instructions in step S3 includes: System sampling: At the beginning of each control cycle, the sensor data of the tandem surgical robotic arm is read, and the joint state of the tandem surgical robotic arm is obtained; Solving for the motion rate: Based on the joint state, process the state vector and substitute it into the enhanced null neural network model to process the state change rate; Instruction generation: The target joint state for the next control cycle is processed through numerical integration using the Euler method; Command execution: The speed or position command corresponding to the target joint state is transmitted to the underlying controller of the serial surgical robot via the communication bus for execution.

9. The control method for a serial surgical robotic arm satisfying RCM constraints according to claim 1, characterized in that: During the iterative execution of step S3, a preset error tolerance value is used as the termination condition. When the decision error is less than the tolerance value, the control convergence is determined and the iterative loop is terminated.

10. An apparatus for use in a tandem surgical robotic arm control method satisfying RCM constraints as described in any one of claims 1-9, characterized in that: The device includes: Constraint modeling module, neural network processing module, and discrete control module; The constraint modeling module is used to model the trajectory tracking constraints, remote center of motion constraints, and physical limit constraints of the serial surgical robotic arm into a nonlinear time-varying equation system. The neural network processing module is an enhanced null neural network module without pseudo-inverses, used to process the nonlinear time-varying equation system output by the constraint modeling module to obtain the continuous motion trend; The discrete control module is used to convert the continuous motion trend output by the neural network processing module into discrete instructions for the serial surgical robotic arm hardware, and control the serial surgical robotic arm to execute iteratively in a high-frequency control loop.

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