Quadruped robot path optimization method and system

Abstract

The invention provides a quadruped robot path optimization method and system, and the method comprises the steps: building an overlapping operation window recognition mechanism through obtaining the state information and topographic data of a robot, generating a risk map based on a conflict probability, and constructing a hierarchical task chain; establishing path-terrain mapping, identifying a vortex region through an energy flow channel and flow field rotation characteristics, and forming a path dominant region; performing task density analysis on the dominant region, and forming a complementary rhythm through peak-valley separation and frequency analysis to generate an equilibrium flow; main and auxiliary path assignment is carried out on the balanced flow, and high-density path reserve is formed through load analysis and compression processing; performing risk detection on the main path to obtain an early warning, triggering reserve release according to the early warning, and performing cross weaving with the main path to form a reinforcing network; a cooperative propagation matrix is constructed based on a reinforcement network, flow field diffusion analysis is carried out to generate discrete path configuration, a convergence center is established, a unified control command is output, and the cooperative path optimization problem under the complex terrain is effectively solved.

Description

Technical Field

[0001] The present invention relates to the technical field of robot collaborative control, and in particular to a quadruped robot path optimization method and system. Background Art

[0002] With the rapid development of quadruped robot technology, the demand for multi-robot collaborative operations in complex terrain environments is growing. In scenarios such as search and rescue, inspection, and transportation, multiple quadruped robots must collaborate to complete tasks in rugged terrain, posing unprecedented challenges to path planning technology. Existing single-robot path planning methods struggle to handle spatiotemporal conflicts among multiple robots, while traditional multi-robot coordination methods lack the ability to deeply perceive and adaptively process complex terrain features.

[0003] Current path planning methods for multi-quadruped robots have limited capabilities for detecting spatiotemporal conflicts, leading to frequent path collisions and resource competition during multi-robot execution. Existing methods are insufficiently adaptable to complex terrain and are unable to effectively identify and avoid dangerous and inaccessible areas within the terrain, resulting in inefficient robot operation and even safety incidents. Furthermore, traditional task scheduling mechanisms are relatively simplistic, lacking adaptive load distribution and backup path management capabilities, making them difficult to cope with dynamically changing operating environments. When the system faces emergencies, existing emergency response mechanisms are inadequate, with limited fault recovery and path reconstruction capabilities, severely restricting the efficiency and safety of multi-quadruped collaborative operations in complex environments. Summary of the Invention

[0004] The present invention provides a quadruped robot path optimization method system. By constructing an overlapping operation window recognition and conflict prediction mechanism, a path-terrain mapping system and eddy current area recognition technology are established, task density analysis and frequency complementation technology are used to generate a dynamically balanced task flow, a high-density path reserve mechanism and a reinforcement network fusion technology based on early warning are constructed, and unified coordinated control is achieved through a collaborative propagation matrix and a path convergence center. The method provides a path optimization solution for the collaborative operation of multiple quadruped robots in complex terrain environments.

[0005] A first aspect of the present invention provides a quadruped robot path optimization method, comprising the following steps: Acquiring status information and terrain data of each quadruped robot, identifying overlapping operation windows based on the status information, generating a path strategy through the overlapping operation windows, and constructing a hierarchical task chain based on the path strategy and the terrain data; Building a path-terrain mapping relationship by combining the hierarchical task chain and the terrain data, identifying an eddy current area through the path-terrain mapping relationship, and avoiding the eddy current area to form a path advantage area; Performing task density analysis on the path advantage area to form a density fluctuation curve, performing peak-valley separation based on the density fluctuation curve to generate a high-density task flow and a low-density task flow, using frequency analysis to make the high-density task flow and the low-density task flow form a complementary rhythm, and using the complementary rhythm to generate a balanced task flow; Performing task assignment on the task balancing flow to generate a primary path and an auxiliary path, performing load analysis on the auxiliary path to extract path redundant resources, and compressing the path redundant resources to form a high-density path reserve; Performing risk detection on the main path to obtain a terrain warning, triggering the release of the high-density path reserve according to the terrain warning, and fusing the released high-density path reserve with the main path to generate a reinforcement path network; A collaborative propagation matrix is ​​constructed based on the reinforced path network, a flow field diffusion analysis is performed on the collaborative propagation matrix to generate a discrete path configuration, a path convergence center is established based on the discrete path configuration, and the discrete path configuration is integrated into a control command through the path convergence center.

[0006] A second aspect of the present invention provides a quadruped robot path optimization system, comprising: a data acquisition module for acquiring status information and terrain data of each quadruped robot, identifying overlapping operation windows based on the status information, generating a path strategy based on the overlapping operation windows, and constructing a hierarchical task chain based on the path strategy and the terrain data; a path generation module, configured to construct a path-terrain mapping relationship by combining the hierarchical task chain and the terrain data, identify eddy current areas through the path-terrain mapping relationship, and avoid the eddy current areas to form a path advantage area; a task scheduling module configured to perform task density analysis on the path advantage area to form a density fluctuation curve, perform peak-valley separation based on the density fluctuation curve to generate a high-density task flow and a low-density task flow, perform frequency analysis to enable the high-density task flow and the low-density task flow to form a complementary rhythm, and generate a balanced task flow using the complementary rhythm; a path dispatching module configured to dispatch tasks to the task balancing flow to generate a primary path and an auxiliary path, perform load analysis on the auxiliary path to extract path redundant resources, and compress the path redundant resources to form a high-density path reserve; a dynamic fusion module, configured to perform risk detection on the primary path to obtain a terrain warning, trigger the release of the high-density path reserve according to the terrain warning, and fuse the released high-density path reserve with the primary path to generate a reinforcement path network; A collaborative control module is used to construct a collaborative propagation matrix based on the reinforced path network, perform flow field diffusion analysis on the collaborative propagation matrix to generate discrete path configurations, establish a path convergence center based on the discrete path configurations, and integrate the discrete path configurations into control commands through the path convergence center.

[0007] The beneficial effects of the present invention are reflected in the following points: 1. Through overlapping operation window identification and spatiotemporal cross analysis, the multi-robot collaborative relationship is quantified into overlap and risk distribution, achieving accurate conflict prediction and active avoidance. Combined with the path-terrain mapping system and flow field rotation feature identification, the vortex area in complex terrain is accurately captured, forming a path advantage area, and effectively eliminating mutual interference between robots. 2. Using task density analysis and peak-valley separation technology, high and low density task flows are coordinated through frequency complementary rhythm to solve the problems of uneven task distribution and load imbalance. At the same time, a high-density path reserve mechanism is constructed, and distributed redundant resources are integrated through time folding and compressed potential energy technology to achieve a transition from static planning to dynamic resource management. 3. A reserve release and reinforcement mechanism based on terrain warning is established, and the path network structure is dynamically adjusted according to real-time risks to achieve the organic integration of the main path and reserve resources. Through collaborative propagation matrix flow field analysis and unified control of the path convergence center, a complete process from path configuration to control command is established to ensure that multiple quadruped robots can work together efficiently in complex terrain.

[0008] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The accompanying drawings herein illustrate specific examples of the technical solutions described in the present invention, and together with the specific implementation methods constitute a part of the specification, and are used to explain the technical solutions, principles and effects of the present invention.

[0010] Unless otherwise specified, the same reference numerals in different drawings represent the same or similar technical features, and the same or similar technical features may also be represented by different reference numerals.

[0011] Figure 1 It is a flow chart of a quadruped robot path optimization method of the present invention.

[0012] Figure 2 It is a structural block diagram of a quadruped robot path optimization system of the present invention. DETAILED DESCRIPTION

[0013] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0014] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or collections thereof.

[0015] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in this specification do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0016] The technical solutions of the embodiments of this application are introduced below.

[0017] like Figure 1 As shown, an embodiment of the present invention provides a quadruped robot path optimization method, comprising the following steps S110 to S160: Step S110 , obtaining status information and terrain data of each quadruped robot, identifying overlapping operation windows based on the status information, generating a path strategy through the overlapping operation windows, and constructing a hierarchical task chain based on the path strategy and terrain data.

[0018] Specifically, the system acquires status information and terrain data for each quadruped robot. This information includes key parameters such as the robot's position, velocity, attitude angle, battery charge, payload status, and sensor data. Real-time data exchange is achieved through a wireless communication network between the robots. Position coordinates are determined using a fusion of GPS and inertial navigation, achieving centimeter-level accuracy. Velocity is measured using encoders and IMU sensors, and attitude angles are acquired using a three-axis gyroscope and accelerometer. Terrain data is collected through a multi-sensor fusion approach, including lidar, stereo vision, and ultrasonic sensors, to create a high-precision three-dimensional terrain model containing information such as ground elevation, slope, roughness, and obstacle distribution. Data collection utilizes a high-frequency, real-time method to ensure real-time awareness of the robot's motion status and terrain changes. Data transmission utilizes multi-channel backup to minimize transmission latency. Data preprocessing includes noise filtering, coordinate transformation, and time synchronization to establish a unified data format and coordinate system.

[0019] Overlapping windows are identified based on state information. Overlapping windows are identified by analyzing the temporal and spatial extents of multiple robots' operations and calculating the spatiotemporal intersection of each robot's operating area. The degree of overlap, R_ij, is calculated as (A_intersection / A_union) × (T_intersection / T_union), where A represents the spatial area and T represents the temporal duration. Intervals where the degree of overlap exceeds a preset threshold are marked as overlapping windows. Window identification utilizes a spatiotemporal voxelization method, dividing the four-dimensional spacetime into discrete cells and labeling the robot occupancy of each cell. Overlap is categorized into three types: spatial overlap (multiple robots appearing simultaneously in the same spatial area), temporal overlap (multiple robots performing tasks simultaneously), and task overlap (multiple robots performing the same or related tasks). The overlap intensity is calculated by combining the number of overlapping robots and the duration of overlap. Window windows with high overlap intensity are prioritized and addressed. A geometric bounding algorithm is used to determine the window boundaries, with the minimum bounding area encompassing all overlapping robots serving as the window boundary.

[0020] In some embodiments, generating a path strategy through the overlapping job windows includes: performing a spatiotemporal cross-analysis on the overlapping job windows to obtain window overlap; calculating the task conflict probability based on the window overlap to generate a conflict risk graph; performing a task decoupling operation according to the conflict risk graph to determine a decomposition boundary; and constructing a path strategy using the decomposition boundary.

[0021] Spatiotemporal intersection analysis is performed on overlapping work windows to determine the degree of window overlap. This analysis establishes a four-dimensional space-time coordinate system, represents the robot's work activities as space-time volumes, and analyzes the degree of intersection between the space-time volumes of different robots' work. Spatial intersection analysis uses a volume intersection algorithm to calculate the overlapping volume of each robot's work area in three-dimensional space. The degree of spatial overlap is determined by the ratio of the overlapping volume to the total volume. Temporal intersection analysis calculates the overlapping intervals along the work time axis and determines the degree of temporal overlap by the ratio of the temporal overlap length to the total work time. The overall degree of overlap is determined by a weighted combination of spatial and temporal overlap, with the weight coefficient determined by task type and priority. Overlap grading categorizes overlapping windows into three levels: high overlap, medium overlap, and low overlap, with different handling strategies corresponding to each level. The overlap calculation takes into account the robot's trajectory prediction, using motion models to estimate the position distribution in future time periods and identify potential overlapping areas in advance.

[0022] The conflict risk map is generated by calculating the task conflict probability based on window overlap. The conflict probability calculation takes into account the combined influence of multiple factors, including overlap, the number of robots, and task complexity. The conflict probability P_conflict = 1-(1-R_total)^N, where R_total represents the overall overlap and N represents the number of robots in the overlap area. The probability reflects the likelihood of task conflict. Conflict types identified include path conflict (multiple robots competing for the same path), resource conflict (multiple robots competing for the same task), and timing conflict (conflicts in task execution time). Conflict intensity is calculated by combining conflict duration and impact range, reflecting the impact of the conflict on the overall task. The conflict risk map is constructed using a gridding method, dividing the task area into grid cells and labeling each cell with the conflict probability and intensity. The risk map is color-coded, with red indicating high-risk areas, yellow indicating medium-risk areas, and green indicating low-risk areas. Conflict risk propagation analysis considers the diffusion effect of conflict in space and time, using a diffusion model to predict the impact range and duration of the conflict.

[0023] Decomposition boundaries are determined by performing task decoupling based on the conflict risk graph. Task decoupling reduces interference between robots by breaking down complex coupled tasks into independent subtasks. Decoupling strategies include temporal decoupling (staggering execution times), spatial decoupling (separating work areas), and functional decoupling (division of work and collaboration). Decomposition boundary identification analyzes the risk gradient in the conflict risk graph and identifies areas with drastic changes in risk density as decomposition boundaries. Boundary strength is determined by calculating the gradient of conflict probability, with areas with large gradients being suitable as decomposition boundaries. Boundary connectivity analysis ensures good connectivity among the decomposed sub-areas to avoid isolated work areas. Boundaries are categorized into hard boundaries (strict separation, no crossing allowed) and soft boundaries (limited crossing allowed, requiring coordination). Decomposition boundaries are represented geometrically using polygons, containing attributes such as vertex coordinates, edge lengths, and boundary type.

[0024] Path strategies are constructed using decomposition boundaries. Path strategy construction divides the overall work area into multiple sub-areas based on the decomposition boundaries, and an independent path planning scheme is developed for each robot within each sub-area. Strategies include three basic modes: avoidance (circumventing high-risk areas), coordination (time-sequential coordination to reduce conflicts), and division of labor (dividing tasks and executing them in parallel). The path generation algorithm uses a path search algorithm, incorporating conflict risk as a key component of the path cost: C_path = C_distance + λ × C_risk + μ × C_time, where C_distance is the distance cost, C_risk is the risk cost, and C_time is the time cost, and λ and μ are weighting coefficients. A policy adaptability mechanism selects an appropriate path strategy based on the characteristics of the decomposition boundaries. Avoidance strategies are used in areas with clear boundaries, while coordination strategies are used in areas with ambiguous boundaries. Path strategies include complete information such as path node sequences, speed plans, time schedules, and contingency plans. A policy coordination mechanism ensures compatibility between path strategies in different sub-areas, enabling seamless integration between strategies through boundary interfaces. Path strategy execution monitoring establishes a real-time feedback mechanism, adjusting policy parameters based on actual execution results to ensure efficient and safe multi-robot collaboration.

[0025] A hierarchical task chain is constructed based on path strategies and terrain data. This hierarchical task chain decomposes complex multi-robot collaborative tasks into multiple layers, including a global planning layer, a local planning layer, and an execution control layer. Data interfaces enable information transmission and coordinated control between these layers. The global planning layer is responsible for overall task allocation and macro-path planning, combining terrain data to determine each robot's operating area and primary path. The local planning layer is responsible for local path optimization and obstacle avoidance, adjusting path details based on real-time terrain information. The execution control layer is responsible for specific motion control and action execution, converting path commands into motor control signals. The task chain structure is organized hierarchically, with tasks at each layer coordinated through priorities and dependencies. Terrain adaptability analysis considers the impact of different terrain conditions on task execution, with flat terrain being suitable for high-speed mobility tasks and rough terrain being suitable for delicate manipulation tasks. The task chain's dynamic adjustment mechanism adjusts task parameters and execution strategies at each layer in real time based on terrain changes and task progress.

[0026] Step S120 , combining the hierarchical task chain and terrain data to construct a path-terrain mapping relationship, identifying eddy current areas through the path-terrain mapping relationship, and avoiding the eddy current areas to form path advantage areas.

[0027] Specifically, a path-terrain mapping relationship is constructed by combining hierarchical task chains and terrain data. Using a multi-level mapping approach, paths at the global planning layer are mapped to macro-terrain features (such as mountains, rivers, and plains); paths at the local planning layer are mapped to meso-terrain features (such as slope, elevation, and vegetation); and paths at the execution control layer are mapped to micro-terrain features (such as rocks, potholes, and obstacles). The mapping relationship M(p,t)=f(P_path,T_terrain) is defined, where P_path represents the path parameters, T_terrain represents the terrain parameters, and f represents the mapping function. Terrain features extracted include key parameters such as ground slope, surface roughness, soil hardness, vegetation density, and obstacle distribution. High-precision terrain information is acquired through multi-sensor fusion. Mapping accuracy is controlled through a gridding method, dividing the terrain into high-precision grid cells, each containing complete terrain characteristic parameters. The dynamic update mechanism of the path-terrain mapping uses terrain perception data during robot motion to correct and improve the mapping relationship in real time, ensuring mapping accuracy and timeliness.

[0028] In some embodiments, identifying the eddy zone through the path-terrain mapping relationship includes: establishing an energy flow channel based on the path-terrain mapping relationship; monitoring the flow resistance along the energy flow channel to obtain the resistance distribution; inferring the flow field rotation characteristics based on the resistance distribution; and marking the flow field rotation characteristics as an eddy zone.

[0029] Energy flow channels are established based on the path-terrain mapping relationship. Energy flow channels are the paths through which energy is transferred and consumed as the robot moves through the terrain. They are established by analyzing the energy variations in the path-terrain mapping relationship. Channel establishment relies on the principle of energy conservation to analyze energy distribution, including the conversion of kinetic energy, potential energy, and dissipated energy. The geometry of the flow channel is determined by both the terrain undulation and the path curvature. Flat terrain forms wide flow channels, while rugged terrain forms narrow ones. The channel width is determined by the energy diffusion range, and the channel orientation follows the direction of maximum energy gradient. The bifurcation and convergence of the flow channel reflect the complexity of the terrain, with bifurcations corresponding to terrain obstacles and convergences corresponding to terrain depressions. Channel connectivity is analyzed using network analysis methods to establish the topology of the channel network and identify key nodes and connecting paths. Energy flow channels are visualized using streamline diagrams, where streamline density indicates energy flow intensity and streamline direction indicates energy flow direction.

[0030] Flow resistance is monitored along the energy flow channel to obtain the resistance distribution. By analyzing the magnitude and distribution of resistance encountered by the robot as it moves through the channel, areas of resistance concentration are identified. Resistance sources include ground friction, air resistance, terrain resistance, and inertial resistance. The total resistance, F_total, equals F_friction + F_air + F_terrain + F_inertia. Resistance measurement utilizes a combination of force and power sensors to infer resistance magnitude by measuring the robot's drive power and motion state. The resistance distribution is obtained using data interpolation techniques, interpolating data from a limited number of measurement points to obtain the resistance distribution for the entire channel. The resistance distribution analysis incorporates terrain characteristic parameters. Areas with steep slopes experience increased terrain resistance, areas with high roughness experience increased frictional resistance, and areas with dense obstacles generate additional detour resistance. The resistance density is determined by the ratio of resistance to contact area, reflecting the magnitude of resistance per unit area. The rate of change of resistance is calculated using its time derivative. Areas with large rates of change indicate rapidly changing resistance and the presence of potentially complex flow field structures. Statistical characteristics of the resistance distribution, including mean, variance, skewness, and kurtosis, describe the shape of the resistance distribution. Drag anomaly detection identifies abnormally high drag areas by setting thresholds. These areas usually correspond to terrain obstacles or flow field singularities.

[0031] The flow field rotation characteristics are inferred from the drag distribution. Based on the spatial variation pattern of the drag distribution, the rotational flow is identified by analyzing the drag gradient and curl. The rotation characteristics are calculated using numerical calculation methods. The rotation intensity is calculated by the spatial derivative of the drag component. The rotation direction is determined by the right-hand rule, with counterclockwise rotation as a positive value and clockwise rotation as a negative value. The spatial scale of the flow field rotation is analyzed by correlation length, reflecting the spatial range of the rotation phenomenon. The rotation center is identified by finding the local extreme point of the rotation intensity, which corresponds to the center position of the rotating flow. The temporal evolution of the flow field rotation is analyzed through continuous monitoring to identify the temporal variation pattern of the rotation intensity. Multi-scale rotation analysis considers rotation phenomena at different spatial scales. Large-scale rotation corresponds to macroscopic features of the terrain, and small-scale rotation corresponds to local terrain details. The stability of the rotation characteristics is evaluated by the consistency of multiple measurements. Stable rotation characteristics are used to mark eddy zones.

[0032] Flow field rotational features are marked as eddy zones. Eddy zones are areas of terrain where resistance to robot motion exhibits a rotational distribution due to factors such as ground undulation and obstacle distribution. These areas increase the robot's energy consumption and motion complexity. Eddy zone marking is based on comprehensive characteristics of the flow field rotational features, including intensity, range, and persistence. Areas that meet the eddy criteria are marked as eddy zones. The eddy criteria include three conditions: rotation intensity exceeding a preset threshold, rotation range exceeding a minimum area, and duration exceeding a minimum duration. The eddy zone boundary is defined by contour lines at specific rotational intensities, which form the eddy zone boundary. Eddy zone classification categorizes eddy zones into three levels based on rotational intensity: strong eddy zones, medium eddy zones, and weak eddy zones, with different avoidance strategies corresponding to each level. Eddy zone codes are named using identifiers in the format of VZ-number-level for easy system identification and management. Eddy zone attribute information includes complete parameters such as center coordinates, boundary range, rotation intensity, rotation direction, duration, and impact radius. The spatial relationship analysis of eddy zones identifies the interactions between adjacent eddy zones, and the avoidance strategies of eddy zones that influence each other require overall consideration.

[0033] Avoid eddy currents to create path-dominant regions. By eliminating eddy currents and other unfavorable terrain areas, terrain regions suitable for efficient robot movement are identified. Advantageous region evaluation metrics include terrain flatness, accessibility, safety, and energy efficiency. The advantage score S = w1 × flatness + w2 × accessibility + w3 × safety + w4 × efficiency, where w1 - w4 are weighting coefficients. Region screening utilizes multiple constraints, prioritizing areas with suitable slopes, no large obstacles, and distance from eddy currents. Advantageous region connectivity analysis ensures good connectivity between selected advantageous regions, forming a continuous advantageous path network. Region classification categorizes advantageous regions into three levels: primary (optimal accessibility), secondary (good accessibility), and tertiary (acceptable accessibility). Path-dominant regions are geometrically represented using polygons, containing attributes such as region boundaries, area, advantage score, and connectivity.

[0034] Step S130 , performing task density analysis on the path advantage area to form a density fluctuation curve, performing peak-valley separation based on the density fluctuation curve to generate high-density task flows and low-density task flows, and using frequency analysis to make the high-density task flows and the low-density task flows form a complementary rhythm, and using the complementary rhythm to generate a balanced task flow.

[0035] Specifically, task density analysis is performed on the path advantage area to generate a density fluctuation curve. Task density is defined as the number of tasks per unit space and per unit time. Task density ρ(x,y,t) = N_tasks / (ΔA×Δt), where N_tasks is the number of tasks, ΔA is the spatial area, and Δt is the time interval. Density calculation uses a sliding window method, with a spatial window of 10 meters by 10 meters and a temporal window of 5 minutes. Continuous density distribution data is obtained by sliding the window. Task types are categorized into mobility tasks, manipulation tasks, perception tasks, and communication tasks. Different task types are assigned different weight coefficients, with manipulation tasks receiving the highest weight and communication tasks receiving the lowest. The density fluctuation curve is generated through time series analysis, with time on the horizontal axis and task density on the vertical axis. The curve reflects the temporal variation of task density. The density fluctuation function uses a trigonometric function model combined with random perturbations and includes parameters such as base density, fluctuation amplitude, angular frequency, phase, and random perturbations. Fluctuation characteristic parameters extracted include key indicators such as fluctuation period, fluctuation amplitude, fluctuation frequency, and trend direction.

[0036] Peak-valley separation based on the density fluctuation curve generates high-density and low-density task flows. By analyzing the local extreme values ​​of the density fluctuation curve, peak and valley intervals of task density are identified. Peak-valley separation optimizes separation performance by combining fluctuation characteristic parameters. The peak-valley search window length is determined based on the fluctuation period, and the peak-valley threshold range is set based on the fluctuation amplitude to ensure separation accuracy. Peak detection uses a sliding window extreme value search algorithm with a window length set to 1 / 4 of the fluctuation period. The maximum density point within the window is searched for as the peak point. Valley detection uses a similar approach, searching for the minimum density point as the valley point. The peak and valley thresholds are determined based on the density mean and standard deviation. High-density task flows are defined as time periods where the density exceeds the peak threshold and include tasks with high density, urgent execution, and high resource requirements. Low-density task flows are defined as time periods where the density falls below the valley threshold and include tasks with low density, slow execution, and low resource requirements. Separation quality is assessed using peak-valley separation, which indicates the degree of distinct peak-valley distinction. Task flow temporal feature analysis includes parameters such as duration, interval, and recurrence period. The continuity processing of task flow ensures the time continuity of task flow through time interpolation, avoiding analysis errors caused by missing data.

[0037] In some embodiments, the frequency analysis is used to form a complementary rhythm between the high-density task flow and the low-density task flow, including: extracting the task main frequency from the high-density task flow; extracting the task sub-frequency from the low-density task flow; calculating the beat interval based on the frequency difference between the task main frequency and the task sub-frequency; and performing time mapping on the beat interval to form a complementary rhythm.

[0038] The dominant frequency of tasks is extracted from high-density task streams. Frequency analysis considers separation quality. Task streams with high separation undergo refined frequency analysis, while task streams with low separation employ robust frequency analysis. Spectral analysis of high-density task streams identifies the dominant frequency components of task execution. Spectral calculation uses a window-weighted FFT method, with a Hamming window selected and a window length set to 1 / 8 the signal length. The dominant frequency is determined by finding the maximum value of the power spectral density. The frequency bandwidth around the dominant frequency is determined using a 3dB bandwidth, reflecting the frequency range of the dominant frequency. The stability of the dominant frequency is verified using multi-window analysis, which divides the signal into multiple overlapping windows and calculates the dominant frequency for each window. Stability is measured using the dominant frequency standard deviation. Harmonic analysis of the dominant frequency identifies frequency components that are integer multiples of the dominant frequency. Harmonic components reflect the periodic characteristics of task execution. Short-time Fourier transform analysis is used to analyze the time-varying characteristics of the dominant frequency, identifying how the dominant frequency changes over time. The confidence level of the dominant frequency is assessed by calculating the signal-to-noise ratio. Interpolation improves frequency resolution for dominant frequency extraction, using parabolic interpolation near the dominant frequency to obtain a more accurate frequency value.

[0039] Task sub-frequencies are extracted from low-density task streams. Sub-frequencies are extracted using a similar method to primary frequency extraction, but with parameters adjusted to suit the characteristics of low-density task streams. Low-density task streams have weaker signal strength, requiring longer observation times and higher frequency resolution. Sub-frequencies are determined by finding the maximum value of the power spectral density of the low-density task stream. Sub-frequencies are identified using a peak detection algorithm with a relative threshold set to 10% of the maximum peak value to minimize noise interference. Sub-frequencies are verified through correlation analysis, calculating the correlation coefficient between the sub-frequencies and the original signal. A correlation coefficient greater than 0.5 is considered valid. Sub-frequencies clustering analysis identifies multiple similar sub-frequencies. Clustered sub-frequencies may correspond to different task execution modes. Spectral shape analysis of sub-frequencies includes parameters such as peak sharpness, bandwidth, and sideband structure, reflecting the frequency-domain characteristics of sub-frequencies. Sub-frequencies are analyzed in the time-domain using an inverse transform to convert the sub-frequencies back to the time domain and identify their corresponding temporal characteristics.

[0040] The beat interval is calculated based on the frequency difference between the task's primary and secondary frequencies. The beat interval reflects the temporal coordination between high-density and low-density task flows and is calculated using the frequency difference. The frequency difference is the absolute difference between the primary and secondary frequencies. A larger frequency difference indicates a more pronounced rhythmic difference between the two task flows. The beat interval, T_beat, = 1 / Δf, where Δf is the frequency difference and the beat interval represents the time period required for the two task flows to resynchronize. The physical meaning of the beat interval is the period of the beat frequency phenomenon, which occurs when two signals with similar frequencies are superimposed. Beat stability is determined through frequency stability analysis. The beat interval is stable under small frequency fluctuations. The rationality of the beat interval is verified by constraints such as time rationality (the interval cannot be too long or too short) and task compatibility (effective task adjustments can be completed within the interval). The beat interval's adaptive adjustment mechanism dynamically adjusts the interval length based on system load and task characteristics, shortening the interval under high load and lengthening it under low load. The quantization accuracy of the beat interval is controlled to the second level to ensure accurate timing control.

[0041] Exemplarily, the timing mapping of the beat intervals to form a complementary rhythm includes: constructing a time elastic window based on the beat intervals; performing beat scaling adjustment within the time elastic window to obtain a variable speed beat sequence; applying periodic constraints to the variable speed beat sequence to form a stable oscillation pattern; and outputting a complementary rhythm through the stable oscillation pattern.

[0042] A time elastic window is constructed based on the beat interval. This time elastic window is a time buffer built around the beat interval, allowing the beat to flexibly adjust within a certain range. The size of the elastic window is determined by the system's time tolerance and is a certain proportion of the beat interval. The shape of the elastic window adopts a Gaussian distribution model, with the center corresponding to the ideal beat time and the edges corresponding to the maximum allowable deviation. The elasticity function uses a Gaussian function to represent the tolerance for time deviation. The softness and hardness of the window boundaries are controlled by constraint strength. Soft boundaries allow for minor violations, while hard boundaries strictly restrict violations. The multi-level elastic window design considers the time sensitivity of different tasks. Critical tasks use narrow elastic windows, while common tasks use wide elastic windows. Overlapping elastic windows is handled through a priority mechanism, with higher priority windows assigned to higher priority tasks. The elastic window dynamically adjusts its size in real time based on system load, shrinking the window when the load is high and expanding it when the load is low.

[0043] Beat scaling is performed within a time elasticity window to generate a variable-speed beat sequence. By varying the beat interval within the elasticity window, the system adapts to real-time state changes. Scaling strategies include linear scaling, nonlinear scaling, and adaptive scaling. Linear scaling adjusts the beat interval using a linear function. Nonlinear scaling uses exponential or logarithmic functions to better adapt to nonlinear load variations. Adaptive scaling is implemented through fuzzy control, which comprehensively determines the degree of scaling based on multiple input parameters (such as load, latency, and resource utilization). The generation of variable-speed beat sequences considers scaling continuity to avoid system oscillations caused by sudden beat changes. A smoothing factor is calculated by averaging adjacent beats to reduce the abruptness of beat changes. Variable-speed range control limits the maximum range of beat scaling to prevent excessive scaling from leading to system loss of control. Beat sequence quality is assessed using two metrics: beat consistency and beat stability.

[0044] A stable oscillation pattern is formed by imposing periodic constraints on the variable-speed beat sequence. This periodic constraint ensures that the variable-speed beat sequence maintains its periodic characteristics during long-term operation, preventing accumulated deviations from causing system desynchronization. Constraint methods include three techniques: period reset, phase correction, and frequency locking. Period reset resets the beat sequence at the end of each complete cycle, eliminating accumulated errors. The reset condition is based on the cumulative time reaching a threshold for a set number of cycles. Phase correction dynamically adjusts the phase of subsequent beats by calculating the deviation between the actual and target phases. Frequency locking uses phase-locked loop technology to lock the variable-speed beat sequence to a reference frequency. Characteristic parameters of the stable oscillation pattern include oscillation amplitude, oscillation frequency, and phase stability. Convergence analysis of the oscillation pattern ensures that the system can quickly converge to a stable state. The robustness of the oscillation pattern has been verified through perturbation testing, demonstrating stable oscillation under external interference.

[0045] Complementary rhythms are output through stable oscillation patterns. These outputs convert stable oscillation patterns into specific task scheduling instructions, guiding the coordinated operation of the multi-robot system. The output format includes information such as timestamp, rhythm type, intensity level, and duration. The complementary rhythm R(t) = A_high × cos(ωt) + A_low × cos(ωt + π), where A_high and A_low represent the amplitudes of high- and low-density tasks, respectively. A rhythm synchronization mechanism ensures that all robots execute tasks according to a unified complementary rhythm, broadcasting the rhythm signal via a wireless communication network. Rhythm execution monitoring establishes a feedback mechanism to monitor the rhythm execution of each robot, promptly identifying and correcting execution deviations. Complementary rhythm performance evaluation includes metrics such as task balance, system efficiency, and energy consumption. A rhythm adaptation mechanism adjusts rhythm parameters based on system performance feedback, achieving continuous rhythm optimization. The storage and playback function of complementary rhythms allows rhythm patterns to be saved and reused, providing a reference for similar task scenarios.

[0046] Complementary rhythms are used to generate a balanced task flow. By temporally reorganizing high-density and low-density task flows according to complementary rhythms, a task execution sequence with relatively uniform density is formed. The balancing algorithm uses a dynamic programming approach to minimize the variance of task density while satisfying the complementary rhythm constraint. The objective function is to minimize the variance of the balanced task density. Temporal reorganization strategies include tasks moving forward, moving backward, splitting, and merging, which adjust task execution times. Load balancing is evaluated by calculating a load balancing factor, which reflects the effectiveness of balancing. Constraints on the task balancing flow include task dependencies, resource availability, and time window restrictions, ensuring that balancing operations do not violate basic constraints on task execution. Balancing effectiveness is verified through simulation tests, comparing system performance metrics before and after balancing, including task completion time, resource utilization, and system stability. The output format of the task balancing flow contains complete information, including task sequence, execution time, resource allocation, and priority settings.

[0047] Step S140 , performing task allocation on the task balancing flow to generate a primary path and an auxiliary path, performing load analysis on the auxiliary path to extract path redundant resources, and compressing the path redundant resources to form a high-density path reserve.

[0048] Specifically, the task balancing flow is assigned to generate a primary path and a secondary path. Based on the task balancing flow generated in S130, task assignment is hierarchically distributed among the balanced tasks based on factors such as importance, urgency, and resource requirements. The assignment strategy adopts a dual-path design: the primary path carries critical and high-priority tasks, while the secondary path carries auxiliary and low-priority tasks. The task importance score I = w1 × urgency + w2 × criticality + w3 × complexity, where w1, w2, and w3 are weight coefficients determined by task type. Tasks on the primary path are characterized by high time sensitivity, high execution accuracy requirements, and severe consequences of failure. They generally account for 60-70% of the total task volume. Tasks on the secondary path are characterized by high time tolerance, relatively low execution accuracy requirements, and the ability to be postponed or canceled. They account for 30-40% of the total task volume. Path assignment utilizes a load balancing algorithm to ensure that the primary path is not overloaded and that the secondary path has an appropriate task load. Task dependency analysis ensures that dependent tasks are assigned to the same path or that a coordination mechanism is established between paths. The primary path design utilizes a streamlined structure with low redundancy, emphasizing execution efficiency and reliability. The secondary path design utilizes a flexible structure with high redundancy, providing support and backup for the primary path. The inter-path switching mechanism provides dynamic adjustment capabilities, enabling tasks to be transferred to the secondary path if problems arise with the primary path.

[0049] Load analysis is performed on the secondary path to identify redundant resources. Resource adequacy is verified on the primary path to ensure resource availability for critical tasks and provide a benchmark for subsequent high-density reserve management. Load analysis monitors resource utilization on the secondary path to identify underutilized redundant resources. Resource types include computing resources, storage resources, communication resources, and time resources. Resource utilization (U) = R_used / R_total, where R_used represents used resources and R_total represents total available resources. Redundant resources are identified using a threshold method, with resources with utilization below 60% marked as redundant. Temporal redundancy analysis compares actual task execution time with allocated time to identify time gaps and buffer time. Temporal redundancy (T_redundant) = T_allocated - T_actual. Temporal redundancy can be used for temporary task insertion or emergency task processing. Spatial redundancy analysis identifies space resources that can be optimized by analyzing detours and alternative paths in path planning. Computational redundancy analysis identifies idle computing capacity by monitoring processor load and memory usage. Redundant resource quality assessment includes metrics such as availability, stability, and responsiveness, with high-quality redundant resources prioritized for reserve management. Redundant resource extraction adopts non-destructive methods to ensure that the normal functions of the auxiliary path are not affected.

[0050] In some embodiments, compressing the path redundant resources to form a high-density path reserve includes: time-folding the path redundant resources to obtain folded-state resources; injecting compression potential energy into the folded-state resources to form potential energy accumulation; continuously applying pressure to make the potential energy accumulation reach a critical density; and locking the critical density state to form a high-density path reserve.

[0051] Time folding is performed on redundant path resources to obtain collapsed resources. Path redundant resources are compressed using a multi-dimensional compression method. This folding operation in the time dimension achieves high-density resource reserves. Time folding compresses and reorganizes redundant resources along the time dimension, concentrating resources originally dispersed across different time periods within a specific time window. Time folding comprehensively considers various redundant resources: temporal redundancy is addressed through time compression, spatial redundancy is addressed through path merging, and computational redundancy is addressed through computing power concentration. The folding operation uses a time mapping method to establish a correspondence between the original time and the collapsed time. The folding mapping is controlled by compression ratio and time offset parameters. The size of the collapsed window is determined based on the temporal distribution characteristics of the resources and is a certain proportion of the original time span. Folding strategies include linear, nonlinear, and adaptive. Linear folding maintains the relative temporal relationships of resources, nonlinear folding prioritizes compression of specific time periods, and adaptive folding dynamically adjusts the degree of folding based on resource importance. Characteristics of collapsed resources include increased temporal density, reduced time span, and improved time utilization. Constraints in the folding process include resource dependencies, temporal order requirements, and system stability to ensure that the folding operation does not disrupt normal system functionality. Folded resources are verified through timing simulation to ensure that the folded resources still meet system requirements. The reversibility of the folded resources allows them to be unfolded back to their original state when needed.

[0052] Compressed potential energy is injected into folded state resources to form potential energy accumulation. Compressed potential energy injection adds additional energy reserves to folded state resources, improving their responsiveness and processing capabilities. Potential energy injection methods include pre-allocating resources, pre-loading data, and pre-establishing connections. Potential energy density is determined by the ratio of potential energy to resource volume. Potential energy types include computing potential (pre-allocated computing power), storage potential (pre-allocated storage space), communication potential (pre-established communication links), and time potential (reserved time buffer). The potential energy injection control strategy uses a gradual injection method to avoid sudden large-scale resource allocations that impact the system. The injection rate is dynamically adjusted based on system load. Potential energy accumulation process monitoring ensures stability by real-time monitoring of potential energy levels. The saturation point of potential energy accumulation is determined by system capacity constraints to avoid excessive accumulation and resource waste. Potential energy accumulation distribution optimization uses a spatial distribution algorithm to evenly distribute potential energy across different resource nodes. The quality assessment of potential energy accumulation includes metrics such as accumulation speed, accumulation stability, and accumulation efficiency.

[0053] Continuous pressure is applied to accumulate potential energy to a critical density. Continuous pressure is achieved through continuous compression, pushing potential energy accumulation to a higher density level. Pressure application methods include a combination of time compression, space compression, and functional compression. The pressure intensity is determined by the ratio of pressure intensity to the area of ​​application. The pressure application process employs a multi-stage strategy: low-intensity pressure is used to establish a baseline density in the initial stage, medium-intensity pressure is used to increase the density in the middle stage, and high-intensity pressure is used in the final stage to reach the critical density. The critical density is identified through density monitoring and stability analysis. When the density approaches the maximum value, the system enters a critical state. The pressure application process is controlled using a feedback control mechanism, adjusting pressure parameters based on density changes. Pressure stability is monitored through vibration analysis to avoid harmful vibrations during the pressure application process. Pressure efficiency is assessed using the energy conversion ratio—the ratio of stored energy to input energy. Safety monitoring of the pressure application process includes pressure, temperature, and deformation monitoring to ensure safety. Termination conditions for the pressure application include reaching the critical density, deteriorating system stability, or exceeding safety thresholds.

[0054] Locking the critical density state forms a high-density path reserve. The high-density path reserve primarily serves emergency needs on the primary path, enabling rapid resource utilization when the primary path experiences resource shortages. Locking solidifies the critical density state, ensuring the stability and durability of the high-density path reserve. The locking mechanism utilizes multiple locking techniques, including physical, logical, and time locking. Physical locking ensures that reserve resources are not occupied by other processes by solidifying the resource allocation table. Logical locking restricts unauthorized access to reserve resources through access control. Time locking ensures that reserve resources remain locked for a specified period of time using a timestamp mechanism. Lock strength is determined by the ratio of the number of locked resources to the total number of resources. Lock status monitoring uses a status detector to monitor the lock status in real time, promptly detecting lock failures. Lock maintenance mechanisms include regular checks, automatic repair, and backup and recovery functions to ensure the continued effectiveness of the lock status. Key parameters of the high-density path reserve include reserve capacity, response time, availability, and call cost. The reserve call interface provides standardized call methods to support access to reserve resources for different types of applications.

[0055] Step S150 , performing risk detection on the main path to obtain terrain warnings, triggering the release of high-density path reserves according to the terrain warnings, and fusing the released high-density path reserves with the main path to generate a reinforcement path network.

[0056] Specifically, risk detection is performed on the main path to obtain terrain warnings. Based on the main path generated by the S140, risk detection uses multi-sensor fusion technology to conduct real-time monitoring and forward-looking analysis of terrain conditions along the path. The detection system includes LiDAR, visual sensors, ultrasonic sensors, inertial measurement units, and other equipment, forming a comprehensive perception network. Risk types identified include terrain obstacle risks (rocks, potholes, steep slopes, etc.), dynamic obstacle risks (moving objects, human activity, etc.), environmental change risks (weather changes, lighting conditions, etc.), and path conflict risks (crossing paths of multiple robots, etc.). The risk assessment function R(x, y, t) = Σwi × Ri(x, y, t), where Ri represents the intensity of the i-th risk category and Ri represents the corresponding weight coefficient. Terrain warnings are graded using a four-level system: blue (low risk, normal travel), yellow (medium risk, cautious travel), orange (high risk, prepare emergency measures), and red (extremely high risk, stop or reroute immediately). Warning trigger thresholds are set based on historical data and safety standards, determined based on historical risk means, standard deviations, and safety factors. Risk forecasting utilizes time series analysis and machine learning methods to predict risk trends over the next 5-15 minutes. Warning information includes detailed parameters such as risk type, location, intensity, duration, and impact range.

[0057] The release of high-density path reserves is triggered based on terrain warnings. The reserve release mechanism automatically or manually triggers the high-density path reserves constructed by S140 based on the terrain warning level and risk characteristics. Trigger conditions include the warning level reaching a threshold, the risk duration exceeding a limit, the simultaneous presence of multiple risk sources, and the main path being impassable. The trigger criterion is T_trigger = (W_level ≥ T_level) ∨ (T_duration ≥ T_time) ∨ (N_risks ≥ N_threshold), where W_level is the warning level, T_level is the level threshold, T_duration is the duration, and N_risks is the number of risks. The release strategy comprehensively considers risk characteristic parameters, determining the type of resources to be released based on risk type, optimizing release locations based on risk location, adjusting the release amount based on risk intensity, and determining the release scope based on the impact area. The release strategy uses a graded release mechanism, determining the amount of reserves released based on risk severity. For low-risk situations, 10-20% of the reserves are released; for medium-risk situations, 30-50%; for high-risk situations, 60-80%; and for extremely high-risk situations, the entire reserve is released. The release process uses a gradual release process to avoid system shock caused by the simultaneous release of large amounts of resources. The release rate is dynamically adjusted based on the urgency of the risk. Reserve release is prioritized in the order of immediately available, quickly activated, and then deep reserve, with priority given to the release of quickly responsive reserve resources.

[0058] In some embodiments, the release-based high-density path reserve is fused with the main path to generate a reinforcement path network, including: constructing a release timing map based on the high-density path reserve; extracting a release diffusion path from the release timing map; cross-weaving along the release diffusion path and the main path; and solidifying the cross-weaving result to form a reinforcement path network.

[0059] A release time series map is constructed based on high-density path reserves. The release time series map is a spatiotemporal distribution diagram depicting the release process of reserve resources, reflecting the release patterns of reserve resources in both time and space. The time series map construction integrates release process parameters: the release volume is reflected as the resource density in the map, the release rate is reflected as the diffusion speed, and the release priority is expressed as the map's hierarchical structure. The map is constructed using a three-dimensional coordinate system, with the x- and y-axes representing spatial position and the z-axis representing time. Each point in the map represents the resource release status at a specific spatiotemporal location. The time series map function G(x,y,t)=f(R_release,T_release,P_position), where R_release is the released volume, T_release is the release time, and P_position is the release position. The map resolution is set to 1 meter in space and 10 seconds in time to ensure map precision. Release pattern recognition analyzes the release patterns in the map to identify different release modes, including concentrated release, dispersed release, pulsed release, and continuous release. Map feature extraction includes key parameters such as release center, diffusion direction, diffusion speed, and coverage. The diffusion rate was calculated by the rate of change of the diffusion radius over time.

[0060] The release diffusion path is extracted from the release time series graph. The release diffusion path is the propagation trajectory of the reserve resource during the release process, reflecting the path characteristics of the resource diffusion from the release point to the surrounding area. Path extraction uses a gradient tracing algorithm to trace the diffusion path along the direction of the maximum resource density gradient. The gradient vector calculation includes partial derivatives in space and time, with the gradient direction indicating the primary direction of diffusion. The diffusion path starts at the initial location of resource release and ends at the boundary of the diffusion impact. Path shapes include radial diffusion (uniform diffusion from the center to the surrounding areas), directional diffusion (preferential diffusion along a specific direction), and multi-center diffusion (simultaneous diffusion from multiple release points). Diffusion velocity analysis calculates the diffusion velocity at each point along the path to identify variations in diffusion speed. The local diffusion velocity is calculated as the ratio of the time rate of change to the gradient amplitude. Areas with higher velocities diffuse faster, while areas with lower velocities diffuse slower. Diffusion path branching analysis identifies path forks and junctions, with branch points corresponding to key diffusion nodes. Path connectivity analysis ensures that the extracted diffusion paths have good connectivity, forming a complete diffusion network.

[0061] Cross-weaving is performed along the release diffusion path and the main path. Cross-weaving organically combines the release diffusion path with the main path to form a mutually supportive and complementary path structure. The weaving strategy uses a multi-point crossover method, establishing connections at the intersections of the diffusion path and the main path. Intersection identification is based on a distance threshold; a connection is established when the distance between the diffusion path and the main path is less than the set threshold. Weaving patterns include vertical weaving (where the diffusion path connects perpendicularly to the main path), parallel weaving (where the diffusion path is parallel to the main path), and spiral weaving (where the diffusion path spirals around the main path). Weaving density is determined by the ratio of the number of intersections to the path length. Weaving strength is represented by connection weights; connections with higher weights have greater transmission capacity. Weaving constraints include geometric constraints (avoiding path conflicts), capacity constraints (keeping the path carrying capacity within the limits), and timing constraints (meeting time synchronization requirements). Conflict detection during the weaving process uses spatial conflict analysis to identify and resolve conflicts arising from path intersections.

[0062] The cross-weaving results are solidified to form a reinforcement path network. The solidification process transforms the dynamic weaving results into a stable network structure, ensuring the durability and reliability of the reinforcement path network. Solidification methods include topology solidification, parameter solidification, and state solidification. Topology solidification establishes a stable network topology by determining the relationships between nodes and edges. The network topology matrix records the connection weight relationships between nodes. Parameter solidification sets various network parameter values, including path capacity, transmission delay, and reliability indicators. State solidification locks the network's operating state to prevent external interference from damaging the network structure. Solidification verification ensures the normal operation of the solidified network through network functional testing. Network performance indicators comprehensively evaluate overall performance in terms of connectivity, capacity, delay, and reliability. Documentation of the reinforcement path network provides complete network documentation, including a network topology diagram, parameter list, and operation manual. The network monitoring interface provides standardized monitoring interfaces, enabling external systems to monitor network status in real time.

[0063] Step S160 , constructing a collaborative propagation matrix based on the reinforcement path network, performing flow field diffusion analysis on the collaborative propagation matrix to generate discrete path configurations, establishing a path convergence center based on the discrete path configurations, and integrating the discrete path configurations into control commands through the path convergence center.

[0064] Specifically, a collaborative propagation matrix is ​​constructed based on the reinforced path network. This matrix, based on the reinforced path network generated by S150, describes the coordinated motion and information propagation characteristics of multiple robots in the network. Graph theory is used to construct the matrix, converting the topological structure of the reinforced path network into a mathematical matrix representation. The collaborative propagation matrix C[i,j] = w_ij × p_ij × t_ij, where C[i,j] represents the collaborative propagation capability from node i to node j, w_ij is the path weight, p_ij is the propagation probability, and t_ij is the propagation delay. The matrix dimensions are n×n, where n is the number of nodes in the network, and the matrix elements reflect the collaborative propagation capability between nodes. Propagation weight calculation comprehensively considers factors such as path length, capacity, and safety. Paths with shorter distances, higher capacity, and higher safety are given higher weights. Propagation probability is obtained from historical data statistics and reflects the likelihood of successful information propagation along a specific path. Propagation delay consists of both physical propagation delay and processing delay. Matrix symmetry analysis verifies the matrix's symmetry. A symmetric matrix indicates equal bidirectional propagation capability, while an asymmetric matrix indicates a unidirectional propagation advantage. Matrix eigenvalue analysis identifies the main propagation direction and propagation mode of the network by calculating eigenvalues ​​and eigenvectors.

[0065] In some embodiments, the flow field diffusion analysis of the collaborative propagation matrix to generate a discrete path configuration includes: decomposing the collaborative propagation matrix into a mainstream diffusion component and a tributary diffusion component; performing streamline tracing on the mainstream diffusion component to form a mainstream path; performing divergence analysis on the tributary diffusion component to determine the branch boundary; and generating a discrete path configuration based on the spatial relationship between the mainstream path and the branch boundary.

[0066] The co-propagation matrix is ​​decomposed into mainstream diffusion components and tributary diffusion components. Matrix decomposition fully utilizes the parametric characteristics of the co-propagation matrix. The propagation weights w_ij influence the component amplitudes, the propagation probabilities p_ij influence the component stability, and the propagation delays t_ij influence the component phase characteristics, ensuring that the decomposition results reflect the propagation characteristics of the original matrix. Matrix decomposition uses eigenvalue decomposition to decompose the co-propagation matrix into different diffusion patterns. The mainstream diffusion component corresponds to the eigenvector with the largest eigenvalue and reflects the primary propagation direction in the network. The tributary diffusion components correspond to the eigenvectors with other eigenvalues ​​and reflect secondary propagation directions. Component importance is ranked by eigenvalue, with components with larger eigenvalues ​​being more important. Component orthogonality verification ensures orthogonality among the components to avoid mutual interference. Component physical meaning analysis explains the physical meaning of each component: the mainstream component corresponds to the primary channel, and the tributary components correspond to the auxiliary channels.

[0067] Streamline tracing is performed on the mainstream diffusion component to form the mainstream path. Numerical integration methods are used to ensure tracking accuracy and numerical stability. The integration step size is determined by comparing the minimum step size with the local characteristic length to ensure the stability of the numerical calculation. The streamline starting point selection is based on the key nodes of the network, including important locations such as source nodes, sink nodes, and connection points. Streamline termination conditions include reaching the boundary, the flow velocity dropping to zero, and the tracking length exceeding the limit. The geometric characteristics of the mainstream path are analyzed, including parameters such as path length, curvature, and turning points. Streamline density control is achieved through adaptive step size adjustment to increase streamline density in areas with drastic flow field changes. The branching and confluence analysis of the mainstream path identifies the bifurcation points and convergence points of the path, which correspond to the key nodes of the network. Streamline quality is verified by indicators such as streamline continuity, smoothness, and physical rationality. The mainstream path is visualized using streamline diagrams, where the thickness of the streamlines indicates the flow intensity and the color of the streamlines indicates the flow velocity.

[0068] Divergence analysis of the tributary diffusion component is performed to determine branch boundaries. By calculating the divergence of the tributary diffusion component, divergent and convergent regions of the flow field are identified. Divergence calculation uses numerical differentiation methods, calculating the sum of the partial derivatives of the velocity field in all directions. Divergent regions correspond to areas with positive divergence, indicating that the fluid is diffusing outward from these regions. Convergent regions correspond to areas with negative divergence, indicating that the fluid is converging toward these regions. Branch boundaries are identified by the zero divergence line, which forms the boundary between divergent and convergent regions. Boundaries are categorized as hard (strict separation) and soft (limited permeability). Boundary strength is measured by the divergence gradient, with larger gradients indicating stronger separation. Boundary stability is analyzed through time evolution analysis; stable boundaries remain relatively stable over time. Multiscale boundary analysis considers boundary characteristics at different spatial scales, with large-scale boundaries corresponding to primary separation and small-scale boundaries corresponding to localized separation. Boundary processing involves boundary smoothing to eliminate jagged features and improve boundary regularity.

[0069] Discrete path configurations are generated based on the spatial relationship between the mainstream path and the branch boundary. The spatial layout of the path configuration is determined by calculating the geometric relationship between the mainstream path and the branch boundary. Relationship types include intersection (paths crossing the boundary), tangency (paths running along the boundary), and separation (paths moving away from the boundary). The configuration generation strategy uses different configuration methods based on spatial relationships: multi-path configurations are used in intersecting areas, and single-path configurations are used in separation areas. Path priority assignment considers the importance of the mainstream path, with mainstream paths receiving higher priority and receiving more resources. Configuration weighting comprehensively considers factors such as path importance, boundary strength, and spatial distance. Discretization discretizes continuous spatial relationships into a limited number of configuration options. Configuration constraints include geometric constraints, capacity constraints, safety constraints, and other restrictions to ensure configuration feasibility. Configuration selection uses a Pareto optimal approach to select configurations that perform well across multiple objectives.

[0070] A path aggregation center is established based on discrete path configurations. The path aggregation center is the control node that coordinates multiple discrete path configurations, integrating distributed path information and generating a unified control strategy. The geometric center method is used to select the aggregation center location. The center's location is calculated by taking a weighted average of the locations of all path nodes. Center weighting takes into account factors such as path importance, node connectivity, and geographic location, with higher weights assigned to important paths. The aggregation range is determined by the influence radius, which is calculated based on the coverage area and range coefficient. The multi-center architecture design addresses the needs of large-scale networks and establishes a hierarchical aggregation system consisting of local and global aggregation centers. Inter-center communication utilizes a star topology, with each path configuration connected to the aggregation center via communication links. The aggregation algorithm uses a weighted average method, averaging the weighted results of each path configuration. Center load balancing utilizes dynamic load distribution to prevent overloading of a single center. The aggregation center's fault-tolerant design includes backup centers and failover mechanisms to ensure system reliability. Center performance monitoring establishes a real-time monitoring system to track the operating status and processing capacity of the aggregation centers.

[0071] In some embodiments, integrating the discrete path configurations into control commands through the path convergence center includes: obtaining the gravitational range of the path convergence center; generating a gravitational gradient distribution based on the gravitational range; pulling the discrete path configurations along the gravitational gradient distribution to perform centripetal aggregation to form an aggregated path beam; and performing vector synthesis on the aggregated path beam to output a control command.

[0072] Obtain the gravitational range of the path convergence center. The gravitational range is the spatial region that the convergence center can effectively influence and control, similar to the concept of a gravitational field in physics. The gravitational model uses a modified Newtonian gravitational formula. The magnitude of gravity is proportional to the center mass and the path mass, and inversely proportional to the square of the distance. The range is determined by a gravitational strength threshold; when the gravitational strength falls below the effective threshold, it is the boundary of the range. The spatial distribution of the gravitational field uses a Gaussian decay model, with the gravitational force decreasing with distance from the center. The superposition of multi-center gravitational fields uses the principle of vector superposition, accounting for the combined effects of multiple convergence centers. The anisotropy of the gravitational field accounts for differences in gravitational force in different directions, with stronger gravitational forces along the main paths. The dynamic adjustment of the gravitational range adjusts the range in real time based on network load and path density, expanding the range when load is high and reducing it when load is low. The gravitational field strength grading divides the range into three levels: strong, medium, and weak gravitational zones. Gravitational boundary effects are handled to avoid sudden changes in gravitational force at boundaries, using a smooth transition function to process boundary regions.

[0073] A gravitational gradient distribution is generated based on the range of gravitational influence. The gravitational gradient distribution describes the rate of change of the gravitational field in space, indicating the direction and intensity of the path configuration's movement toward the center of convergence. Gradient calculation uses numerical differentiation to calculate the rate of change of the gravitational field in all directions. The gradient direction indicates the direction of increasing gravity, and the gradient magnitude indicates the severity of the gravitational change. Normalization of the gradient direction ensures that the directional information of the gradient vector is not affected by the magnitude. Topological analysis of the gradient field identifies critical points in the gradient field, including special locations such as saddle points, extreme points, and center points. Gradient line tracing plots the trajectory of gravitational lines by integrating along the gradient direction. Variance analysis is used to analyze the inhomogeneity of the gradient distribution; a large variance indicates an uneven distribution. The stability of the gradient field is verified using Lyapunov analysis to ensure that the gradient field has convergent properties. A gradient correction mechanism addresses singularities and discontinuities in the gradient field, correcting anomalous gradients using interpolation and smoothing methods.

[0074] Discrete path configurations are pulled along the gravitational gradient distribution to converge centripetally, forming a converged path bundle. Centripetal convergence is the process of converging dispersed path configurations towards a convergence center under the influence of the gravitational gradient field. The pulling algorithm uses gradient descent to update the path position based on the gradient direction of the current position. The dynamic equations of the convergence process consider the combined effects of gravity, drag, inertia, and other factors. Convergence speed is controlled through adaptive step size adjustment, dynamically adjusting the movement step size based on the convergence rate. The path bundle formation process consists of three stages: initial dispersion, gradual convergence, and final bundle formation. Geometric analysis of the converged path bundle includes parameters such as bundle width, bundle density, and bundle convergence. Convergence quality is controlled using the convergence degree metric, which is measured as the ratio of the position standard deviation to the initial dispersion radius. Convergence stability analysis ensures the stability and controllability of the convergence process by observing the convergence characteristics of the convergence process. The branching and merging of the convergent bundle considers the interactions between multiple bundles and establishes a coordination mechanism between bundles.

[0075] Vector synthesis is performed on the aggregated path bundle to output control commands. Vector synthesis combines multiple path information within the aggregated path bundle into a unified control command, enabling the transition from path planning to motion control. The synthesis method uses weighted vector averaging, averaging each path vector according to its weight. Weight assignment takes into account factors such as path importance, reliability, and execution difficulty, with higher weights given to important paths. Command component decomposition decomposes the synthesized vector into components such as position, velocity, and direction commands. The position command is calculated by multiplying the synthesized vector by the execution time. The velocity command considers dynamic constraints to ensure that the generated velocity command is within the robot's capabilities. The direction command is determined by calculating the angle of the velocity vector using the inverse tangent function. Command scheduling considers the execution order and time coordination of commands to establish a command execution schedule. Command priority assignment ensures that important commands are executed first, and urgent commands can interrupt ongoing normal commands. Control command formatting converts the vector synthesis results into a standard robot control protocol format. The command output interface provides a standardized command output interface that supports command reception and execution by different robot types, ultimately completing the path optimization of the quadruped robot.

[0076] In order to implement the quadruped robot path optimization method corresponding to the above method embodiment, to achieve the corresponding functions and technical effects. Figure 2 , Figure 2 The following is a block diagram of a quadruped robot path optimization system 200 provided in an embodiment of the present application. For ease of explanation, only the parts related to this embodiment are shown. The quadruped robot path optimization system 200 provided in an embodiment of the present application includes: A data acquisition module 201 is configured to obtain status information and terrain data of each quadruped robot, identify overlapping operation windows based on the status information, generate a path strategy based on the overlapping operation windows, and construct a hierarchical task chain based on the path strategy and the terrain data; A path generation module 202 is configured to construct a path-terrain mapping relationship by combining the hierarchical task chain and the terrain data, identify eddy current areas through the path-terrain mapping relationship, and avoid the eddy current areas to form a path advantage area; The task scheduling module 203 is configured to perform task density analysis on the path advantage area to form a density fluctuation curve, perform peak-valley separation based on the density fluctuation curve to generate a high-density task flow and a low-density task flow, perform frequency analysis to make the high-density task flow and the low-density task flow form a complementary rhythm, and generate a balanced task flow using the complementary rhythm; A path allocation module 204 is configured to allocate tasks to the task balancing flow to generate a primary path and an auxiliary path, perform load analysis on the auxiliary path to extract path redundancy resources, and compress the path redundancy resources to form a high-density path reserve; A dynamic fusion module 205 is configured to perform risk detection on the primary path to obtain a terrain warning, trigger the release of the high-density path reserve according to the terrain warning, and fuse the released high-density path reserve with the primary path to generate a reinforcement path network; The collaborative control module 206 is used to construct a collaborative propagation matrix based on the reinforced path network, perform flow field diffusion analysis on the collaborative propagation matrix to generate a discrete path configuration, establish a path convergence center based on the discrete path configuration, and integrate the discrete path configuration into a control command through the path convergence center.

[0077] The quadruped robot path optimization system 200 can implement the quadruped robot path optimization method of the above-mentioned method embodiment. The optional options in the above-mentioned method embodiment also apply to this embodiment and will not be described in detail here. The remaining contents of the embodiment of this application can refer to the contents of the above-mentioned method embodiment and will not be repeated in this embodiment.

[0078] The purpose of the above embodiments is to exemplify and deduce the technical solution of the present invention, and to fully describe the technical solution, purpose and effect of the present invention. Its purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosed content of the present invention, and it does not limit the scope of protection of the present invention.

[0079] The above embodiments are not exhaustive and may include many other embodiments not listed above. Any replacements and improvements made without violating the concept of the present invention are within the scope of protection of the present invention.

Claims

1. A quadruped robot path optimization method, characterized in that: include: Acquiring status information and terrain data of each quadruped robot, identifying overlapping operation windows based on the status information, generating a path strategy through the overlapping operation windows, and constructing a hierarchical task chain based on the path strategy and the terrain data; Building a path-terrain mapping relationship by combining the hierarchical task chain and the terrain data, identifying an eddy current area through the path-terrain mapping relationship, and avoiding the eddy current area to form a path advantage area; Performing task density analysis on the path advantage area to form a density fluctuation curve, performing peak-valley separation based on the density fluctuation curve to generate a high-density task flow and a low-density task flow, using frequency analysis to make the high-density task flow and the low-density task flow form a complementary rhythm, and using the complementary rhythm to generate a balanced task flow; Performing task assignment on the task balancing flow to generate a primary path and an auxiliary path, performing load analysis on the auxiliary path to extract path redundant resources, and compressing the path redundant resources to form a high-density path reserve; Performing risk detection on the main path to obtain a terrain warning, triggering the release of the high-density path reserve according to the terrain warning, and fusing the released high-density path reserve with the main path to generate a reinforcement path network; A collaborative propagation matrix is ​​constructed based on the reinforced path network, a flow field diffusion analysis is performed on the collaborative propagation matrix to generate a discrete path configuration, a path convergence center is established based on the discrete path configuration, and the discrete path configuration is integrated into a control command through the path convergence center.

2. The method according to claim 1, characterized in that Generating a path strategy through the overlapping operation windows includes: Performing spatiotemporal cross analysis on the overlapping operation windows to obtain window overlap; Calculating the task conflict probability based on the window overlap to generate a conflict risk graph; Performing a task decoupling operation according to the conflict risk graph to determine a decomposition boundary; A path strategy is constructed using the decomposition boundary.

3. The method according to claim 1, characterized in that The identifying of the eddy current area by the path-terrain mapping relationship includes: establishing an energy flow channel based on the path-terrain mapping relationship; monitoring flow resistance along the energy flow channel to obtain resistance distribution; inferring the flow field rotation characteristics based on the resistance distribution; The flow field rotation features are marked as vortex regions.

4. The method according to claim 1, wherein The step of forming a complementary rhythm between the high-density task flow and the low-density task flow through frequency analysis includes: Extracting the task main frequency from the high-density task stream; extracting a task sub-frequency from the low-density task stream; Calculating a beat interval based on a frequency difference between the task main frequency and the task secondary frequency; The beat intervals are time-mapped to form a complementary rhythm.

5. The method according to claim 1, wherein The compressing the redundant path resources to form a high-density path reserve includes: Performing time folding on the redundant path resources to obtain folded state resources; injecting compression potential energy into the folded state resource to form potential energy accumulation; The potential energy is accumulated to a critical density by continuously applying pressure; Locking the critical density state forms a high-density path reserve.

6. The method according to claim 1, characterized in that The released high-density path reserve is merged with the main path to generate a reinforcement path network, including: constructing a release timing map based on the high-density pathway reserve; extracting a release diffusion path from the release timing profile; Cross-weaving along the release diffusion path and the main path; The cross-weaving result is solidified to form a reinforcement path network.

7. The method according to claim 1, characterized in that The performing flow field diffusion analysis on the collaborative propagation matrix to generate a discrete path configuration includes: Decomposing the cooperative diffusion matrix into a mainstream diffusion component and a tributary diffusion component; Performing streamline tracing on the mainstream diffusion component to form a mainstream path; Performing a divergence analysis on the tributary diffusion component to determine branch boundaries; A discrete path configuration is generated based on a spatial relationship between the main flow path and the branch boundaries.

8. The method according to claim 1, characterized in that The integrating the discrete path configurations into control commands through the path convergence center includes: Obtaining the gravitational range of the path convergence center; generating a gravitational gradient distribution based on the gravitational action range; Pulling the discrete path configuration along the gravitational gradient distribution to perform centripetal aggregation to form an aggregated path bundle; Perform vector synthesis on the aggregated path bundle and output a control command.

9. The method according to claim 4, characterized in that The performing time mapping on the beat intervals to form a complementary rhythm comprises: constructing a time elastic window based on the beat interval; Performing beat expansion and contraction adjustment within the time elastic window to obtain a variable speed beat sequence; Applying periodic constraints to the variable speed beat sequence to form a stable oscillation mode; A complementary rhythm is output through the stable oscillation pattern.

10. A quadruped robot path optimization system, characterized in that: include: a data acquisition module for acquiring status information and terrain data of each quadruped robot, identifying overlapping operation windows based on the status information, generating a path strategy based on the overlapping operation windows, and constructing a hierarchical task chain based on the path strategy and the terrain data; a path generation module, configured to construct a path-terrain mapping relationship by combining the hierarchical task chain and the terrain data, identify eddy current areas through the path-terrain mapping relationship, and avoid the eddy current areas to form a path advantage area; a task scheduling module configured to perform task density analysis on the path advantage area to form a density fluctuation curve, perform peak-valley separation based on the density fluctuation curve to generate a high-density task flow and a low-density task flow, perform frequency analysis to enable the high-density task flow and the low-density task flow to form a complementary rhythm, and generate a balanced task flow using the complementary rhythm; a path dispatching module configured to dispatch tasks to the task balancing flow to generate a primary path and an auxiliary path, perform load analysis on the auxiliary path to extract path redundant resources, and compress the path redundant resources to form a high-density path reserve; a dynamic fusion module, configured to perform risk detection on the primary path to obtain a terrain warning, trigger the release of the high-density path reserve according to the terrain warning, and fuse the released high-density path reserve with the primary path to generate a reinforcement path network; A collaborative control module is used to construct a collaborative propagation matrix based on the reinforced path network, perform flow field diffusion analysis on the collaborative propagation matrix to generate discrete path configurations, establish a path convergence center based on the discrete path configurations, and integrate the discrete path configurations into control commands through the path convergence center.

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