Parametric decoupled drive compensation method for multi-segment rope-driven continuum robots

Abstract

The application discloses a parameterized decoupling driving compensation method for a multi-segment rope-driven continuum robot, which comprises the following steps: a variable-curvature kinematics model of the multi-segment rope-driven continuum robot based on a generalized antagonistic factor is established, and a recursive rope tension solver based on adaptive damping fixed-point iteration is constructed; in a dynamic motion process, a linear interpolation model is constructed by using normalized hysteresis progress, and the generalized antagonistic factor is corrected in real time; a feedforward compensation instruction containing cable elastic elongation and skeleton axial compression is constructed based on a lumped parameter model; and step-by-step parameter identification is performed by adopting a sequential locking strategy from a base to an end. Compared with the prior art, the application can compensate the comprehensive error caused by multi-segment coupling, friction hysteresis and structural elasticity accurately without an external sensor by only simple calibration, so that the end pose control precision of the robot is improved.

Description

Technical Field

[0001] This invention belongs to the field of continuum robot control, and in particular relates to a parametric decoupling drive compensation method for multi-segment rope driven continuum robots that takes into account friction and coupling effects. Background Technology

[0002] Cable-driven continuum robots (CDCRs) have shown irreplaceable potential in minimally invasive surgery (MIS) and confined space operations due to their compliant structure and remote actuation capabilities. By adjusting the length of the cables, their slender skeletons can be controlled to bend flexibly in complex environments to complete tasks, but precise control remains a challenge.

[0003] In practical applications, relying on traditional geometric kinematics or mechanical models to control multi-segment rope-driven continuum robots faces significant challenges:

[0004] 1. Difficulty in accurately modeling nonlinear transmission errors: The driving force needs to be transmitted over long distances through a slender guide channel. During this process, the friction between the driving cable and the guide hole, the elastic elongation of the cable itself, and the axial compression of the flexible skeleton are coupled together, resulting in severe hysteresis nonlinearity. Existing error compensation methods usually treat this as a fixed parameter model for fitting. However, the actual friction and hysteresis characteristics are highly time-varying and configuration-dependent, and simple measurement fitting cannot adapt to varying bending conditions; moreover, because the "relaxation" effect caused by the shortening of the skeleton under compression is ignored, the input displacement is often swallowed up by the system's elasticity, resulting in a severe lag in the end-effector response.

[0005] 2. Path-dependent coupling effects in multi-segment configurations: Existing compensation strategies are mostly designed for single-segment robots and often fail in multi-segment serial systems. This is because complex path-dependent coupling exists in multi-segment continuums. The bending of the proximal joint not only changes its own shape but also alters the cable transmission path that passes through the segment and drives the distal joint, resulting in a change in the cumulative contact angle. According to the Capstan equation, this change in contact angle exponentially amplifies friction, making the driving force transmission efficiency of the distal joint not only dependent on its own load but also deeply coupled to the historical motion trajectory of the proximal joint, making distal motion extremely difficult to predict. Simultaneously, the coupled motion of the distal joint may also cause antagonistic internal forces to be generated in the proximal joint, further complicating the path-dependent coupling.

[0006] 3. Limitations of High-Precision Models and Sensors: Current control schemes present an irreconcilable contradiction between "model accuracy" and "real-time performance." Accurate continuum mechanics models (such as Cosserat rod theory) involve solving complex two-point boundary value problems (BVP), resulting in excessive computational loads that struggle to meet the demands of high-frequency real-time control. Furthermore, they fail to account for transmission factors such as friction. Data-driven neural network methods, on the other hand, exhibit poor generalization ability; once mechanical wear causes a shift in the friction coefficient, the model becomes ineffective. While closed-loop feedback can improve accuracy, integrating end-effector force or position sensors in extremely confined spaces, such as minimally invasive surgery, is extremely difficult due to size limitations (millimeter-scale diameter) and stringent sterilization procedures.

[0007] 4. Positive Kinematic Representation Errors: Existing kinematic models struggle to accurately describe the effects of friction and tension antagonism on the bending shape of a continuum. In practical applications, the cumulative friction between the drive cable and the guide hole causes the cable tension to decrease exponentially along the robot skeleton. Multi-cable drives generate internal antagonistic tensions, and frictional torque significantly alters the local torque balance of the skeleton, resulting in a nonlinear spatial decay distribution of the actual curvature along the axial direction. This renders the constant curvature assumption of the PCC model completely invalid. While precise mechanical models such as the Cosserat rod can describe this deformation, their solutions heavily rely on the frictional force field distributed along the rod as input. Due to the lack of distributed force sensors, the specific distribution of friction is unknown, preventing the model from calculating the true shape without accurate frictional input. Furthermore, the Cosserat model involves solving complex boundary value problems, resulting in extremely high computational costs and making it difficult to meet real-time control requirements.

[0008] Therefore, there is an urgent need for a sensorless control method that can quantitatively describe and compensate for this path-dependent coupling effect and nonlinear hysteresis. Summary of the Invention

[0009] The purpose of this invention is to provide a parameterized decoupling drive compensation method for multi-segment rope-driven continuum robots. This method first establishes a variable curvature kinematic model based on a generalized antagonistic factor, parameterizing the shape attenuation effect caused by anisotropic friction and multi-cable antagonism. Then, a recursive rope tension solver considering multi-cable coupling is constructed. Using an adaptive damping fixed-point iterative algorithm, the internal tension distribution of the entire robot segment is solved from the end effector to the base under sensorless conditions, solving the numerical convergence problem under high curvature conditions. For frictional hysteresis in dynamic motion, a linear interpolation equivalent model based on normalized hysteresis progress is established for real-time correction. Finally, based on a lumped parameter model, precise feedforward compensation is performed on the elastic elongation of the cables and the axial compression of the skeleton caused by path-dependent friction, thereby improving the robot's end effector pose control accuracy.

[0010] The technical solution to achieve the objective of this invention is: a parameter decoupling drive compensation method for a multi-segment rope-driven continuum robot, the specific steps of which are as follows:

[0011] We establish the curvature shape distribution function of any segment of a multi-segment rope-driven continuum robot based on a generalized antagonistic factor, and analyze the non-uniform shape decay caused by anisotropic friction and multi-segment rope antagonism.

[0012] A recursive rope tension solver considering the coupling of multi-cable friction and antagonistic forces is constructed to solve the numerical convergence problem caused by tension-friction-shape coupling.

[0013] During the dynamic motion of the continuum robot, a linear interpolation model is constructed using normalized hysteresis progress to correct the generalized antagonistic factor in real time.

[0014] The actual input rope length parameters for multi-segment continuum drive are constructed based on feedforward elastic compensation of lumped parameters.

[0015] Step-by-step parameter identification employs a sequential locking strategy from the base to the end.

[0016] Furthermore, the generalized antagonism factor is the projection ratio of the friction-weighted torque onto the net driving torque, used to uniformly describe the shape attenuation effect caused by anisotropic friction and multi-cable antagonism, and is defined by the following formula:

[0017] ;

[0018] In the formula, For segment numbers of a continuum robot. For the first continuum robot Generalized antagonistic factor of the cross section of a segmental continuum robot. For the first continuum robot Cable serial numbers for the cross-section of a segmental continuum robot. This indicates that it includes all passages through the first... Cables in the cross-section of a segmental continuum robot; For the first The first cable Tension within the segment; Indicates the first The moment arm vector of the cable within its cross-section, where Let be the position vector of the cable within its cross-section. It is a unit vector along the local tangent; For the first The signed coefficient of friction of the cable.

[0019] Furthermore, the curvature shape distribution function of any segment of the multi-segment rope-driven continuum robot is:

[0020] ;

[0021] In the formula, For segment numbers of a continuum robot. For scalar curvature amplitude, The position is along the arc length of the skeleton. ; This is the total arc length of the robot segment; This represents the macroscopic bending angle of the robot segment. For the first continuum robot Generalized antagonistic factor of cross section of segmental continuum robot.

[0022] Furthermore, in constructing the recursive rope tension solver, the rope tension of any segment of a continuous body is solved based on the principle of virtual work and the curvature distribution of the continuous body; the end tension of any segment of the continuous body required to maintain the target pose is calculated. The formula is:

[0023] ;

[0024] in, For the first Local drive set for segmental continuum robots The tension vector of all cables in the system; For the first The elastic potential energy gradient of the segment itself, The cumulative coupled driving torque from the distal segment, For the first The moment arm matrix of the segment, For the first The Moore-Penrose pseudo-inverse matrix of the moment arm matrix of the segment; It is the identity matrix; It is a zero-space vector.

[0025] Furthermore, in order to adhere to the minimum adversarial control strategy and ensure physical feasibility, the cable can only be subjected to tension, not compression, and the zero-space vector... Set as:

[0026] ;

[0027] This ensures that all calculated tensions are non-negative and that the internal preload is minimized.

[0028] Furthermore, in the recursive solution of the reverse rope tension and the adaptive fixed-point iteration, the fixed-point iterative mapping function for the generalized antagonistic factor is constructed as follows:

[0029] ;

[0030] In the formula, This is a fixed-point iterative mapping function for the generalized antagonistic factor based on the moment projection ratio. The true value of the continuum near the adjacent end segments is obtained through fixed-point iteration. And the rope tension in that section;

[0031] Using the chain rule, the total derivative of this mapping function is decomposed into the product of four physical gains: friction sensitivity, equilibrium gain, stiffness gain, and shape sensitivity.

[0032] ;

[0033] To characterize the effect of cable tension variation on the calculated value of the generalized antagonism factor; To characterize the geometric proportion by which torque demand is converted into tension; , The stiffness matrix represents the skeleton. This characterizes the effect of changes in frictional state on curvature distribution.

[0034] Furthermore, an adaptive damping factor is introduced. The iteration process is relaxed, and the iteration step size is dynamically adjusted based on the real-time estimated generalized antagonistic factor:

[0035] ;

[0036] ;

[0037] In the formula: It serves as the base step size for rapid convergence under low-friction conditions. These are sensitivity calibration parameters used to suppress gain under conditions of high friction or large bending. For the first The estimated value of the generalized antagonistic factor at the next iteration.

[0038] Furthermore, in the process of correcting the generalized antagonistic factor, an equivalent antagonistic model based on normalized hysteresis progress is established by linear interpolation; the change in the current bending angle relative to the starting point of the reverse motion is calculated and normalized to obtain a dimensionless hysteresis progress factor; using the hysteresis progress factor, linear interpolation is performed between the stable friction state before reversal and the theoretical target friction state based on the assumption of complete slip, to calculate the equivalent generalized antagonistic factor corrected at the current moment.

[0039] Furthermore, in the actual input rope length parameters of the multi-segment continuum drive constructed based on the feedforward elastic compensation of lumped parameters, the final first... Duan Di Motor position command of root drive cable It consists of four superimposed parts: geometric path length, cable elongation compensation, skeleton compression compensation, and hysteresis compensation.

[0040] ;

[0041] In the formula: Let be the theoretical path length calculated based on geometric kinematics, where Indicates the first The first segment of the continuum The amount of coupling drive required to change when the root rope is in the m-th segment before it passes through; This is the compensation amount for the elastic elongation of the cable; This is the sum of the axial compression compensation for all the near-end skeleton segments (1 to j) through which the cable passes; This is the system hysteresis compensation constant. Ensure that the compensation direction is consistent with the motion direction.

[0042] Furthermore, (1) the root cable drive number Cable elastic elongation compensation for segmented continuum robots for:

[0043] ;

[0044] In the formula, For lumped transmission stiffness, The cable tension at the base of the continuum is given. Let m be the cable segment stiffness of the m-th segment of the driving rope path of the j-th segment of the continuum. Let be the cumulative attenuation factor of the m-th segment of the path of the i-th driving rope in the j-th segment of the continuum. The variable curvature tension distribution factor of the m-th segment of the drive rope path of the j-th segment of the continuum; the cable elastic elongation compensation is the sum of the elongation of the base transmission segment and the elongation within each segment of the robot body, and the elongation of each segment has been corrected by path friction attenuation.

[0045] (2) Explicitly calculate all passages through the first Axial compressive deformation of the skeleton caused by the resultant force of the cable segment And reverse compensation is performed in the drive command to eliminate control slack caused by skeleton shortening: axial compression deformation of the skeleton for:

[0046] ;

[0047] In the formula, To achieve lumped frame compressive stiffness, The variable curvature tension distribution factor of the j-th segment of the continuum.

[0048] Compared with existing technologies, the beneficial effects of the present invention are as follows:

[0049] (1) High precision of multi-segment decoupling: This invention proposes the concept of "generalized antagonistic factor" to parameterize the complex anisotropic friction and multi-cable antagonistic effect, and analyzes the non-uniform curvature attenuation characteristics along the continuum. This model can accurately reconstruct the true shape of the proximal skeleton distorted by friction, thereby accurately quantifying the "cumulative contact angle" and tension attenuation of the distal driving cable on the proximal path. It solves the nonlinear coupling interference of proximal posture changes on the distal driving force, and realizes a high-precision shape and force transmission description of multi-segment continuum robots.

[0050] (2) Recursive Tension Estimation Strategy: This invention addresses the strongly coupled algebraic loop problem of "tension-friction-shape" by constructing a chain-like derivative structure for the iterative mapping function. The total derivative of the update law is physically decomposed into four transmission terms: friction-defined sensitivity, geometric scale, stiffness gain, and shape sensitivity. Through worst-case gain analysis of this chain structure, the physical nature of the positive correlation between the closed-loop gain and the system strain energy (square of the bending angle) is revealed. Based on this, an adaptive damping update law is designed, dynamically adjusting the iteration step size according to the real-time estimated generalized antagonistic factor. This solves the problem that existing mechanical models cannot obtain accurate internal tension as input when end-effector force sensors are lacking; particularly, it solves the technical challenge of numerical divergence and non-convergence of conventional iterative algorithms caused by excessive nonlinear gain in a multi-segment continuous body under high load or large bending angle "high-energy state". This method enables the numerically stable inverse solution of the internal tension distribution of the entire robot segment within the entire workspace using only joint position input. It eliminates the dependence on bulky end effectors and ensures robustness of the solution under various extreme configurations through an adaptive mechanism, providing accurate physical model input for subsequent precise feedforward compensation.

[0051] (3) Path-dependent coupling compensation model: This invention physically decouples the nonlinear transmission error of a multi-segment continuum robot into four types of lumped constants: dynamic friction coefficient, system hysteresis, transmission stiffness, and skeleton compression stiffness. An analytical compensation model is constructed using the derived variable curvature tension distribution factor (Ψ) and cumulative attenuation factor (Φ). This solves the problems of existing precise mechanical models (such as the Cosserat rod) having excessively high computational costs due to complex differential equation numerical integration, making it difficult to meet real-time control requirements, and traditional geometric models (such as PCC) neglecting skeleton axial compression and path friction, resulting in severely insufficient compensation accuracy. This allows the controller to accurately calculate and compensate for cable elastic elongation and skeleton axial compression through efficient algebraic operations using only the four types of constants identified offline and the base tension calculated in real time, greatly reducing computational requirements and enabling real-time deployment of a high-precision mechanical model on embedded systems. Attached Figure Description

[0052] Figure 1 A schematic diagram of the path-dependent geometric coupling mechanism of a multi-segment cable-driven continuum robot;

[0053] Figure 2 A schematic diagram of the path-dependent frictional coupling mechanism of a multi-segment cable-driven continuum robot;

[0054] Figure 3 In coefficient of friction Below, the bending shape and end trajectory of the 0.3m continuous segment;

[0055] Figure 4 A flowchart for the recursive tension estimation strategy;

[0056] Figure 5 The diagram illustrates the friction reversal wavefront and equivalent hysteresis model. (a) shows a complete unidirectional friction reversal process, with the friction reversal wavefront... Propagating from the base to the end, the skeleton is divided into a new state region at the near end and an old state region at the far end; (b) shows a simplified assumption when the inverted intermediate state is inverted again, that is, the multiple nested wavefront states caused by rapid switching of direction (middle figure) are simplified to a single wavefront state (right figure) to reduce computational complexity. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the appendices in the embodiments of this application will be described below. Figures 1-5 The technical solutions in the embodiments of this application are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0058] This application provides a parameter-based decoupling drive compensation method for multi-segment cable-driven continuum robots, aiming to solve the problem of low control accuracy caused by path-dependent coupling, frictional hysteresis, and structural elasticity in multi-segment continuum robots. The core steps of this method are as follows:

[0059] Step 1: Establish the curvature shape distribution function of any segment of a multi-segment rope-driven continuum robot based on the generalized antagonistic factor.

[0060] To address the failure of the constant curvature assumption in the PCC model mentioned in the background art, this invention establishes a curvature shape distribution model based on the "generalized antagonistic factor".

[0061] Step 1.1: Define the generalized antagonist factor

[0062] The generalized antagonism factor η is defined as the projection ratio of the friction-weighted torque onto the net driving torque, used to uniformly describe the shape attenuation effect caused by anisotropic friction and multi-cable antagonism. Its definition formula is:

[0063] ;

[0064] In the formula, For segment numbers of a continuum robot. , This represents the total number of segments in the continuum robot. For the first continuum robot Generalized antagonistic factor of cross-section, For the first continuum robot Cable serial number of the cross section This indicates that it includes all passages through the first... The cross-section of the cable in a segmental continuum robot; For the first The first cable Tension within the segment; Indicates the first The moment arm vector of the cable within its cross-section, where Let be the position vector of the cable within its cross-section. It is a unit vector along the local tangent. For the first The signed coefficient of friction of a cable is defined as follows: ,in The coefficient of kinetic friction is . Indicates the direction of movement; during stretching, it is... Positive values ​​indicate release, while negative values ​​indicate release. The numerator of the formula represents the projection of the friction-weighted torque onto the direction of the net driving torque, and the denominator is the square of the magnitude of the net driving torque.

[0065] Step 1.2: Establish the curvature shape distribution function of any segment of a multi-segment rope-driven continuum robot.

[0066] For an n-segment continuum, based on the generalized adversarial factor , establish the first Scalar curvature of segment continuum robot Along its skeletal length The curvature evolution differential equation:

[0067] ;

[0068] To describe the actual configuration of the robot in three-dimensional space, this invention uses curvature vectors. Parameterized as scalar curvature amplitude With constant curvature plane angle The combination of these elements results in the spatial curvature vector being expressed as:

[0069] ;

[0070] In the formula, For the first The bending plane angle of a segmented continuum robot is determined by the direction of the resultant tension of the drive cable in that segment, and is considered constant within a single segment. This is because the macroscopic bending angle of any segment of the continuum robot... The curvature profile is subject to a strict constraint on the length of the drive cable, thus imposing a definite integral condition. By analytically integrating the above curvature evolution differential equation, we obtain the curvature shape distribution function of any segment of the continuum robot:

[0071] ;

[0072] In the formula, The position is along the arc length of the skeleton. ; This is the total arc length of the robot segment; This represents the macroscopic bending angle of the robot segment.

[0073] This curvature distribution model shows that the curvature distribution of any segment of a continuum robot is determined solely by the geometric parameters of that segment. ) and broad-sense antagonist factors Decision. Among them... It includes the internal force properties of the segment itself and other cables passing through it, thus enabling the reconstruction of a true, non-uniform bending shape while stripping the coupling between segments.

[0074] For a simplified symmetrical antagonistic drive configuration (e.g., only one pair of cables driving in the same plane, cable 1 stretching, cable 2 releasing, and both having a coefficient of friction...), The generalized antagonistic factor can be simplified to a scalar tension ratio form:

[0075]

[0076] like Figure 3 As shown, when the continuum is in the driven stretching phase, the corresponding generalized antagonistic factor is... The curvature distribution exhibits a "proximal concentration" characteristic, with a larger curvature at the proximal end and a smaller curvature at the distal end; when the continuum is in the driving release phase, the corresponding generalized antagonistic factor... The curvature distribution exhibits a "distal concentration" characteristic, with smaller curvature at the proximal end and larger curvature at the distal end. Compared to the traditional constant curvature model (dashed line in the figure), this model (solid line in the figure) can accurately describe the non-uniform spatial curvature caused by friction and antagonistic forces.

[0077] Step 2: Construct a recursive rope tension solver that considers the coupling of multi-cable friction and antagonistic forces.

[0078] To address the challenge of obtaining internal tension without sensors, this invention employs a reverse recursive rope tension solution strategy "from far end to near end," combined with an adaptive fixed-point iterative algorithm to inversely solve the tension across the entire segment (the process is as follows). Figure 4 (As shown).

[0079] Step 2.1: Solving for the tension of a rope in any segment of a continuous body based on the principle of virtual work and the curvature distribution of the continuous body.

[0080] Starting from the segment with the least coupling influence (segment n), the tension at the end of any segment of the continuum required to maintain the target pose is calculated using the principle of virtual work. :

[0081]

[0082] in, For the first Local drive set for segmental continuum robots (Indicates termination at the ) The tension vector of all cables in the cable set (which drives the segment's end); For the first The elastic potential energy gradient of the segment itself (i.e., elastic restoring torque). ,in Here is the stiffness matrix. for The curvature vector at that point; For from the distant segment ( to The cumulative coupled driving torque of ) for the last end ( ), ; For the first The moment arm matrix of the segment is defined as follows: , Its Moore-Penrose pseudo-inverse matrix; It is the identity matrix; It is a zero-space vector used to adjust internal tension.

[0083] To adhere to the "least confrontation" control strategy and ensure physical feasibility (the cable can only be subjected to tension, not compression), we will use the null space vector. Set as:

[0084] ;

[0085] This setting ensures that all calculated tensions are non-negative and that the internal preload is minimized.

[0086] Step 2.2: Recursive solution and adaptive fixed-point iteration of reverse rope tension

[0087] From the The process is reversed from the first segment to the base segment (the second segment). (Section). For the current first... The force balance equation of a segment must include not only its own elastic restoring moment, but also the force generated by all the distal driving cables (driving the first segment). to The cumulative frictional coupling torque generated when the cable (of a segment) passes through the segment, while the tension solution of the continuum of adjacent segments has a strongly coupled algebraic loop problem of "tension-friction-shape", which cannot be solved directly.

[0088] To address the problem of strongly coupled algebraic loops in the tension solution process, this invention constructs a generalized antagonistic factor. Fixed-point iterative mapping function:

[0089] ;

[0090] In the formula, This is a fixed-point iterative mapping function for the generalized antagonistic factor based on the moment projection ratio. This function calculates the antagonistic factor guess obtained from the coupled load transmitted from the remote end. As input, the continuum shape is first reconstructed using the current antagonistic factor estimate, and the elastic potential energy gradient is calculated. Then, the rope tension distribution satisfying force equilibrium is solved by combining the far-end load. Finally, the projection ratio of the total frictional torque, including the contribution from the far-end cable, onto the direction of the elastic restoring torque is calculated, thereby obtaining a new generalized antagonistic factor estimate. The true extent of the continuum at adjacent end segments can be solved through fixed-point iteration. And the rope tension in that section.

[0091] The algorithm calculates the rope tension of the furthest segment of the continuum as the initial condition for recursive solution, starting from the robot's farthest end (the segment least affected by coupling). (Segment) begins. Since there is no other load following this segment, the principle of virtual work can be directly used to calculate the target macroscopic bending angle to maintain it. Required end tension vector This is used as the initial value input for the recursive tension solver.

[0092] Using the chain rule, the total derivative of this mapping function is decomposed into the product of four physical gains: friction sensitivity, equilibrium gain, stiffness gain, and shape sensitivity.

[0093] ;

[0094] This characterizes the effect of cable tension variation on the calculated value of the generalized antagonism factor; This represents the geometric proportion by which torque demand is converted into tension. The bending stiffness of the frame determines the stiffness of the frame. The stiffness matrix represents the skeleton. This characterizes the effect of friction state changes on curvature distribution. Through worst-case gain analysis of each term, the total closed-loop gain is found... With system strain energy (bending angle) The square of the product is positively correlated:

[0095] ;

[0096] This indicates that under high curvature (high strain energy) conditions, the total product of chain gains may be greater than 1, causing conventional iterative algorithms to diverge.

[0097] To prevent iterative divergence under high curvature conditions, this invention designs an adaptive damped fixed-point iterative algorithm. An adaptive damping factor is introduced. The iteration process is relaxed, and the iteration step size is dynamically adjusted based on the real-time estimated generalized antagonistic factor:

[0098] ;

[0099] ;

[0100] In the formula: It serves as the base step size for rapid convergence under low-friction conditions. These are sensitivity calibration parameters used to suppress gain under conditions of high friction or large bending. For the first The estimated value of the generalized antagonism factor at the next iteration. When two adjacent iterations... The difference is less than the threshold At that time, the tension distribution of the current segment and the load at the base end are output as the basis for the next segment ( Input of (segment).

[0101] This adaptive damping fixed-point iterative algorithm ensures that the Lipschitz constant of the mapping function is always less than 1 throughout the entire workspace, thus guaranteeing the global convergence of the sensorless tension solution. The solver can be completed in 3-5 iterations.

[0102] Step 3: Correcting the generalized antagonistic factor η during the dynamic motion of the continuum robot.

[0103] To address the issue of the highly time-varying and path-dependent nature of frictional hysteresis, in dynamic processes involving reverse motion, it is essential to consider the frictional state (generalized antagonistic factor). Real-time corrections are made to reflect the hysteresis loop characteristics.

[0104] Step 3.1: Establish a linear interpolation equivalent antagonistic factor model based on normalized hysteresis progress.

[0105] As shown in Figure 5(a), when the driving cable changes its direction of motion (e.g., from tension to release), the reversal of friction is not instantaneous, but rather forms a friction reversal wavefront that propagates from the base to the end. Wavefront Serving as a dividing point: its proximal region ( The region has entered a new state of frictional equilibrium, while the far-end region ( It remains "locked" in the old frictional state. As the motion continues, the wavefront moves toward the end until it is completely reversed.

[0106] Figure 5 (b) represents a simplified assumption regarding the phenomenon of intermediate state reversal (complex nesting): if the driving direction changes again before the wavefront reaches its end (i.e., in an intermediate state), multiple wavefronts moving in opposite directions will exist simultaneously on the skeleton (e.g., ...). Figure 5 (As shown in the middle of b), this forms a multi-layered, nested friction distribution region. Directly calculating the dynamics of such multiple wavefronts is extremely difficult.

[0107] To enable real-time control based on the first two models, this invention establishes a linear interpolation equivalent antagonistic model based on normalized hysteresis progress. Based on the integral mean value theorem, it ignores the microscopic distribution details of multiple wavefronts, and equates the resulting macroscopic hysteresis effect to a unified equivalent parameter. This parameter is obtained by linear interpolation between the "old state" and the "new theoretical state," thus avoiding the tracking calculation of complex wavefront positions while ensuring macroscopic pose accuracy.

[0108] First, based on the current geometric parameters and the friction state at the moment of bending reversal, calculate the total angular travel required to complete one cycle from "fully loaded" to "fully released" (or vice versa), i.e., the total hysteresis angle threshold. :

[0109]

[0110] In the formula, This represents the stable frictional state before reversal (i.e., the generalized antagonistic factor at the starting point). The terminal curvature at the current moment. For the first The length of the segment. This threshold physically represents the total change in bending angle required for the friction wavefront to propagate from the base to the end.

[0111] Next, the normalized hysteresis progress is defined. The change in the current bending angle relative to the starting point of the reverse motion is calculated and normalized to obtain the dimensionless hysteresis progress factor. :

[0112] In the formula, The current macroscopic bending angle. The angle is the starting point of this reverse motion. This indicates that the frictional state has not yet begun to change. This indicates that the direction of friction has been completely reversed.

[0113] Finally, utilize delayed progress. We perform weighted linear interpolation between the "old state" and the "new theoretical state" to obtain the equivalent generalized antagonistic factor at the current moment. :

[0114] ;

[0115] In the formula, This represents the theoretical target friction state calculated at the current moment based on the assumption of complete slip (i.e., assuming the wavefront has instantaneously reached its end). This linear interpolation model achieves a smooth, equivalent description of the complex nonlinear friction characteristics within the hysteresis loop.

[0116] An equivalence analysis was conducted based on the integral mean value theorem and the principle of spatial low-pass filtering: Although the simplified equivalent smoothing model Compared with the actual wavefront segmentation model There is a deviation in local curvature However, since both are constrained by the same macroscopic bending angle constraint (i.e. The local deviation exhibits oscillatory characteristics in space; the end position error is the second integral of the curvature deviation. Since the integration process is equivalent to performing a spatial low-pass filter on the high-frequency oscillating curvature deviation, the positive and negative deviations cancel each other out, making the two highly equivalent at the end pose level.

[0117] Step 3.2: Establish an antagonist factor update strategy for the dynamic coupling process.

[0118] In multi-segment coupled motion, attitude changes in the distal segment will cause the motion to pass through the proximal segment (the first segment). The cable tension in the segment changes continuously, leading to the theoretical target friction state in the near-end segment. It evolves dynamically over time. This method treats this coupling process as a quasi-static process, within each control cycle:

[0119] (1) First, the theoretical target friction state is solved recursively using step two. ;

[0120] (2) Update the delayed progress ;

[0121] (3) Calculate the corrected equivalent generalized antagonistic factor using the above interpolation formula. This strategy ensures the equivalent generalized antagonist factor. The smoothness in the time domain avoids abrupt changes in near-end shape calculation caused by fluctuations in far-end load.

[0122] Step 4: Constructing the actual input rope length parameters for multi-segment continuum drive based on feedforward elastic compensation using lumped parameters

[0123] Based on the variable curvature shape determined in step one and the tension distribution calculated in step two, the final motor drive command is calculated using the following model. To compensate for cable elongation and skeleton compression:

[0124] Step 4.1: Decoupling the physical parameters of nonlinear transmission error in a multi-segment continuum robot.

[0125] The nonlinear transmission error of a multi-segment continuum robot is physically decoupled into four types of independent lumped constants:

[0126] Dynamic friction coefficient ( ): Characterizes the contact friction between the cable and the guide hole;

[0127] System hysteresis ( ): Characterizes the commutation dead zone;

[0128] Lumped transmission stiffness ( ): Characterizes the flexibility of the transmission path from the drive unit to the base;

[0129] Lumped frame compressive stiffness ( ) and cable segment stiffness ( ): Characterizes the structural flexibility within the robot body.

[0130] Step 4.2: Characterizing the tension transmission loss of the multi-segment continuum coupling process based on cumulative contact angle.

[0131] When calculating tension transfer, the cumulative contact angle before segment j (the sum of bending angles before segment j) is introduced. The concept is used to quantify the coupling effect of multiple segments. The root drive cable (wire) reaches the first Before the segment, all proximal segments must be traversed ( arrive (segment). This invention defines a cumulative decay factor. :

[0132] ,

[0133] In the formula, This is the sum of the macroscopic bending angles of all near-end segments along the cable's path. For the first The signed coefficient of friction of the cable. This factor quantitatively describes the tension transmission loss caused by near-end bending. Multiplying the rope tension at the base of the root drive cable by this factor gives the initial position in segment j. ( ) rope tension.

[0134] Step 4.3: Construct a cable elongation compensation model based on variable curvature tension distribution.

[0135] To accurately calculate elongation under variable curvature distribution, a variable curvature tension distribution factor derived from the curvature shape distribution of the j-th segment of the continuous bending is introduced.

[0136]

[0137] In the formula, This is the effective attenuation index. This factor directly calculates the equivalent average tension ratio of the cable within the variable curvature bending section. Combining the above factors, the [missing information] is calculated. root cable drive number Total elastic elongation over a period of time :

[0138] ;

[0139] The formula shows that the cable elongation is the sum of the elongation of the base transmission section and the elongation of each segment of the robot body, and the elongation of each segment has been corrected for path friction attenuation.

[0140] Step 4.4: Construct a skeleton compression compensation model for a multi-segment continuum robot.

[0141] Explicitly calculate all passages through the first Axial compressive deformation of the skeleton caused by the resultant force of the cable segment Furthermore, reverse compensation is performed in the drive command (i.e., an additional compression compensation is added on top of the motor's extension length) to eliminate control slack caused by frame shortening. The frame compression deformation is:

[0142] ;

[0143] Step 4.5: Construct the actual input rope length parameters for multi-segment continuum drive.

[0144] The final Duan Di Motor position command of root drive cable It consists of four superimposed parts: geometric path length, cable elongation compensation, skeleton compression compensation, and hysteresis compensation.

[0145]

[0146] In the formula: Let be the theoretical path length calculated based on geometric kinematics, where Indicates the first The first segment of the continuum The required change in coupling drive when the rope reaches the m-th segment before passing through can be obtained by the following formula: ,in Let m represent the curvature of the m-th segment. Let be the position vector of the cable within the cross-section of the m-th segment; This is the cable elastic elongation compensation amount calculated in step 4.3; For all proximal skeleton segments along the cable's path (from the base to the first...) The sum of the axial compression compensation of the segments (calculated by step 4.4); This is the system backlash compensation constant. Ensure that the compensation direction is consistent with the motion direction.

[0147] Step 5: Step-by-step parameter identification:

[0148] To accurately obtain the four types of lumped constants in the above model, a sequential locking strategy "from base to end" is adopted:

[0149] Step 5.1: First, lock all segments at the far end into a straight line state, then drive only the base segment. By comparing the theoretical model with the actual encoder data, identify the friction coefficient μ and system hysteresis of this segment. ) and lumped stiffness parameter ( , , ).

[0150] Step 5.2: Keeping the base segment stationary, unlock the next segment. Use the identified base segment parameters to decouple the near-end transmission error of the current segment, thereby independently identifying the characteristic parameters of each segment. This step-by-step identification method effectively isolates the parameter coupling between multiple segments and improves the identification accuracy.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it; although

[0152] The present invention has been described in detail with reference to the foregoing embodiments. Those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A parameter-decoupling drive compensation method for a multi-segment rope-driven continuum robot, characterized in that, The specific steps of the method are as follows: We establish the curvature shape distribution function of any segment of a multi-segment rope-driven continuum robot based on a generalized antagonistic factor, and analyze the non-uniform shape decay caused by anisotropic friction and multi-segment rope antagonism. A recursive rope tension solver considering the coupling of multi-cable friction and antagonistic forces is constructed to solve the numerical convergence problem caused by tension-friction-shape coupling. During the dynamic motion of the continuum robot, a linear interpolation model is constructed using normalized hysteresis progress to correct the generalized antagonistic factor in real time. The actual input rope length parameters for multi-segment continuum drive are constructed based on feedforward elastic compensation of lumped parameters. Step-by-step parameter identification employs a sequential locking strategy from the base to the end.

2. The parameter decoupling drive compensation method according to claim 1, characterized in that, The generalized antagonism factor is the projection ratio of the friction-weighted torque onto the net driving torque, used to uniformly describe the shape attenuation effect caused by anisotropic friction and multi-cable antagonism, and is defined by the following formula: ； In the formula, For segment numbers of a continuum robot. For the first continuum robot Generalized antagonistic factor of the cross section of a segmental continuum robot. For the first continuum robot Cable serial numbers for the cross-section of a segmental continuum robot. This indicates that it includes all passages through the first... Cables in the cross-section of a segmental continuum robot; For the first The first cable Tension within the segment; Indicates the first The moment arm vector of the cable within its cross-section, where Let be the position vector of the cable within its cross-section. It is a unit vector along the local tangent; For the first The signed coefficient of friction of the cable.

3. The parameter decoupling drive compensation method according to claim 1, characterized in that, The curvature shape distribution function of any segment of the multi-segment rope-driven continuum robot is: ； In the formula, For segment numbers of a continuum robot. For scalar curvature amplitude, The position is along the arc length of the skeleton. ; This is the total arc length of the robot segment; This represents the macroscopic bending angle of the robot segment. For the first continuum robot Generalized antagonistic factor of cross section of segmental continuum robot.

4. The parameter decoupling drive compensation method according to claim 1, characterized in that, In constructing the recursive rope tension solver, the rope tension of any segment of a continuous body is solved based on the principle of virtual work and the curvature distribution of the continuous body; the end tension of any segment of the continuous body required to maintain the target pose is calculated. The formula is: ； in, For the first Local drive set for segmental continuum robots The tension vector of all cables in the system; For the first The elastic potential energy gradient of the segment itself, The cumulative coupled driving torque from the distal segment, For the first The moment arm matrix of the segment, For the first The Moore-Penrose pseudo-inverse matrix of the moment arm matrix of the segment; It is the identity matrix; It is a zero-space vector.

5. The parameter decoupling drive compensation method according to claim 4, characterized in that, To adhere to the minimum adversarial control strategy and ensure physical feasibility, the cable can only be subjected to tension, not compression, and the zero-space vector... Set as: ； This ensures that all calculated tensions are non-negative and that the internal preload is minimized.

6. The parameter decoupling drive compensation method according to claim 4, characterized in that, In the recursive solution of the reverse rope tension and the adaptive fixed-point iteration, the fixed-point iterative mapping function for the generalized antagonistic factor is constructed as follows: ； In the formula, This is a fixed-point iterative mapping function for the generalized antagonistic factor based on the moment projection ratio. The true value of the continuum near the adjacent end segments is obtained through fixed-point iteration. And the rope tension in that section; Using the chain rule, the total derivative of this mapping function is decomposed into the product of four physical gains: friction sensitivity, equilibrium gain, stiffness gain, and shape sensitivity. ； To characterize the effect of cable tension variation on the calculated value of the generalized antagonism factor; To characterize the geometric proportion by which torque demand is converted into tension; , represents the stiffness matrix of the skeleton; This characterizes the effect of changes in frictional state on curvature distribution.

7. The parameter decoupling drive compensation method according to claim 6, characterized in that, Introducing an adaptive damping factor The iteration process is relaxed, and the iteration step size is dynamically adjusted based on the real-time estimated generalized antagonistic factor: ； ； In the formula: It serves as the base step size for rapid convergence under low-friction conditions. These are sensitivity calibration parameters used to suppress gain under conditions of high friction or large bending. For the first The estimated value of the generalized antagonistic factor at the next iteration.

8. The parameter decoupling drive compensation method according to claim 1, characterized in that, In the process of correcting the generalized antagonistic factor, an equivalent antagonistic model based on normalized hysteresis progress is established by linear interpolation; the change of the current bending angle relative to the starting point of the reverse motion is calculated and normalized to obtain a dimensionless hysteresis progress factor; using the hysteresis progress factor, linear interpolation is performed between the stable friction state before reversal and the theoretical target friction state based on the assumption of complete slip, and the corrected equivalent generalized antagonistic factor at the current moment is calculated.

9. The parameter decoupling drive compensation method according to claim 1, characterized in that, In the actual input rope length parameters of the multi-segment continuum drive constructed by the feedforward elastic compensation based on lumped parameters, the final first... Duan Di Motor position command of root drive cable It consists of four superimposed parts: geometric path length, cable elongation compensation, skeleton compression compensation, and hysteresis compensation. ； In the formula: Let be the theoretical path length calculated based on geometric kinematics, where Indicates the first The first segment of the continuum The amount of coupling drive required to change when the root rope is in the m-th segment before it passes through; This is the compensation amount for the elastic elongation of the cable; This is the sum of the axial compression compensation amounts of all the near-end skeleton segments through which the cable passes; This is the system hysteresis compensation constant. Ensure that the compensation direction is consistent with the motion direction.

10. The parameter decoupling drive compensation method according to claim 9, characterized in that, (1) No. root cable drive number Cable elastic elongation compensation for segmented continuum robots for: ； In the formula, For lumped transmission stiffness, The cable tension at the base of the continuum is given. Let m be the cable segment stiffness of the m-th segment of the driving rope path of the j-th segment of the continuum. Let be the cumulative attenuation factor of the m-th segment of the path of the i-th driving rope in the j-th segment of the continuum. The variable curvature tension distribution factor of the m-th segment of the drive rope path of the j-th segment of the continuum; the cable elastic elongation compensation is the sum of the elongation of the base transmission segment and the elongation within each segment of the robot body, and the elongation of each segment has been corrected by path friction attenuation. (2) Explicitly calculate all passages through the first Axial compressive deformation of the skeleton caused by the resultant force of the cable segment And reverse compensation is performed in the drive command to eliminate control slack caused by skeleton shortening: axial compression deformation of the skeleton for: ； In the formula, To achieve lumped frame compressive stiffness, The variable curvature tension distribution factor of the j-th segment of the continuum.

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