A steady-state fast construction method and system for artificial potential field

Abstract

The application provides a steady-state fast construction method and system for an artificial potential field, comprising the following steps: step 1: equivalent the artificial potential field to the potential field generated by a single gravitational point, model a 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, speed and uncorrected node position of the nodes by setting a simulation step; step 3: the uncorrected node position is gradually corrected to a projection corrected position meeting the length constraint of the rigid rod by using an iterative projection method until converging to a steady-state shape; and step 4: output the converged projection corrected position as a steady-state solution of the artificial potential field. The application realizes significant improvement of the steady-state construction speed, and simultaneously considers the low complexity and high feasibility of the steady-state state construction of the physical components.

Description

Technical Field

[0001] This invention belongs to the field of equivalent artificial potential energy field technology, and particularly relates to a method and system for the rapid steady-state construction of artificial potential energy fields. Background Technology

[0002] In recent years, with the development of artificial intelligence, automatic control, and intelligent systems, an increasing number of engineering problems have been abstracted and transformed into physical modeling problems in order to obtain efficient solution methods using classical mechanics principles. Among these, the mechanical equivalence principle has become an effective modeling tool, widely applied in scenarios such as UAV trajectory design, path planning, and robot navigation. This method equates the complex path planning task to the steady-state shape problem of a rope system under an artificial potential energy field, and then uses a mechanical model to solve for the force equilibrium state of the rope, mapping it to the trajectory of the target system. Through this equivalent model, the computational complexity of directly solving for the path in a high-dimensional nonlinear space can be avoided to some extent.

[0003] However, in practical applications, problems based on artificial potential energy fields often exhibit high non-convexity and complex coupling relationships among multiple variables, making the solution for the steady-state shape of a rope essentially a highly nonlinear and strongly non-convex optimization problem. Traditional convex optimization methods, gradient descent methods, or numerical iteration methods often face problems such as slow convergence speed and susceptibility to local optima in these problems, making it difficult to meet the dual requirements of real-time performance and reliability in engineering. Therefore, how to construct a fast-converging, simple, and easy-to-implement steady-state solution scheme for ropes in complex artificial potential energy fields has become one of the hot research and application issues in this field. Breakthroughs in related technologies will provide more efficient and robust support for trajectory planning of intelligent systems in complex environments. Summary of the Invention

[0004] To address the problems of high model complexity, slow steady-state simulation speed, and difficulty in meeting engineering deployment requirements of existing steady-state construction methods, this invention proposes a rapid steady-state construction method and scheme for artificial potential energy fields, which can significantly improve the steady-state construction speed while taking into account the low complexity and high feasibility of constructing the steady-state state of physical components.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] A method for rapid steady-state construction of artificial potential energy fields 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.

[0007] 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;

[0008] Step 3: Using an iterative projection method, the uncorrected node positions are gradually corrected to projected corrected positions that satisfy the rigid rod length constraint until they converge to a steady-state shape;

[0009] Step 4: Output the converged projection correction position as the steady-state solution of the artificial potential field.

[0010] Furthermore, the equivalent physical model in step 1 includes:

[0011] Artificial potential energy fields and their components;

[0012] Physical components;

[0013] The artificial potential energy field and its components include a single particle and the potential energy field formed by the particle's own gravity; the physical components include several nodes and rigid rods connecting the nodes.

[0014] Furthermore, the nodes have mass, but their volume is negligible; the rigid rods are of fixed length and have no mass; a rigid rod is connected between every two nodes to form a steel chain, and the rigid rods can rotate around the nodes; the first and last nodes of the steel chain are fixed.

[0015] Furthermore, the initialization operation in step 1 includes:

[0016] Set the simulation step size and simulation iteration time;

[0017] Calculate the maximum number of outer layer iterations based on the simulation step size and simulation iteration time;

[0018] Calculate the straight-line distance based on the coordinates of the first and last nodes of the steel chain;

[0019] Based on the coordinates of the first and last nodes, the number of nodes, and the straight-line distance, the steel chain node coordinate vector is linearly initialized;

[0020] Initialize the velocity vectors of each node to zero.

[0021] Further, step 2 includes:

[0022] Calculate the distance vector from each node to the gravitational particle in the previous iteration;

[0023] Calculate the acceleration vector of each node of the steel chain in the current iteration based on the distance vector from each node of the steel chain to the gravitational particle, the coordinates of the gravitational particle, and the coordinate vector of each node of the steel chain in the previous iteration.

[0024] Calculate the velocity vector of each node in the current iteration based on the acceleration vector of each node in the current iteration, the velocity vector of each node in the previous iteration, and the simulation step size.

[0025] Update the coordinate vectors of the steel chain nodes for the outermost iteration and initial constraint projection iteration at the current iteration number based on the velocity vectors of each node and the simulation step size.

[0026] Furthermore, the iterative projection method in step 3 includes multiple loops:

[0027] Inner iterative loop: constrained projection iteration;

[0028] Outer iterative loop: Traverse each node of the steel chain and gradually correct the uncorrected node positions to the projected corrected positions according to the spacing constraints.

[0029] Furthermore, step 3, which involves progressively correcting the uncorrected node positions to projected corrected positions that satisfy the rigid rod length constraint, includes three types of processing:

[0030] First node correction: Correct the position of the second node based on the coordinates of the first node of the steel chain;

[0031] Intermediate node correction: Correct the position of intermediate nodes based on the distance constraint between adjacent nodes;

[0032] End node correction: Correct the position of the second to last node based on the coordinates of the last node of the steel chain.

[0033] Further, step 3 includes:

[0034] Based on the coordinates of the first node of the steel chain, the distance from the first node to the second node of the steel chain is calculated using the coordinate vectors of the outermost iteration and the previous constraint projection iteration under the current iteration number.

[0035] Based on the distance from the first node to the second node of the steel chain in the outermost iteration and the previous constraint projection iteration under the current iteration number, and the spacing between steel chain nodes, calculate the distance adjustment parameters from the first node to the second node of the steel chain in the outermost iteration and the previous constraint projection iteration under the current iteration number; and calculate and correct the first element of the coordinate vector of the steel chain node in the outermost iteration and the current constraint projection iteration under the current iteration number.

[0036] Repeat the above steps to calculate the intermediate elements of the steel chain node coordinate vectors of the outermost iteration and the current constraint projection iteration in turn;

[0037] Based on the coordinates of the last node of the steel chain, calculate the last element of the steel chain node coordinate vector for the outermost iteration and the current constraint projection iteration under the corrected current iteration number.

[0038] Furthermore, the constraint projection iteration includes a termination condition:

[0039] The maximum number of constraint projection iterations is reached, or

[0040] The node spacing error is less than the set threshold.

[0041] On the other hand, the present invention also provides a steady-state rapid construction system for artificial potential energy fields, comprising:

[0042] Equivalent physical model construction module: It is used to convert the artificial potential energy field into the potential energy field generated by a single gravitational particle, and to model the target trajectory as a steel chain system composed of several nodes and rigid rods of fixed length, to establish the equivalent physical model and to initialize the equivalent physical model;

[0043] Iterative calculation module; it is used to perform force analysis on several nodes in a steel chain based on an equivalent physical model and according to the gravitational effect, and iteratively update the acceleration, velocity and uncorrected node position of the nodes by setting the simulation step size;

[0044] Constraint Projection Correction Module: It is used to gradually correct the uncorrected node positions to the projected corrected positions that satisfy the rigid rod length constraints using an iterative projection method until it converges to a steady-state shape; Result Output Module: It is used to output the converged projected corrected positions as the steady-state solution of the artificial potential energy field.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] This invention addresses the steady-state steel chain shape problem under an artificial potential energy field induced by a gravitational particle, and designs a rapid steady-state construction method. In this method, an equivalent artificial potential energy field induced by a single gravitational particle in the region is established, and the force, acceleration, velocity, and initial position of each steel chain node are calculated iteratively during the iteration process. Subsequently, a node adjustment mechanism with constant spacing constraints is designed, and an iterative constraint projection method is used to progressively correct the positions of the steel chain nodes until convergence, outputting the final steel chain shape that satisfies the system constraints. Compared with existing methods based on reinforcement learning or complex nonlinear optimization models, this invention has low algorithm complexity, fast steady-state construction speed, abandons high-complexity models, and is easy to implement online or embedded deployment; it has strong physical interpretability and high stability, which helps to understand and analyze the motion behavior of physical components; it satisfies various engineering constraints and can flexibly introduce various practical limitations such as velocity, time, steel chain length, and node spacing. In summary, the steel chain design scheme proposed in this invention establishes an effective bridge between theoretical modeling and engineering applications, providing a practical technical route for low-complexity, high-efficiency steady-state construction design. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0048] Figure 1 This is a simplified flowchart of the algorithm in an embodiment of the present invention;

[0049] Figure 2 This is an example diagram showing the distribution of steel chain nodes, start point, and end point according to an embodiment of the present invention;

[0050] Figure 3 This is a simplified flowchart of the algorithm for step 3 in this embodiment of the invention;

[0051] Figure 4 This is a diagram illustrating the steady-state construction results of an embodiment of the present invention. Detailed Implementation

[0052] 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.

[0053] Example 1

[0054] The invention will now be further described with reference to the accompanying drawings.

[0055] 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.

[0056] like Figure 2 As shown, the equivalent physical model in step 1 includes:

[0057] Artificial potential energy fields and their components;

[0058] Physical components;

[0059] 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.

[0060] 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 .

[0061] The specific steps are as follows:

[0062] 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 Coordinates of the end node of the steel chain Straight-line distance from start to finish Number of steel chain nodes Calculate the initial x-coordinate vector of the steel chain node and initialize the ordinate vector of the steel chain node Define and initialize the x-coordinate velocity vector of the steel chain nodes. and initialize the longitudinal velocity vector of the steel chain node Initialize the outermost frame iteration count. .

[0063] Step 1, based on simulation step size Simulation iteration time Calculate the maximum number of iterations for the outermost frame. for:

[0064]

[0065] in, The maximum number of iterations for the outermost frame. For simulation iteration time, For simulating step size, This is for rounding operations.

[0066] Step 1 is 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 for:

[0067]

[0068] in, The straight-line distance between the start and end points. The coordinates of the first node of the steel chain. These are the coordinates of the end node of the steel chain.

[0069] In step 1, based on the coordinates of the first node of the steel chain Coordinates of the end node of the steel chain Number of steel chain nodes Calculate the initial x-coordinate vector of the steel chain node for:

[0070]

[0071] in, For the first Initial x-coordinates of each steel chain node To initialize the x-coordinate vector of the steel chain nodes, The number of steel chain nodes. The coordinates of the end node of the steel chain. These are the coordinates of the first node of the steel chain.

[0072] 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:

[0073]

[0074] 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.

[0075] Define and initialize the x-coordinate velocity vector of the steel chain node. for:

[0076]

[0077] in, To initialize the x-coordinate velocity vector of the steel chain node, its vector length is... All elements are 0.

[0078] Step 1 defines the initialization of the longitudinal velocity vector of the steel chain node. for:

[0079]

[0080] in To initialize the velocity vector of the steel chain node's ordinate, its length is... All elements are 0.

[0081] 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;

[0082] 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:

[0083]

[0084] in, For the first The distance vector from the steel chain node to the gravitational mass in the second outermost iteration. For the first The distance vector from the steel chain node to the gravitational particle in the second outermost iteration is... One element, The number of steel chain nodes. For the first The ordinate vector of the steel chain node in the second outermost iteration For the first The x-coordinate vector of the steel chain node in the second outermost iteration These are the coordinates of the gravitational particle.

[0085] Step 2.2: 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 distance vector from the steel chain node to the gravitational particle in the second outermost iteration Calculate the first The x-coordinate acceleration vector of the steel chain node in the second outermost iteration for:

[0086]

[0087] in, For the first The x-coordinate acceleration vector of the steel chain node in the second outermost iteration For the first The outermost iteration of the steel chain node's x-coordinate acceleration vector... One element, The number of steel chain nodes. For the first The distance vector from the steel chain node to the gravitational mass in the second outermost iteration. For the first The x-coordinate vector of the steel chain node in the second outermost iteration These are the coordinates of the gravitational particle.

[0088] Based on the coordinates of the gravitational particle , No. The ordinate vector of the steel chain node in the second outermost iteration , No. The distance vector from the steel chain node to the gravitational particle in the second outermost iteration Calculate the first The acceleration vector of the ordinate of the steel chain node in the second outermost iteration for:

[0089]

[0090] in, For the first The acceleration vector of the ordinate of the steel chain node in the second outermost iteration For the first The acceleration vector of the ordinate of the steel chain node in the second outermost iteration. One element, The number of steel chain nodes. For the first The distance vector from the steel chain node to the gravitational mass in the second outermost iteration. For the first The ordinate vector of the steel chain node in the second outermost iteration These are the coordinates of the gravitational particle.

[0091] Step 2.3: According to the first The x-coordinate velocity vector of the steel chain node in the second outermost iteration , No. The x-coordinate acceleration vector of the steel chain node in the second outermost iteration Simulation step size Calculate the first The x-coordinate velocity vector of the steel chain node in the second outermost iteration for:

[0092]

[0093] in, For the first The x-coordinate velocity vector of the steel chain node in the second outermost iteration For the first The x-coordinate velocity vector of the steel chain node in the second outermost iteration. One element, The number of steel chain nodes. For the first The x-coordinate acceleration vector of the steel chain node in the second outermost iteration This is the simulated step size.

[0094] According to the The velocity vector of the steel chain node in the second outermost iteration , No. The acceleration vector of the ordinate of the steel chain node in the second outermost iteration Simulation step size Calculate the first The velocity vector of the steel chain node in the second outermost iteration for:

[0095]

[0096] in, For the first The velocity vector of the steel chain node in the second outermost iteration. For the first The velocity vector of the ordinate of the steel chain node in the second outermost iteration. One element, The number of steel chain nodes. For the first The acceleration vector of the ordinate of the steel chain node in the second outermost iteration This is the simulated step size.

[0097] Step 2.4: According to the first The x-coordinate vector of the steel chain node in the second outermost iteration , No. The x-coordinate velocity vector of the steel chain node in the second outermost iteration Simulation step size Calculate the first before correction The x-coordinate vector of the steel chain node in the second outermost iteration and the initial constraint projection iteration. for:

[0098]

[0099] in, To correct the previous one The outermost iteration and the initial constraint projection iteration of the steel chain node x-coordinate vector. To correct the previous one The outermost iteration and initial constraint projection iteration of the steel chain node x-coordinate vector. One element, The number of steel chain nodes. For the first The x-coordinate velocity vector of the steel chain node in the second outermost iteration This is the simulated step size.

[0100] According to the The ordinate vector of the steel chain node in the second outermost iteration , No. The velocity vector of the steel chain node in the second outermost iteration Simulation step size Calculate the first before correction The ordinate vector of the steel chain node in the second outermost iteration and the initial constraint projection iteration for:

[0101]

[0102] in, To correct the previous one The ordinate vectors of the steel chain nodes in the second outermost iteration and the initial constraint projection iteration. To correct the previous one The outermost iteration and initial constraint projection iteration of the steel chain node ordinate vector. One element, The number of steel chain nodes. For the first The velocity vector of the steel chain node in the second outermost iteration. This is the simulation step size. Initialize the number of constraint projection iterations. .

[0103] Step 3: Using an iterative projection method, the uncorrected node positions are progressively corrected to projected corrected positions that satisfy the rigid rod length constraint until convergence to a steady-state shape; for example... Figure 3 As shown,

[0104] Step 3.1: Based on the coordinates of the first 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 x-coordinate distance from the first node to the second node of the steel chain in the next constraint projection iteration. 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 Calculate the first 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. .

[0105]

[0106]

[0107] in, For the first The second outermost iteration and the... The x-coordinate 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 x-coordinate vector of the steel chain node in the next constraint projection iteration. These are the coordinates of the first node of the steel chain. 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. 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.

[0108] 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. .

[0109]

[0110]

[0111] 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.

[0112] Step 3.3: 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 , No. 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. , No. 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. Calculate the first before correction The second outermost iteration and the... The first element of the x-coordinate vector of the steel chain node in the next constraint projection iteration. According to the original version The second outermost iteration and the... The ordinate vector of the steel chain node in the second constraint projection iteration , No. 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. , 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 before correction The second outermost iteration and the... The first element of the y-coordinate vector of the steel chain node in the next constraint projection iteration Initialize the number of steel chain nodes. .

[0113]

[0114]

[0115] in, To correct the previous one The second outermost iteration and the... The first element of the x-coordinate vector of the steel chain node in the next constraint projection iteration. For the first The second outermost iteration and the... The x-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 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 y-coordinate vector of the steel chain node in the next constraint projection iteration. For the first The second outermost iteration and the... The ordinate distance between the first node and the second node of the steel chain in the next constraint projection iteration.

[0116] Step 3.4: 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 Calculate the first The second outermost iteration and the... The first constraint projection iteration x-coordinate distance vector of each steel chain node According to the original version The second outermost iteration and the... The ordinate 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 Distance vector of the ordinate of each steel chain node .

[0117]

[0118]

[0119] in, For the first The second outermost iteration and the... The first constraint projection iteration x-coordinate distance vector of each steel chain node For the first The second outermost iteration and the... The first constraint projection iteration The x-coordinate distance vector of the nth steel chain node One element, The number of 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. For the first The second outermost iteration and the... The first constraint projection iteration Distance vector of the ordinate of each steel chain node For the first The second outermost iteration and the... The first constraint projection iteration The distance vector between the ordinate coordinates of the nth steel chain node and the first... One element, The number of steel chain nodes. 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.

[0120] Step 3.5: According to the first The second outermost iteration and the... The distance vector of the steel chain node's x-coordinate in the first constraint projection iteration, the first... The second outermost iteration and the... The first constraint projection iteration Distance vector of the ordinate of each steel chain node Calculate the first The second outermost iteration and the... The first constraint projection iteration Distance vector between steel chain nodes According to the first The second outermost iteration and the... The first constraint projection iteration Distance vector between steel chain nodes Number of steel chain nodes Steel chain node spacing Calculate the first The second outermost iteration and the... The first constraint projection iteration Steel chain node distance adjustment parameter vector .

[0121]

[0122]

[0123] in, For the first The second outermost iteration and the... The first constraint projection iteration Distance vector between steel chain nodes For the first The second outermost iteration and the... The first constraint projection iteration The distance vector between the nth steel chain node One element, The number of steel chain nodes. For the first The second outermost iteration and the... The first constraint projection iteration Distance vector of the ordinate of each steel chain node For the first The second outermost iteration and the... The distance vector of the horizontal coordinate of the chain node in the next constraint projection iteration. For the first The second outermost iteration and the... The first constraint projection iteration The distance adjustment parameter vector for each steel chain node For the first The second outermost iteration and the... The first constraint projection iteration The parameter vector for adjusting the distance between steel chain nodes. Each element.

[0124] Step 3.6: 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 , No. The second outermost iteration and the... The first constraint projection iteration Steel chain node distance adjustment parameter vector , No. The second outermost iteration and the... The first constraint projection iteration x-coordinate distance vector of each steel chain node Calculate the first before correction The second outermost iteration and the... The first iteration of the constraint projection iteration is the x-coordinate vector of the steel chain node. element According to the original version The second outermost iteration and the... The ordinate vector of the steel chain node in the second constraint projection iteration , No. The second outermost iteration and the... The first constraint projection iteration Steel chain node distance adjustment parameter vector , No. The second outermost iteration and the... The first constraint projection iteration Distance vector of the ordinate of each steel chain node Calculate the first before correction The second outermost iteration and the... The first constraint projection iteration of the steel chain node ordinate vector element .

[0125]

[0126]

[0127] in, To correct the previous one The second outermost iteration and the... The first iteration of the constraint projection iteration is the x-coordinate vector of the steel chain node. One element, For the first The second outermost iteration and the... The first constraint projection iteration The distance adjustment parameter vector 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. 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 Distance vector of the ordinate 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.

[0128] Step 3.7: 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 , No. The second outermost iteration and the... The first constraint projection iteration Steel chain node distance adjustment parameter vector , No. The second outermost iteration and the... The first constraint projection iteration x-coordinate distance vector of each steel chain node Calculate the first before correction The second outermost iteration and the... The first iteration of the constraint projection iteration is the x-coordinate vector of the steel chain node. element According to the original version The second outermost iteration and the... The ordinate vector of the steel chain node in the second constraint projection iteration , No. The second outermost iteration and the... The first constraint projection iteration Steel chain node distance adjustment parameter vector , No. The second outermost iteration and the... The first constraint projection iteration Distance vector of the ordinate of each steel chain node Calculate the first before correction The second outermost iteration and the... The first constraint projection iteration of the steel chain node ordinate vector element .

[0129]

[0130]

[0131] in, To correct the previous one The second outermost iteration and the... The first iteration of the constraint projection iteration is the x-coordinate vector of the steel chain node. One element, The number of steel chain nodes. For the first The second outermost iteration and the... The first constraint projection iteration x-coordinate distance vector of each steel chain node For the first The second outermost iteration and the... The first constraint projection iteration The distance adjustment parameter vector 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. 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 Distance vector of the ordinate of each steel chain node Before the revision The second outermost iteration and the... The vertical coordinate vector of the steel chain node in the second constraint projection iteration.

[0132] Step 3.8: Use replace ,judge Is it true? If so... If yes, return to step 3.4; otherwise, proceed to step 3.9.

[0133] 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 x-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 .

[0134]

[0135]

[0136] 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.

[0137] Step 3.10: According to 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 , No. 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 Calculate 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 According to 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 Number of steel chain nodes Steel chain node spacing Calculate the first The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first Distance adjustment parameters for each steel chain node .

[0138]

[0139]

[0140] in, 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 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 No. 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. 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.

[0141] Step 3.11: 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 , No. The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first Distance between steel chain nodes , No. 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 Calculate the first before correction The second outermost iteration and the... The first iteration of the constraint projection iteration is the x-coordinate vector of the steel chain node. element According to the original version The second outermost iteration and the... The x-coordinate vector of the steel chain node in the second constraint projection iteration , No. The second outermost iteration and the... The first constraint projection iteration The steel chain node to the first Distance adjustment parameters for each steel chain node , No. 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 Calculate the first before correction The second outermost iteration and the... The first constraint projection iteration of the steel chain node ordinate vector element .

[0142]

[0143]

[0144] in, To correct the previous one The second outermost iteration and the... The first iteration of the constraint projection iteration is the x-coordinate vector of the 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.

[0145] Step 3.12: Use replace ,judge Is it true? If so... If yes, return to step 3.1; otherwise, proceed to step 4.

[0146] Step 4: Output the converged projection correction position as the steady-state solution of the artificial potential field.

[0147] 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... The ordinate vector of the steel chain node in the second constraint projection iteration Definition of the first The ordinate vector of the steel chain node in the second outermost iteration .

[0148]

[0149]

[0150] in, For the first The x-coordinate vector of the steel chain node in the second outermost iteration 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. For the first The ordinate vector of the steel chain node in the second outermost iteration 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.

[0151] Step 4.2: Use replace ,judge Is it true? If so... Return to step 2.1; otherwise, output the result, such as... Figure 4 As shown.

[0152] It should be noted that, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0153] Although this invention uses terms such as artificial potential field, gravitational node, steel chain node, and rigid rod frequently, the possibility of using other terms is not excluded. These terms are used merely for the convenience of describing and explaining the essence of this invention; interpreting them as any additional limitation would contradict the spirit of this invention.

[0154] Example 2

[0155] This embodiment provides a steady-state rapid construction system for artificial potential energy fields, including:

[0156] Equivalent physical model construction module: It is used to convert the artificial potential energy field into the potential energy field generated by a single gravitational particle, and to model the target trajectory as a steel chain system composed of several nodes and rigid rods of fixed length, to establish the equivalent physical model and to initialize the equivalent physical model;

[0157] Iterative calculation module. It is used to perform force analysis on several nodes in a steel chain based on an equivalent physical model and according to the gravitational effect. The acceleration, velocity and uncorrected node position of the nodes are updated iteratively by setting the simulation step size.

[0158] Constraint Projection Correction Module: It is used to gradually correct the uncorrected node positions to the projected corrected positions that satisfy the rigid rod length constraints using an iterative projection method until it converges to a steady-state shape; Result Output Module: It is used to output the converged projected corrected positions as the steady-state solution of the artificial potential energy field.

[0159] It should be understood that any parts not described in detail in this specification belong to the prior art.

[0160] It should be understood that the above description of the preferred embodiments is quite detailed, but this should not be construed as limiting the scope of protection of this invention. It is neither necessary nor possible to exhaustively describe all possible implementations. Those skilled in the art, guided by this invention, can make substitutions or modifications without departing from the scope of the claims, all of which fall within the scope of protection of this invention. The scope of protection of this invention should be determined by 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, 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 coordinate 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 it converges 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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