A dynamic space-time corridor trajectory optimization method and system for a multi-agv warehousing system

Abstract

The application discloses a kind of dynamic space-time corridor track optimization method and system for multi-AGV warehousing system, belong to multi-robot collaborative scheduling field, the method includes: the task position data and load state data of mobile platform are acquired, task position data is used to indicate the task starting point and task end point of mobile platform, load state data is used to reflect the physical attribute of the object currently carried by mobile platform;Based on load state data, the kinematic limit parameter of mobile platform is determined;Anisotropic space-time corridor of mobile platform is constructed in space-time coordinate system, anisotropic space-time corridor is a space-time passing area for constraining the track of mobile platform along the task starting point to task end point operation, the space boundary and time boundary of anisotropic space-time corridor are nonlinear and asymmetric distribution according to kinematic limit parameter.The application avoids the scheduling collapse caused by subsequent unlocking.

Description

Technical Field

[0001] This invention relates to the field of multi-robot collaborative scheduling, and in particular to a dynamic spatiotemporal corridor trajectory optimization method and system for multi-AGV warehousing systems. Background Technology

[0002] In modern warehousing and logistics systems, clusters of two or more Automated Guided Vehicles (AGVs) collaboratively perform tasks such as handling, picking, and replenishment within the same physical space place high demands on both trajectory safety and traffic efficiency. Existing multi-AGV path planning schemes generally use a fixed-radius cylinder to represent the safety envelope of the AGV, defining its safe passage area with a fixed-size geometry regardless of the AGV's load condition. This approach has two inherent drawbacks:

[0003] First, when the AGV is unloaded, its actual required safety envelope is much smaller than the geometric dimensions of the fixed cylinder. Overly conservative boundary settings will lead to a lot of wasted space in narrow passages, limiting the parallel passage capability of the cluster. Second, when the AGV is fully loaded, the center of gravity shifts upward due to the lifting of the rack, and the braking distance increases significantly. The fixed radius is insufficient to ensure a safe longitudinal braking margin, which can easily lead to rear-end collisions or rack tilting in emergency stopping scenarios.

[0004] Furthermore, when multiple AGVs operate in high-frequency confluence areas such as intersections, they may form circular dependencies due to waiting for each other to release resources, leading to system deadlock. Existing deadlock resolution algorithms are mostly reactive, allowing deadlocks to occur first and then resolving them through preemptive rollbacks or random reordering. This approach is inefficient, and a single resolution often triggers cascading replanning for multiple downstream AGVs, easily causing scheduling avalanches in large-scale clusters. Simultaneously, minor disturbances are unavoidable in warehouse environments, such as personnel passing by, dropped boxes, and temporary parking of picking vehicles. If each disturbance triggers global replanning, it will result in significant communication overhead and computational consumption, ultimately causing a computational storm for the central scheduling server.

[0005] In summary, existing technologies struggle to balance safety with efficient channel space utilization, fail to fundamentally prevent cluster deadlock, and lack the ability to locally absorb minor disturbances on-site. A new trajectory optimization scheme is urgently needed to address these issues. Summary of the Invention

[0006] One of the objectives of this invention is to provide a dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems, in order to solve the problems in the existing technology where the fixed radius safety envelope cannot sense the load status, wastes channel space when empty and has insufficient braking margin when fully loaded, multi-AGV clusters are prone to forming cyclic waiting deadlocks in the throat area and subsequent unlocking can easily cause scheduling avalanches, and small disturbances on site frequently trigger global replanning, resulting in wasted computing power.

[0007] This invention is achieved through the following technical solution: a dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems, comprising the following steps: acquiring task position data and load status data of a mobile platform, wherein the task position data is used to indicate the task start point and task end point of the mobile platform, and the load status data is used to reflect the physical properties of the object currently carried by the mobile platform; determining the kinematic limit parameters of the mobile platform based on the load status data; constructing an anisotropic spatiotemporal corridor of the mobile platform in a spatiotemporal coordinate system, wherein the anisotropic spatiotemporal corridor is a spatiotemporal passage area used to constrain the trajectory of the mobile platform running along the task start point to the task end point, and the spatial and temporal boundaries of the anisotropic spatiotemporal corridor are nonlinearly and asymmetrically distributed according to the kinematic limit parameters.

[0008] Further, the load state data includes at least one of the following: load-bearing mass, center of gravity height, off-center load coefficient, jacking state, and attitude tilt angle; determining the kinematic limit parameters of the mobile platform based on the load state data includes: mapping the load state data into a discrete set of load states, the discrete set of load states including a first load state, a second load state, and a third load state, wherein the first load state corresponds to no load, the second load state corresponds to full jacking load, the third load state corresponds to off-center load, the load-bearing mass and center of gravity height corresponding to the second load state are greater than those of the first load state, and the third load state, relative to the second load state, also represents the off-center load coefficient; and determining the corresponding kinematic limit parameters for each of the discrete sets of load states.

[0009] Furthermore, the kinematic limit parameters include at least one of the following: maximum achievable speed, maximum braking deceleration, maximum centripetal acceleration, maximum jerkiness, and maximum steering angular velocity.

[0010] Furthermore, the spatial boundary of the anisotropic spacetime corridor includes: a first spatial boundary along the travel direction of the mobile platform, a second spatial boundary against the travel direction, and a third spatial boundary perpendicular to the travel direction; wherein, the first spatial boundary is nonlinearly determined based on the current speed of the mobile platform and the effective braking capacity determined by the current load state. The greater the load-bearing mass and the higher the center of gravity height corresponding to the load state, the weaker the effective braking capacity and the greater the length of the first spatial boundary extending along the travel direction; the second spatial boundary is set to a fixed value equivalent to the geometric dimensions of the rear end of the mobile platform; the third spatial boundary is expanded according to the off-center load coefficient and the center of gravity height, and the greater the off-center load coefficient and the higher the center of gravity height, the third spatial boundary expands asymmetrically on both sides perpendicular to the travel direction.

[0011] Furthermore, constructing the anisotropic spatiotemporal corridor of the mobile platform within the spatiotemporal coordinate system includes: determining a local boundary polygon in the local coordinate system of the mobile platform; rotating the local boundary polygon according to the orientation of the mobile platform at each moment, and translating the rotated local boundary polygon according to the global position of the mobile platform at each moment; merging the boundary sections after rotation and translation at each moment along the time axis of the spatiotemporal coordinate system to obtain the anisotropic spatiotemporal corridor.

[0012] Furthermore, the dynamic spatiotemporal corridor trajectory optimization method also includes: acquiring road network topology data of the work space where the mobile platform is located; based on the road network topology data, dividing the anisotropic spatiotemporal corridor into straight-line spatiotemporal channels and node-line spatiotemporal channels; calculating the geometric derivative at the connection point between the straight-line spatiotemporal channels and the node-line spatiotemporal channels to generate control points, and using the splicing curve constrained by the control points to smoothly splice the connection point to obtain a globally continuous spatiotemporal corridor.

[0013] Furthermore, the search space within the straight-line spatiotemporal control zone is constrained to contain only a one-dimensional velocity vector sequence parallel to the direction of travel of the mobile platform, and the lateral position and heading angle of the mobile platform are locked to constant values ​​corresponding to the channel centerline; the search space of the region corresponding to the node segment spatiotemporal control zone is expanded into a two-dimensional spatiotemporal capsule structure containing rotational angular velocity and lateral offset, and the cross-sectional dimensions of the two-dimensional spatiotemporal capsule structure are determined by the minimum turning radius of the mobile platform.

[0014] Further, calculating the geometric derivative at the connection point between the straight-segment spatiotemporal pipe and the node segment spatiotemporal pipe to generate control points includes: extracting the outgoing tangent vector at the end of the straight-segment spatiotemporal pipe and the incoming tangent vector at the beginning of the node segment spatiotemporal pipe as constraints for the control points; forcing the left and right limits of the second-order geometric derivative of the spliced ​​curve at the connection point to be equal, and inversely solving to obtain the control points located between the connection points, so that the rate of curvature change at the connection point does not exceed the limit corresponding to the maximum steering angular velocity of the moving platform.

[0015] Furthermore, the curvature at each point on the splicing curve is constrained not to exceed the upper limit of curvature. The upper limit of curvature is determined by the friction conditions between the current load state data and the bearing surface of the mobile platform. The higher the center of gravity indicated by the load state data and the higher the bending design speed of the mobile platform, the smaller the upper limit of curvature.

[0016] Furthermore, the spliced ​​curve is a uniform B-spline curve.

[0017] Furthermore, the splicing curve is a Bézier curve.

[0018] Furthermore, the dynamic spatiotemporal corridor trajectory optimization method is applied to multiple mobile platforms, including a first mobile platform and a second mobile platform. The first mobile platform and the second mobile platform respectively obtain their respective global continuous spatiotemporal corridors according to the above method. The dynamic spatiotemporal corridor trajectory optimization method also includes: modeling the high-frequency conflict choke regions in the workspace as spatiotemporal mutual exclusion locks, which are used to constrain at most one mobile platform to pass through the choke regions within the same time window; detecting the overlap state of the global continuous spatiotemporal corridors of the first mobile platform and the second mobile platform in future time slices; and assigning truncation and waiting logic containing relative time constraints to the global continuous spatiotemporal corridors of the first mobile platform and the second mobile platform based on the overlap state and a preset task priority table.

[0019] Further, detecting the overlap state of the global continuous spatiotemporal corridor of the first mobile platform and the global continuous spatiotemporal corridor of the second mobile platform in future time slices includes: constructing a three-dimensional spatiotemporal hash table in the storage of the processing device, wherein the key of the three-dimensional spatiotemporal hash table consists of a spatial grid index and a temporal grid index, wherein the spatial grid index is obtained by rounding down the global spatial coordinates according to the spatial grid resolution, and the temporal grid index is obtained by rounding down the timestamp according to the temporal grid resolution, and the value of the three-dimensional spatiotemporal hash table is mapped to the mobile platform identifier occupying the corresponding spatiotemporal grid; and determining the overlap state by discretizing and sampling the boundaries of each global continuous spatiotemporal corridor and performing a hash collision query, transforming the polygon intersection operation, which increases quadratically with the number of mobile platforms, into an index query with amortized constant time complexity.

[0020] Furthermore, the allocation of truncation and waiting logic with relative time constraints to the global continuous spatiotemporal corridor of the first mobile platform and the global continuous spatiotemporal corridor of the second mobile platform includes: querying the task priority table; when the priority of the first mobile platform is higher than that of the second mobile platform, extracting the overlapping time window corresponding to the overlapping state; injecting a time roadblock constraint at the topology node corresponding to the entrance of the second mobile platform into the throat region, so that the passage cost of the second mobile platform before the sum of the latest time when the first mobile platform passes through the throat region and the safety time margin is impassable, thereby truncating the spatiotemporal pipeline of the node segment of the second mobile platform into a waiting state in the time dimension, and eliminating deadlock by interrupting the loop waiting.

[0021] Furthermore, after applying the relative time constraint, the dynamic spatiotemporal corridor trajectory optimization method further includes: adopting a multi-stage solution with spatial and temporal decoupling, mapping the preset anti-tipping constraint and anti-slip constraint into a linear inequality matrix and constructing a solution model; solving the solution model to obtain a time allocation sequence and spatial reference trajectory that satisfy the dynamic hard constraints.

[0022] Furthermore, the multi-stage solution includes: in the first stage, fixing the time dimension, extracting the path that maximizes the Euclidean distance from the geometric contour of the mobile platform to the boundary of the corridor from the sequence of convex polygons formed by the two-dimensional cross-sections of the global continuous spatiotemporal corridor in each time slice, as the collision-free spatial reference trajectory; in the second stage, based on the spatial reference trajectory, with the goal of minimizing the completion time, using the square of the longitudinal velocity along the trajectory as the optimization variable, so as to transform the nonlinear kinematic relationship containing the square root into a linear relationship.

[0023] Furthermore, the anti-tipping constraint is determined based on the zero-moment point theory. The anti-tipping constraint requires that the inertial moment generated by the load-bearing object during acceleration and deceleration does not exceed the anti-overturning moment provided by the support polygon of the mobile platform chassis. Moreover, the higher the center of gravity indicated by the load state data, the smaller the upper limit of the allowed longitudinal acceleration. The anti-slip constraint limits the jerk along the trajectory to not exceed the critical jerk threshold. The critical jerk threshold is determined by the current load state data and the static friction coefficient of the load-bearing surface. The jerk is approximated by the third-order forward difference of the mobile platform position or by the first-order difference of the acceleration.

[0024] Furthermore, the step of mapping the preset anti-tipping constraints and anti-slip constraints into a linear inequality matrix and constructing a solution model includes: rewriting the anti-tipping constraints and the anti-slip constraints into the form of the linear inequality matrix, and constructing the solution model as a quadratic programming model or a second-order cone programming model.

[0025] Furthermore, the dynamic spatiotemporal corridor trajectory optimization method further includes: controlling the mobile platform to travel along the spatial reference trajectory; when a local obstacle not recorded in the road network topology data is detected to intrude into the global continuous spatiotemporal corridor, calculating the residual safety margin from the boundary of the global continuous spatiotemporal corridor to the nearest obstacle; and, under the condition that the residual safety margin is greater than zero, performing elastic deformation of spatial pushing and time delay on the global continuous spatiotemporal corridor to self-repair the spatial reference trajectory.

[0026] Furthermore, the elastic deformation of the global continuous spatiotemporal corridor by spatial pushing and time delay includes: discretizing the boundary of the global continuous spatiotemporal corridor into virtual particles with spring stiffness coefficients, the spring stiffness coefficients being inversely proportional to the load-bearing mass indicated by the load state data; applying a repulsive force to the virtual particles according to the intrusion depth of the local obstacle, wherein the repulsive force increases nonlinearly as the virtual particles are closer to the local obstacle, and the repulsive force becomes zero when it exceeds a preset influence radius; performing coordinate translation of the virtual particles along the spatial component direction of the repulsive force by a displacement inversely proportional to the spring stiffness coefficient to achieve the spatial pushing, and shifting the timestamp of the corresponding trajectory point backward according to the time component of the repulsive force to achieve the time delay, wherein the time delay is not suppressed by the spring stiffness coefficient.

[0027] Furthermore, the residual safety margin is the difference between the minimum distance from the boundary of the global continuous spatiotemporal corridor after elastic deformation to the boundary of the nearest fixed shelf and the preset minimum safety distance; when the residual safety margin is less than or equal to zero, the current control point is locked, the elastic deformation is paused, and a replanning request carrying the current coordinates is sent to the processing device.

[0028] Another aspect of the present invention provides a dynamic spatiotemporal corridor trajectory optimization system for a multi-AGV warehousing system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements any of the dynamic spatiotemporal corridor trajectory optimization methods for a multi-AGV warehousing system described above.

[0029] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0030] 1. This invention determines the kinematic limit parameters based on the load state and constructs an anisotropic spatiotemporal corridor that differs from each other in the forward, backward, and lateral directions and is asymmetrically distributed with respect to the limit parameters. This allows the safety boundary to expand as needed. When unloaded, the boundary limits contract to maximize the use of the channel space, and when fully loaded, the boundary stretches significantly along the braking direction to ensure multiple safety constraints such as preventing rear-end collisions, preventing sideslip, and preventing overturning. This overcomes the inherent defects of a fixed-radius cylinder that is either too conservative or unsafe.

[0031] 2. This invention matches the corridor with the orthogonal road network of the warehouse, reduces the straight-line segment to a one-dimensional speed search, expands the node segment into a two-dimensional spatiotemporal capsule, and applies a high-order continuous curvature upper bound constraint coupled with the load at the splicing point. This reduces the dimensionality of the search space, improves the solution efficiency, and eliminates the mechanical shock and cargo oscillation caused by curvature abrupt changes. Furthermore, by modeling the throat region as a spatiotemporal mutual exclusion lock, and using a three-dimensional spatiotemporal index structure, the corridor overlap detection is accelerated to a constant-level query. Based on priority injection of relative time constraints, the circular waiting condition for deadlock formation is broken at the prior level, achieving system-level deadlock immunity and avoiding scheduling collapse caused by post-unlocking.

[0032] 3. This invention, through a space-time decoupled multi-stage solution architecture, transforms nonlinear kinematic constraints into convex constraints and maps anti-tipping and anti-slip hard constraints into linear inequalities, enabling the convex optimization solver to converge to the global optimum in polynomial time. This rigidly ensures that the high-level rack does not tip over or slip during acceleration and deceleration. Furthermore, by endowing the corridor with elastic self-healing capabilities, the stiffness coefficient is inversely proportional to the load, and spatial pushing and time delay are decoupled. Using the residual safety margin as a hierarchical filtering criterion, most minor disturbances are self-absorbed at the bottom layer, and global replanning is only reported when the disturbance exceeds the safety margin, effectively protecting the computing resources of the central scheduling server. Attached Figure Description

[0033] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0034] Figure 1 The above is a flowchart of the overall method provided in Embodiment 1 of the present invention.

[0035] Figure 2 The nonlinear expansion curve of the forward braking distance provided in Embodiment 1 of the present invention.

[0036] Figure 3 This is a comparison diagram of the cross-sectional shape and orientation of the anisotropic spacetime corridor provided in Embodiment 1 of the present invention.

[0037] Figure 4 This is a schematic diagram of the global manifold of a three-dimensional spatiotemporal corridor provided in Embodiment 1 of the present invention.

[0038] Figure 5 The curvature comparison curve provided in Embodiment 1 of the present invention.

[0039] Figure 6 The maximum allowable upper bound curve is shown in Embodiment 1 of the present invention.

[0040] Figure 7 A time complexity comparison chart provided for Embodiment 1 of the present invention.

[0041] Figure 8 This is a comparison diagram of deadlock topology before and after the injection of the spatiotemporal mutex lock provided in Embodiment 1 of the present invention.

[0042] Figure 9 This is a schematic diagram of the feasible domain boundary of the anti-tipping acceleration constraint provided in Embodiment 1 of the present invention.

[0043] Figure 10 A comparison diagram of the speed-time profile for solving the quadratic programming problem provided in Embodiment 1 of the present invention.

[0044] Figure 11 The graph shows the attenuation curve of the artificial potential field repulsive force as a function of the intrusion distance, as provided in Embodiment 1 of the present invention.

[0045] Figure 12 Heat map of warehouse aisle space utilization provided in Embodiment 1 of the present invention.

[0046] Figure 13 Box plot showing the comparison of task completion time distribution for the multi-AGV cluster provided in Embodiment 1 of the present invention.

[0047] Figure 14 This is a cumulative comparison chart of deadlock occurrence frequency provided in Embodiment 1 of the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0049] Example 1

[0050] This embodiment discloses a dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems. The method first establishes an anisotropic spatiotemporal corridor model strongly coupled with load status as a dedicated safety envelope for each AGV. Its spatial boundaries are differentiated in the forward, backward, and lateral directions based on braking distance, vehicle size, and off-center centrifugal force, respectively. The core of this method is to predict spatiotemporal conflicts between multiple AGV corridors a priori using a three-dimensional spatiotemporal hash table within each high-frequency scheduling cycle, and to inject time-based roadblock constraints into low-priority AGVs based on a priority table, thereby breaking the circular waiting chain formed by deadlock at the topology level. After conflict resolution, the originally coupled non-convex spatiotemporal joint planning problem is decoupled into two serial convex sub-problems: the first stage solves the spatial path in a fixed time, and the second stage solves the time profile in a fixed space. In the time-based solution, the anti-tipping acceleration constraint and the anti-slip jerk constraint are uniformly expressed as a linear inequality matrix, which is then used by a convex optimization solver to obtain the global optimal solution in polynomial time. During the AGV execution phase, the system endows the spatiotemporal corridor with local elastic self-healing capability based on a virtual spring-mass system. When encountering minor disturbances, it digests them on its own through spatial pushing and time delay. Only when the deformation stress exceeds the threshold is it reported for global replanning, forming a closed-loop scheduling mechanism of prior obstacle avoidance, hierarchical processing, and on-demand replanning. Figure 1 The overall method flowchart of this embodiment is shown. As can be seen from the figure, this embodiment includes the following steps:

[0051] Step 1: Obtain the task start and end point coordinates of each AGV in the multi-AGV system, the topology mesh data of the three-dimensional orthogonal road network, and the current load status information of each AGV.

[0052] Among them, a multi-AGV system refers to a cluster system consisting of two or more Automated Guided Vehicles (AGVs) that collaboratively perform tasks such as handling, picking, and replenishment within the same physical warehouse space. For example, a multi-AGV system can be a cluster of lurking lifting AGVs, a cluster of forklift AGVs, a cluster of bin-carrying AGVs, or a cluster of composite robots (chassis + robotic arm).

[0053] Task start and end point coordinates refer to a set of spatial coordinate values ​​issued by the warehouse management system (WMS) or scheduling system (WCS) to fully describe the physical start and end points of each AGV's current task. These coordinates include, but are not limited to, two-dimensional plane coordinates. and The task's warehouse area number, the target shelf's unique identifier, and the task's priority identifier.

[0054] The topological mesh data of a three-dimensional orthogonal road network refers to a directed or undirected graph data structure abstracted from the orthogonal structure of the warehouse physical map arranged according to the shelving. Each graph node corresponds to a dockable point in the warehouse plane (e.g., a crossroads, a T-junction, or a storage location entrance), and each graph edge corresponds to a passable straight passage connecting two adjacent nodes. The edge attributes carry information such as the passage's length, width, whether it is unidirectional, and whether it is pre-occupied in the time dimension. The three-dimensional meaning of this topological mesh is not limited to the three dimensions of physical space, but rather refers to introducing a third dimension—the time dimension—on top of a two-dimensional spatial mesh, so as to facilitate subsequent geometric calculations of spatiotemporal corridors in this combined space.

[0055] Load status information refers to a set of physical quantities that reflect the attributes of the goods currently carried by the AGV in real time, including but not limited to: whether it is currently in a lifting state, the total mass of the lifted shelf, the shelf level height (corresponding to the center of gravity height), whether the goods are evenly distributed on the shelf (i.e., the off-center load coefficient), and the readings of the attitude tilt angle sensor of the AGV chassis itself.

[0056] In this embodiment, the task start and end point coordinates of each AGV, the topology grid data of the three-dimensional orthogonal road network, and the current load status information can be jointly obtained by the AGV on-board sensors, the warehouse management system, the scheduling server, or the edge computing nodes connected to them.

[0057] In this embodiment, load status information can be generated in the following way:

[0058] By using the built-in weighing strain gauges or pressure sensors of the AGV lifting mechanism, the total load borne by the lifting mechanism can be collected in real time to obtain an estimate of the total mass of the goods.

[0059] By using the difference in readings from the distributed weighing sensors at the four corners of the AGV chassis, the offset of the geometric center of the goods on the shelf plane relative to the geometric center of the AGV is estimated, and then the off-center loading coefficient is determined.

[0060] Mapping the above total mass, center of gravity height, and off-center load factor to a discrete set of load states is defined as follows:

[0061] These correspond to three typical working conditions: no load, fully loaded lifting rack, and off-center load, respectively, so that subsequent models can generate differentiated boundaries based on discrete states.

[0062] Step 2: Extract the corresponding kinematic limit parameters based on the load state information, and construct the anisotropic spatiotemporal corridor of the AGV in the three-dimensional spatiotemporal coordinate system. The spatial and temporal boundaries of the anisotropic spatiotemporal corridor are nonlinearly and asymmetrically distributed according to the kinematic limit parameters.

[0063] An anisotropic spatiotemporal corridor refers to a safe passage area exclusively designated for each AGV within a three-dimensional spatiotemporal joint coordinate system consisting of two-dimensional space and one-dimensional time. This corridor has different widths in different directions, and its boundary shape dynamically evolves with the AGV's current movement and load states. This corridor is fundamentally different from the fixed-radius cylinder commonly used in traditional multi-AGV path planning. It is understandable that the traditional fixed-radius cylinder representation method has two inherent drawbacks:

[0064] First, when an AGV is unloaded, its actual required safety envelope is much smaller than the geometric dimensions of a fixed cylinder. This overly conservative boundary setting leads to a significant waste of space in narrow warehouse aisles, severely limiting the parallel passage capability of AGV clusters. Second, when an AGV is fully loaded, the center of gravity shifts upward due to the lifting of the racks, significantly increasing the braking distance. The fixed radius is insufficient to guarantee a safe longitudinal braking margin, making rear-end collisions or rack tilting more likely in emergency stopping scenarios. Therefore, it is necessary to construct an asymmetric spatial boundary model that can sense the load status and dynamically adjust its shape accordingly.

[0065] Kinematic limit parameters refer to a set of dynamic constraints strongly coupled to the current load state of the AGV, including but not limited to maximum achievable speed, maximum braking deceleration, maximum centripetal acceleration, maximum permissible jerk, and maximum steering angular velocity. These parameters are not fixed constants, but rather reflect the current load state. The function will change dynamically depending on the actual working conditions of the AGV.

[0066] In this embodiment, to ensure that the constructed safety envelope matches the AGV's actual kinematic capabilities under the current load in the forward, backward, and lateral directions, thereby maximizing the utilization of the limited space in the storage aisle while guaranteeing multiple safety constraints such as rear-end collision prevention, sideslip prevention, and rollover prevention, an anisotropic spatiotemporal corridor for the AGV is constructed in a three-dimensional spatiotemporal coordinate system, including:

[0067] Parse the load status information and map it into a discrete set of states;

[0068] For each discrete load state, the spatial boundaries of the AGV in the forward, backward, and lateral directions are determined respectively;

[0069] Based on the determination of spatial boundaries in all directions, the boundaries are stretched along the time axis to obtain a three-dimensional spacetime corridor.

[0070] Specifically, in this embodiment, the discretization of the load state may include:

[0071] Analyze the load state information and map it to a discrete state set. These correspond to the empty load state, the fully loaded lifting rack state, and the off-center load state, respectively. The total mass of the current AGV is denoted as... The height of the center of gravity is recorded as .

[0072] Understandably, when hour, Take the AGV's own curb weight. Take the geometric center of gravity height of the AGV chassis; when hour, Take the total mass of the AGV, the lifted shelf, and the goods. The weighted average center of gravity height of the entire system is taken; this value will shift significantly upwards when the shelves are lifted. At that time, In addition to the above, an off-center load factor is introduced. It is used to characterize the degree to which the center of gravity deviates from the geometric center on the horizontal plane.

[0073] Specifically, in this embodiment, the nonlinear stretching of the forward spatial boundary may include:

[0074] For a fully loaded AGV with a lifting rack, the maximum forward braking distance and minimum turning radius are calculated based on the load mass and center of gravity height. The core design principle for the forward boundary is to incorporate the minimum braking distance required to stop into the boundary calculation. The braking distance itself depends on the current vehicle speed and the effective braking capacity, which is closely related to the load. When the AGV is fully loaded, the increased rack height shifts the center of gravity upwards, resulting in a significant forward weight shift effect during braking. This reduces the rear axle's adhesion to the ground, thus weakening the effective braking force. This effect needs to be reflected by introducing a decay term related to the center of gravity height and mass into the braking force calculation.

[0075] For example, in this embodiment, the forward boundary can be calculated using the following formula:

[0076]

[0077] in, This is the reference front end length of the AGV vehicle body; This represents the current speed of the AGV. This is the coefficient of friction between the tire and the ground. It is the acceleration due to gravity; This is the attenuation coefficient of the center of gravity effect, used to quantify the degree to which the height and mass of the center of gravity weaken the effective braking force; This represents the height of the center of gravity under the current load condition. This represents the total mass of the AGV under the current load condition. This is a safety margin related to the load condition. Figure 2 The diagram shows the nonlinear expansion curve of the forward braking distance of the AGV under load in this embodiment. Three curves are plotted in the diagram: no load (L=0), full load (L=1), and off-center load (L=2), and a traditional fixed radius corridor is superimposed as a horizontal baseline.

[0078] It should be noted that in the above formula, It is a braking distance term based on kinematics. Its denominator... This represents the maximum braking deceleration that tire friction can provide under ideal conditions, while This is a correction for the attenuation of the ideal braking force: when the AGV is fully loaded ( )hour, and As both the numerator and denominator increase, the required braking distance increases non-linearly, and the forward boundary is stretched significantly, thus ensuring sufficient braking margin to prevent rear-end collisions; when the AGV is unloaded ( )hour, and The values ​​are all very small, the attenuation term approaches zero, and the forward boundary is extremely contracted, maximizing the use of the limited space of the storage channel. This on-demand expansion design is the key technological advantage of the anisotropic spacetime corridor compared to the traditional fixed cylindrical model.

[0079] Specifically, in this embodiment, the differentiated design of the backward and lateral spatial boundaries may include:

[0080] The backward boundary can be determined by the following formula:

[0081]

[0082] in, This represents the length of the vehicle's base rear end, with the negative sign indicating the direction along the negative X-axis of the AGV's local coordinate system. It's understandable that since the AGV doesn't actively brake or move backward at high speed during normal operation, setting the rearward boundary to a fixed value equivalent to the vehicle's geometric dimensions is sufficient to meet safety requirements. This design avoids meaningless boundary expansion along the negative X-axis, further ensuring efficient utilization of the passageway space. Figure 3The diagram shows a comparison of the cross-sectional shape of the anisotropic spatiotemporal corridor in polar coordinates in this embodiment. The diagram depicts the closed polygonal outline of the spatial boundary under three working conditions: no load, full load, and off-center load. It shows that the corridor is asymmetrically distributed in the forward, backward, and lateral directions, especially the asymmetrical feature of the lateral boundary expanding to one side under the off-center load condition.

[0083] The lateral boundary needs to consider the lateral offset caused by centrifugal force when the AGV turns, especially under off-center loading conditions. In these conditions, the center of gravity of the cargo is not at the geometric center of the vehicle, leading to an asymmetrical distribution of lateral offset. Therefore, the lateral boundary should be differentiated based on the off-center loading coefficient and the center of gravity height. The calculation formula is:

[0084]

[0085] in, The reference half-width of the AGV body; This refers to the maximum permissible turning angular velocity of the AGV. This is the off-center load factor, which is used when an off-center load is detected. )hour, Take a larger value to make the side boundary expand asymmetrically, so as to prevent the cargo from scraping against the side due to the centrifugal force of turning; It was also included in the calculation of the lateral boundary, reflecting the additional risk of a high center of gravity in lateral motion—the higher the center of gravity, the greater the risk of cargo slippage or shelf tilting under the same lateral acceleration, and the greater the required lateral safety margin.

[0086] Specifically, in this embodiment, the mapping from local boundaries to the global spatiotemporal corridor may include:

[0087] After determining the spatial boundaries in each direction, the asymmetric polygons defined in the AGV's local coordinate system need to be mapped to the global coordinate system and stretched along the time axis to form a complete three-dimensional spatiotemporal corridor. The local polygons are aligned to the AGV's orientation at each moment using a rotation matrix, and then placed at the AGV's global position at that moment using a translation vector. Finally, the two-dimensional sections from all moments are joined along the time dimension to form a three-dimensional manifold.

[0088] For example, in this embodiment, an anisotropic spacetime corridor The mathematical expression in the global coordinate system can be obtained by calculating the following formula:

[0089]

[0090] in, To determine the time based on the AGV heading angle The constructed two-dimensional rotation matrix is ​​used to rotate the boundary polygon in the local coordinate system to align with the global coordinate system; For AGV at any time The global position vector is used to translate the rotated polygon to the correct global position; Based on the current speed and load status The calculated anisotropic space boundary polygon; and These represent the start and end times of the planning time domain, respectively. Representation of time The Cartesian product is used to upgrade the two-dimensional spatial slices to a three-dimensional spatiotemporal space. This formula, by taking the union of the two-dimensional sections at each moment, fully expresses the spatial occupancy within the entire planning time domain as a three-dimensional spatiotemporal corridor. Figure 4 The diagram shows a global manifold of the three-dimensional spatiotemporal corridor in this embodiment. The XY axes of the diagram are the warehouse plane coordinates, and the Z axis is the time axis. It depicts the three-dimensional tubular manifold formed by the stretching of the spatial boundary polygon along the time dimension when the fully loaded AGV travels along the straight channel.

[0091] Understandably, the nonlinear and asymmetric distribution of the time boundary is also reflected in this union operation: when the AGV is fully loaded, due to the decay of acceleration, the time to reach the target speed is prolonged, thus the corridor exhibits a nonlinear extension with a gentle beginning and a steeper end in the T-axis direction; conversely, when unloaded, it exhibits a rapid decay pattern with a steep beginning and a gentle end. This asymmetric characteristic in the time dimension, together with the asymmetric characteristic in the spatial dimension, constitutes the complete physical connotation of the name anisotropy.

[0092] Step 3: Based on the topological mesh data of the three-dimensional orthogonal road network, the anisotropic spatiotemporal corridor is divided into straight-segment spatiotemporal pipes and node segment spatiotemporal pipes. Control points are generated by calculating the geometric derivatives at the connection points of the two pipes, and the boundaries are smoothly spliced ​​using polynomial curve constraints to generate a globally continuous spatiotemporal corridor.

[0093] After constructing an anisotropic spatiotemporal corridor for each AGV, it is necessary to further match the corridor structure with the physical topology of the warehouse road network. Since the channels in the warehouse environment are highly orthogonal, the motion trajectory of the AGV is essentially composed of alternating straight segments and turning node segments. Therefore, the dimensionality of the search space can be reduced and the dynamic feasibility of the trajectory can be ensured by segmenting the corridor into straight tubes and node capsules and applying smooth constraints at the splicing points.

[0094] Specifically, in the straight section, the AGV's motion freedom is limited to longitudinal movement along the channel direction, and its lateral position and heading angle are constrained to approximately constants by the channel wall. Therefore, the search space is reduced from a two-dimensional plane to a one-dimensional velocity planning problem.

[0095] In this embodiment, to maximize solution efficiency while ensuring safety, the search space within the spatiotemporal band of the straight-line segment is constrained to contain only a one-dimensional velocity vector sequence parallel to the direction of travel. Specifically, within the time interval corresponding to the straight-line segment, the AGV's state variables are simplified to a single longitudinal displacement. and its time derivative (longitudinal velocity) With longitudinal acceleration ), while the horizontal position and heading angle It is then locked to a constant value corresponding to the channel centerline. By reducing the dimensionality, the complex problem that might have involved two-dimensional pose search is transformed into a single-variable time-optimal control problem, enabling the subsequent convex optimization solver to converge at near real-time speed.

[0096] At turning points, the AGV needs to change its heading angle within a limited space, possessing two-dimensional translational and rotational degrees of freedom. In the crossroads or T-junctions corresponding to the node segment's spatiotemporal conduit, the search space is expanded into a two-dimensional spatiotemporal capsule structure containing rotational angular velocity and lateral offset.

[0097] Understandably, the so-called two-dimensional spatiotemporal capsule refers to abstracting the feasible domain of the AGV into a capsule-shaped geometry with a rounded rectangular cross-section extending along the time axis within the time window corresponding to the node segment. The radius of the capsule's cross-section is determined by the AGV's minimum turning radius, the length of the capsule is determined by the time required to enter and exit the curve, and the capsule's axis is aligned with the diagonal direction of the intersection, i.e., the transition curve from the entrance tangent direction to the exit tangent direction. Through this capsuleification process, the search space of the node segment retains the degrees of freedom necessary for the AGV to rotate and laterally offset, while geometric constraints prevent the disordered diffusion of the search range across the entire intersection plane.

[0098] Furthermore, at the junction of the straight-line pipe section and the node capsule, without proper handling, the trajectory will exhibit abrupt changes or discontinuities in curvature, leading to a step in the angular velocity command received by the steering motor, which in turn can cause mechanical shock and cargo oscillation. Therefore, a parametric curve with high-order continuity needs to be introduced at the junction to achieve a smooth transition. This can be achieved by extracting the end tangent vector of the straight-line segment and the beginning tangent vector of the node segment, and using them as control point pairs for the parametric curve.

[0099] In this embodiment, specifically, it can be adopted Uniform B-spline curves or Bézier curves are used to achieve smooth splicing between straight tubular sections and nodal capsules. B-spline curves naturally possess local support and controllable continuous order. Their control points can be determined by the tangent direction vector at the end of the straight tubular section and the tangent direction vector at the beginning of the nodal tubular section, ensuring the continuity of position and tangent direction at the splice.

[0100] For example, in this embodiment, the B-spline curve at the splice can be expressed by the following formula:

[0101]

[0102] in, For parameters Points on the curve at that location; For the first indivual The B-order spline basis function, recursively defined by the node vector, determines the range and weight of the influence of each control point on the curve shape; For the first There are [number] control points, totaling [number] points. The values ​​of the control points are constrained by the outgoing tangent vector at the end of the straight pipe strip and the incoming tangent vector at the beginning of the node pipe strip. The normalized curve parameters have a range of values. . Figure 5 The figure shows a curve comparison of the curvature of the B-spline smooth splicing and the traditional hard splicing in this embodiment. As can be seen from the figure, the B-spline splicing eliminates the curvature abrupt change and limits the rate of curvature change to within the maximum steering angular velocity limit of the AGV, thus avoiding the step jump in steering motor commands.

[0103] It should be noted that the specific method for generating this control point is as follows: the geometric first derivative is calculated at the end of the straight segment. Obtain the outgoing tangent vector and calculate the geometric first derivative at the beginning of the nodal segment. Obtain the incident tangent vector and force The left and right limits are equal at the splice point (i.e., the second derivative is continuous). (Conditions), and thus solve the system of equations to find the intermediate control points. The coordinates are determined by continuously calculating the intermediate insertion point using the forced second derivative, thus strictly limiting the rate of curvature change at the splicing boundary to within the maximum steering angular velocity limit of the AGV, thereby eliminating the step jump in steering motor commands.

[0104] After determining the parametric expression of the splicing curve, to ensure that the AGV does not cause the fully loaded rack to tip over or the goods to slip due to excessive centripetal acceleration when turning, it is also necessary to apply an upper bound constraint on the curvature of the curve coupled with the load state. From a physical point of view, when the AGV moves on a curve, the centripetal acceleration experienced by the goods is directly proportional to the square of the velocity and inversely proportional to the turning radius. The reciprocal of the turning radius is the curvature. Therefore, it is necessary to limit the curvature of the curve at all positions to not exceed the maximum value allowed by the current load and friction conditions.

[0105] For example, in this embodiment, the curvature constraint can be expressed by the following formula:

[0106]

[0107] in, For the curve in parameters The curvature at a point is given by the first derivative of the curve. and second derivative It is calculated using standard differential geometry formulas; The coefficient of static friction between the cargo and the AGV's bearing surface; It is the acceleration due to gravity; The design speed for the AGV when navigating a curve; The coefficient representing the influence of center of gravity height; This represents the height of the center of gravity under the current load condition. Figure 6 The graph showing the maximum permissible upper bound of curvature variation for load-state coupling in this embodiment is illustrated. Figure 6 As can be seen, when fully loaded and lifted, the center of gravity height increases under the current load condition, which compresses the upper limit of the allowable curvature, forcing a smoother turning trajectory, thus ensuring anti-rollover safety from a mathematical perspective.

[0108] It should be noted that in the above equation, the right side of the inequality... This represents the maximum curvature allowed under the current load conditions. (Molecule) The acceleration corresponding to the maximum lateral support force provided by static friction is expressed in the denominator. This reflects the physical law that the higher the speed, the smaller the allowable curvature. This introduces the amplifying effect of center of gravity height on rollover risk—when the AGV is fully loaded and lifted, The increase in curvature further reduces the maximum permissible curvature, thus forcing a smoother turning trajectory. By requiring the B-spline curve to satisfy the condition of continuous second derivative, the angular velocity command received by the steering motor is ensured to be smoothly transitioned, eliminating the mechanical shock caused by abrupt changes in curvature. This is completely equivalent to the description in claim 3, which limits the rate of curvature change to the maximum steering angular velocity limit of the AGV.

[0109] After the above processing, the originally fragmented straight-line segment spacetime continuum and nodal segment spacetime continuum were seamlessly spliced ​​into a single continuum. A continuous overall geometric structure, namely a globally continuous spatiotemporal corridor.

[0110] Step 4: Model the high-frequency conflict throat region as a spatiotemporal mutual exclusion lock, detect the multidimensional overlap state of multiple global continuous spatiotemporal corridors in future time slices, and assign truncation and waiting logic containing relative time constraints to the conflict corridors based on the overlap state and the preset task priority table to eliminate deadlock topology.

[0111] After constructing a spatiotemporal corridor coupled with the load and completing road network matching for each AGV through the aforementioned steps, when multiple AGVs are running in the same warehousing environment, spatiotemporal overlap of corridors is inevitable, i.e., potential collision conflicts. Especially in choke areas such as aisle intersections, multiple AGVs may form a circular dependency by waiting for each other to release resources, leading to system deadlock.

[0112] Understandably, traditional deadlock resolution algorithms are reactive, meaning the system first allows a deadlock to occur and then resolves it through preemptive rollback, random reordering, or other means. The fundamental flaw of this approach is its low efficiency and potential for cascading effects—a single deadlock resolution often triggers cascading replanning of multiple downstream AGVs, easily leading to scheduling avalanches in large-scale clusters. Therefore, it is necessary to predict the collision topology in the spatiotemporal domain in advance and fundamentally disrupt the necessary conditions for deadlock formation through proactive time constraint injection, achieving prior-level deadlock immunity.

[0113] A spacetime mutex lock is a logical control unit configured for specific bottleneck areas in a warehouse road network (e.g., a crossroads where multiple channels converge, a T-junction leading only to the charging area, a narrow passage at the entrance of a storage location, etc.) to restrict that at most one AGV can pass through at any given time. This mutex lock is conceptually similar to a mutex lock in an operating system, but its holding and releasing events do not occur at a point in time, but rather within a time window.

[0114] Within the region where the spatiotemporal mutex lock is activated, the spatiotemporal corridor set of the first AGV is periodically calculated. Collection of time and space corridors with the second AGV .

[0115] In large-scale AGV cluster scenarios, if polygon intersection operations are directly performed on the spatiotemporal corridors of each pair of AGVs, the computational complexity will increase quadratically with the number of AGVs. This is unacceptable for warehousing systems that often have hundreds of AGVs operating simultaneously.

[0116] Therefore, in this embodiment, a three-dimensional spatiotemporal hash table is constructed in the main control memory, and the three-dimensional key-value pair of this hash table is determined by... Composition, in which, and A discrete grid index for the physical base map of the warehouse, divided according to the dimensions of the AGVs themselves. For discrete time step index; the hash table value is mapped to the pointer of the unique identifier of the AGV occupying that spatiotemporal grid.

[0117] For example, in this embodiment, a three-dimensional spatiotemporal discrete hash map is first constructed. For any AGV its corridor The discretized key values ​​can be calculated using the following formula:

[0118]

[0119] in, The global spatial coordinates of a point within the corridor; This is the timestamp corresponding to that point; This refers to the grid resolution in the spatial direction; The grid resolution is in the time direction; The floor function is used to transform continuous spatiotemporal coordinates into discrete grid indices. Through this discretization, each spatiotemporal grid cell can serve as a key in a hash table, with its corresponding value being the set of all AGV numbers occupying that grid. Figure 7 A comparison chart showing the time complexity of 3D spatiotemporal hash query and traditional polygon intersection in this embodiment is presented.

[0120] Corridor overlap detection can be represented by the intersection of sets:

[0121]

[0122]

[0123] in, For keys in a hash table The corresponding set of AGV numbers; The numbers of the two AGVs that clashed; This is the priority function for the AGV. When... When it is not empty, it indicates that there is a spatiotemporal conflict.

[0124] It should be noted that the core advantage of this hash mapping mechanism lies in transforming the polygon intersection operation, which originally required a continuous space (whose computational complexity increases quadratically with the number of AGVs), into a hash query based on a discrete grid index (where the amortized time complexity of a single query is constant). By discretizing and sampling the spatiotemporal corridor boundaries of each AGV and performing hash collision queries in parallel, the... The time complexity of corridor intersection detection is reduced to deterministic memory access operations based on hash lookup, which is the computing power guarantee for high-frequency scheduling of large-scale AGV clusters.

[0125] Once determined That is, there are physically overlapping time slices. Then, the preset task priority table is queried. Assuming the first AGV has a higher priority than the second AGV, the overlapping time window is extracted. A time-barrier penalty function is injected into the low-priority AGV (i.e., the second AGV) before it enters the throat node.

[0126] Forcefully modify the topology mesh node properties of the second AGV, and add a hard time roadblock constraint at the entrance of the overlapping region of the spatial mesh:

[0127]

[0128] The time barrier can be more fully represented by the following formula:

[0129]

[0130] in, The time-related roadblock penalty is injected into the low-priority AGV path cost function; The latest time for a high-priority AGV to pass through the throat node; This provides an additional safety margin to compensate for sensor measurement errors and actuator response delays; This is a choke point in the space where a conflict occurs. When a low-priority AGV attempts to enter this choke point before a high-priority AGV has passed through, its passage cost is set to infinity. This forces the underlying speed planner to output a waiting curve with a speed of zero, causing the spatiotemporal pipeline of the second AGV's node segment to be truncated into a waiting state in the time dimension. This forces the first AGV to release the mutex lock before it can pass. From the perspective of the resource allocation graph, this mechanism breaks the necessary condition for deadlock formation at the prior level (the circular waiting condition in the Coffman condition is broken) by forcibly interrupting the circular waiting chain, thus achieving system-level deadlock immunity. Figure 8 This diagram illustrates a comparison of deadlock topologies before and after the injection of a spatiotemporal mutex lock in this embodiment. The diagram includes two parallel Gantt charts: the left chart shows the deadlock where two AGVs form a loop at the throat node without the injection of a temporal barrier; the right chart shows the deadlock after the injection of a hard temporal barrier. Afterwards, low-priority AGVs are truncated to a waiting state, while high-priority AGVs release their mutexes first.

[0131] Step 5: After applying relative time constraints, a multi-stage solution architecture with space-time decoupling is adopted to map the preset anti-tipping jerkness constraints and velocity constraints into linear inequality matrices, construct a quadratic programming or second-order cone programming model, and solve for the time allocation sequence and spatial reference trajectory that satisfy the dynamic hard constraints.

[0132] After determining the collision-free spatial corridor for each AGV through the aforementioned steps, it is necessary to assign an optimal time profile to the corridor, that is, to determine the passing speed of the AGV at each position in the corridor.

[0133] Understandably, joint planning of multiple agents in three-dimensional spacetime is a non-convex problem with extremely high computational complexity, making direct solutions infeasible in large-scale clusters. Therefore, we can leverage the premise that the spatial corridor is fixed to decouple the problem into a velocity optimization problem along the trajectory longitudinally. By cleverly substituting variables, we can transform the nonlinear kinematic constraints into convex constraints, thereby obtaining the global optimum in polynomial time using an efficient convex optimization solver.

[0134] The first stage of spatial solution: fix each time step, take the global continuous spatiotemporal corridor as the feasible region of the convex polygon, and extract the Euclidean distance maximization path between the AGV geometric contour and the boundary of the convex polygon as the collision-free spatial trajectory.

[0135] Specifically, in this stage, the time dimension is temporarily frozen, and the problem degenerates into a purely geometric problem—finding a spatial path that maximizes the Euclidean distance from the geometric center of the AGV to the boundary of the corridor within a sequence of convex polygons formed by the two-dimensional cross-sections of the anisotropic spatiotemporal corridor at each time slice. This maximization operation is mathematically equivalent to solving a Chebyshev center problem, and its physical meaning is to walk along the exact center of the corridor, thus leaving the maximum margin for possible subsequent elastic deformation.

[0136] The second stage involves time calculation: based on the given spatial trajectory, a function is established with the shortest completion time as the objective function. For a multi-order optimization model with linear constraints, where Let the time interval vector and constraint matrix be... With boundary vector The speed and acceleration upper limits are determined by mapping the maximum output torque and maximum braking current of the hardware motor.

[0137] The trajectory is discretized into a finite number of time steps, and acceleration and the square of velocity are defined as optimization variables at each time step. By using the square of velocity instead of velocity itself as the variable, the nonlinear kinematic relationship that originally contained the square root (such as...) is optimized. The objective function and constraints of the entire optimization problem are transformed into linear relationships, making them convex sets, thus ensuring that the convex optimization solver can converge efficiently.

[0138] For example, in this embodiment, a discrete time step is set. The state variable is the longitudinal displacement along the trajectory. ,make Indicates acceleration. Let represent the square of the velocity. The optimization problem aiming to minimize runtime and smoothness can be expressed as follows:

[0139]

[0140] in, For the first Minimizing the negative of the square of the step speed is equivalent to maximizing the speed and thus minimizing the total running time. The weighting coefficients for the jerkiness smoothing term are used to balance the relationship between time optimality and motion smoothness. For the first The speed of movement.

[0141] Furthermore, in this embodiment, the optimization objective is to minimize the total running time while maintaining smooth motion, all while satisfying all safety constraints. The anti-tipping constraint is based on the Zero Moment Point (ZMP) theory, requiring that the inertial torque generated by the cargo during acceleration and deceleration must not exceed the anti-tipping torque provided by the chassis support polygon.

[0142] The anti-tipping acceleration constraint based on zero-moment point theory can be expressed by the following formula:

[0143]

[0144] in, and These represent the distances from the front and rear ends of the polygon supporting the AGV chassis to the projection point of the center of gravity, respectively, and represent the lever arms that the chassis resists tilting forward and backward. The total mass under the current load condition; It is the acceleration due to gravity; This is the current center of gravity height. Figure 9 This diagram illustrates the feasible domain boundary of the anti-tipping acceleration constraint under full load conditions in this embodiment.

[0145] It should be noted that in the above formula, The design of being positioned in the denominator has a clear physical meaning: when the AGV is fully loaded and the rack is raised, the center of gravity height is... The magnitude is significantly increased, and the maximum allowable acceleration boundary on the right side of the inequality is strictly compressed, thus the mathematical model rigidly guarantees that the high-level rack will not tilt forward or backward during the longitudinal acceleration and deceleration phases. (The remaining text appears to be incomplete and requires further context.) It can then be seen that the upper bound of the allowable acceleration is... It is directly proportional, that is, the wider the chassis and the lower the center of gravity, the greater the allowable acceleration, which is completely consistent with physical intuition.

[0146] Jerk is the derivative of acceleration with respect to time, representing the rate of change of acceleration. Even if the acceleration itself is within a safe range, if its change is too drastic, the instantaneous inertial impact can cause the goods to slip on the AGV's carrying surface. Therefore, jerk constraints limit the rate of change of acceleration to prevent goods from slipping due to dynamic impacts caused by sudden jumps in acceleration. This embodiment provides two equivalent expressions:

[0147] The first expression is based on discrete time steps. AGV position coordinates below The current jerkness value is approximated by a forward finite difference equation:

[0148]

[0149] The second equivalent expression is based on acceleration. First-order difference:

[0150]

[0151] It should be noted that these two forms are mathematically equivalent: the third difference of position equals the first difference of acceleration (at constant velocity). Assuming the following, one of the forms can be flexibly selected based on the solver's preference for decision variables (either location or acceleration).

[0152] Based on the center of gravity height and chassis support polygon area under full load conditions, calculate the critical jerk threshold that prevents the cargo from tipping over. In the time allocation solution stage, the inequalities will be... This is transformed into a linear matrix row vector related to the time interval variation component, i.e.:

[0153]

[0154] in, To determine based on the current load status and the static friction coefficient between the cargo and the bearing surface The maximum permissible level of jerkiness is determined.

[0155] The aforementioned anti-tipping constraints and jerkiness constraints are rewritten in the form of a standard linear inequality matrix. :

[0156]

[0157] Among them, matrix The structure is jointly determined by acceleration boundary constraints and abrupt change difference constraints between adjacent time steps; vector For acceleration decision variables, The transpose of a matrix; a vector Each component is an upper bound determined by the anti-tipping condition and the jerkiness limit. By unifying all constraints into matrix inequality form, the entire velocity optimization problem is rigorously constructed as a quadratic programming (QP) or second-order cone programming (SOCP) problem, and convex optimization solvers (such as OSQP, ECOS, Mosek, etc.) can converge to the global optimum in polynomial time.

[0158] Forced into a quadratic programming or second-order cone programming model, ensuring that the optimized output curve meets the physical anti-tipping requirements. The output obtained from the solution includes two parts: the time allocation sequence. and the corresponding spatial reference trajectory . Figure 10 This example shows a speed-time profile comparison of the quadratic programming solution in this embodiment. Figure 10 It can be seen The jerkiness hard constraint ensures that the velocity curve of the optimized output meets the physical anti-slip requirements, while approximating the time-optimal solution in polynomial time.

[0159] Step 6: Control the AGV to travel along the spatial reference trajectory. When a local physical disturbance deviating from the reference trajectory is detected, calculate the residual safety margin from the current corridor boundary to the nearest obstacle. If the residual safety margin is greater than zero, perform elastic deformation of the current spatiotemporal corridor with local spatial pushing and time delay to self-repair the trajectory.

[0160] After completing the corridor construction, road network matching, collision detection, and speed optimization through the aforementioned steps, it is also necessary to consider the unavoidable real-time disturbances in the warehouse environment. Understandably, in actual operation, temporary minor obstacles often appear in the warehouse environment, such as people passing by, fallen cardboard boxes, or temporarily parked picking carts. If every such disturbance triggers global replanning, it will lead to significant communication overhead and computational resource consumption, and in severe cases, may even cause a computing power storm on the central scheduling server. Therefore, it is necessary to endow the spatiotemporal corridor with local self-healing capabilities, enabling it to absorb minor disturbances within a certain range, and only report to the global scheduling layer for replanning when the disturbance exceeds the local repair capacity.

[0161] By collecting environmental point cloud data in real time, when a local static or dynamic obstacle not in the topology grid data is detected intruding into the current spatiotemporal corridor, an elastic self-repair mechanism is triggered.

[0162] Specifically, the AGV's onboard LiDAR or depth camera continuously scans the surrounding environment at a high frame rate (e.g., above 20Hz), performs differential calculations between the original point cloud and the static obstacle map in the topological mesh data, and the resulting residual is the unregistered local obstacle; when the position coordinates of any unregistered obstacle fall within the geometric boundary of the current spatiotemporal corridor, the elastic self-repair mechanism is activated.

[0163] Then, drawing on the ideas in elasticity mechanics, the boundary of the spacetime corridor is regarded as a system of point masses connected by virtual springs. The boundary of the current spacetime corridor is discretized into virtual point masses containing spring stiffness coefficients, which are inversely proportional to the load state information.

[0164] For example, in this embodiment, the current spatiotemporal corridor boundary is discretized into a set of virtual particles. And define the corridor spring stiffness coefficient as:

[0165]

[0166] in, The reference stiffness constant; This is the quality impact coefficient; This represents the total mass of the AGV under the current load condition.

[0167] It should be noted that this formula reflects the design intent of lower stiffness with heavier loads. Understandably, this design is contrary to intuition, as heavy loads usually mean stiffer. However, in the context of this application, low stiffness means smaller spatial displacement per unit force. That is, when the corridor of a fully loaded AGV is disturbed, the deformation resistance in the spatial direction is greater. The system tends to avoid the conflict by delaying the time (i.e., slowing down and waiting) rather than by moving laterally (i.e., going around). The purpose of this design is that sharp lateral turns of AGVs under full load can easily cause the shelves to tip over. Therefore, longitudinal deceleration should be prioritized to mitigate disturbances.

[0168] When an intruding obstacle is detected At that time, the repulsive force vector is calculated based on the intrusion depth of the intrusion obstacle. The repulsive force of the artificial potential field on each virtual particle can be calculated by the following formula:

[0169]

[0170] in, The environmental stiffness coefficient characterizes the strength of the repulsive force field of the obstacle; For the first The distance from a virtual point mass to an obstacle; The radius of influence of the potential field is such that when the distance between the particle and the obstacle is greater than this radius, it is not affected by the repulsive force. The gradient direction of the distance field is the direction of the repulsive force. A key characteristic of this potential field function is that the repulsive force increases rapidly and non-linearly as the particle gets closer to the obstacle, resulting in excellent obstacle avoidance performance. Figure 11 The graph shows the attenuation curve of the repulsive force of the artificial potential field with the invasion distance in this embodiment. It can be seen from the graph that the repulsive force... It increases rapidly and nonlinearly, while... The zero-time property verifies the obstacle avoidance effectiveness of the artificial potential field.

[0171] Under the influence of repulsive force, and provided that the hard constraints of the surrounding shelf legs and other AGV corridor boundaries are not breached, the virtual particle undergoes coordinate translation (spatial pushing) along the direction of the repulsive force vector, and simultaneously shifts the timestamp of the corresponding trajectory point backward (time delay). (Particle) Given spatial translation and time delay, the corridor deformation update equation can be calculated using the following formula:

[0172]

[0173]

[0174] in, This represents the displacement of a point mass in a spatial dimension; This is the projection of the repulsive force onto the spatial component (i.e., the xy plane); The aforementioned stiffness coefficient related to the load; This represents the delay of the particle in the time dimension; This is the projection of the repulsive force onto the time component (i.e., the T-axis); This is the proportional coefficient for time delay.

[0175] Understandably, spatial compression components With stiffness coefficient Inversely proportional, while the time delay component It is not suppressed by the stiffness coefficient. This decoupling design makes the deformation in the spatial dimension suppressed in the fully loaded scenario (low stiffness, i.e., stiff spring), and the disturbance is mainly absorbed by the time delay; conversely, in the unloaded scenario (high stiffness, i.e., soft spring), the system tends to quickly bypass the disturbance by spatial lateral displacement without having to reduce the speed.

[0176] Step 7: Finally, after the corridor completes local deformation, the residual safety margin is used to determine whether the self-healing trajectory was successful. This embodiment further provides deformation stress reporting logic as a filter connecting the underlying reactive obstacle avoidance and the upper-level global planning and scheduling.

[0177] Define the deformation stress value ,in This represents the physical distance between the current spacetime corridor boundary after elastic deformation and the nearest absolutely static obstacle in the surrounding area. The minimum mechanical redundancy error limit set for the system. This stress value can be calculated using the following formula:

[0178]

[0179] in, This is the set of virtual particles after deformation; The boundary of the nearest fixed shelf; This refers to the minimum safe distance that must be maintained between the AGV and the rack.

[0180] When repulsive forces accumulate due to continuous disturbances, the deformation stress value at the next moment is calculated. When the deformation exceeds the stress threshold, the reprogramming trigger criterion is determined. The reprogramming trigger criterion can be expressed by the following formula:

[0181]

[0182] At this point, the current control point is locked, elastic self-repair is paused, and a forced replanning request identifier carrying the current coordinates is sent to the central scheduling server via the communication bus.

[0183] It should be noted that this criterion acts as a filter connecting the lower-level reactive obstacle avoidance and the upper-level global planning and scheduling. When the obstacle is small and the intrusion distance is short, the repulsive force is limited, and the corridor only experiences slight local expansion or time stamp delay. Disturbances are absorbed automatically at the bottom level without needing to be reported; only when an obstacle is large enough to push the corridor boundary to interfere with the fixed shelving... A global replanning request is only triggered when a minor disturbance occurs. Through this layered filtering mechanism, most minor disturbances are intercepted and processed at the lower level, effectively protecting the computing resources of the central scheduling server and avoiding computing storms caused by frequent invalid replanning requests.

[0184] Based on the above steps, simulation experiments were conducted. The simulation experiments show that in a large-scale warehouse scenario with 200 AGVs operating simultaneously, compared with the traditional fixed cylindrical corridor + centralized conflict detection scheme, the channel space utilization rate of the method in this application is increased from about 62% to 89%, the frequency of deadlock is reduced from 4.3 times per hour to 0 times, the shelf shaking event caused by excessive abrupt movement under full load is reduced from 17 times per thousand tasks to 0.4 times, and the replanning request frequency of the central scheduling server is reduced by about 78%. Figure 12 The simulation experiment in this embodiment shows the heat map of the warehouse aisle space utilization rate of the proposed scheme and the traditional scheme. The map contains two side by side warehouse plan heat maps. The left map shows the aisle occupancy rate distribution under the traditional fixed cylindrical corridor; the right map shows the aisle occupancy rate distribution under the anisotropic corridor of the proposed scheme. The color intensity represents the actual utilization rate of the aisle space. Figure 13 A box plot comparing the task completion time distribution of the multi-AGV cluster in the simulation experiment of this embodiment is shown. Figure 14 The diagram shows a cumulative comparison of the deadlock frequency of the proposed scheme and the traditional scheme in the simulation experiment of this embodiment.

[0185] Example 2

[0186] This embodiment discloses a dynamic spatiotemporal corridor trajectory optimization system for multi-AGV warehousing systems.

[0187] Specifically, this system can be integrated into electronic devices, such as terminals and servers. Terminals can be AGV-mounted industrial control computers, handheld dispatch terminals, smart Bluetooth devices, laptops, or personal computers. Servers can be a single central dispatch server or a server cluster consisting of multiple servers; for example, it can be a distributed cluster including a path planning master node, conflict detection slave nodes, and elastic deformation coprocessing nodes.

[0188] In this embodiment, the dynamic spatiotemporal corridor trajectory optimization system for multi-AGV warehousing systems can also be integrated into multiple electronic devices. For example, the system can be integrated into multiple servers, with multiple servers working together to implement the trajectory optimization method of this application. One part of the servers is specifically responsible for global topology network maintenance and mutual exclusion lock management, while another part of the servers is specifically responsible for the underlying anisotropic corridor calculation and elastic deformation solution.

[0189] In this embodiment, the server can also be implemented as an AGV on-board main controller, that is, some lightweight computing modules that originally ran on the central server, such as local elastic self-healing modules, are moved to the AGV end to reduce communication latency.

[0190] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for dynamic spatiotemporal corridor trajectory optimization in a multi-AGV warehousing system, characterized in that, The dynamic spatiotemporal corridor trajectory optimization method includes: The task location data and load status data of the mobile platform are obtained. The task location data is used to indicate the task start and end point of the mobile platform. The load status data is used to reflect the physical attributes of the object currently carried by the mobile platform. The load status data includes: load capacity, center of gravity height and off-center load factor. Based on the load status data, the kinematic limit parameters of the mobile platform are determined, including the maximum steering angular velocity; An anisotropic spatiotemporal corridor is constructed within the spatiotemporal coordinate system. The anisotropic spatiotemporal corridor is a spatiotemporal passage area used to constrain the trajectory of the mobile platform along the mission start point to the mission end point. The spatial and temporal boundaries of the anisotropic spatiotemporal corridor are nonlinear and asymmetrically distributed according to the kinematic limit parameters. The spatial boundary of the anisotropic spacetime corridor includes: A first spatial boundary along the direction of travel of the mobile platform, a second spatial boundary against the direction of travel, and a third spatial boundary perpendicular to the direction of travel; wherein, The first spatial boundary is nonlinearly determined based on the current speed of the mobile platform and the effective braking capacity determined by the current load state. The length of the first spatial boundary extending along the travel direction is determined as the sum of the reference front length of the mobile platform, the braking distance term, and the safety margin related to the current load state. The braking distance term is calculated with the square of the current speed as the numerator and the difference between the ideal braking term and the center of gravity effect attenuation term as the denominator. The ideal braking term is determined by twice the product of the friction coefficient between the tires and the ground of the mobile platform and the gravitational acceleration. The center of gravity effect attenuation term is proportional to the product of the center of gravity height under the current load state and the load-bearing mass under the current load state. The greater the load-bearing mass and the higher the center of gravity height corresponding to the load state, the greater the center of gravity effect attenuation term, the smaller the denominator, the weaker the effective braking capability, and the greater the length of the first spatial boundary extending along the travel direction. The second spatial boundary extends in the local coordinate system of the mobile platform in the opposite direction to the direction of travel. The extension length of the second spatial boundary in this direction is set to a fixed value equal to the reference rear end length of the mobile platform, and does not change with the current speed and the load state. The third spatial boundary is expanded according to the off-center load coefficient and the center of gravity height. The magnitude of the third spatial boundary on both sides perpendicular to the direction of travel is determined as the sum of the reference half-width of the mobile platform and the lateral expansion term. The lateral expansion term is the product of the maximum steering angular velocity, the off-center load coefficient under the current load state, and the center of gravity height under the current load state. The larger the off-center load coefficient and the higher the center of gravity height, the larger the lateral expansion term and the more asymmetrical the expansion of the third spatial boundary on both sides perpendicular to the direction of travel.

2. The dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems according to claim 1, characterized in that, The load status data also includes at least one of the lifting status and attitude tilt angle; Determining the kinematic limit parameters of the mobile platform based on the load state data includes: Load status data is mapped to a discrete set of load statuses, which includes a first load status, a second load status, and a third load status. The first load state corresponds to no load, the second load state corresponds to full load with jacking, and the third load state corresponds to off-center load. The load-bearing mass and center of gravity height corresponding to the second load state are greater than those of the first load state, and the third load state, relative to the second load state, also represents the off-center load factor; And determine the corresponding kinematic limit parameters for each of the discrete sets of load states; The kinematic limit parameters also include at least one of the following: maximum achievable speed, maximum braking deceleration, maximum centripetal acceleration, and maximum jerk.

3. The dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems according to claim 1, characterized in that, The spatial boundary of the anisotropic spacetime corridor includes: Determine the local boundary polygon in the local coordinate system of the mobile platform; The local boundary polygon is rotated according to the orientation of the mobile platform at each moment, and the rotated local boundary polygon is translated according to the global position of the mobile platform at each moment. The boundary sections after rotation and translation at each moment are merged along the time axis of the spatiotemporal coordinate system to obtain the anisotropic spatiotemporal corridor.

4. The dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems according to claim 1, characterized in that, The dynamic spatiotemporal corridor trajectory optimization method also includes: Obtain the road network topology data of the workspace where the mobile platform is located; Based on the road network topology data, the anisotropic spatiotemporal corridor is divided into straight-line spatiotemporal corridor and node spatiotemporal corridor. Calculate the geometric derivative at the connection point between the straight-line segment spatiotemporal duct and the nodal segment spatiotemporal duct to generate control points. The connection points are then smoothly spliced ​​using the splicing curve constrained by the control points to obtain a globally continuous spatiotemporal corridor. The search space within the spatiotemporal control zone of the straight section is constrained to contain only a one-dimensional velocity vector sequence parallel to the direction of travel of the mobile platform, and the lateral position and heading angle of the mobile platform are locked to constant values ​​corresponding to the centerline of the channel. The search space corresponding to the spatiotemporal tube of the node segment is expanded into a two-dimensional spatiotemporal capsule structure containing rotational angular velocity and lateral offset. The cross-sectional dimensions of the two-dimensional spatiotemporal capsule structure are determined by the minimum turning radius of the mobile platform.

5. The dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems according to claim 4, characterized in that, The step of calculating the geometric derivative at the connection point between the straight-segment spatiotemporal duct and the nodal segment spatiotemporal duct to generate control points includes: Extract the outgoing tangent vector at the end of the straight-line spatiotemporal conduit and the incoming tangent vector at the beginning of the node segment spatiotemporal conduit, and use them as the constraint conditions for the control point; The left and right limits of the second geometric derivative of the splicing curve at the connection point are forced to be equal, and the control points located between the connection points are obtained by inverse solution, so that the rate of curvature change at the connection point does not exceed the limit corresponding to the maximum steering angular velocity of the mobile platform. The curvature at all points on the spliced ​​curve is constrained to not exceed the upper bound of curvature, which is determined by the friction conditions between the current load state data and the bearing surface of the mobile platform. Furthermore, the higher the center of gravity indicated by the load status data, the higher the cornering design speed of the mobile platform, and the smaller the upper bound of the curvature.

6. The dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems according to claim 4, characterized in that, The dynamic spatiotemporal corridor trajectory optimization method is applied to multiple mobile platforms, including a first mobile platform and a second mobile platform. The first mobile platform and the second mobile platform respectively obtain their respective global continuous spatiotemporal corridors according to claim 4. Furthermore, the dynamic spatiotemporal corridor trajectory optimization method also includes: The high-frequency conflict choke zone in the workspace is modeled as a spatiotemporal mutual exclusion lock, which is used to restrict at most one mobile platform from passing through the choke zone within the same time window. Detect the overlap between the global continuous spatiotemporal corridor of the first mobile platform and the global continuous spatiotemporal corridor of the second mobile platform in future time slices; Based on the overlapping state and the preset task priority table, the passage priority is determined for the first mobile platform and the second mobile platform, and a relative time constraint is applied to the mobile platform with lower priority, so that the spatiotemporal pipeline of the node segment corresponding to the mobile platform with lower priority is in a waiting state within the overlapping time window corresponding to the overlapping state.

7. The dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems according to claim 6, characterized in that, The detection of the overlap between the global continuous spatiotemporal corridor of the first mobile platform and the global continuous spatiotemporal corridor of the second mobile platform in future time slices includes: A three-dimensional spatiotemporal hash table is constructed in the storage of the processing device. The key of the three-dimensional spatiotemporal hash table consists of a spatial grid index and a temporal grid index. The spatial grid index is obtained by rounding down the global spatial coordinates according to the spatial grid resolution. The temporal grid index is obtained by rounding down the timestamp according to the temporal grid resolution. The value of the three-dimensional spatiotemporal hash table is mapped to the mobile platform identifier that occupies the corresponding spatiotemporal grid. By discretizing the boundaries of each global continuous spatiotemporal corridor and performing hash collision queries, the polygon intersection operation, which increases quadratically with the number of mobile platforms, is transformed into an index query with amortized constant time complexity to determine the overlap state. The relative time constraint includes: querying the task priority table; when the priority of the first mobile platform is higher than that of the second mobile platform, extracting the overlapping time window corresponding to the overlapping state; injecting a time roadblock constraint at the topology node corresponding to the entrance of the second mobile platform into the throat region; setting the passage cost of the second mobile platform through the topology node before the sum of the latest time when the first mobile platform passes through the throat region and the safety time margin as an impassable value, so that the spatiotemporal pipeline of the node segment of the second mobile platform remains in a waiting state before the first mobile platform passes through the throat region, and eliminating deadlock by interrupting the loop waiting.

8. The dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems according to claim 7, characterized in that, After applying the relative time constraint, the dynamic spatiotemporal corridor trajectory optimization method further includes: A multi-stage solution with spatial and temporal decoupling is adopted, and the preset anti-tipping constraints and anti-slip constraints are mapped into linear inequality matrices and a solution model is constructed. Solving the solution model yields the time allocation sequence and spatial reference trajectory that satisfy the dynamic hard constraints. The multi-stage solution includes: In the first stage, with a fixed time dimension, the path that maximizes the Euclidean distance from the geometric contour of the mobile platform to the boundary of the corridor is extracted from the sequence of convex polygons formed by the two-dimensional cross-sections of the global continuous spatiotemporal corridor at each time slice, and is used as the collision-free spatial reference trajectory. The second stage, based on the given spatial reference trajectory, aims to minimize the completion time by discretizing the spatial reference trajectory into a finite number of time steps. At each time step, acceleration and the square of velocity are defined as optimization variables. By using the square of velocity instead of velocity itself as the optimization variable, the nonlinear kinematic relationship containing the square root is transformed into a linear relationship.

9. The dynamic spatiotemporal corridor trajectory optimization method for multi-AGV warehousing systems according to claim 8, characterized in that, The anti-tipping constraint is determined based on the zero-moment point theory. The anti-tipping constraint requires that the inertial moment generated by the load-bearing object during acceleration and deceleration does not exceed the anti-tipping moment provided by the mobile platform chassis support polygon. Furthermore, the higher the center of gravity indicated by the load status data, the smaller the upper limit of the allowable longitudinal acceleration; The anti-slip constraint limits the jerk along the trajectory to no more than a critical jerk threshold, which is determined by the current load state data and the static friction coefficient of the bearing surface. The jerkiness is obtained by approximating the third-order forward difference of the position of the moving platform, or by approximating the first-order difference of the acceleration.

10. A dynamic spatiotemporal corridor trajectory optimization system for multi-AGV warehousing systems, characterized in that, The dynamic spatiotemporal corridor trajectory optimization system includes: processor; The memory stores a computer program that, when executed by a processor, implements a dynamic spatiotemporal corridor trajectory optimization method for a multi-AGV warehousing system as described in any one of claims 1 to 9.

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