Path planning method and system for cooperative ball change of neutron multi-ball spectrometer

Abstract

The invention provides a path planning method and system for cooperative ball change of a neutron multi-ball spectrometer, and relates to the field of data processing. In the method, a real contact condition is obtained by superposing an irradiation field, a temperature field and a structural vibration field in a three-dimensional model, an attitude evolution law of a sphere in an initial contact state is extracted, and a phase-locked cone region and a phase-locked circulation track are calibrated; and dividing a far area, an approaching area and a phase-locked window area in the multi-ball stacking area according to the distance, the approaching area and the phase-locked window area so as to generate a macroscopic approaching path. In the execution process, a sensor is used for detecting initial contact, and a phase-locked circulation track is superposed in a phase-locked time window, so that the posture of the ball tends to be a stable posture attractor; after phase locking is completed, amplitude is gradually reduced, clamping force is increased, and stable locking is achieved. And finally, a complete ball changing path plan is obtained by fusing the local phase locking path and the macroscopic approaching path. By implementing the technical scheme, the problem that the ball changing task is influenced by the attitude degradation uncertainty of the ball in the initial contact state is solved.

Description

Technical Field

[0001] This application relates to the technical field of data processing, specifically to a path planning method and system for collaborative ball changing in a neutron multi-sphere spectrometer. Background Technology

[0002] In the fields of radiation detection and nuclear metrology, neutron multisphere spectrometers, as key devices for assessing neutron doses in different energy ranges, are widely deployed in nuclear facilities environments characterized by high radiation, high temperature gradients, and strong structural vibrations. During long-term operation, these devices require periodic replacement of spheres with different specifications and shielding parameters to ensure measurement accuracy and energy range coverage.

[0003] Unlike traditional industrial material handling tasks, sphere replacement tasks in neutron multi-sphere spectrometers involve spheres typically made of high-density materials with highly symmetrical geometries. Their outer surfaces exhibit extremely low friction and low adhesion under long-term irradiation, cooling cycles, and structural vibration. When the gripper contacts the sphere during replacement, the clamping force in the initial contact state has not yet been established. The sphere maintains relative attitude stability only through weak contact friction. At this time, changes in the temperature gradient inside the irradiation cavity, slight vibrations of the supporting structure, and minute excitations from the gripper's end effector can all trigger unpredictable micro-rotations of the sphere. Because the attitude degradation process of the sphere in the initial contact state is highly random, its attitude evolution often deviates from the attitude boundaries preset in the path planning stage. This results in the original planned path failing to effectively constrain the sphere's attitude during actual execution, further increasing the risk of slippage, attitude instability, or contact failure, and making subsequent clamping, extraction, or replacement actions unreliable. Therefore, existing path planning methods cannot solve the problem of the uncertainty of sphere attitude degradation in the initial contact state affecting the sphere replacement task.

[0004] Therefore, there is an urgent need for a path planning method and system for collaborative ball changing in neutron multi-sphere spectrometers. Summary of the Invention

[0005] This application provides a path planning method and system for collaborative ball replacement in a neutron multi-sphere spectrometer, which helps to solve the problem of the ball replacement task being affected by the uncertainty of the ball attitude degradation in the initial contact state.

[0006] The first aspect of this application provides a path planning method for collaborative ball replacement in a neutron multi-sphere spectrometer. The method includes: acquiring a three-dimensional model of the multi-sphere stacking structure, the inner wall structure of the irradiation cavity, the support structure, and the grasper structure of the neutron multi-sphere spectrometer; superimposing irradiation field distribution, temperature field distribution, and structural vibration field distribution onto the three-dimensional model to obtain the contact friction characteristics and contact stiffness variation range of the spheres; based on the contact friction characteristics and the contact stiffness variation range, applying a micro-vibration sequence and a micro-oscillation trajectory to the spheres in the initial contact state through simulation and experiment to determine the sphere attitude evolution behavior; calibrating the sphere attitude to converge to the phase-locked cone region of the stable attitude attractor based on the sphere attitude evolution behavior; and constructing a phase-locked loop trajectory corresponding to the phase-locked cone region; mapping the phase-locked cone region to the multi-sphere stacking area; dividing the area into a distant region, a near region, and a phase-locked window region based on the sphere position and reachable space; and generating a phase-locked loop trajectory that satisfies preset constraints. A macroscopic approach path is defined, and the time interval corresponding to the path segment intersecting with the phase-locked window region within the macroscopic approach path is defined as the phase-locked time window. During the ball-changing process, if the sensor group determines that the gripper has entered the initial contact state and is within the phase-locked window region, the process switches to phase-locked training mode, and the phase-locked loop trajectory is superimposed within the phase-locked time window to control the gripper end to perform micro-vibration and micro-oscillation actions at the contact point region with the ball, so that the ball's attitude converges towards the stable attitude attractor. In phase-locked training mode, if the ball's attitude is determined to have completed phase-locking based on changes in contact force distribution, contact stiffness, and end-micro-vibration response, the vibration amplitude of the phase-locked loop trajectory is reduced, and the gripper clamping force is increased, so that the ball smoothly transitions from the initial contact state to the fully locked state. Based on the local phase-locked path corresponding to the phase-locked loop trajectory and the macroscopic approach path, the final path planning for the collaborative ball-changing of the neutron multi-sphere spectrometer is obtained.

[0007] A second aspect of this application provides a path planning system for collaborative ball replacement in a neutron multi-sphere spectrometer. The system includes an acquisition module and a processing module. The acquisition module acquires a three-dimensional model of the multi-sphere stack structure, the inner wall structure of the irradiation cavity, the support structure, and the grasper structure of the neutron multi-sphere spectrometer. It then overlays irradiation field distribution, temperature field distribution, and structural vibration field distribution onto the three-dimensional model to obtain the contact friction characteristics and contact stiffness variation range of the spheres. The processing module, based on the contact friction characteristics and contact stiffness variation range, applies a micro-vibration sequence and a micro-oscillation trajectory to the spheres in the initial contact state through simulation and experimentation to determine the sphere attitude evolution behavior. Based on the sphere attitude evolution behavior, it calibrates the sphere attitude to converge to the phase-locked cone region of the stable attitude attractor and constructs a phase-locked loop trajectory corresponding to the phase-locked cone region. The processing module further maps the phase-locked cone region to the multi-sphere stack area, divides the area into a distant region, a near region, and a phase-locked window region based on the sphere position and reachable space, and generates a sequence that satisfies a preset condition. The macroscopic approach path of the constraint conditions is defined, and the time interval corresponding to the path segment intersecting with the phase-locked window region in the macroscopic approach path is determined as the phase-locked time window. The processing module is further configured to, during the ball-changing process, if the sensor group determines that the gripper has entered the initial contact state and is within the phase-locked window region, switch to the phase-locked training mode and superimpose the phase-locked loop trajectory within the phase-locked time window to control the gripper end to perform micro-vibration and micro-oscillation actions at the contact point region with the ball, so that the ball attitude converges to the stable attitude attractor. The processing module is further configured to, in the phase-locked training mode, if the ball attitude is determined to have completed phase-locking based on the changes in contact force distribution, contact stiffness, and end micro-vibration response, reduce the vibration amplitude of the phase-locked loop trajectory and increase the gripper clamping force to smoothly transition the ball from the initial contact state to the fully locked state. The processing module is further configured to, based on the local phase-locked path corresponding to the phase-locked loop trajectory and the macroscopic approach path, obtain the final path planning for the neutron multi-sphere spectrometer collaborative ball changing.

[0008] A third aspect of this application provides an electronic device including a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, and both the user interface and the network interface are used to communicate with other devices. The processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method described above.

[0009] A fourth aspect of this application provides a non-transitory computer-readable storage medium storing instructions that, when executed, perform the method described above.

[0010] In summary, one or more technical solutions provided in this application have at least the following technical effects or advantages: By overlaying irradiation, temperature, and structural vibration field distributions onto a 3D model, path planning is transformed from idealized geometric deduction to physical field-driven modeling based on real irradiation conditions. This allows for the acquisition of the contact friction characteristics and contact stiffness variation range of the sphere under different conditions from the outset, significantly reducing attitude uncertainty. By applying multiple micro-vibration sequences and micro-oscillation trajectories in the initial contact state and analyzing attitude evolution behavior, the natural convergence law of the sphere in a low-friction environment is actively extracted, thereby calibrating the phase-locked cone region and phase-locked loop trajectory, enabling drivable attitude convergence during the contact phase. Path planning further maps the phase-locked cone region to a multi-sphere stacked area, establishing a hierarchical spatial structure of distant, approach, and phase-locked window regions, allowing the macroscopic path to naturally guide the grasper into a spatial domain capable of triggering attitude training. During the execution phase, a sensor array is used to determine the initial contact state in real time and whether it is within the phase-locked window region, thus switching to phase-locked training mode at the correct time. By overlaying the phase-locked loop trajectory, the sphere's attitude is driven to converge towards the stable attractor direction. Subsequently, a smooth and safe transition from initial contact to complete locking is achieved based on changes in contact force distribution, contact stiffness, and micro-vibration response. Finally, by fusing local phase-locked paths and macroscopic access paths, the overall path possesses both global reachability and local stability, enabling stable, reliable, and repeatable execution of multi-ball replacement tasks under low-friction, high-symmetry, and thermal disturbance environments. Therefore, it effectively addresses the problem of the uncertainty of ball attitude degradation in the initial contact state affecting ball replacement tasks. Attached Figure Description

[0011] Figure 1 A flowchart illustrating a path planning method for collaborative ball changing in a neutron multi-sphere spectrometer, provided as an embodiment of this application; Figure 2 A schematic diagram of a path planning system for collaborative ball changing in a neutron multi-sphere spectrometer, provided as an embodiment of this application; Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0012] Explanation of reference numerals in the attached figures: 21. Acquisition module; 22. Processing module; 31. Processor; 32. Communication bus; 33. User interface; 34. Network interface; 35. Memory. Detailed Implementation

[0013] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0014] In the description of the embodiments of this application, the words "for example" or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design that is described as "for example" or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design options. Rather, the use of the words "for example" or "for instance" is intended to present the relevant concepts in a specific manner.

[0015] In the description of the embodiments of this application, the term "multiple" means two or more. For example, multiple systems means two or more systems, and multiple screen terminals means two or more screen terminals. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the indicated technical features. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0016] To address the aforementioned technical problems, this application provides a path planning method for collaborative ball changing in a neutron multi-sphere spectrometer, referring to... Figure 1 , Figure 1 This is a flowchart illustrating a path planning method for collaborative sphere replacement in a neutron multi-sphere spectrometer, provided as an embodiment of this application. The method is applied to a server and includes steps S110 to S160, as follows:

[0017] S110. Obtain a three-dimensional model of the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, the support structure, and the gripper structure for the neutron multi-sphere spectrometer. Then, superimpose the irradiation field distribution, temperature field distribution, and structural vibration field distribution onto the three-dimensional model to obtain the contact friction characteristics and contact stiffness variation range of the spheres.

[0018] Specifically, a multi-sphere neutron spectrometer is a device that uses a multi-layered spherical structure of different sizes and shielding materials to perform spectral measurements and dose assessments of neutrons in different energy ranges. A multi-sphere stacked structure refers to the spherical assembly structure formed by stacking or arranging multiple spheres in a limited space according to a preset order or layout within the multi-sphere neutron spectrometer. The irradiation chamber inner wall structure refers to the geometry and material composition of the inner wall of the irradiation area or experimental chamber where the multi-sphere neutron spectrometer is located. This inner wall structure is made of metal, shielding material, or a composite structure, and its shape, thickness, and opening positions affect the neutron flux distribution, scattering characteristics, and the reachable space of the robotic arm. The support structure refers to the mechanical support components used to support the spheres in the multi-sphere stacked structure, including trays, support rods, positioning grooves, and limiting blocks. These support structures determine the support method, contact position, and displacement characteristics of the spheres in a static state, as well as under force or vibration. The gripper structure refers to the specific structural form of the end effector installed at the end of the robotic arm for gripping the spheres, such as multi-finger grippers, compliant grippers, or wrap-around clamps with concave curved surfaces. The gripper structure includes the shape of the fingertip contact surface, the range of gripping opening, the driving method and compliance characteristics. In the 3D model, it is necessary to accurately describe the surface area where the gripper fingertip may contact the ball in order to carry out contact simulation and path planning in the future.

[0019] The irradiation field distribution refers to the distribution of neutron irradiation intensity at various locations within the spatial range corresponding to the aforementioned three-dimensional model, describing the magnitude of neutron flux and its spatial gradient in different regions within the cavity. The irradiation field distribution is influenced by the neutron source location, neutron energy spectrum, shielding materials, and the multi-sphere stacked structure itself. The temperature field distribution refers to the distribution of surface temperature of various structures and spheres within the spatial range corresponding to the three-dimensional model, determined by neutron irradiation deposition energy, cooling system status, and environmental heat transfer conditions. The structural vibration field distribution refers to the distribution of vibration responses generated by various structures in the three-dimensional model under external excitation, including variations in vibration displacement, vibration velocity, or vibration acceleration at different structural nodes.

[0020] Contact friction characteristics refer to the frictional behavior of the contact surfaces between the sphere and the supporting structure, or between the sphere and the gripper structure, under different irradiation field distributions, temperature field distributions, and structural vibration field distributions. This includes the range of friction coefficient values, the transition characteristics between adhesion and slippage, and the changing trends of frictional performance under temperature variations and irradiation aging. The range of contact stiffness variation refers to the range of equivalent stiffness at the contact interface between the sphere and the supporting structure, or between the sphere and the gripper structure, varying with different operating conditions. Contact stiffness describes the ease with which contact deformation occurs when a small load in a certain direction is applied to the contact area. The range of contact stiffness variation reflects whether the contact interface is relatively soft or relatively rigid under different irradiation field distributions, temperature field distributions, and structural vibration field distributions.

[0021] Furthermore, the server constrains the external dimensions, center position, and stacking method of each sphere in the multi-sphere stacked structure according to engineering drawings and on-site survey data, ensuring that the gap relationship and support position relationship between the spheres are consistent with the actual equipment. The cavity shape, inner wall thickness, opening position, and inspection port position of the irradiation cavity inner wall structure are restored according to the structural design parameters, maintaining the spatial correspondence with the multi-sphere stacked structure. The key components of the support structure, such as the tray, support rod, and limit block that support the spheres, are finely modeled, especially the curved surface areas in contact with the spheres, to accurately describe the contact geometry. The structural elements of the gripper structure, such as the fingertip curved surface in contact with the spheres, the clamping opening limit, and the end-effector attitude range, are modeled together and aligned with the coordinate system of the end flange of the collaborative robotic arm. This allows the multi-sphere stacked structure, the irradiation cavity inner wall structure, the support structure, and the gripper structure to form a complete geometric entity with realistic assembly relationships and motion boundaries in the 3D model, providing a unified spatial basis for subsequent multiphysics superposition and contact analysis simulation.

[0022] After obtaining the 3D model, it was imported into a multiphysics simulation environment to construct irradiation field simulation examples, temperature field simulation examples, and structural vibration simulation examples. In the irradiation field simulation example, by defining the neutron source location, neutron energy spectrum, neutron beam intensity, and material cross-sectional data of the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, and the supporting structure, the irradiation field distribution in 3D space under different irradiation conditions was solved. The neutron flux and energy deposition distribution at each grid cell or node were recorded in the 3D model coordinate system. In the temperature field simulation example, the energy deposition results obtained from the irradiation field simulation example were used as a heat source term. Combined with the cooling duct layout, cooling medium flow rate, environmental heat transfer conditions, and material thermal conductivity parameters, the irradiation field distribution of the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, and the supporting structure were solved under different operating times. The temperature field distribution under different cooling conditions allows for a clear spatial calibration of the temperature gradient on the sphere surface and the local temperature rise of the supporting structure in the three-dimensional model. In the structural vibration simulation example, under dynamic load conditions from cooling equipment, pump sets, or external excitation, the vibration modes and forced responses of the multi-sphere stacked structure, supporting structure, and gripper structure are analyzed. The structural vibration field distribution under different combinations of excitation frequency and excitation amplitude is obtained. The vibration displacement or vibration acceleration response at each key location is mapped back to the three-dimensional model, so that the same three-dimensional model can simultaneously provide a description of the working conditions of irradiation field distribution, temperature field distribution, and structural vibration field distribution in a multiphysics simulation environment.

[0023] In a multiphysics simulation environment, local mesh refinement was performed on the contact surfaces between the sphere and the supporting structure, and between the sphere and the fingertips of the gripper structure. The contact type, contact friction model, and initial parameters of the normal contact stiffness for each contact element were set. External loads and boundary constraints representing the actual ball-changing process were applied under different irradiation, temperature, and structural vibration conditions, including static clamping force, slow displacement loading, and superimposed small-amplitude vibration disturbances. Through contact analysis simulation, the contact pressure distribution, contact slip, and contact area deformation in the contact area under various conditions were collected and compared with measured data obtained from calibration tests. The effective friction parameters and normal contact stiffness parameters for each contact condition were identified in the simulation environment. The contact friction characteristics can be described by the ratio of the contact tangential force to the contact normal force, for example, expressed as a friction coefficient function:

[0024]

[0025] in, The coefficient of friction in contact friction characteristics represents the ability of the contact interface to resist tangential slippage under specific working conditions. This represents the contact force at the contact interface in the tangential direction. Its value is derived from the resultant force of the tangential contact elements in the contact analysis simulation or the tangential load measurement results in the calibration test. The contact force in the normal direction of the contact interface is derived from the resultant force of the normal contact element in the contact analysis simulation or the normal load measurement results in the calibration test. The ratio of the two is used to characterize the slip tendency and anti-slip capability of the contact interface under different working conditions.

[0026] The range of contact stiffness variation can be described by the relationship between the increment of normal contact force and the increment of normal contact displacement, for example, expressed by the normal contact stiffness function as:

[0027] in, The normal contact stiffness represents the response strength of the contact interface to changes in normal load within a small range of displacement variations. This refers to the increment of the normal load applied in contact analysis simulation or calibration test. This represents the increment of normal displacement in the contact area under the applied normal load. This function reflects the trend of the contact interface changing from a soft to a rigid state under different radiation field distributions, temperature field distributions, and structural vibration field distributions. Combining simulation data and calibration test results under multiple operating conditions, the friction coefficient and normal contact stiffness under different operating conditions are statistically analyzed and categorized. Finally, a range of contact friction characteristics and a range of contact stiffness variation are given for each typical operating condition. These ranges serve as the basic parameters for path planning and phase-locked loop (PLL) training strategies, enabling subsequent attitude control and path planning to adaptively adjust to differences in contact stability under different operating conditions.

[0028] S120. Based on the contact friction characteristics and the range of contact stiffness variation, a micro-vibration sequence and a micro-oscillation trajectory are applied to the sphere in the initial contact state through simulation and experiment to determine the sphere's attitude evolution behavior. Based on the sphere's attitude evolution behavior, the sphere's attitude is calibrated to converge to the phase-locked cone region of the stable attitude attractor, and a phase-locked cyclic trajectory corresponding to the phase-locked cone region is constructed.

[0029] Specifically, the initial contact state refers to the state where the sphere and the fingertip contact area of ​​the gripper structure have just made contact, but the gripper's clamping force has not yet increased to a fully locked level. In this state, the sphere has made physical contact with the gripper, but still retains considerable degrees of attitude and sliding freedom. At this point, the contact friction characteristics and the range of contact stiffness variation jointly determine whether the sphere maintains its current attitude or undergoes a significant attitude shift under the influence of micro-vibrations and thermal expansion and contraction. Here, the sphere specifically refers to the spherical detection unit used for neutron energy spectrum measurement in a multi-sphere stacked structure, formed by multiple layers of different materials, with a highly symmetrical geometry, a large mass, and a relatively smooth outer surface. The stable attitude attractor refers to a specific attitude region that the sphere's attitude can naturally converge to, which repeatedly appears in multiple simulations and experiments. This region has self-stability, meaning that after the sphere approaches this attitude region, even with small micro-vibrations and thermal expansion and contraction disturbances, it tends to remain near this attitude and no longer undergoes a significant shift. A stable attitude attractor can be understood as a "set of stable equilibrium attitudes" of a sphere in a contact environment. For example, the sphere automatically finds a position and orientation in the concave geometry of the gripper fingertip that neither slips out nor is easy to clamp later.

[0030] A phase-locked cone region (PLC) refers to the initial attitude region in the attitude state space that can stably converge to a stable attitude attractor under the influence of a specific micro-vibration sequence and micro-oscillation trajectory. In other words, the PLC corresponds to a set of initial contact attitudes. As long as the sphere's attitude falls within this range and a micro-vibration sequence and micro-oscillation trajectory matching the PLC are applied, the sphere's attitude will converge to the corresponding stable attitude attractor along a certain attitude evolution trajectory. A phase-locked cyclic trajectory refers to a type of micro-motion trajectory with a specific temporal structure and spatial pattern corresponding to the PLC. This type of trajectory is executed periodically or quasi-periodically near the contact point region, causing the sphere's attitude to gradually adjust along a direction conducive to convergence in each cycle. PLC cyclic trajectories are "effective micro-motion combinations" selected from simulations and experiments. Under the constraints of contact friction characteristics and the range of contact stiffness variations, they can significantly increase the probability of the sphere's attitude entering the stable attitude attractor and accelerate the convergence speed.

[0031] Furthermore, a synchronous excitation platform was first built for the sphere in its initial contact state in both the co-simulation and experimental environments. In the simulation environment, the 3D models of the multi-sphere stacked structure, support structure, and gripper structure were coupled using a multibody dynamics solver and a finite element solver. In the experimental environment, a test bench with parameters identical to the simulation model was built for the sphere, support structure, and gripper structure. A unified controller was used to send end-effector trajectory commands to the collaborative robotic arm. A family of micro-vibration sequences with different frequencies, amplitudes, and phases were defined for the sphere in its initial contact state. The excitation acceleration of the gripper end-effector near the contact point was described as a vector-time function.

[0032]

[0033] in, This represents the change of the micro-vibration acceleration vector of the gripper tip in three-dimensional space over time. Indicates time, This indicates the number of the first group of damped vibration components. Indicates the first The initial amplitude of each damped vibration component, Indicates the first The attenuation coefficient of each damped vibration component is used to control the rate at which this component gradually weakens over time. Indicates the first The excitation frequency of each damped vibration component Indicates the first The initial phase of each damped vibration component Indicates the first The excitation direction vector of each damped vibration component in three-dimensional space This indicates the number of frequency-modulated vibration components in the second group. Indicates the first The vibration amplitude of each frequency modulation component, This represents the reference frequency used to construct the frequency modulation components. This represents a frequency offset function that changes slowly over time, used for simulating operating condition disturbances or fine-tuning the frequency during adaptive optimization. Indicates the first The initial phase of each frequency modulation component, Indicates the first The excitation direction vector of each frequency modulation component in three-dimensional space. Through this micro-vibration sequence, which includes the superposition of damping and frequency modulation components, multiple frequency and direction combinations can be covered in the same experiment or simulation. This allows the attitude degrees of freedom of the sphere under the constraints of contact friction characteristics and contact stiffness variation range to be fully excited, thus enabling a more comprehensive observation of the attitude evolution law. The micro-oscillation trajectory is constructed spatially around the contact point normal or tangential. By setting the micro-displacement path of the gripper end in the local coordinate system, the end attitude is made to slowly move along small arcs, small-angle oscillations, or spiral paths. These paths are applied synchronously with the aforementioned micro-vibration sequence in time, thereby forming a rich set of excitation condition data in the co-simulation and experimental environments.

[0034] After executing multiple sets of micro-vibration sequences and micro-oscillation trajectories, time-series data on the sphere's attitude, changes in contact force distribution, and changes in contact stiffness were simultaneously acquired in a co-simulation and experimental environment. The sphere's attitude can be represented by an attitude vector relative to the gripper structure. For example, a uniform attitude parameterization method can be used to denot the sphere's attitude at each moment as... The contact force distribution can be represented as a force vector time series containing the normal and tangential force components of each fingertip. The change in contact stiffness can be obtained by performing linear regression or nonlinear fitting on the contact displacement and contact force within small time steps to obtain an equivalent stiffness time series. The collected data... The contact force distribution and contact stiffness state are spliced ​​together at each moment to form a set of state points in the attitude state space. These points are then used to construct state trajectories through time series analysis, and clustering and topological analysis are performed on these trajectories in a high-dimensional attitude state space. To characterize whether a state trajectory converges to a stable attitude attractor along a specific attitude evolution path, an attitude deviation function can be introduced. This function describes the deviation between the current attitude and a candidate stable attitude as a time-varying quantity, used to observe whether the deviation gradually decreases and remains within a finite neighborhood under perturbation conditions. By identifying state trajectories that start from the initial contact state, show a monotonically or gradually decreasing attitude deviation within a finite time, a weakening contact slip trend, and ultimately enter a stable small-range fluctuation interval, the corresponding initial attitude and contact configuration combinations are determined. The connected regions formed by these combinations in the attitude state space are labeled as phase-locked cone regions, making the phase-locked cone regions represent the set of initial attitudes that are "convergent under specific excitation conditions."

[0035] After obtaining multiple phase-locked cone regions, for the attitude evolution characteristics corresponding to each phase-locked cone region, trajectory elements that achieve rapid attitude convergence need to be selected from a large number of micro-vibration sequences and micro-oscillation trajectories. A trajectory element refers to a local control segment with a complete time length, including the excitation parameters and end-space trajectory within that time segment. To quantitatively evaluate the convergence performance of trajectory elements under the constraints of contact friction characteristics and contact stiffness variation range, a comprehensive evaluation function can be constructed for each trajectory element during the data processing stage. For example, a function can be used to evaluate the convergence performance of a trajectory element within a certain time interval. The convergence performance metric within the timeframe is:

[0036]

[0037] in, Indicates the first The overall convergence cost of each trajectory unit; a smaller value indicates better convergence quality. , , These are non-negative weighting parameters used to balance the importance of different evaluation indicators. Indicates the first The trajectory of the sphere's attitude evolution over time under the excitation of individual trajectory units. This represents the reference attitude vector corresponding to the target stable attitude attractor. Indicates the first The deviation vector of the force at each contact point under the excitation of a trajectory unit can be, for example, composed of the difference between the contact force at each fingertip and the desired force distribution. This represents the sum of the absolute values ​​of the deviation vector, used to measure the degree of non-uniformity in force distribution. This represents an index function related to contact slip risk, which can be calculated based on the ratio of tangential to normal force and contact friction characteristics, reflecting whether the slip limit is approaching at any given moment. This is achieved through analysis of each trajectory unit... By performing calculations and sorting, trajectory units that can rapidly reduce attitude deviation, have a relatively balanced contact force distribution, and control slip risk within a finite time can be selected in each phase-locked cone region. These units are then used as a set of candidate trajectory units to provide high-quality basic segments for the subsequent construction of phase-locked cyclic trajectories.

[0038] After obtaining the candidate trajectory unit sets for different phase-locked cone regions, these trajectory units need to be spliced ​​and periodically constructed in time and space to form the phase-locked cyclic trajectory corresponding to the phase-locked cone region. To ensure that the phase-locked cyclic trajectory does not introduce attitude changes or contact force changes at the splicing points during repeated execution, any two candidate trajectory units can be spliced ​​together. and Construct a continuity measure function between them:

[0039]

[0040] in, Indicates the first The end state of the first trajectory unit and the first The continuity cost when directly splicing the initial states of each trajectory unit. , , These are non-negative weighting parameters used to balance the importance of attitude continuity, acceleration continuity, and contact force continuity. Indicates the first The sphere's attitude at the end of each trajectory unit. Indicates the first The sphere's orientation at the initial moment for each trajectory unit. and These represent the acceleration vectors at the end of the grabber at the corresponding time points. and These represent the contact force distribution vectors at corresponding time points. The convergence cost is determined by searching within the candidate trajectory unit set. Smaller and continuous cost A smaller sequence of trajectory units, periodically spliced ​​together and slightly parametrically smoothed, can construct a phase-locked loop trajectory that forms a closed loop in the attitude state space, is repeatable in time, continuous in contact mechanics response, and exhibits stable convergence under constraints of contact friction characteristics and contact stiffness variations. This phase-locked loop trajectory ultimately serves as a control template corresponding one-to-one with the phase-locked cone region, invoked in path planning and phase-locked training modes to drive the sphere's attitude to converge from any point within the phase-locked cone region to the corresponding stable attitude attractor.

[0041] S130. Map the phase-locked cone region to the multi-sphere stacked region. Divide the region into a distant region, a near region, and a phase-locked window region based on the position of the spheres and the reachable space. Generate a macroscopic approach path that satisfies the preset constraints. In the macroscopic approach path, determine the time interval corresponding to the path segment that intersects with the phase-locked window region as the phase-locked time window.

[0042] Specifically, the "far-away region," "approach region," and "phase-locked window region" are hierarchical divisions of the space related to the target sphere within the multi-sphere stacked region. The "far-away region" refers to the area where the gripper is in a safe standby or coarse movement phase before performing a ball swap. This region is a certain distance from the target sphere, will not trigger contact, and is not used for attitude control; it is mainly used for global movement and safe obstacle avoidance. The "approach region" is the spatial region where the gripper has approached the target sphere but has not yet entered the phase-locked sensitive range. Within the approach region, the movement of the gripper's end effector begins to be significantly affected by the multi-sphere stacked structure, support structure, and cavity geometry constraints, but has not yet entered the critical small-scale region where "a slight movement is sufficient to trigger contact and initiate attitude evolution." The phase-locked window region is a critical spatial sub-region determined by the intersection of the mapped phase-locked cone region and the reachable space. When the gripper's end effector is located in the phase-locked window region and makes initial contact with the sphere, the sphere's attitude is highly likely to fall into the phase-locked cone region. As long as the corresponding phase-locked loop trajectory is subsequently executed, attitude convergence can be achieved. Therefore, the phase-locked window region is the spatial "window" used by path planning to trigger the phase-locked acclimatization mode.

[0043] Preset constraints refer to a set of constraint rules that must be satisfied beforehand when generating a macroscopic approach path, including but not limited to obstacle avoidance constraints, radiation dose constraints, joint safety constraints, execution time constraints, and path smoothness constraints. A path segment refers to a continuous trajectory extracted from the complete macroscopic approach path, corresponding to the grasper's movement within a certain time interval. At the spatial intersection of the macroscopic approach path and the phase-locked window region, continuous path segments whose trajectory points fall within the phase-locked window region can be found. A time interval refers to the time period corresponding to each trajectory point in the path segment, that is, the time period during which the grasper's end effector actually resides within the phase-locked window region while moving along the macroscopic approach path. The phase-locked time window explicitly defines this time interval as "the time period during which phase-locked loop trajectories are allowed and appropriate for execution."

[0044] Furthermore, in the attitude state space, the phase-locked cone region is defined as the set of relative poses of the spheres relative to the gripper end effector. This set of relative poses is combined with the poses of the target spheres in the multi-sphere stacked structure in the world coordinate system, and mapped using the forward kinematics model of the collaborative robotic arm to obtain the set of poses of the gripper end effector in the world coordinate system. This mapping relationship can be expressed as:

[0045]

[0046] in, This represents the set of reachable attitude regions of the gripper end effector corresponding to the phase-locked cone region in the world coordinate system. This represents the pose transformation matrix of the grabber's end effector in the world coordinate system. This represents the relative pose transformation matrix of the sphere with respect to the end of the gripper. This represents a pre-defined set of phase-locked cone regions in the attitude state space. This represents the joint angle vector of the collaborative robotic arm. This represents the feasible set of joint space that satisfies joint reachability, joint limits, and joint velocity constraints. This represents the pose transformation matrix of the target sphere in the world coordinate system. The positive kinematics function of the collaborative robotic arm is used to map joint angle vectors to end-effector pose. Through this set of relationships, the "phase-lockable pose of the sphere relative to the gripper" is mathematically transformed into "the achievable pose region of the gripper's end effector in space." Subsequently, occlusion information and the geometric information of the irradiation cavity's inner wall structure are superimposed on the multi-sphere stacked structure, and through... Visibility and collision detection are performed to eliminate postures that geometrically interfere with the multi-sphere stacked structure, the inner wall structure of the irradiated cavity, or the supporting structure. This, combined with the joint accessibility of the collaborative robotic arm structure, further optimizes the process. The area is clipped to a practically accessible and securely reachable phase-locked window region, forming a spatial subset of constraint geometry and kinematic relationships.

[0047] Using the center of the target sphere as a reference point, the space containing the grasper's end effector trajectory is layered in the world coordinate system or local polar coordinate system. Spaces far from the sphere where the grasper's end effector movement will not trigger contact are designated as "far-away regions," while spaces of moderate distance from the sphere where the grasper's end effector may enter a pre-contact posture but has not yet entered the phase-locked window region are designated as "approach regions." The phase-locked window region obtained in the previous step is taken as the innermost region. Furthermore, the reachable space of the collaborative robotic arm is used to define the circumferentially accessible sectors of the sphere in the polar angle dimension. Subsequently, when planning the macroscopic approach path, obstacle avoidance constraints, radiation dose constraints, joint limit constraints, and path continuity constraints are introduced to optimize the grasper's end effector trajectory within the configuration space. The path cost function can be constructed to solve the path from the far region to the near region and into the phase-locked window region. For example, a path cost function that simultaneously penalizes the path length, the degree of proximity to obstacles, and the dwell time in the high-dose region can be used, with the addition of joint limits and smoothness constraints. This ensures that the final macroscopic approach path geometrically avoids the multi-sphere stacked structure and the inner wall structure of the irradiation cavity, controls the cumulative irradiation exposure in terms of irradiation field distribution, satisfies the accessibility and safety of the collaborative robotic arm in the joint space, and inevitably falls into the phase-locked window region at the end of the path, thus providing a spatial entry point for subsequent phase-locked training.

[0048] After the macroscopic approach path is generated, it is represented as a time-parameterized grasper end-effector trajectory, establishing a correspondence between the grasper end-effector pose at each moment and the path's time parameters. Within this time-parameterized trajectory, it is determined point-by-point whether the grasper end-effector pose falls within the aforementioned phase-locked window region. By performing ensemble detection on all path points, continuous time intervals within the phase-locked window region are identified. For example, the macroscopic approach path is denoted as... ,in The path execution time parameter is determined by analyzing each time step. judge The system determines whether a position belongs to the phase-locked window region set, identifies all time intervals that satisfy the condition "pose is within the phase-locked window region," performs continuity analysis on these intervals, and defines the longest or most suitable time interval for use as the phase-locked phase as the phase-locked time window. The phase-locked time window consists of a start time and an end time, corresponding to the period during which the grasper's end point on the macroscopic approach path both geometrically enters the phase-locked window region and meets preset constraints. Within this time period, the server can switch to phase-locked training mode after the sensor group detects the grasper entering the initial contact state and overlays the phase-locked loop trajectory. Outside the phase-locked time window, the system maintains the macroscopic approach path tracking mode, thus providing a strict and repeatable trigger boundary for phase-locked control in the time dimension.

[0049] S140. During the ball-changing process, if the sensor group determines that the gripper has entered the initial contact state and is in the phase-locked window area, then switch to the phase-locked training mode and superimpose the phase-locked loop trajectory within the phase-locked time window to control the gripper end to perform micro-vibration and micro-oscillation actions in the contact point area with the ball, so that the ball's attitude converges to the stable attitude attractor.

[0050] Specifically, phase-locked taming mode is a special control mode relative to ordinary path tracking mode. In this mode, the server no longer just tracks the pre-planned macroscopic geometric path, but focuses on executing the pre-calibrated phase-locked loop trajectory to actively adjust the sphere's attitude through micro-movements in specific time and space structures.

[0051] Furthermore, the contact process between the gripper's fingertip and the ball is first synchronously sampled using tactile sensors, force sensors, micro-accelerometers, and near-field vision sensors in the sensor array. The various sensor signals are aligned on a unified time axis, and a feature set for identifying the initial contact state is constructed. Multi-source observations at the same time can be combined into a feature vector, and a contact state criterion function can be defined.

[0052]

[0053] in, Indicates at time The comprehensive criterion value for the initial contact state is such that a larger value indicates the state is closer to the initial contact state. , , These are non-negative weighting coefficients used to balance the influence of different features on the comprehensive criterion. This indicates the magnitude of the contact force in the normal direction measured by the force sensor at the fingertips of the gripper. and These represent the lower and upper limits of the threshold range defining the initial contact state, respectively. This represents a smooth step function, used to characterize the transition characteristics of contact force from "no contact" to "within the threshold range of the initial contact state". This quantity, obtained by normalizing the contact-related characteristic energy in the spectrum of the micro-accelerometer, is used to reflect whether there is an energy abrupt change in the contact characteristic frequency band in the end-effector micro-vibration response. This represents the overlap between the local contour of the sphere reconstructed by a near-field vision sensor and the contact area of ​​the grasper's fingertip, expressed as a normalized overlap area or overlap voxel ratio, indicating spatial features. When When the preset judgment threshold is exceeded within several consecutive sampling periods, the server believes that the contact force of the gripper fingertip has changed from zero to a stable value within the initial contact state threshold range. The contact characteristic spectrum changes in the end micro-vibration response and the local contour of the sphere enters the contact area of ​​the gripper fingertip are obtained, thus obtaining a feature set including contact force characteristics, vibration characteristics and visual characteristics, which is used for subsequent control mode switching judgment.

[0054] Assuming the grasper enters the initial contact state based on the feature set, the server must also simultaneously satisfy the conditions that the grasper's end-effector pose falls within the phase-locked window region and the current moment is within the phase-locked time window before switching the control mode from the macroscopic approach path trajectory tracking mode to the phase-locked training mode. Therefore, the macroscopic approach path has already been included in the path planning phase. The phase-locked window region and phase-locked time window are bound together, and the current pose of the gripper end effector is calculated during the execution phase using real-time joint encoders and positive kinematics. And determine whether it belongs to the phase-locked window region. Simultaneously determine the time parameter Does it fall within the phase-locked time window? This can be achieved by introducing a pattern indicator function:

[0055]

[0056] in, This is a mode switching indicator. A value of 1 indicates that all conditions for entering the phase-locked loop (PLL) training mode are met, while a value of 0 indicates that the trajectory tracking mode, which is close to the macroscopic path, continues to be maintained. This is an indicator function that takes the value 1 if the condition is true and 0 otherwise. The threshold for determining the initial contact state. The current pose of the gripper end effector. For the set of phase-locked window regions, This is the phase-locked loop time window interval. The server calculates this in each control cycle. When the transition from 0 to 1 triggers a mode switch, it changes the original single tracking... The control law is switched to a phase-locked loop training control law superimposed with the phase-locked loop trajectory, and the control law is changed when the phase-locked time window ends or the contact state degrades. It is restored to 0, returning to the trajectory tracking mode of macroscopic approach path, thereby achieving reliable triggering and exit of phase-locked loop training mode under the dual constraints of time and space.

[0057] Within the phase-locked loop (PLL) time window, the server needs to select a target PLL trajectory from the PLL trajectory library that fits the current contact configuration and superimpose this target PLL trajectory onto the macroscopic approach path. This is used to control the gripper's end effector to perform micro-vibration and micro-oscillation movements in the contact point region, causing the sphere's attitude to converge towards the stable attitude attractor. Therefore, the current contact configuration can be described as a high-dimensional feature vector including the contact point location, contact normal direction, contact force distribution, and contact stiffness state. And for each candidate phase-locked loop trajectory in the phase-locked loop trajectory library Establish the adaptation cost function:

[0058]

[0059] in, Indicates at time The first The adaptation cost when using a phase-locked loop trajectory as the target phase-locked loop trajectory; the smaller the value, the better it is suited to the current contact configuration. , , These are non-negative weighting parameters used to balance the importance of three types of characteristics: contact normal, contact force distribution, and contact stiffness. This represents the normal direction vector at the current contact point. Indicating the construction of the first The calibration normal direction corresponding to the phase-locked loop trajectory. This represents the current multi-finger contact force distribution vector. Indicates the first The desired contact force distribution corresponding to the phase-locked loop trajectory. This represents the current contact stiffness characteristic, which can be estimated from the relationship between contact force and contact micro-displacement. Indicates the first The reference contact stiffness characteristic quantity for calibrating a phase-locked loop trajectory. This is calculated by applying the formula to all candidate phase-locked loop trajectories. The trajectory with the lowest cost is selected as the target phase-locked loop trajectory. And align it with the current execution time on the time scale, representing the target pose trajectory at the end of the grabber as:

[0060]

[0061] in, Indicates at time The end-effector integrated command trajectory to be sent to the servo controller This represents the smooth pose trajectory corresponding to the macroscopic approximation path. Indicates the target phase-locked loop trajectory The incremental trajectories of micro-vibration and micro-oscillation poses are mapped to the world coordinate system. Through this superposition method, the grasper end effector still evolves slowly along the macroscopic approach path as a whole, while micro-vibration and micro-oscillation movements with specific frequency structures and spatial patterns are superimposed in the local contact point region. This causes the sphere's attitude to gradually converge towards the stable attitude attractor under the constraints of contact friction characteristics and the range of contact stiffness variation, thereby achieving a controllable transition from an uncertain initial contact attitude to a stable locked attitude within the phase-locked time window.

[0062] S150. In phase-locked acclimatization mode, if the ball's posture is determined based on changes in contact force distribution, contact stiffness, and end-effector micro-vibration response to complete phase-locking, then the vibration amplitude of the phase-locked cycle trajectory is reduced, and the gripper clamping force is increased, so that the ball smoothly transitions from the initial contact state to the fully locked state.

[0063] Specifically, firstly, during the execution of the phase-locked loop trajectory, the distribution of contact force at the gripper fingertips, changes in contact stiffness, and the micro-vibration response at the end are statistically analyzed using a sliding time window to construct a comprehensive criterion for determining whether the sphere's attitude has completed phase-locking. This can be done within a length of... Within the sliding time window, the time series of normal contact forces at each fingertip are normalized and the distribution uniformity is calculated. The contact force at the fingertips is denoted as Let the normalized contact force be... A distribution uniformity index is constructed using the variance of the contact force distribution:

[0064]

[0065] in, Indicates at time The degree of uniformity of contact force distribution; the closer the value is to 1, the more uniform the force on each fingertip is within the sliding time window. The length of the sliding time window. For integration time variable, For a moment No. Normalized contact force at the fingertips, For at any time The average of the normalized contact forces at all fingertips. The stability of the contact stiffness can be described by an energy measure of the slope of the instantaneous contact stiffness change within a sliding time window, assuming the instantaneous normal contact stiffness is... ,definition:

[0066]

[0067] in, Indicates contact stiffness stability. For at any time The smaller the absolute value of the first derivative of contact stiffness with respect to time, the more gradual the change in stiffness. A value closer to 1 indicates greater stability in stiffness variation. The convergence of the end-effector micro-vibration response can be described by the time decay trend of the contact-related frequency band energy in the acceleration spectrum. Let the normalized frequency band energy in a certain phase-locked sensitive frequency band be... The following is given:

[0068]

[0069] in, Indicates the convergence of the end-micro-vibration response. This represents the target frequency band energy level obtained after calibration near the stable attitude attractor. Reconstruct the integrated phase-locked loop criterion:

[0070]

[0071] in, For at any time A comprehensive indicator used to determine whether the sphere's attitude has completed phase locking. , , These are non-negative weighting coefficients used to balance the importance of contact force distribution uniformity, contact stiffness stability, and vibration response convergence; when within multiple consecutive sliding time windows... When the force continuously exceeds the preset threshold, the control system determines that the sphere's attitude has completed phase locking, meaning that the contact force distribution tends to be balanced, the slope of the contact stiffness change continues to decrease, and the end micro-vibration response exhibits stable characteristics.

[0072] After determining that the sphere's attitude has completed phase-locking, to prevent attitude reversal drift caused by a sudden disappearance of excitation, the control system gradually reduces the vibration amplitude of the phase-locked loop trajectory according to a preset reduction rhythm, and continuously monitors contact stability during the reduction process. The vibration amplitude envelope of the phase-locked loop trajectory can be denoted as... At the time of phase-locking completion Take the current amplitude as Then, the reduction process is performed according to the exponentially increasing gradually varying function, as follows:

[0073]

[0074] in, For at any time The target vibration amplitude of the phase-locked loop trajectory. The initial vibration amplitude at the moment the phase-locking is completed. A weighting parameter between 0 and 1, used to weight exponential decay and gradual decay. Indicates the rate of exponential decay. This represents the decay factor of the decay term of a rational function. When... When it increases, It monotonically decreases and eventually approaches zero. During the reduction process, the control system uses the same contact force distribution uniformity, contact stiffness stability, and vibration response convergence indices as before, for each control cycle. , and Monitoring should be conducted; if it is found that the vibration amplitude decreases at a certain stage, or Significant decrease, or If a reversal or worsening trend emerges, the reduction should be temporarily suspended or maintained for a short period. The amplitude remains unchanged, with minor adjustments made if necessary, to ensure that the reduction process does not induce the sphere's attitude to drift in the opposite direction from the stable attitude attractor neighborhood to the unfavorable attitude region.

[0075] When the vibration amplitude of the phase-locked loop trajectory is gradually reduced according to the above amplitude reduction strategy and drops to the preset threshold... At this point, the control system begins to gradually increase the gripper's clamping force in a slow, gradual manner, smoothly integrating the local phase-locked path back to the macroscopic approach path during this process to ensure the continuity of the gripper's end-effector trajectory and the mechanical state of the contact interface. The target clamping force curve can be represented as... The moment when the boost begins is recorded as Corresponding to the initial clamping force The clamping force of the target in the fully locked state is The evolution of clamping force is controlled by a piecewise gradual increase function:

[0076]

[0077] in, For a moment The target clamping force, The initial clamping force is the small clamping force in the initial contact state. The clamping force for a fully locked target state. The clamping force escalation rate parameter, This is a piecewise modulation function used to fine-tune the clamping force growth rhythm based on real-time contact stability. Its value varies between 0 and 1, and it is activated when the contact state is detected to be extremely stable. Approaching 1, it accelerates the convergence towards the target value; when a trend of marginal deterioration in contact force distribution or stiffness stability is detected... Reduce and slow down the rate of increase in clamping force. While the clamping force increases gradually, the end-point command trajectory is progressively transitioned from a superposition of "macroscopic approach path plus local phase-locked path" to tracking only the macroscopic approach path. This can be achieved through a time weighting function. The path fusion is achieved as follows:

[0078]

[0079] in, For a moment The final comprehensive target trajectory, This represents the terminal trajectory corresponding to the local phase-locked path. This represents the terminal trajectory corresponding to the macroscopic approximation path. The fusion weights are monotonically decreasing over time, in the initial stage. As the clamping force gradually approaches 1, , The force is gradually reduced to near zero, so that the end motion smoothly transitions from a local phase-locked path to a macroscopic approach path. During this process, the contact force distribution, contact stiffness stability and vibration response convergence are continuously monitored to ensure that trajectory fusion and the gradual increase of clamping force do not disrupt the continuity of the mechanical state of the contact interface, and finally the sphere smoothly transitions from the initial contact state to the fully locked state.

[0080] S160. Based on the local phase-locked path and macroscopic approach path corresponding to the phase-locked loop trajectory, the final path plan for collaborative ball replacement in the neutron multi-sphere spectrometer is obtained.

[0081] Specifically, the macroscopic approach path and the corresponding local phase-locked paths in the phase-locked loop trajectory are synchronized in time and corrected in space within a unified path space to ensure consistency in pose continuity and contact interface mechanical state between the two types of paths. Within the phase-locked time window calibrated in the macroscopic approach path, the local phase-locked paths are embedded into the macroscopic approach path according to the start and end times of this time window. This allows the gripper end effector to gradually transition from the macroscopic approach path to the local phase-locked path as it approaches the sphere, and then smoothly transition back to the macroscopic approach path after completing attitude phase-locking and gradual increase in clamping force. This ensures that the spatial trajectory, velocity distribution, and contact force evolution of the gripper end effector remain continuous and controllable before and after phase-locking. Subsequently, time reparameterization and velocity profile optimization are performed on the fused overall trajectory to ensure its executability under the joint limits, velocity limits, acceleration limits, and obstacle avoidance constraints of the collaborative robotic arm. Key sections of the path involving multi-sphere stacking structures, support structures, and the inner wall structure of the irradiation cavity are re-verified to ensure that the embedding of the local phase-locked path does not introduce new collision risks or irradiation exposure exceeding limits. The final trajectory is a complete final path plan that includes the macroscopic approach path, phase-locked time window, local phase-locked path, and transition segment after full locking. It can simultaneously achieve global reachability, local attitude stability, and robustness of the execution process throughout the entire ball-changing process.

[0082] In one possible implementation, the neutron multi-sphere spectrometer further includes a main robotic arm structure and an auxiliary robotic arm structure. In a 3D model, the reachable space, obstacle avoidance space, and dynamic constraint space of the main and auxiliary robotic arm structures are jointly modeled. Based on the occlusion relationship between the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, and the support structure, the cooperative target pose region of the auxiliary robotic arm is determined, and a cooperative support path is generated to enable the auxiliary robotic arm to enter the cooperative target pose region. During the process of the main robotic arm approaching the sphere along the macroscopic approach path, a cooperative approach path is generated to enable the auxiliary robotic arm to synchronously approach the sphere based on the overlap relationship of the reachable spaces of the main and auxiliary robotic arms and the temporal coupling constraints. When the main robotic arm enters the phase-locked window region and switches to the phase-locked training mode, a cooperative local phase-locked path is generated based on the phase-locked cone region and the phase-locked loop trajectory to enable the auxiliary robotic arm to perform phase-matching support actions within the phase-locked time window. The cooperative support path, cooperative approach path, and cooperative local phase-locked path realize the coordinated movement between the main and auxiliary robotic arms, thereby constructing a cooperative convergence path that enhances the convergence of the sphere's attitude towards the stable attitude attractor.

[0083] Specifically, firstly, the reachable space, obstacle avoidance space, and dynamic constraint space of the main and auxiliary robotic arm structures are jointly modeled in a 3D model. Based on the joint structure parameters, joint angle range, joint velocity, and joint acceleration limits of the main and auxiliary robotic arms, the end-effector reachable spaces of both arms in the world coordinate system are obtained through forward and inverse kinematics solutions. Under the constraints of the geometric models of the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, and the support structure, the obstacle avoidance space and safe working space of both arms are constructed through collision detection and visibility analysis. Subsequently, in this joint space, based on the occlusion relationship between the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, and the support structure on the visibility around the spheres and the support direction, the cooperative target pose region where the auxiliary robotic arm can provide lifting, support, or limiting functions without interfering with the macroscopic approach path of the main robotic arm is determined using visibility cone constraints and normal support direction constraints. This region is defined as a set of end-effector poses and is modified through the following feasibility screening constraints:

[0084]

[0085] in, This represents the set of target pose regions for collaborative use by the assistive robotic arm. This represents the pose matrix of the end effector of the robotic arm in the world coordinate system. This represents the positive kinematic mapping of the auxiliary robotic arm. This represents the joint angle vector of the auxiliary robotic arm. This represents the feasible set of joint spaces that satisfy the joint angle range, joint velocity, and joint acceleration constraints of the auxiliary robotic arm. This represents a collection of obstacles consisting of a multi-sphere stacked structure, an irradiation cavity inner wall structure, and a supporting structure. This indicates that the end-effector pose does not intersect with any obstacles. This is represented as the pre-specified expected support normal direction vector for collaborative support. This represents the actual support direction vector derived from the end-effector pose. This represents the support direction consistency threshold. After obtaining the cooperative target pose region, through... Internally, path optimization with obstacle avoidance and dynamic constraints is performed to generate a collaborative support path that allows the end effector of the auxiliary robotic arm to smoothly enter the collaborative target pose region from the initial safe standby pose, and ensures that each state along the path simultaneously satisfies joint accessibility and irradiation field safety constraints.

[0086] During the process of the main robotic arm approaching the sphere along the macroscopic approach path, a cooperative approach path needs to be generated based on the overlap relationship of the reachable spaces of the main and auxiliary robotic arms and the constraints of temporal coupling, so that the auxiliary robotic arm enters the cooperative target pose region synchronously with the main robotic arm in time. To this end, firstly, a Cartesian product set of the end-effector reachable spaces of the main and auxiliary robotic arms is constructed in the joint configuration space. Through intersection operations, the joint reachable space in which the two arms can move simultaneously without collision is obtained. Then, the end-effector trajectory of the macroscopic approach path of the main robotic arm is... Projecting onto the joint reachability space, determining parameters at each time step. The set of selectable end-effector poses for the auxiliary robotic arm is given. Then, a collaborative approach path optimization problem for the auxiliary robotic arm is constructed with temporal coupling as a constraint. A cost function simultaneously penalizes the path length, joint motion, and deviation from the cooperative target pose region of the auxiliary robotic arm. For example, a joint cost function can be constructed as follows:

[0087]

[0088] in, Cost of optimizing the approach path for collaboration and These represent the start and end times of the collaboration approach phase, respectively. Indicates the time of the auxiliary robotic arm The joint angular velocity vector, , , These are non-negative weight parameters. This indicates the pose of the end effector of the robotic arm as it changes over time. This represents the projection operator that projects the current end-effector pose onto the cooperative target pose region. Indicates the time of the end effector of the main robotic arm. Pose along the macroscopic approach path. Let represent the collision penalty function between the main robotic arm and the auxiliary robotic arm, whose value increases as the distance between the two arms decreases. By solving this optimization problem, under the premise of ensuring that the two arms do not collide with each other, that there is no collision environment, and that the auxiliary robotic arm remains coupled with the macroscopic approach path of the main robotic arm in time, a cooperative approach path is obtained in which the auxiliary robotic arm synchronously approaches the sphere from its initial pose and converges to the cooperative target pose region.

[0089] In practice, the first step is to match the current phase-locked cone region index of the main robotic arm with the currently executing phase-locked loop trajectory. Extract the reference phase function to describe the local micro-vibration and micro-oscillation of the main robotic arm. With reference frequency function Then, based on the force distribution and support direction of the sphere within the cooperative target pose area, the target support micro-motion trajectory of the auxiliary robotic arm end effector near the support point is designed. The two must satisfy phase matching constraints in time:

[0090] in, and These represent the time intervals of the auxiliary robotic arm. Corresponding to the instantaneous phase and instantaneous frequency of the micro-motion, and These represent the instantaneous phase and instantaneous frequency of the main robotic arm's phase-locked loop trajectory, respectively. The pre-designed phase offset is used to create a favorable energy dissipation mode between the support point and the contact point. and To account for phase and frequency error tolerances, the auxiliary robot arm's local trajectory, satisfying the above constraints, is solved within the phase-locked time window. This ensures that the cooperative local phase-locked path maintains phase matching with the main robot arm's phase-locked cyclic trajectory in time, and maintains stable support for the sphere in space while suppressing unfavorable attitude degrees of freedom. Consequently, a local convergence field is formed during the phase-locking phase, resulting in the synergistic effect of the main robot arm's "excitation-attitude adjustment" and the auxiliary robot arm's "support-constraint drift."

[0091] Finally, the macroscopic approach path, local phase-locked path, and exit path after phase-locking are concatenated in time to form a complete main path. The cooperative support path, cooperative approach path, and cooperative local phase-locked path of the auxiliary robotic arm are aligned in time to form a complete auxiliary path. Joint time reparameterization ensures that the two paths are strictly synchronized at key event moments, such as entering the approach area, entering the phase-locked window area, starting the phase-locked loop trajectory, and beginning the gradual increase of clamping force. Furthermore, multi-body collision detection, irradiation exposure assessment, and dynamic feasibility verification are introduced into the joint path. If any local segment is found to be unsatisfied with constraints, the local segment is fine-tuned or re-solved at the joint planning level. The resulting collaborative convergence path enables the main robotic arm to execute the phase-locked loop trajectory at the contact point to complete attitude training, while the auxiliary robotic arm executes phase-matching support actions at the support point to enhance attitude convergence. The two robotic arms form a coordinated control effect with temporal coordination and spatial complementarity throughout the ball-changing process, enabling the ball to converge more quickly and reliably to the stable attitude attractor and achieve safe locking under low friction, high symmetry, and multi-source disturbance environments.

[0092] This application also provides a path planning system for collaborative ball changing in a neutron multi-sphere spectrometer, referring to... Figure 2 , Figure 2This application provides a schematic diagram of a path planning system for collaborative ball replacement in a neutron multi-sphere spectrometer. The system is a server, comprising an acquisition module 21 and a processing module 22. The acquisition module 21 acquires three-dimensional models of the multi-sphere stacking structure, the inner wall structure of the irradiation cavity, the support structure, and the grasper structure of the neutron multi-sphere spectrometer. It then overlays irradiation field distribution, temperature field distribution, and structural vibration field distribution onto the three-dimensional models to obtain the contact friction characteristics and contact stiffness variation range of the spheres. The processing module 22, based on the contact friction characteristics and contact stiffness variation range, applies micro-vibration sequences and micro-oscillation trajectories to the spheres in their initial contact state through simulation and experimentation to determine the sphere attitude evolution behavior. Based on the sphere attitude evolution behavior, it calibrates the sphere attitude to converge to the phase-locked cone region of the stable attitude attractor and constructs the phase-locked loop trajectory corresponding to the phase-locked cone region. The processing module 22 also maps the phase-locked cone region to the multi-sphere stacking area, dividing the area into distant, near, and phase-locked regions based on the sphere positions and reachable spaces. The processing module 22 is used to generate a macroscopic approach path that meets preset constraints within a window region. The time interval corresponding to the path segment intersecting the phase-locked window region within the macroscopic approach path is defined as the phase-locked time window. The processing module 22 is also used to switch to phase-locked training mode if, during the ball-changing process, the sensor group determines that the gripper has entered the initial contact state and is within the phase-locked window region. A phase-locked loop trajectory is then superimposed within the phase-locked time window to control the gripper's end-effector to perform micro-vibration and micro-oscillation actions at the contact point with the ball, so that the ball's attitude converges towards the stable attitude attractor. The processing module 22 is also used to reduce the vibration amplitude of the phase-locked loop trajectory and increase the gripper's clamping force if, in phase-locked training mode, the ball's attitude is determined to have completed phase-locking based on changes in contact force distribution, contact stiffness, and end-effector micro-vibration response, so that the ball smoothly transitions from the initial contact state to the fully locked state. The processing module 22 is also used to obtain the final path planning for collaborative ball changing using the neutron multi-sphere spectrometer based on the local phase-locked path and macroscopic approach path corresponding to the phase-locked loop trajectory.

[0093] It should be noted that the above embodiments of the apparatus are only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus and method embodiments provided in the above embodiments belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.

[0094] This application also provides an electronic device, with reference to... Figure 3 , Figure 3This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: at least one processor 31, at least one network interface 34, a user interface 33, a memory 35, and at least one communication bus 32.

[0095] The communication bus 32 is used to enable communication between these components.

[0096] The user interface 33 may include a display screen and a camera. Optionally, the user interface 33 may also include a standard wired interface and a wireless interface.

[0097] The network interface 34 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0098] The processor 31 may include one or more processing cores. The processor 31 connects to various parts of the server via various interfaces and lines, executing instructions, programs, code sets, or instruction sets stored in the memory 35, and calling data stored in the memory 35 to perform various server functions and process data. Optionally, the processor 31 may be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor 31 may integrate one or a combination of several of the following: Central Processing Unit (CPU), Graphics Processing Unit (GPU), and modem. The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content to be displayed on the screen; and the modem handles wireless communication. It is understood that the modem may also not be integrated into the processor 31 and may be implemented as a separate chip.

[0099] The memory 35 may include random access memory (RAM) or read-only memory. Optionally, the memory 35 may include a non-transitory computer-readable storage medium. The memory 35 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 35 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch function, sound playback function, image playback function, etc.), instructions for implementing the above-described method embodiments, etc.; the data storage area may store data involved in the above-described method embodiments, etc. Optionally, the memory 35 may also be at least one storage device located remotely from the aforementioned processor 31. Figure 3 As shown, the memory 35, which serves as a computer storage medium, may include an operating system, a network communication module, a user interface module, and an application program for a path planning method for collaborative ball changing in a neutron multi-sphere spectrometer.

[0100] exist Figure 3 In the electronic device shown, the user interface 33 is mainly used to provide an input interface for the user and to obtain the user input data; while the processor 31 can be used to call an application program stored in the memory 35 for a path planning method for cooperative ball changing in a neutron multi-sphere spectrometer. When executed by one or more processors, the electronic device executes one or more methods as described in the above embodiments.

[0101] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0102] This application also provides a non-transitory computer-readable storage medium storing instructions. When executed by one or more processors, these instructions cause an electronic device to perform one or more of the methods described in the above embodiments.

[0103] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of other embodiments of this disclosure upon considering the specification and the disclosure of practical truth. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A path planning method for collaborative ball changing in a neutron multi-sphere spectrometer, characterized in that, The method includes: A three-dimensional model of the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, the support structure, and the gripper structure of the neutron multi-sphere spectrometer is obtained. The irradiation field distribution, temperature field distribution, and structural vibration field distribution are superimposed on the three-dimensional model to obtain the contact friction characteristics and contact stiffness variation range of the spheres. Based on the contact friction characteristics and the range of contact stiffness variation, a micro-vibration sequence and a micro-oscillation trajectory are applied to the sphere in the initial contact state through simulation and experiment to determine the sphere attitude evolution behavior. Based on the sphere attitude evolution behavior, the sphere attitude is calibrated to converge to the phase-locked cone region of the stable attitude attractor, and a phase-locked loop trajectory corresponding to the phase-locked cone region is constructed. The phase-locked cone region is mapped to a multi-sphere stacked region. Based on the sphere positions and reachable space, the region is divided into a distant region, a near region, and a phase-locked window region. A macroscopic approach path that satisfies preset constraints is generated. The time interval corresponding to the path segment that intersects with the phase-locked window region in the macroscopic approach path is determined as the phase-locked time window. During the ball-changing process, if the sensor group determines that the gripper has entered the initial contact state and is in the phase-locked window area, the mode is switched to phase-locked training mode, and the phase-locked loop trajectory is superimposed within the phase-locked time window to control the gripper end to perform micro-vibration and micro-oscillation actions in the contact point area with the ball, so that the ball's attitude converges to the stable attitude attractor. In phase-locked training mode, if the ball posture is determined to complete phase-locking based on changes in contact force distribution, contact stiffness, and end-micro-vibration response, the vibration amplitude of the phase-locked cycle trajectory is reduced, and the clamping force of the gripper is increased, so that the ball smoothly transitions from the initial contact state to the fully locked state. Based on the local phase-locked path corresponding to the phase-locked loop trajectory and the macroscopic approach path, the final path plan for the collaborative ball replacement of the neutron multi-sphere spectrometer is obtained.

2. The path planning method for collaborative ball changing in a neutron multi-sphere spectrometer according to claim 1, characterized in that, The process involves acquiring a three-dimensional model of the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, the support structure, and the gripper structure for the neutron multi-sphere spectrometer. Then, the irradiation field distribution, temperature field distribution, and structural vibration field distribution are superimposed onto the three-dimensional model to obtain the contact friction characteristics and contact stiffness variation range of the spheres. Specifically, this includes: In a unified modeling environment, based on engineering drawings, structural design parameters and on-site survey data, a detailed geometric entity of the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, the support structure and the gripper structure is established and assembled to obtain the three-dimensional model. The three-dimensional model is imported into a multiphysics simulation environment. By constructing irradiation field simulation examples, temperature field simulation examples, and structural vibration simulation examples, the irradiation field distribution, temperature field distribution, and structural vibration field distribution under different working conditions are solved. In the three-dimensional model, contact analysis simulation is performed on the contact areas between the sphere and the gripper structure and between the sphere and the support structure. The contact pressure distribution, contact slip and contact area deformation are collected, and the contact friction characteristics and contact stiffness variation range are determined based on the simulation results and calibration test results under different working conditions.

3. The path planning method for collaborative ball changing in a neutron multi-sphere spectrometer according to claim 1, characterized in that, Based on the contact friction characteristics and the range of contact stiffness variation, a micro-vibration sequence and a micro-oscillation trajectory are applied to the sphere in the initial contact state through simulation and experimentation to determine the sphere's attitude evolution behavior. The sphere's attitude evolution behavior is then used to calibrate and converge the sphere's attitude to the phase-locked cone region of the stable attitude attractor, and a phase-locked loop trajectory corresponding to the phase-locked cone region is constructed. Specifically, this includes: In a joint simulation and experimental environment, multiple sets of micro-vibration sequences with different frequencies, amplitudes and phase structures, as well as micro-oscillation trajectories constructed around the contact point normal or tangential, are synchronously executed on a sphere in the initial contact state. The time series of the sphere's attitude, the change in contact force distribution, and the change in contact stiffness are collected after the micro-vibration sequence is executed. The response data is then mapped into the attitude state space to identify the contact configuration region that can induce the sphere's attitude to converge to a stable attitude attractor along a specific attitude evolution channel. The contact configuration region is then labeled as a phase-locked cone region. Based on the attitude evolution characteristics corresponding to each phase-locked cone region, trajectory units that can achieve rapid attitude convergence under the constraints of the contact friction characteristics and the range of contact stiffness variation are selected from the micro-vibration sequence and the micro-oscillation trajectory. Based on the trajectory unit, a phase-locked loop trajectory corresponding to the phase-locked cone region is constructed.

4. The path planning method for collaborative ball changing in a neutron multi-sphere spectrometer according to claim 1, characterized in that, The process involves mapping the phase-locked cone region to a multi-sphere stacked region, dividing the region into a distant region, a near region, and a phase-locked window region based on the sphere positions and reachable space, and generating a macroscopic approach path that satisfies preset constraints. The time interval corresponding to the path segment intersecting the phase-locked window region within the macroscopic approach path is determined as the phase-locked time window. Specifically, this includes: The attitude range of the gripper relative to the sphere corresponding to the phase-locked cone region is transformed into the reachable attitude region of the gripper end in space. After considering the occlusion relationship of the multi-sphere stacked structure, the geometric limitations of the inner wall structure of the irradiation cavity, and the joint reachability of the collaborative robotic arm structure, the reachable attitude region is trimmed into the actual accessible phase-locked window region. Based on the phase-locked window region, the sphere is divided into a far-away region, an approach region, and a phase-locked window region in the circumference. Under the conditions of satisfying obstacle avoidance constraints, irradiation dose constraints, joint limit constraints, and path continuity constraints, a macroscopic approach path is generated from the far-away region through the approach region to the phase-locked window region. The time interval during which the grasper end pose enters the phase-locked window region is identified in the macroscopic approach path, and the time interval is used as the phase-locked time window.

5. The path planning method for collaborative ball changing in a neutron multi-sphere spectrometer according to claim 1, characterized in that, During the ball-changing process, if the sensor group determines that the gripper has entered the initial contact state and is within the phase-locked window region, then the process switches to phase-locked training mode, and the phase-locked loop trajectory is superimposed within the phase-locked time window to control the gripper end to perform micro-vibration and micro-oscillation movements at the contact point with the ball, so that the ball's attitude converges towards the stable attitude attractor. Specifically, this includes: The sensor group uses tactile sensors, force sensors, micro-accelerometers, and near-field vision sensors to detect in real time the transition characteristics of the gripper fingertip contact force from zero to one, the stability characteristics of the contact force amplitude within the initial contact state threshold range, the spectral changes of contact characteristics appearing in the end-effector micro-vibration response, and the spatial characteristics of the local contour of the sphere entering the gripper fingertip contact area, thus obtaining a feature set. Under the premise that the gripper enters the initial contact state based on the feature set, and based on the condition that the gripper end pose falls into the phase-locked window area and the current time is within the phase-locked time window, the control mode is switched from the trajectory tracking mode of the macro approach path to the phase-locked taming mode. Within the phase-locked time window, a target phase-locked loop trajectory adapted to the current contact configuration is selected from the phase-locked loop trajectory and superimposed onto the macroscopic approach path to control the gripper end to perform micro-vibration and micro-oscillation actions in the contact point area according to the target phase-locked loop trajectory, so as to guide the sphere attitude to converge toward the stable attitude attractor.

6. The path planning method for cooperative ball changing in a neutron multi-sphere spectrometer according to claim 1, characterized in that, In the phase-locked training mode, if the ball's posture is determined based on changes in contact force distribution, contact stiffness, and end-effector micro-vibration response to complete phase-locking, then the vibration amplitude of the phase-locked cycle trajectory is reduced, and the gripper's clamping force is increased, allowing the ball to smoothly transition from the initial contact state to the fully locked state. Specifically, this includes: During the execution of the phase-locked loop trajectory, the distribution uniformity of the contact force at the fingertips of the gripper, the stability of the contact stiffness, and the convergence of the end-effector micro-vibration response are monitored. When it is determined, based on the distribution uniformity, the stability, and the convergence, that the contact force distribution tends to be uniform, the slope of the contact stiffness change continues to decrease, and the end-effector micro-vibration response exhibits stable characteristics, the sphere attitude is determined to complete the phase-locking. The vibration amplitude of the phase-locked loop trajectory is reduced according to a preset reduction rhythm, and the contact stability is monitored synchronously during the reduction of vibration amplitude to avoid triggering attitude reverse drift; After the vibration amplitude of the phase-locked loop trajectory drops to a preset threshold, the gripper clamping force is gradually increased in a slow manner to allow the ball to transition from the initial contact state to the fully locked state. During the transition, the local phase-locked path is smoothly integrated into the macroscopic approach path to ensure the continuity of the gripper end trajectory and the mechanical state of the contact interface.

7. The path planning method for cooperative ball changing in a neutron multi-sphere spectrometer according to claim 1, characterized in that, The neutron multisphere spectrometer further includes a main robotic arm structure and an auxiliary robotic arm structure, and the method further includes: In the three-dimensional model, the reachable space, obstacle avoidance space and dynamic constraint space of the main robotic arm structure and the auxiliary robotic arm structure are jointly modeled. Based on the occlusion relationship between the multi-sphere stacked structure, the inner wall structure of the irradiation cavity and the support structure, the cooperative target pose region of the auxiliary robotic arm is determined, and a cooperative support path that enables the auxiliary robotic arm to enter the cooperative target pose region is generated. During the process of the main robotic arm approaching the sphere along the macroscopic approach path, a cooperative approach path is generated based on the reachable spatial overlap relationship and temporal coupling constraint between the main robotic arm and the auxiliary robotic arm, so that the auxiliary robotic arm can synchronously approach the sphere. When the main robotic arm enters the phase-locked window area and switches to the phase-locked training mode, a cooperative local phase-locked path is generated based on the phase-locked cone area and the phase-locked loop trajectory, which enables the auxiliary robotic arm to perform phase-matching support actions within the phase-locked time window. The cooperative movement between the main robotic arm and the auxiliary robotic arm is achieved through the cooperative support path, the cooperative approach path, and the cooperative local phase-locked path, so as to construct a cooperative convergence path that enhances the convergence of the sphere's attitude to the stable attitude attractor.

8. A path planning system for collaborative sphere changing in a neutron multi-sphere spectrometer, characterized in that, The system is used to execute the path planning method for cooperative ball changing in a neutron multi-sphere spectrometer as described in any one of claims 1 to 7. The system includes an acquisition module and a processing module, wherein... The acquisition module is used to acquire a three-dimensional model of the multi-sphere stacked structure, the inner wall structure of the irradiation cavity, the support structure, and the gripper structure of the neutron multi-sphere spectrometer, and to superimpose the irradiation field distribution, temperature field distribution, and structural vibration field distribution on the three-dimensional model to obtain the contact friction characteristics and contact stiffness variation range of the spheres. The processing module is used to apply a micro-vibration sequence and a micro-oscillation trajectory to the sphere in the initial contact state through simulation and experiment based on the contact friction characteristics and the range of contact stiffness variation, so as to determine the sphere attitude evolution behavior, and to calibrate the sphere attitude to converge to the phase-locked cone region of the stable attitude attractor according to the sphere attitude evolution behavior, and to construct the phase-locked loop trajectory corresponding to the phase-locked cone region. The processing module is further configured to map the phase-locked cone region to a multi-sphere stacked region, divide the region into a distant region, a near region, and a phase-locked window region based on the position of the spheres and the reachable space, and generate a macroscopic approach path that satisfies preset constraints. In the macroscopic approach path, the time interval corresponding to the path segment that intersects with the phase-locked window region is determined as the phase-locked time window. The processing module is also used to switch to phase-locked training mode if the sensor group determines that the gripper has entered the initial contact state and is in the phase-locked window area during the ball exchange process, and to superimpose the phase-locked loop trajectory within the phase-locked time window to control the end of the gripper to perform micro-vibration and micro-oscillation actions in the contact point area with the ball so that the ball's attitude converges to the stable attitude attractor. The processing module is also used to reduce the vibration amplitude of the phase-locked loop trajectory and increase the clamping force of the gripper in the phase-locked training mode if the ball posture is determined to complete phase-locking based on the changes in contact force distribution, contact stiffness and end micro-vibration response. This allows the ball to smoothly transition from the initial contact state to the fully locked state. The processing module is further configured to obtain the final path plan for the collaborative ball replacement of the neutron multi-sphere spectrometer based on the local phase-locked path corresponding to the phase-locked loop trajectory and the macroscopic approach path.

9. An electronic device, characterized in that, The electronic device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions. The user interface and the network interface are both used to communicate with other devices. The processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores instructions that, when executed, perform the method as described in any one of claims 1 to 7.

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