Steady-state rapid construction method and system for artificial potential energy field

Abstract

The invention provides a steady-state rapid construction method and system for an artificial potential energy field, and the method comprises the steps: 1, enabling the artificial potential energy field to be equivalent to a potential energy field generated by a single gravitational mass point, and carrying out the modeling of a target trajectory into a steel chain system composed of a plurality of nodes and rigid rods with fixed lengths, establishing an equivalent physical model and carrying out initialization operation on the equivalent physical model; step 2, based on the equivalent physical model, carrying out stress analysis on a plurality of nodes in the steel chain according to the gravitational action, and iteratively updating the acceleration, the speed and the uncorrected node position of the nodes by setting a simulation step size; step 3, adopting an iterative projection method to gradually correct the uncorrected node position into a projection correction position meeting the length constraint of the rigid rod until the position is converged to a steady state shape; and 4, outputting the converged projection correction position as a steady-state solution of the artificial potential energy field. According to the method, the steady-state construction speed is remarkably increased, and low complexity and high feasibility of steady-state construction of the physical component are considered.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of equivalent artificial potential field, and particularly relates to a steady-state fast construction method and system for artificial potential field. BACKGROUND

[0002] In recent years, with the development of artificial intelligence, automatic control and intelligent systems, more and more engineering problems are abstracted and transformed into physical modeling problems, so as to obtain an efficient solving method by means of classical mechanics principles. Among them, the mechanical equivalent principle becomes an effective modeling means and is widely used in scenes such as unmanned aerial vehicle trajectory design, path planning, robot navigation and the like. The method equivalent the complex path planning task to the steady-state shape problem of the rope system in the artificial potential field, and then solves the force balance state of the rope by means of the mechanical model, so as to map the running trajectory of the target system. Through the equivalent model, the calculation complexity brought by directly solving the path in the high-dimensional nonlinear space can be avoided to a certain extent.

[0003] However, in actual application, the problem constructed based on the artificial potential field often has high non-convexity and complex coupling relationship between multiple variables, so that the solving problem of the steady-state shape of the rope is essentially a highly nonlinear and strongly non-convex optimization problem. The traditional convex optimization method, gradient descent method or numerical iteration method often faces problems such as slow convergence speed and easy to fall into local optimal solution in such problems, and it is difficult to meet the dual requirements of real-time and reliability in engineering. Therefore, how to construct a fast-converging, simple-form and easy-to-implement steady-state solving scheme of the rope in a complex artificial potential field has become one of the hot issues in the current research and application of the field. The breakthrough of related technology will provide more efficient and robust support for intelligent system trajectory planning in complex environment. SUMMARY

[0004] In view of the problems of high model complexity, slow steady-state simulation implementation speed and difficulty in meeting the requirements of engineering deployment of the existing steady-state construction method, the application provides a steady-state fast construction method and scheme for artificial potential field, so as to realize the significant improvement of the steady-state construction speed, and also consider the low complexity and high feasibility of the steady-state state construction of the physical components.

[0005] To solve the above technical problems, the application provides the following technical scheme: A steady-state fast construction method for artificial potential field, comprising the following steps: step 1: equivalent the artificial potential field to the potential field generated by a single gravitational particle, and model the target trajectory as a steel chain system composed of a plurality of nodes and rigid rods with fixed length, establish an equivalent physical model and perform an initialization operation on the equivalent physical model; Step 2. Based on the equivalent physical model, force analysis is performed on several nodes in the steel chain under the action of gravity, and the acceleration, velocity and uncorrected node position of the nodes are iteratively updated by setting a simulation step; Step 3: The uncorrected node position is gradually corrected to a projection corrected position that satisfies the length constraint of the rigid rod by using an iterative projection method until it converges to a steady state shape; Step 4: Output the converged projection corrected position as the steady state solution of the artificial potential field.

[0006] Further, the equivalent physical model in step 1 includes: An artificial potential field and its components; Physical components; The artificial potential field and its components include a single particle and a potential field formed by the gravity of the particle itself; the physical components include several nodes and rigid rods connecting the nodes.

[0007] Further, the nodes have mass, and their volume is ignored; the rigid rods have fixed length and no mass; each two nodes are connected by a rigid rod, forming a steel chain, and the rigid rod can rotate around the node; the first node and the last node of the steel chain are fixed.

[0008] Further, the initialization operation in step 1 includes: Setting a simulation step and a simulation iteration time; Calculating the maximum outer iteration number based on the simulation step and the simulation iteration time; Calculating the straight-line distance based on the coordinates of the first node and the last node of the steel chain; Linearly initializing the node coordinate vector of the steel chain based on the coordinates of the first node and the last node, the number of nodes and the straight-line distance; Initializing the velocity vector of each node to a zero vector.

[0009] Further, step 2 includes: Calculating the distance vector of each node to the gravity particle at the last iteration number; Calculating the acceleration vector of each node of the steel chain at the current iteration number based on the distance vector of each node of the steel chain to the gravity particle at the last iteration number, the coordinates of the gravity particle, and the node coordinate vector of the steel chain at the last iteration number; Calculating the velocity vector of each node of the steel chain at the current iteration number based on the acceleration vector of each node at the current iteration number, the velocity vector of each node of the steel chain at the last iteration number and the simulation step; Updating the node coordinate vector of the steel chain for the outermost iteration and the initialization constraint projection iteration at the current iteration number based on the velocity vector of each node of the steel chain at the current iteration number and the simulation step.

[0010] Further, the step 3 iterative projection method comprises a multi-layer loop: Inner iteration loop: constraint projection iteration; Outer iteration loop: traversing each node of the steel chain, step by step modifying the uncorrected node position to the projection corrected position according to the interval constraint.

[0011] Further, the step 3 of step by step modifying the uncorrected node position to the projection corrected position satisfying the rigid rod length constraint comprises three types of processing: First node correction: modifying the second node position based on the coordinate of the first node of the steel chain; Intermediate node correction: modifying the intermediate node position based on the interval constraint between adjacent nodes; Last node correction: modifying the second last node position based on the coordinate of the last node of the steel chain.

[0012] Further, the step 3 comprises: Based on the coordinate of the first node of the steel chain, the distance from the first node to the second node of the steel chain in the outermost iteration and the last constraint projection iteration under the current iteration number is calculated based on the node coordinate vector of the steel chain in the outermost iteration and the last constraint projection iteration under the current iteration number. Based on the distance from the first node to the second node of the steel chain in the outermost iteration and the last constraint projection iteration under the current iteration number, the distance adjustment parameter from the first node to the second node of the steel chain in the outermost iteration and the last constraint projection iteration under the current iteration number is calculated; and the first element of the node coordinate vector of the steel chain in the outermost iteration and the last constraint projection iteration under the current iteration number is calculated. Repeat the above steps to sequentially calculate the intermediate elements of the node coordinate vector of the steel chain in the outermost iteration and the last constraint projection iteration under the current iteration number. Based on the coordinate of the last node of the steel chain, the last element of the node coordinate vector of the steel chain in the outermost iteration and the last constraint projection iteration under the current iteration number is calculated.

[0013] Further, the constraint projection iteration comprises a termination condition: The maximum constraint projection iteration number is reached, or The node interval error is less than a set threshold.

[0014] In another aspect, the present application also provides a steady-state fast construction system for artificial potential field, comprising: Equivalent physical model construction module: for equivalent to the artificial potential field as the potential field generated by a single gravitational point, and modeling the target trajectory as a steel chain system composed of a plurality of nodes and rigid rods with fixed length, establishing an equivalent physical model and initializing the equivalent physical model; An iterative calculation module is configured to perform force analysis on the nodes in the steel chain based on the equivalent physical model according to the gravitational effect, and iteratively update the acceleration, velocity and uncorrected node position of the nodes by setting a simulation step; A constraint projection correction module is configured to correct the uncorrected node position to a projection correction position meeting the length constraint of the rigid rod by using an iterative projection method until a steady state shape is reached.

[0015] Compared with the prior art, the present application has the following beneficial effects: The present application is directed to the steady state steel chain shape problem caused by the artificial potential field of the gravitational particle, and a steady state fast construction method is designed. In the method, the equivalent artificial potential field caused by a single gravitational particle in the region is established, and the force, acceleration, velocity and uncorrected position of each steel chain node in the iteration process are calculated step by step. Then, by designing a node adjustment mechanism with constant spacing constraint, the node position is corrected step by step by using an iterative constraint projection method until the final steel chain shape meeting the system constraint condition is converged and output. Compared with the existing method based on reinforcement learning or complex nonlinear optimization model, the algorithm complexity of the present application is low, the steady state construction speed is fast, the high complexity model is abandoned, and the online or embedded deployment is facilitated; the physical interpretability is strong, the stability is high, and the motion behavior of the physical components is helpful to understand and analyze; various engineering constraints such as speed, time, steel chain length, node spacing and other practical restrictions can be flexibly introduced; in summary, the steel chain design scheme proposed in the present application establishes an effective bridge between theoretical modeling and engineering application, and provides a feasible technical route for low complexity and high efficiency steady state construction design. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the present application or prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0017] Figure 1 It is an algorithm flowchart of the embodiment of the present application; Figure 2 It is a steel chain node, starting point and end point distribution example diagram of the embodiment of the present application; Figure 3 It is an algorithm flowchart of step 3 in the embodiment of the present application; Figure 4 It is a steady state construction result display diagram of the embodiment of the present application. DETAILED DESCRIPTION

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0019] Example 1 The invention will now be further described with reference to the accompanying drawings.

[0020] like Figure 1 The following is a flowchart of the method of the present invention. The implementation process includes the following steps: Step 1: The artificial potential energy field is equivalent to the potential energy field generated by a single gravitational particle, and the target trajectory is modeled as a steel chain system consisting of several nodes and rigid rods of fixed length. An equivalent physical model is established and the equivalent physical model is initialized. like Figure 2 As shown, the equivalent physical model in step 1 includes: Artificial potential energy fields and their components; Physical components; The artificial potential energy field and its components include a single point mass and the potential energy field formed by the point mass's own gravity; the physical components include several nodes and rigid rods connecting the nodes. The nodes have mass, but their volume is negligible; the rigid rods are of fixed length and have no mass; a rigid rod connects every two nodes, forming a steel chain, and the rigid rods can rotate around the nodes; the first and last nodes of the steel chain are fixed.

[0021] This embodiment introduces the coordinates of the first node of the steel chain. Coordinates of the end node of the steel chain Coordinates of a gravitational particle Length of rigid rod Define the number of steel chain nodes. Simulation step size Simulation iteration time Maximum number of constraint projection iterations .

[0022] The specific steps are as follows: Step 1: Based on simulation step size Simulation iteration time Calculate the maximum number of iterations for the outermost frame. Based on the coordinates of the first node of the steel chain Coordinates of the end node of the steel chain Calculate the straight-line distance between the start and end points Based on the coordinates of the first node of the steel chain , the last node coordinate of the steel chain , the straight-line distance between the start and end points , the number of nodes of the steel chain calculating the initial steel chain node horizontal coordinate vector and the initial steel chain node vertical coordinate vector defining the initial steel chain node horizontal coordinate velocity vector and the initial steel chain node vertical coordinate velocity vector initializing the number of outermost frame iterations .

[0023] the simulation step length based on step 1 , the simulation iteration time calculating the maximum number of outermost frame iterations is:

[0024] wherein, is the maximum number of outermost frame iterations, is the simulation iteration time, is the simulation step length, is a rounding operation.

[0025] the first node coordinate of the steel chain based on step 1 , the last node coordinate of the steel chain calculating the straight-line distance between the start and end points is:

[0026] wherein, is the straight-line distance between the start and end points, is the first node coordinate of the steel chain, is the last node coordinate of the steel chain.

[0027] the first node coordinate of the steel chain based on step 1 , the last node coordinate of the steel chain , the number of nodes of the steel chain calculating the initial steel chain node horizontal coordinate vector is:

[0028] wherein, is the initial horizontal coordinate of the th node of the steel chain, is the initial steel chain node horizontal coordinate vector, is the number of nodes of the steel chain, is the last node coordinate of the steel chain, is the first node coordinate of the steel chain.

[0029] In step 1, based on the coordinates of the first node of the steel chain Coordinates of the end node of the steel chain Straight-line distance from start to finish Number of steel chain nodes Calculate the initial ordinate vector of the steel chain node for:

[0030] in, For the first Initial ordinates of each steel chain node To initialize the y-coordinate vector of the steel chain nodes, For the number of steel chain nodes, The straight-line distance between the start and end points. The spacing between steel chain nodes. , for The first vector Each element.

[0031] Define and initialize the x-coordinate velocity vector of the steel chain node. for:

[0032] in, To initialize the x-coordinate velocity vector of the steel chain node, its vector length is... All elements are 0.

[0033] Step 1 defines the initialization of the longitudinal velocity vector of the steel chain node. for:

[0034] in To initialize the velocity vector of the steel chain node's ordinate, its length is... All elements are 0.

[0035] Step 2. Based on the equivalent physical model, perform force analysis on several nodes in the steel chain according to the gravitational effect, and iteratively update the acceleration, velocity and uncorrected node position of the nodes by setting the simulation step size; Step 2.1: Based on the coordinates of the gravitational particle , No. The x-coordinate vector of the steel chain node in the second outermost iteration , No. The ordinate vector of the steel chain node in the second outermost iteration Calculate the first The distance vector from the steel chain node to the gravitational particle in the second outermost iteration for:

[0036] where, is the distance vector from the steel chain node to the gravitation mass in the th outermost iteration, is the th element of the distance vector from the steel chain node to the gravitation mass in the th outermost iteration, is the number of steel chain nodes, is the longitudinal coordinate vector of the steel chain nodes in the th outermost iteration, is the lateral coordinate vector of the steel chain nodes in the th outermost iteration, is the gravitation mass coordinate.

[0037] Step 2.2: Calculate the lateral coordinate acceleration vector of the steel chain nodes in the th outermost iteration from the gravitation mass coordinate , the lateral coordinate vector of the steel chain nodes in the th outermost iteration, , the distance vector from the steel chain nodes to the gravitation mass in the th outermost iteration, is:

[0038] where, is the lateral coordinate acceleration vector of the steel chain nodes in the th outermost iteration, is the th element of the lateral coordinate acceleration vector of the steel chain nodes in the th outermost iteration, is the number of steel chain nodes, is the distance vector from the steel chain nodes to the gravitation mass in the th outermost iteration, is the lateral coordinate vector of the steel chain nodes in the th outermost iteration, is the gravitation mass coordinate.

[0039] Calculate the longitudinal coordinate acceleration vector of the steel chain nodes in the th outermost iteration from the gravitation mass coordinate , the longitudinal coordinate vector of the steel chain nodes in the th outermost iteration, , the distance vector from the steel chain nodes to the gravitation mass in the th outermost iteration, is:​ is:

[0040] wherein is the th outermost iteration steel chain node longitudinal coordinate acceleration vector, is the th element of the th outermost iteration steel chain node longitudinal coordinate acceleration vector, is the number of steel chain nodes, is the th outermost iteration steel chain node distance vector to the gravitating mass, is the th outermost iteration steel chain node longitudinal coordinate vector, is the gravitating mass coordinate.

[0041] Step 2.3: Calculate the th outermost iteration steel chain node transversal coordinate velocity vector , the th outermost iteration steel chain node transversal coordinate acceleration vector , and the simulation step size , from the th outermost iteration steel chain node transversal coordinate velocity vector is:

[0042] wherein is the th outermost iteration steel chain node transversal coordinate velocity vector, is the th element of the th outermost iteration steel chain node transversal coordinate velocity vector, is the number of steel chain nodes, is the th outermost iteration steel chain node transversal coordinate acceleration vector, is the simulation step size.

[0043] Calculate the th outermost iteration steel chain node longitudinal coordinate velocity vector , the th outermost iteration steel chain node longitudinal coordinate acceleration vector , and the simulation step size , from the th outermost iteration steel chain node longitudinal coordinate velocity vector is:

[0044] wherein is the steel chain node longitudinal coordinate velocity vector in the k-th outermost iteration, is the steel chain node longitudinal coordinate velocity vector in the k-th outermost iteration, is the k-th element of the steel chain node longitudinal coordinate velocity vector in the k-th outermost iteration, is the number of steel chain nodes, is the steel chain node longitudinal coordinate acceleration vector in the k-th outermost iteration, is the simulation step size. Step 2.4: Calculate the steel chain node transversal coordinate vector before the correction of the k-th outermost iteration and initialization of the constraint projection iteration from the steel chain node longitudinal coordinate vector in the k-th outermost iteration, the steel chain node transversal coordinate velocity vector

[0045] in the k-th outermost iteration, and the simulation step size as: wherein is the steel chain node transversal coordinate vector before the correction of the k-th outermost iteration and initialization of the constraint projection iteration, is the k-th element of the steel chain node transversal coordinate vector before the correction of the k-th outermost iteration and initialization of the constraint projection iteration, is the number of steel chain nodes, is the steel chain node transversal coordinate velocity vector in the k-th outermost iteration, is the simulation step size.

[0046] Calculate the steel chain node longitudinal coordinate vector in the k-th outermost iteration and initialization of the constraint projection iteration from the steel chain node longitudinal coordinate vector in the k-th outermost iteration, the steel chain node longitudinal coordinate velocity vector in the k-th outermost iteration, and the simulation step size as: wherein is the steel chain node longitudinal coordinate vector in the k-th outermost iteration and initialization of the constraint projection iteration, is the k-th element of the steel chain node longitudinal coordinate vector in the k-th outermost iteration and initialization of the constraint projection iteration,

[0047] is the number of steel chain nodes, is the steel chain node longitudinal coordinate acceleration vector in the k-th outermost iteration, is the simulation step size. wherein is the steel chain node longitudinal coordinate vector in the k-th outermost iteration and initialization of the constraint projection iteration, is the k-th element of the steel chain node longitudinal coordinate vector in the k-th outermost iteration and initialization of the constraint projection iteration, is the number of steel chain nodes, is the steel chain node longitudinal coordinate acceleration vector in the k-th outermost iteration,

[0048] is the simulation step size. is the steel chain node longitudinal coordinate vector in the k-th outermost iteration and initialization of the constraint projection iteration, ​​the steel chain node longitudinal coordinate vector of the second outermost iteration and the initialization constraint projection iteration, the first outermost iteration and the initialization constraint projection iteration, the first outermost iteration and the initialization constraint projection iteration, the first outermost iteration and the initialization constraint projection iteration, the number of steel chain nodes, the first outermost iteration and the initialization constraint projection iteration, the steel chain node longitudinal coordinate velocity vector in the second outermost iteration, the simulation step length. The number of constraint projection iterations in the initialization,

[0049] Step 3: using the iterative projection method, the uncorrected node position is gradually corrected to the projection corrected position which satisfies the rigid bar length constraint until it converges to the steady state shape; as shown in Figure 3 Step 3.1: according to the first node coordinate of the steel chain , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction

[0050]

[0051]

[0052] , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction , the first outermost iteration and the first constraint projection iteration before correction ​​The distance between the first node and the second node of the steel chain in the next constraint projection iteration. To correct the previous one The second outermost iteration and the... The first element of the longitudinal coordinate vector of the steel chain node in the second constraint projection iteration.

[0053] Step 3.2: According to the first The second outermost iteration and the... The x-coordinate distance from the first node to the second node of the steel chain in the next constraint projection iteration. , No. The second outermost iteration and the... The ordinate distance from the first node to the second node of the steel chain in the next constraint projection iteration. Calculate the first The second outermost iteration and the... The distance from the first node to the second node of the steel chain in the next constraint projection iteration According to the first The second outermost iteration and the... The distance from the first node to the second node of the steel chain in the next constraint projection iteration Number of steel chain nodes Steel chain node spacing Calculate the first The second outermost iteration and the... The distance adjustment parameter between the first node and the second node of the steel chain in the next constraint projection iteration. .

[0054]

[0055]

[0056] in, For the first The second outermost iteration and the... The distance from the first node to the second node of the steel chain in the next constraint projection iteration. For the first The second outermost iteration and the... The distance between the first node and the second node of the steel chain in the next constraint projection iteration. For the first The second outermost iteration and the... The horizontal coordinate distance between the first node and the second node of the steel chain in the next constraint projection iteration. For the first The second outermost iteration and the... The distance adjustment parameter from the first node to the second node of the steel chain in the next constraint projection iteration. This refers to the spacing between steel chain nodes.

[0057] Step 3.3: Calculate the first element of the steel chain node vertical coordinate vector for the previous outermost iteration and the previous constraint projection iteration. Step 3.4: Calculate the second element of the steel chain node vertical coordinate vector for the previous outermost iteration and the previous constraint projection iteration. Step 3.5: Calculate the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration. Step 3.6: Calculate the distance for the first node of the steel chain to the second node of the steel chain in the vertical coordinate for the previous outermost iteration and the previous constraint projection iteration. Step 3.7: Calculate the first element of the steel chain node vertical coordinate vector for the previous outermost iteration and the previous constraint projection iteration. Step 3.8: Calculate the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration. Step 3.9: Calculate the distance for the first node of the steel chain to the second node of the steel chain in the vertical coordinate for the previous outermost iteration and the previous constraint projection iteration. Step 3.10: Calculate the first element of the steel chain node vertical coordinate vector for the previous outermost iteration and the previous constraint projection iteration. Step 3.11: Calculate the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration. Step 3.12: Calculate the distance for the first node of the steel chain to the second node of the steel chain in the vertical coordinate for the previous outermost iteration and the previous constraint projection iteration. Step 3.13: Calculate the first element of the steel chain node vertical coordinate vector for the previous outermost iteration and the previous constraint projection iteration. Step 3.14: Calculate the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration. Step 3.15: Calculate the distance for the first node of the steel chain to the second node of the steel chain in the vertical coordinate for the previous outermost iteration and the previous constraint projection iteration. Step 3.16: Calculate the steel chain node vertical coordinate vector for the previous outermost iteration and the previous constraint projection iteration. Step 3.17: Calculate the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration. Step 3.18: Calculate the distance for the first node of the steel chain to the second node of the steel chain in the vertical coordinate for the previous outermost iteration and the previous constraint projection iteration. Step 3.19: Calculate the first element of the steel chain node vertical coordinate vector for the previous outermost iteration and the previous constraint projection iteration. Step 3.20: Calculate the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration. Step 3.21: Calculate the distance for the first node of the steel chain to the second node of the steel chain in the vertical coordinate for the previous outermost iteration and the previous constraint projection iteration. Step 3.22: Calculate the first element of the steel chain node vertical coordinate vector for the previous outermost iteration and the previous constraint projection iteration. Step 3.23: Calculate the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration. Step 3.24: Calculate the distance for the first node of the steel chain to the second node of the steel chain in the vertical coordinate for the previous outermost iteration and the previous constraint projection iteration. Step 3.25: Calculate the first element of the steel chain node vertical coordinate vector for the previous outermost iteration and the previous constraint projection iteration. Step 3.26: Initialize the number of steel chain nodes. .

[0058]

[0059]

[0060] wherein, is the first element of the steel chain node horizontal coordinate vector for the previous outermost iteration and the previous constraint projection iteration, is the horizontal coordinate distance for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration, is the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain. is the first element of the steel chain node horizontal coordinate vector for the previous outermost iteration and the previous constraint projection iteration, is the horizontal coordinate distance for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration, is the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain. is the first element of the steel chain node horizontal coordinate vector for the previous outermost iteration and the previous constraint projection iteration, is the horizontal coordinate distance for the first node of the steel chain to the second node of the steel chain for the previous outermost iteration and the previous constraint projection iteration, is the distance adjustment parameter for the first node of the steel chain to the second node of the steel chain. is the first element of the steel chain node horizontal coordinate vector for the previous outermost iteration and the previous constraint projection iteration,​ the first element of the steel chain node longitudinal coordinate vector of the the first element of the steel chain node longitudinal coordinate vector of the the first element of the steel chain node longitudinal coordinate vector of the the first element of the steel chain node longitudinal coordinate vector of the the first element of the steel chain node longitudinal coordinate vector of the

[0061] Step 3.4: Calculate the steel chain node transverse coordinate distance vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the the first element of the steel chain node transverse coordinate vector of the .

[0062]

[0063]

[0064] wherein, the first element of the steel chain node transverse coordinate distance vector of the the first element of the steel chain node transverse coordinate distance vector of the the first element of the steel chain node transverse coordinate distance vector of the the first element of the steel chain node transverse coordinate distance vector of the the first element of the steel chain node transverse coordinate distance vector of the the first element of the steel chain node transverse coordinate distance vector of the the first element of the steel chain node transverse coordinate distance vector of the the first element of the steel chain node transverse coordinate distance vector of the the first element of the steel chain node transverse coordinate distance vector of the the number of steel chain nodes, the steel chain node transverse coordinate vector of the the steel chain node transverse coordinate vector of the the steel chain node transverse coordinate vector of the the first element of the steel chain node longitudinal coordinate distance vector of the the first element of the steel chain node longitudinal coordinate distance vector of the the first element of the steel chain node longitudinal coordinate distance vector of the the first element of the steel chain node longitudinal coordinate distance vector of the the first element of the steel chain node longitudinal coordinate distance vector of the the first element of the steel chain node longitudinal coordinate distance vector of the the first element of the steel chain node longitudinal coordinate distance vector of the the steel chain node longitudinal coordinate distance vector, the steel chain node longitudinal coordinate distance vector, the number of steel chain nodes, the steel chain node longitudinal coordinate distance vector, the steel chain node longitudinal coordinate distance vector, the steel chain node longitudinal coordinate distance vector.

[0065] Step 3.5: calculating the steel chain node distance vector the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector the steel chain node distance vector, the steel chain node distance vector the steel chain node distance vector the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector, the number of steel chain nodes, the steel chain node distance, the steel chain node distance adjustment parameter vector the steel chain node distance adjustment parameter vector the steel chain node distance adjustment parameter vector the steel chain node distance adjustment parameter vector .

[0066]

[0067]

[0068] wherein, the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector, the steel chain node distance vector, the number of steel chain nodes, the steel chain node longitudinal coordinate distance vector, the steel chain node longitudinal coordinate distance vector, the steel chain node longitudinal coordinate distance vector, the steel chain node longitudinal coordinate distance vector, the steel chain node longitudinal coordinate distance vector, the outermost iteration and the steel chain node horizontal coordinate distance vector for the outermost iteration and the outermost iteration and the adjustment parameter vector for the outermost iteration and the outermost iteration and the outermost iteration and the adjustment parameter vector for the element of the adjustment parameter vector for the outermost iteration and the

[0069] Step 3.6: Calculate the outermost iteration and the horizontal coordinate vector for the outermost iteration and the outermost iteration and the adjustment parameter vector for the outermost iteration and the outermost iteration and the horizontal coordinate distance vector for the outermost iteration and the element of the horizontal coordinate vector for the outermost iteration and the outermost iteration and the vertical coordinate vector for the element of the vertical coordinate vector for the outermost iteration and the vertical coordinate vector for the outermost iteration and the adjustment parameter vector for the outermost iteration and the vertical coordinate distance vector for the element of the vertical coordinate vector for the outermost iteration and the outermost iteration and the vertical coordinate distance vector for the element of the vertical coordinate distance vector for the outermost iteration and the outermost iteration and the element of the vertical coordinate vector for the outermost iteration and the .

[0070]

[0071]

[0072] wherein, is the jth element of the steel chain node horizontal coordinate vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration, is the jth element of the steel chain node horizontal coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth element of the steel chain node horizontal coordinate vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration, is the jth element of the steel chain node horizontal coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth steel chain node distance adjustment parameter vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration, is the jth steel chain node distance adjustment parameter vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth steel chain node horizontal coordinate distance vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration, is the jth steel chain node horizontal coordinate distance vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration, is the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration. is the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth element of the steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration, is the jth element of the steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth element of the steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration, is the jth element of the steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth steel chain node vertical coordinate distance vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration, is the jth steel chain node vertical coordinate distance vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration. is the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, is the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration. is the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration.

[0073] Step 3.7: Calculate the jth element of the steel chain node horizontal coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration from the steel chain node horizontal coordinate vector for the (k - 1)th outermost iteration and the (j - 1)th constraint projection iteration, the jth steel chain node distance adjustment parameter vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node horizontal coordinate distance vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node distance adjustment parameter vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node horizontal coordinate distance vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration. the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration. the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration. the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration, the jth steel chain node vertical coordinate vector for the (k - 1)th outermost iteration and the jth constraint projection iteration. the j-th steel chain node distance adjustment parameter vector , the -th outermost iteration and the -th constraint projection iteration the j-th steel chain node longitudinal coordinate distance vector the j-th element of the steel chain node longitudinal coordinate vector of the -th outermost iteration and the -th constraint projection iteration before correction .

[0074]

[0075]

[0076] wherein, the j-th element of the steel chain node transversal coordinate vector of the -th outermost iteration and the -th constraint projection iteration before correction is the number of steel chain nodes, the j-th steel chain node transversal coordinate distance vector of the -th outermost iteration and the -th constraint projection iteration the j-th steel chain node distance adjustment parameter vector of the -th outermost iteration and the -th constraint projection iteration the steel chain node transversal coordinate vector of the -th outermost iteration and the -th constraint projection iteration before correction the j-th element of the steel chain node longitudinal coordinate vector of the -th outermost iteration and the -th constraint projection iteration before correction the j-th steel chain node longitudinal coordinate distance vector of the -th outermost iteration and the -th constraint projection iteration the steel chain node longitudinal coordinate vector of the -th outermost iteration and the -th constraint projection iteration before correction

[0077] Step 3.8: replace with , and determine whether is true. If ​​​​​​If yes, return to step 3.4; otherwise, proceed to step 3.9.

[0078] Step 3.9: Based on the coordinates of the end node of the steel chain Before the revision The second outermost iteration and the... The x-coordinate vector of the steel chain node in the second constraint projection iteration Calculate the first The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first The horizontal coordinate distance of each steel chain node Based on the coordinates of the first node of the steel chain Before the revision The second outermost iteration and the... The ordinate vector of the steel chain node in the second constraint projection iteration Number of steel chain nodes Calculate the spacing between steel chain nodes Calculate the first The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first Distance of the vertical coordinate of each steel chain node .

[0079]

[0080]

[0081] in, For the first The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first The x-coordinate distance of each steel chain node To correct the previous one The second outermost iteration and the... The x-coordinate vector of the steel chain node in the second constraint projection iteration These are the coordinates of the end node of the steel chain. For the first The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first Distance of the vertical coordinate of each steel chain node To correct the previous one The second outermost iteration and the... The vertical coordinate vector of the steel chain node in the second constraint projection iteration.

[0082] Step 3.10: According to the first the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration .

[0083]

[0084]

[0085] wherein, the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the first outermost iteration and the first constraint projection iteration the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node.

[0086] Step 3.11: Calculate the jth element of the steel chain node horizontal coordinate vector of the (i-1)th outer iteration and the (j-1)th constraint projection iteration before correction. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node.

[0087] the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node.

[0088] the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node.

[0089] wherein, the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. the distance adjustment parameter of the jth steel chain node to the kth steel chain node. One element, For the first The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first The x-coordinate distance of each steel chain node For the first The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first Distance between steel chain nodes To correct the previous one The second outermost iteration and the... The horizontal coordinate vector of the steel chain node in the next constraint projection iteration. To correct the previous one The second outermost iteration and the... The first constraint projection iteration of the steel chain node ordinate vector One element, For the first The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first Distance of the vertical coordinate of each steel chain node For the first The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first The distance adjustment parameters for each steel chain node. To correct the previous one The second outermost iteration and the... The horizontal coordinate vector of the steel chain node in the next constraint projection iteration.

[0090] Step 3.12: Use replace ,judge Is it true? If so... If yes, return to step 3.1; otherwise, proceed to step 4.

[0091] Step 4: Output the converged projection correction position as the steady-state solution of the artificial potential field.

[0092] Step 4.1: Based on the original version... The second outermost iteration and the... The x-coordinate vector of the steel chain node in the second constraint projection iteration Definition of the first The x-coordinate vector of the steel chain node in the second outermost iteration According to the original version The second outermost iteration and the... Steel chain node longitudinal coordinate vector of the second constraint projection iteration Steel chain node longitudinal coordinate vector of the first outermost iteration Steel chain node longitudinal coordinate vector of the second outermost iteration .

[0093]

[0094]

[0095] Steel chain node longitudinal coordinate vector of the first outermost iteration Steel chain node longitudinal coordinate vector of the second outermost iteration Steel chain node longitudinal coordinate vector of the first outermost iteration Steel chain node longitudinal coordinate vector of the second outermost iteration Steel chain node longitudinal coordinate vector of the first outermost iteration Steel chain node longitudinal coordinate vector of the second outermost iteration Steel chain node longitudinal coordinate vector of the first outermost iteration Steel chain node longitudinal coordinate vector of the second outermost iteration Steel chain node longitudinal coordinate vector of the first outermost iteration Steel chain node longitudinal coordinate vector of the second outermost iteration Steel chain node longitudinal coordinate vector of the first outermost iteration Steel chain node longitudinal coordinate vector of the second outermost iteration

[0096] Step 4.2: replace with, and determine whether is established. If, return to step 2.1; otherwise, output the result, as shown in. Figure 4

[0097] It should be noted that, according to the needs of implementation, each step / component described in the present application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into a new step / component, to achieve the purpose of the present application.

[0098] Although the present application uses terms such as artificial potential field, gravity node, steel chain node, and rigid rod more frequently, the possibility of using other terms is not excluded. The use of these terms is merely for the convenience of describing and explaining the essence of the present application; any kind of additional limitation by interpreting them is contrary to the spirit of the present application.

[0099] Embodiment 2 The present embodiment provides an artificial potential field oriented steady-state fast construction system, comprising: An equivalent physical model construction module: which is used to equivalently convert the artificial potential field into the potential field generated by a single gravity particle, model the target trajectory as a steel chain system composed of a plurality of nodes and rigid rods with fixed length, establish an equivalent physical model and perform an initialization operation on the equivalent physical model; ​​​​An iterative calculation module is configured to perform force analysis on the nodes in the steel chain according to gravitational force based on an equivalent physical model, and iteratively update the acceleration, velocity and uncorrected node position of the nodes by setting a simulation step; A constraint projection correction module is configured to correct the uncorrected node position to a projection correction position meeting the length constraint of the rigid rod by using an iterative projection method until a stable state shape is reached, and a result output module is configured to output the projection correction position after convergence as a stable state solution of the artificial potential field.

[0100] It should be understood that parts not elaborated in the specification are all prior art.

[0101] It should be understood that the above description of the preferred embodiments is detailed and should not be considered as limiting the scope of patent protection of the present application. It is not necessary or possible to enumerate all the embodiments. Those skilled in the art can make substitutions or modifications without departing from the scope of the claims, which fall within the scope of the present application. The scope of patent protection of the present application shall be subject to the appended claims.

Claims

1. A method for constructing a steady-state of an artificial potential field, characterized in that, The method comprises the following steps: Step 1: equivalent the artificial potential field to the potential field generated by a single gravitational point, and model the target trajectory as a steel chain system composed of a plurality of nodes and rigid rods with fixed lengths, establish an equivalent physical model and perform an initialization operation on the equivalent physical model; Step 2: based on the equivalent physical model, perform stress analysis on the plurality of nodes in the steel chain according to the gravitational action, and iteratively update the acceleration, velocity and uncorrected node position of the nodes by setting a simulation step; Step 3: using an iterative projection method, gradually correct the uncorrected node position to a projection corrected position meeting the rigid rod length constraint until converging to a steady state shape; Step 4: output the converged projection corrected position as the steady state solution of the artificial potential field.

2. The method of claim 1, wherein, The equivalent physical model in the step 1 comprises: An artificial potential field and components thereof; Physical components; The artificial potential field and components thereof comprise a single point and a potential field formed by the gravitational force of the point itself; the physical components comprise a plurality of nodes and rigid rods connecting the nodes.

3. The method of claim 2, wherein, The nodes have mass and ignore their volume; the rigid rods have fixed lengths and no mass; each two nodes are connected by a rigid rod, forming a steel chain, and the rigid rod can rotate around the node; the first node and the last node of the steel chain are fixed.

4. The method of claim 2, wherein, The initialization operation in the step 1 comprises: Setting a simulation step and a simulation iteration time; Calculating the maximum outer iteration number based on the simulation step and the simulation iteration time; Calculating the straight line distance based on the coordinates of the first node and the last node of the steel chain; Linearly initializing the node coordinate vector of the steel chain based on the coordinates of the first node and the last node, the number of nodes and the straight line distance; Initializing the velocity vector of each node as a zero vector.

5. The method of claim 4, wherein, The step 2 comprises: Calculating the distance vector of each node to the gravitational point in the last iteration number; Calculating the acceleration vector of each node of the steel chain in the current iteration number based on the distance vector of each node of the steel chain to the gravitational point in the last iteration number, the coordinates of the gravitational point and the node coordinate vector of the steel chain in the last iteration number; Calculating the velocity vector of each node of the steel chain in the current iteration number based on the acceleration vector of each node in the current iteration number, the velocity vector of each node of the steel chain in the last iteration number and the simulation step; Updating the node coordinate vector of the steel chain in the current iteration number for the outermost iteration and the constraint projection iteration based on the velocity vector of each node of the steel chain in the current iteration number and the simulation step.

6. The method of claim 5, wherein, The iterative projection method in the step 3 comprises a plurality of loops: Inner iteration loop: constraint projection iteration; Outer iteration loop: traversing each node of the steel chain, and gradually correcting the uncorrected node position to a projection corrected position meeting the interval constraint.

7. The method of claim 6, wherein, The step 3 of gradually correcting the uncorrected node position to a projection corrected position meeting the rigid rod length constraint comprises three types of processing: First node correction: correcting the second node position based on the coordinate of the first node of the steel chain; Intermediate node correction: correcting the intermediate node position based on the interval constraint between adjacent nodes; Last node correction: correcting the second last node position based on the coordinate of the last node of the steel chain.

8. The method of claim 5, wherein, The step 3 comprises: calculating the distance adjustment parameter of the first node to the second node of the steel chain in the outermost iteration and the last constraint projection iteration based on the distance of the first node to the second node of the steel chain in the outermost iteration and the last constraint projection iteration, and the distance between the nodes of the steel chain in the current iteration, and calculating the first element of the node coordinate vector of the steel chain in the outermost iteration and the last constraint projection iteration in the current iteration; repeating the above steps to sequentially calculate the intermediate elements of the node coordinate vector of the steel chain in the outermost iteration and the last constraint projection iteration in the current iteration; calculating the last element of the node coordinate vector of the steel chain in the outermost iteration and the last constraint projection iteration in the current iteration based on the coordinates of the last node of the steel chain. The constraint projection iteration includes a termination condition:

9. The method of claim 6, wherein, the maximum number of constraint projection iterations is reached, or the error of the distance between the nodes is less than a set threshold. It includes:

10. A steady-state fast construction system for artificial potential fields, characterized in that, an equivalent physical model construction module for equivalent to the artificial potential field as the potential field generated by a single gravitational point, and modeling the target trajectory as a steel chain system composed of a number of nodes and rigid rods of fixed length, establishing an equivalent physical model and initializing the equivalent physical model; an iterative calculation module for performing force analysis on the nodes in the steel chain based on the equivalent physical model according to the gravitational effect, and iteratively updating the acceleration, velocity and uncorrected node position of the nodes by setting a simulation step; a constraint projection correction module for using an iterative projection method to gradually correct the uncorrected node position to a projection corrected position that satisfies the length constraint of the rigid rod, until converging to a steady state shape; and a result output module for outputting the converged projection corrected position as the steady state solution of the artificial potential field; The artificial potential field-oriented steady state fast construction system is used to perform the steps of the artificial potential field-oriented steady state fast construction method of any one of claims 1-9.

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