Multi-ball-pair self-adaptive palm structure and shape sensing method and system thereof

Abstract

The invention discloses a multi-spherical-pair self-adaptive palm structure and a shape sensing method and system thereof, and relates to the technical field of robot tactile perception, and the method comprises the steps: firstly obtaining the position and normal vector of an object surface contact point through kinematics modeling; selecting a hyper-quadratic surface equation as a parameterized model; constructing an optimization objective function fusing the position error and the normal deviation; a least square method optimizer capable of being iteratively reconstructed is used for solving, in each iteration, balance factors are adaptively updated according to error statistical distribution of all contact points so as to balance contribution of two kinds of heterogeneous errors, and a dynamic weight is calculated for each contact point so as to suppress noise and abnormal points; and finally, outputting a fitted hyper-quadric surface parameter. According to the method, the problems that multi-source errors are difficult to balance and are sensitive to measurement noise in shape perception are solved, and high-precision and high-robustness online object shape estimation is realized.

Description

Technical Field

[0001] This invention relates to the field of robot tactile perception technology, specifically a multi-spherical adaptive palm structure and its shape perception method and system. Background Technology

[0002] In the field of robotic grasping and manipulation, enabling robotic hands to perceive object shapes in real time and accurately is crucial for achieving stable grasping, precise manipulation, and environmental interaction. In recent years, tactile sensing hands with flexible or adaptive structures have attracted attention due to their ability to passively conform to object contours and acquire information from multiple contact points. Among these, the multi-spherical adaptive hand structure, through a series of freely rotatable spherical joints, can naturally conform to the object surface during grasping. Furthermore, by using attitude sensors integrated within the spherical joints, it calculates the spatial position and normal vector of each contact point, providing a valuable data source for shape estimation. However, existing technologies for 3D shape reconstruction based on such sparse contact point data, especially for regular geometries such as ellipsoids and cubes commonly encountered in grasping scenarios, typically face two interrelated core challenges, leading to inaccurate and unreliable perception results:

[0003] The challenge of balancing heterogeneous errors from multiple sources: Shape perception requires the simultaneous use of two types of information: the position of the contact point and the normal vector. The former reflects "where the point is," while the latter reflects "which direction it faces." Most existing fitting methods only optimize positional errors (such as the distance from the point to the model surface), failing to effectively utilize the normal vector information, which contains stronger geometric constraints. Even the few methods that attempt to introduce normal constraints face a fundamental challenge: positional errors (usually measured in millimeters) and normal deviations (measured in radians or cosine values) differ greatly in physical dimensions and numerical scales. Existing technologies lack an adaptive mechanism to reasonably balance the contributions of these two types of heterogeneous errors to the optimization objective, typically relying on empirically set fixed weights. This makes the optimization process easily dominated by one type of error, thus failing to obtain an accurate shape model that simultaneously satisfies positional fit and normal alignment, and the fitting results often exhibit systematic bias. The challenge of lack of robustness under sensor noise and outlier interference: In actual grasping, the measurement information of the contact point is inevitably affected by factors such as sensor noise, slight slippage, and structural elastic deformation, producing unreliable "outliers." Traditional fitting methods based on ordinary least squares aim to minimize the sum of squared errors across all points, making them extremely sensitive to outliers. A single large, noisy point can pull the entire fitting result in the wrong direction, severely compromising the accuracy of shape estimation. Existing techniques lack effective mechanisms for dynamically identifying and suppressing these outliers during iterative optimization, resulting in poor robustness and unstable perception results in practical applications. Summary of the Invention

[0004] This invention provides a multi-spherical adaptive palm structure and its shape perception method and system, which solves the problems mentioned in the background art of how to adaptively balance the contributions of position and normal heterogeneous errors in shape fitting, and how to suppress measurement noise and outlier interference, thereby achieving high-precision and high-robustness online shape perception.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A multi-spherical adaptive palm structure shape perception method includes the following steps:

[0007] S1: Perform kinematic modeling on the multi-spherical adaptive palm structure to obtain the position coordinates of multiple contact points on the surface of the grasped object and the corresponding contact point normal vectors.

[0008] S2: Select the hyperquadratic surface equation as the parameterized model representing the shape of the grasped object;

[0009] S3: Construct an optimization objective function, which is a weighted sum of the position error term and the normal vector direction deviation term for all contact points;

[0010] S4: Solve the objective function using an iteratively reconfigurable least squares optimizer to determine the parameters of the hyperquadratic surface equation; wherein the solution process includes at least the following iterative steps:

[0011] S41: Based on the current iteration's estimated hyperquadratic surface parameters, calculate the position error and orientation deviation of each contact point;

[0012] S42: Based on the statistical distribution of position errors and orientation deviations of all contact points obtained in step S41, adaptively calculate the balance factor. The balance factor Used to adjust the relative weights of the position error term and the orientation deviation term in the optimization objective function;

[0013] S43: Calculate the dynamic weight of the position error for each contact point separately. Dynamic weights relative to directional deviation Among them, for contact points with errors greater than a preset statistical threshold, their corresponding dynamic weights are reduced.

[0014] S44: Use the updated balance factor and dynamic weights , We construct a weighted optimization objective function and perform least squares optimization to obtain a new round of hyperquadratic surface parameter estimates.

[0015] S5: Repeat steps S41 to S44 until the convergence condition is met, and output the final hyperquadratic surface parameters as the shape-aware result.

[0016] As a preferred embodiment of the present invention, the balance factor in step S42 The calculation method is as follows: calculate the ratio of the first statistical value of the absolute value of the position error of all contact points to the second statistical value of the absolute value of the direction deviation of all contact points; wherein, the first statistical value and the second statistical value are both medians or means.

[0017] As a preferred technical solution of the present invention, the balance factor The specific calculation formula is as follows:

[0018]

[0019] in, For the positional error of the contact point, For the directional deviation of the contact point, This indicates the median operation.

[0020] As a preferred technical solution of the present invention, in step S43, the preset statistical threshold is determined based on the statistical dispersion of the position error and direction deviation of all contact points in the current iteration.

[0021] As a preferred technical solution of the present invention, in step S43, dynamic weights and The calculation formula is:

[0022]

[0023] in, and These represent the position errors of all contact points in the current iteration. and directional deviation The median of A constant factor, A function that is cropped to the interval [0,1].

[0024] As a preferred embodiment of the present invention, in step S3, the position error term is expressed as Sampson distance. The calculation formula is as follows:

[0025]

[0026] in, This is the implicit expression for the equation of the hyperquadratic surface. Its gradient.

[0027] As a preferred embodiment of the present invention, in step S2, the equation of the hyperquadratic surface is in the form of:

[0028]

[0029] in, Let the coordinates be the center coordinates of the surface. , , These are the scale parameters along the three principal axes. This is the shape index.

[0030] As a preferred embodiment of the present invention, before the first iteration in step S4, the method further includes: setting initial estimates of the parameters of the hyperquadratic surface equation and setting the equilibrium factor. Dynamic weights and Assign initial values.

[0031] The present invention also provides a multi-spherical adaptive palm structure shape perception system, the system being configured to execute the above-described multi-spherical adaptive palm structure shape perception method, and comprising:

[0032] The kinematic modeling module is used to perform kinematic modeling on the multi-spherical adaptive palm structure to obtain the position coordinates of multiple contact points on the surface of the grasped object and the corresponding contact point normal vectors.

[0033] The model selection module is used to select the hyperquadratic surface equation as the parametric model representing the shape of the grasped object;

[0034] The objective function construction module is used to construct the optimization objective function, which is a weighted sum of the position error term and the normal vector direction deviation term for all contact points;

[0035] An iterative optimization solution module is used to solve the objective function using an iteratively reconfigurable least squares optimizer to determine the parameters of the hyperquadratic surface equation; wherein, the iterative optimization solution module is configured to execute an iterative process, the iterative process including:

[0036] Based on the current iteration's estimated hyperquadratic surface parameters, calculate the position error and orientation deviation of each contact point;

[0037] Based on the statistical distribution of position errors and orientation deviations of all contact points obtained from the calculation, a balance factor for adjusting the weights of the two errors is adaptively calculated. ;

[0038] Based on the degree of deviation of the position error and orientation deviation of each contact point relative to their respective statistical scales, a dynamic weight of the position error is calculated for each contact point. Dynamic weights relative to directional deviation ;

[0039] Use the updated balance factor and dynamic weights , We construct a weighted optimization objective function and perform least squares optimization to obtain a new round of hyperquadratic surface parameter estimates.

[0040] The process is iteratively executed until the convergence condition is met, and the final hyperquadratic surface parameters are output as the shape-aware result.

[0041] The present invention also provides a multi-spherical adaptive palm structure, comprising: a base;

[0042] And a plurality of rotatable ball joints connected to the base in a multi-stage series manner, wherein at least the last-stage ball joint is used to contact the object being grasped; wherein each stage of the ball joint integrates an attitude sensor for measuring its own rotation angle;

[0043] The hand structure is configured such that the data acquired by the attitude sensor can be used to execute the aforementioned multi-spherical adaptive hand structure shape perception method.

[0044] The present invention has the following advantages:

[0045] In step S42, the balance factor is dynamically calculated in each iteration based on the statistical distribution (such as the median) of the errors at all contact points. This mechanism enables real-time, automated adjustment of the relative importance of two types of errors. It ensures that the optimization process simultaneously and evenly approximates the position and normal constraints of the contact point, resulting in a hyperquadratic surface that not only spatially matches the measurement point but also whose local surface orientation is highly consistent with the measurement normal vector. This significantly improves the geometric accuracy and physical reliability of shape estimation and solves the optimization bias problem caused by fixed weights.

[0046] In step S43, dynamic weights are introduced and iteratively updated for each contact point. and The weights are calculated based on the deviation of each point's error from the overall statistical scale (such as a multiple of the median), automatically reducing the contribution of outliers. This iteratively reconstructible optimization process transforms standard least-squares optimization into a robust estimation. It can automatically identify and suppress unreliable data points caused by noise, slippage, and other factors, greatly reducing the impact of outliers on the overall fitting results. Therefore, the method of this invention exhibits excellent stability and reliability in environments with actual measurement noise, ensuring the consistency and accuracy of shape-sensing results.

[0047] In summary, this invention organically integrates the adaptive error balancing mechanism (S42) and the dynamic noise-resistant weighting strategy (S43) into a unified iterative optimization framework (S4), working synergistically to fundamentally overcome the two major bottlenecks in the prior art. This enables the multi-spherical adaptive hand structure not only to "sense" contact but also to infer accurate and robust object geometry from sparse, noisy tactile data, thereby greatly enhancing the robot gripper's environmental understanding and adaptive interaction capabilities. Attached Figure Description

[0048] Figure 1 This is a flowchart of the multi-spherical adaptive palm structure shape perception method in the embodiment;

[0049] Figure 2 The flowchart of the iteratively reconfigurable least squares optimizer (IRLS) in this embodiment is shown.

[0050] Figure 3 This is a schematic diagram of the experimental device for the multi-spherical adaptive palm structure robotic hand used in the embodiment.

[0051] Figure 4 This is a schematic diagram illustrating the kinematic modeling of the multi-spherical adaptive palm structure in the embodiment.

[0052] Figure 5 This is a schematic diagram illustrating the principle of surface fitting based on the least squares method in the embodiment.

[0053] Figure 6 This is a comparison chart of experimental results for shape perception of spheres of different sizes in the examples.

[0054] In the diagram: 1. The object being grasped; 2. Linkage fingers; 3. Base; 4. Signal acquisition board; 5. Motor; 6. Multi-ball adaptive palm structure. Detailed Implementation

[0055] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0056] This invention provides a multi-spherical adaptive palm structure and its shape perception method and system. The method aims to robustly and accurately estimate the geometry of the object being grasped, particularly regular objects such as ellipsoids and cubes, online using sparse contact point information acquired by sensors embedded in the palm structure.

[0057] Example 1: This example provides a multi-spherical adaptive palm structure shape perception method. Through the adaptive balancing mechanism and dynamic weight strategy in the iterative optimization framework, it achieves high-precision and high-robust online shape perception. It solves the problem mentioned in the background technology that the difference in the dimensions and numerical scale between position error (millimeter level) and normal deviation (radian level) makes the optimization process easily dominated by a certain type of error, as well as the problem that the traditional least squares method is sensitive to outliers, resulting in unstable fitting results.

[0058] Specifically, such as Figure 1 As shown, it includes the following steps S1 to S5.

[0059] S1: Perform kinematic modeling on the multi-spherical adaptive palm structure to obtain the position coordinates of multiple contact points on the surface of the grasped object and the corresponding contact point normal vectors.

[0060] Specifically, such as Figure 3 and Figure 4 As shown, the multi-spherical adaptive palm structure used in this embodiment consists of a base and multiple rotatable spherical pairs connected to the base in a multi-level series manner. At least the last-level spherical pair (i.e., the spherical pair that directly contacts the object) is used to contact the object being grasped, and each level of the spherical pair integrates an attitude sensor (such as an inertial measurement unit, IMU) to measure its own rotation angle (Euler angle).

[0061] The modeling process includes:

[0062] Distinguish and name the spherical pairs: those with a radius of The spherical sub-sub ... The ball pair is named a tertiary ball pair (final contact ball pair). It is labeled with (…). () A unique identifier for a third-level ball, in which This indicates the secondary ball sub-number to which it belongs. This indicates the number of the third-level ball set on its corresponding second-level ball set.

[0063] Deriving contact point information using the transformation matrix:

[0064] Contact point location calculation: Level 3 ball joint ( The center of rotation (which can be considered as the contact point) in the world coordinate system The position vector below It can be derived step by step through the transformation matrix:

[0065]

[0066] in, It is a secondary ball deputy The position of the center of rotation, From the second-level ball deputy The center of rotation points to the third-level ball pair ( The vector of the center of rotation can be further expressed as:

[0067]

[0068] here, It is a secondary ball deputy The rotation transformation matrix obtained by the Euler angle transformation measured by the internal sensor represents the rotation of its coordinate system relative to the world coordinate system; It is a level three ball assistant ( The initial position vector in its corresponding second-order spherical sub-coordinate system.

[0069] Finally, the coordinates of the contact point are: .

[0070] Contact point normal vector calculation: third-order ball joint ( Normal vector at the contact point (Assuming the contact point is located on a fixed direction on the outer surface of the ball joint, such as initially along the Z-axis of the local coordinate system of the ball joint) is:

[0071]

[0072] in, It is composed of three-level ball assistants ( The rotation transformation matrix is ​​obtained by transforming Euler angles measured by the internal sensor.

[0073] S2: Select the hyperquadratic surface equation as the parameterized model representing the shape of the grasped object.

[0074] Considering the shapes of common objects (such as ellipsoids, cubes, cylinders, etc.) encountered in robot grasping scenarios, this invention selects the hyperquadratic surface equation as the basic model for fitting, because it can flexibly express the aforementioned shapes in a unified mathematical form. The explicit form of this equation is:

[0075]

[0076] in, Indicates the center position of the surface; , , These are the scale parameters (semi-axis lengths) of the surface in the three principal axis directions. For shape index (when When it is close to 2, it represents an ellipsoid. When the value is greater than 2, it tends to represent a cube or a cylinder.

[0077] For ease of calculation, it is written in implicit form. :

[0078]

[0079] At any point The gradient at that point (i.e., the direction of the normal vector of the surface at that point) is:

[0080]

[0081] in Represents the symbolic function, that is:

[0082]

[0083] S3: Construct an optimization objective function, which is a weighted sum of the position error term and the normal vector direction deviation term for all contact points.

[0084] To fully utilize the position and normal information of the contact point, the following objective function is constructed. :

[0085]

[0086] in: For the position error term, the Sampson distance is used to approximate the shortest distance from the contact point to the hyperquadratic surface. The calculation formula is as follows:

[0087]

[0088] For directional deviation This indicates the inconsistency between the measured normal vector and the processed normal vector of the fitted surface at the corresponding projection point. The calculation formula is:

[0089]

[0090] in, It is the contact point The coordinates of an orthogonal projection point on the hyperquadratic surface can be calculated using the following formula:

[0091]

[0092] in It is a balancing factor used to adjust the relative weights of position error and orientation deviation in the overall objective function.

[0093] S4: Solve the objective function using an iteratively reconfigurable least squares optimizer (IRLS) to determine the parameters of the hyperquadratic surface equation.

[0094] This step is the core of the method, and its purpose is to robustly solve for the objective function. Minimize hyperquadratic surface parameters The optimizer uses an iterative process, such as... Figure 2 As shown, the specific steps are as follows:

[0095] S41: Initialization: Set parameters of the hyperquadratic surface A set of initial estimates Initial equilibrium factor and the dynamic weight of each contact point. , All values ​​can be set to 1.

[0096] S42: Calculate the error and adaptively update the balance factor based on the current parameters. .

[0097] Use the current parameter estimate Calculate for all contact points and .

[0098] Then, based on the error statistical distribution of all contact points in this iteration, the balance factor is adaptively updated. This allows it to balance the magnitude difference between the two types of heterogeneous errors. The updated formula is:

[0099]

[0100] in, This indicates that the median is used. The formula uses the median to represent the overall error level, and its ratio can be automatically adjusted. This ensures that the position error term and the orientation deviation term contribute equally to the optimization process, preventing either one from dominating the optimization process.

[0101] S43: Calculate the dynamic weight of each contact point and .

[0102] To suppress the effects of noise and outliers, a dynamic weight is introduced for each contact point j. and The weight is calculated based on the degree of deviation of the error at that point from the overall error dispersion; the greater the deviation, the lower the weight. The calculation formula is as follows:

[0103]

[0104] in:

[0105] , , representing the scales of position error and orientation deviation, respectively.

[0106] For constant factors (e.g., can be taken as) =3, corresponding to " The "Principles" are used to define the threshold for outliers.

[0107] The function will The error is limited to the range 0 to 1. This means that when the error at a certain point exceeds... When the median scale is 1 times larger, its weight will be reduced to 0, thus effectively suppressing it in this iteration.

[0108] S44: Perform weighted least squares optimization.

[0109] Using the updated balance factor and dynamic weights , Construct the weighted objective function for this iteration:

[0110]

[0111] Minimize using a nonlinear least squares optimization algorithm (e.g., a function in the SciPy library that uses the Trust Region Reflection (TRF) algorithm). At the same time, parameters can be set. Reasonable boundary constraints (such as) , Solving this equation yields a new round of parameter estimates. .

[0112] S45: Determine whether the convergence is successful.

[0113] Check if the convergence condition is met (e.g., the parameter change is less than a threshold, or the maximum number of iterations has been reached). If convergence has not occurred, then let... Return to step S42 for the next iteration; if convergence has been achieved, proceed to step S5.

[0114] S5: Output the final hyperquadratic surface parameters as shape-aware results.

[0115] After iterative convergence, the final hyperquadratic surface parameters are output. This parameter characterizes the perceived shape of the object. Simultaneously, two evaluation metrics can be calculated to quantify the fit:

[0116] Mean square error : Reflects the overall fit of the position.

[0117]

[0118] Average angle deviation : Reflects the overall normal consistency.

[0119]

[0120] in, This indicates calculating the average value.

[0121] In this embodiment, an experiment was conducted using a robotic hand with a multi-spherical adaptive palm structure, and a robotic hand as described above was constructed. Figure 3 The experimental setup shown includes: a multi-spherical adaptive hand structure 6, connecting fingers 2, a base 3, a signal acquisition board 4, and a motor 5. The multi-spherical adaptive hand structure 6 consists of multiple spherical joints of different sizes, each of which can rotate freely, and each spherical joint contains an embedded attitude sensor.

[0122] The linkage finger 2 is a linkage structure that provides centripetal grasping force, with all three fingers driven by the same power source. The entire device grasps the object 1 by bending the fingers, providing a grasping force. The multi-ball joint adaptive palm structure 6 conforms to the shape of the object under the action of the grasping force. After the grasp is stable, the pose signal of the sensor inside the ball joint is collected and input into the IRLS optimizer to calculate the fitting result. The device is used to grasp standard spheres of different sizes (radius RS from 30mm to 45mm), collect contact point data, and run the shape perception algorithm of this invention.

[0123] A schematic diagram of the fitting process is shown below. Figure 5 As shown, the algorithm flow is as follows: Figure 2 As shown. The final shape-perceived result (taking the fitted sphere radius as an example) is compared with the true value as follows: Figure 6 As shown. Experimental results show that the fitting results obtained by the method of this invention (especially the IRLS optimizer that introduces adaptive λ update and dynamic weight mechanism) have significantly better MSE and AVG indices than methods that only use position error or use fixed weights, demonstrating the beneficial effects of this invention in improving geometric accuracy and algorithm robustness.

[0124] Example 2, another embodiment of the present invention provides a multi-spherical adaptive palm structure shape perception system, which can be integrated into a robot controller or host computer in a software, hardware, or a combination of software and hardware. The system includes:

[0125] The kinematic modeling module is configured to execute step S1, receiving raw Euler angle data from the hand structure posture sensor, and calculating and outputting the position coordinates of each contact point using a built-in transformation matrix formula. and normal vector .

[0126] Model selection module: Configured to determine the hyperquadratic surface equation as the fitting model and provide its implicit functions. and gradient The computing interface.

[0127] The objective function construction module is configured to execute step S3, which calculates the objective function for each point based on the input contact point information and the current surface parameters. and And construct the objective function according to the formula. .

[0128] Iterative optimization solution module: Configured to execute step S4. This module is the core of the system, internally implementing the IRLS optimization process. Specifically, it includes:

[0129] Parameter and weight initialization unit.

[0130] The error statistics and balance factor update unit is used to perform step S42.

[0131] The dynamic weight calculation unit is used to execute step S43.

[0132] The weighted least squares optimization solution unit is used to execute step S44 and call the underlying optimization algorithm library.

[0133] Convergence determination unit, used to control the iteration loop.

[0134] The results output module is configured to execute step S5 and output the final shape parameters and fitting evaluation index.

[0135] Example 3: Another embodiment of the present invention provides a multi-spherical adaptive palm structure, which is a hardware platform capable of implementing the above method, as shown in the figure, and includes:

[0136] Base: Used to connect to the wrist or finger drive mechanism of the robotic arm.

[0137] Multiple rotatable ball joints: flexibly connected to the base in a multi-stage (e.g., two-stage, three-stage) series configuration. Relative rotation is allowed between each stage of the ball joints, and between the ball joints and the base, via hinges or flexible connectors. The outer surface of the final stage ball joint (three-stage ball joint) is used for direct contact with the object being grasped.

[0138] Attitude sensor: integrated inside each ball joint, preferably a miniature inertial measurement unit (IMU), used to measure the rotation angle (roll, pitch, yaw) of the ball joint relative to its initial attitude in real time.

[0139] Signal acquisition and processing unit (optional integration): Used to acquire data from each sensor, perform preliminary processing, and upload the data.

[0140] When the hand structure grasps an object, under the action of the grasping force, each ball joint passively rotates to adapt to the object's contour, thus forming multiple contact points between the final ball joint and the object's surface. By reading the data from the sensors within all ball joints and combining it with the kinematic model described in Example 1, the precise positions and normal directions of these contact points can be calculated, providing input for subsequent shape perception algorithms.

[0141] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-spherical adaptive palm structure shape perception method, characterized in that, Includes the following steps: S1: Perform kinematic modeling on the multi-spherical adaptive palm structure to obtain the position coordinates of multiple contact points on the surface of the grasped object and the corresponding contact point normal vectors. S2: Select the hyperquadratic surface equation as the parameterized model representing the shape of the grasped object; S3: Construct an optimization objective function, which is a weighted sum of the position error term and the normal vector direction deviation term for all contact points; S4: Solve the objective function using an iteratively reconfigurable least squares optimizer to determine the parameters of the hyperquadratic surface equation; wherein the solution process includes at least the following iterative steps: S41: Based on the current iteration's estimated hyperquadratic surface parameters, calculate the position error and orientation deviation of each contact point; S42: Based on the statistical distribution of position errors and orientation deviations of all contact points obtained in step S41, adaptively calculate the balance factor. The balance factor Used to adjust the relative weights of the position error term and the orientation deviation term in the optimization objective function; S43: Calculate the dynamic weight of the position error for each contact point separately. Dynamic weights relative to directional deviation Among them, for contact points with errors greater than a preset statistical threshold, their corresponding dynamic weights are reduced. S44: Use the updated balance factor and dynamic weights , We construct a weighted optimization objective function and perform least squares optimization to obtain a new round of hyperquadratic surface parameter estimates. S5: Repeat steps S41 to S44 until the convergence condition is met, and output the final hyperquadratic surface parameters as the shape-aware result.

2. The multi-spherical adaptive palm structure shape perception method according to claim 1, characterized in that, Balance factor in step S42 The calculation method is as follows: calculate the ratio of the first statistical value of the absolute value of the position error of all contact points to the second statistical value of the absolute value of the direction deviation of all contact points; wherein, the first statistical value and the second statistical value are both medians or means.

3. The multi-spherical adaptive palm structure shape perception method according to claim 2, characterized in that, The balance factor The specific calculation formula is as follows: in, For the positional error of the contact point, For the directional deviation of the contact point, This indicates the median operation.

4. The multi-spherical adaptive palm structure shape perception method according to claim 1, characterized in that, In step S43, the preset statistical threshold is determined based on the statistical dispersion of the position error and direction deviation of all contact points in the current iteration.

5. The multi-spherical adaptive palm structure shape perception method according to claim 4, characterized in that, In step S43, dynamic weights and The calculation formula is: in, and These represent the position errors of all contact points in the current iteration. and directional deviation The median of A constant factor, A function that is cropped to the interval [0,1].

6. The multi-spherical adaptive palm structure shape perception method according to claim 1, characterized in that, In step S3, the position error term uses Sampson distance. The calculation formula is as follows: in, This is the implicit expression for the equation of the hyperquadratic surface. Its gradient.

7. The multi-spherical adaptive palm structure shape perception method according to claim 1, characterized in that, In step S2, the equation of the hyperquadratic surface is in the form of: in, Let the coordinates be the center coordinates of the surface. , , These are the scale parameters along the three principal axes. This is the shape index.

8. The multi-spherical adaptive palm structure shape perception method according to claim 1, characterized in that, Before the first iteration in step S4, the method further includes: setting initial estimates for the parameters of the hyperquadratic surface equation and setting the equilibrium factor. Dynamic weights and Assign initial values.

9. A multi-spherical adaptive palm structure shape sensing system, characterized in that, The system is configured to perform a multi-spherical adaptive palm structure shape perception method according to any one of claims 1 to 8, and includes: The kinematic modeling module is used to perform kinematic modeling on the multi-spherical adaptive palm structure to obtain the position coordinates of multiple contact points on the surface of the grasped object and the corresponding contact point normal vectors. The model selection module is used to select the hyperquadratic surface equation as the parametric model representing the shape of the grasped object; The objective function construction module is used to construct the optimization objective function, which is a weighted sum of the position error term and the normal vector direction deviation term for all contact points; An iterative optimization solution module is used to solve the objective function using an iteratively reconfigurable least squares optimizer to determine the parameters of the hyperquadratic surface equation; wherein, the iterative optimization solution module is configured to execute an iterative process, the iterative process including: Based on the current iteration's estimated hyperquadratic surface parameters, calculate the position error and orientation deviation of each contact point; Based on the statistical distribution of position errors and orientation deviations of all contact points obtained from the calculation, a balance factor for adjusting the weights of the two errors is adaptively calculated. ; Based on the degree of deviation of the position error and orientation deviation of each contact point relative to their respective statistical scales, a dynamic weight of the position error is calculated for each contact point. Dynamic weights relative to directional deviation ; Use the updated balance factor and dynamic weights , We construct a weighted optimization objective function and perform least squares optimization to obtain a new round of hyperquadratic surface parameter estimates. The process is iteratively executed until the convergence condition is met, and the final hyperquadratic surface parameters are output as the shape-aware result.

10. A multi-spherical adaptive palm structure, characterized in that, include: Base; And a plurality of rotatable ball joints connected to the base in a multi-stage series manner, wherein at least the last-stage ball joint is used to contact the object being grasped; Each of the rotatable ball joints integrates an attitude sensor for measuring its own rotation angle; The palm structure is configured such that data acquired by the attitude sensor can be used to perform a multi-spherical adaptive palm structure shape perception method as described in any one of claims 1 to 8.

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