Global path planning method for pure electric automatic driving commercial vehicle in logistics park scene

By preprocessing the high-definition map into a topological map and calculating energy consumption in combination with the vehicle dynamic model, the problem of ignoring road characteristics and vehicle characteristics in the existing technology is solved, and more efficient global path planning is achieved, reducing the energy consumption and transportation costs of commercial vehicles.

CN120027812APending Publication Date: 2025-05-23CHONGQING UNIV

Patent Information

Application Number
CN202510195331.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-02-21
Publication Date
2025-05-23

AI Technical Summary

Technical Problem

When conducting global path planning, the existing technology ignores the road characteristics and characteristics of pure electric autonomous driving commercial vehicles in the logistics park's characteristic scenarios, and fails to effectively consider the impact of factors such as load mass changes, energy recovery, road slope, curve curvature and other factors on energy consumption and efficiency.

Method used

By obtaining high-definition maps and preprocessing them into topological maps, the three-dimensional information, curvature and slope of the road are calculated, and energy consumption and recovery are calculated in combination with the vehicle's longitudinal dynamic model, and a comprehensive weighting algorithm is constructed to optimize path planning.

Benefits of technology

It realizes more accurate energy consumption calculation and efficiency evaluation, optimizes the global path planning of commercial vehicles in the logistics park, reduces energy consumption and transportation costs, and improves operating efficiency.

✦ Generated by Eureka AI based on patent content.

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Abstract

A global path planning method for a pure electric automatic driving commercial vehicle in a logistics park scene is characterized by comprising the following steps: step 1, acquiring a high-definition map of a target logistics park, and preprocessing the high-definition map into a topological map; 2, calculating the arc length, curvature and gradient between any two adjacent points on the topological map; 3, calculating energy consumption / recovery of the vehicle between two adjacent points on the topological map according to the vehicle longitudinal dynamic model; 4, calculating the running time of the vehicle between two adjacent points on the topological map; 5, constructing a comprehensive weight algorithm of energy consumption and efficiency between two adjacent points on the topological map; 6, calculating the weight of each path on the topological map according to a comprehensive weight algorithm; 7, constructing a cost function by adopting an A * algorithm; 8, constructing a heuristic function according to the characteristics of the topological map; and 9, searching an optimal global path of the vehicle by adopting an improved A * algorithm according to the position information of the starting point and the ending point of the vehicle on the topological map.
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Description

Technical Field

[0001] The present invention relates to the technical field of commercial vehicle path planning, and in particular to a global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario. Background Art

[0002] In recent years, the commercial application of autonomous driving technology has developed rapidly. In closed or semi-closed logistics parks, the autonomous driving of pure electric self-driving commercial vehicles will gradually replace traditional manual driving. As a means of production, the operating cost of commercial vehicles is a very critical indicator in the actual operation process. Autonomous driving technology consists of five major parts: perception, positioning, decision-making, planning and control. Among them, the global path planning in trajectory planning has a very important impact on the energy consumption and efficiency of commercial vehicles. The global path planning for pure electric self-driving commercial vehicles in specific scene areas of park logistics is significantly different from the global path planning of passenger cars:

[0003] (1) The load capacity of commercial vehicles varies widely, and different load capacities have different effects on energy consumption on different routes;

[0004] (2) A large amount of global path planning is usually performed on a two-dimensional grid map, ignoring the height information of the road. However, for pure electric self-driving commercial vehicles, the energy recovery function can be used to charge the battery and reduce energy consumption when driving downhill;

[0005] (3) The curvature characteristics of the road cannot be described on the raster map. Different road curvatures have an impact on the speed of commercial vehicles. Even when the road curvature is smaller than the minimum turning radius of the vehicle, the vehicle speed will be smaller and the required efficiency cost will be higher.

[0006] Disadvantages of existing technologies: Currently, map-based vehicle global path planning methods include A* and Dijkstra methods based on graph theory, which are generally performed on grid maps. When performing global path planning, they do not take into account the road characteristics of the logistics park scenes and the characteristics of pure electric self-driving commercial vehicles, and ignore the impact of factors such as road slope, curves, changes in cargo mass, energy recovery, and the vehicle's minimum turning radius on energy consumption and efficiency. Summary of the invention

[0007] The present invention provides a global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario, which improves operating efficiency and reduces energy consumption of point-to-point transportation of vehicles while realizing global path planning of the commercial vehicle.

[0008] To achieve the above-mentioned purpose, the present invention provides a global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario, which comprises the following steps:

[0009] Step 1: Obtain a high-definition map of the target logistics park, and preprocess the high-definition map into a topological map;

[0010] Step 2: According to the three-dimensional spatial coordinates of each point on the topological map, calculate the distance L, curvature k and slope θ between any two adjacent points on the topological map;

[0011] Step 3: Calculate the energy consumption / recovery E between two adjacent points on the topological map according to the vehicle longitudinal dynamics model;

[0012] Step 4: According to the vehicle running speed v, calculate the running time T between two adjacent points on the topological map;

[0013] Step 5: Based on the energy consumption / recovery E and running time T of the vehicle at two points on the topological map, a comprehensive weight algorithm for energy consumption and efficiency between two adjacent points on the topological map is constructed;

[0014] Step 6: Calculate the weight w of each path on the topological map according to the comprehensive weight algorithm;

[0015] Step 7: Use the A* algorithm to construct the cost function f(N);

[0016] Step 8: Construct the heuristic function h(N) according to the characteristics of the topological map;

[0017] Step 9: Based on the starting and ending position information of the vehicle on the topological map, the improved A* algorithm is used to search for the optimal global path of the vehicle.

[0018] Through the above design, the high-precision map is first preprocessed to obtain a topological map with three-dimensional information and curvature; then, when calculating the energy consumption of each section of the topological map, the slope, length, curvature of the road and the energy consumption under different load capacities are considered according to the longitudinal dynamics model of the vehicle, so that the calculated energy consumption between two points is more accurate and consistent with the actual application scenario; when calculating the operating efficiency of the vehicle under each section of the topological map, the three-dimensional information of the road is considered, so that the road distance is more accurate, and the arrival speed of the vehicle under different curvatures changes dynamically, and the calculated time is closer to the actual operation situation.

[0019] Preferably, in step 2, according to the triangle principle, the slope θ between two adjacent points is calculated by using the three-dimensional spatial coordinates of two adjacent points on the topological map:

[0020]

[0021] Among them, (x 1 ,y 1 ,z 1 ) and (x 2 ,y 2 ,z2 ) are the three-dimensional spatial coordinates of two adjacent points on the topological map;

[0022] The curvature k is approximately calculated by the coordinates of three consecutive points, and the calculation formula is:

[0023]

[0024] Among them, d 12 d 13 d 23 They represent the length of the chord between the three points; S represents the area of ​​the triangle formed by the three points;

[0025] The area of ​​the triangle S is calculated according to Heron's formula, and the expression is as follows:

[0026]

[0027] Using the distance formula between two points in three-dimensional space, calculate the length of the chord d between the two points:

[0028]

[0029] According to the curvature k between two points, the radius of the arc is obtained

[0030] According to the calculation formula of chord length d and arc length L:

[0031]

[0032] L=Rα

[0033] The relationship between the chord length d and the arc length L is obtained, that is, the distance L between the two points is:

[0034]

[0035] Preferably, in step 3, the vehicle longitudinal dynamics model expression is as follows:

[0036] F t =ma+F r +F a +F g

[0037] F r =f r mgcosθ

[0038]

[0039] F g =mgsinθ

[0040]

[0041] Among them, F t represents driving force, m represents vehicle mass, a represents acceleration, F r Indicates rolling resistance, F a Indicates air resistance, F g represents the gravitational resistance, f r represents the rolling coefficient, θ represents the vehicle driving slope, g represents the acceleration of gravity, ρ represents the air density, C d represents the air resistance coefficient, A represents the frontal area, v represents the vehicle speed, T e Represents the driving motor torque, i g Indicates the gear ratio, i 0 Indicates the speed ratio of the reducer, n t represents efficiency, and r represents the rolling radius of the tire.

[0042] Preferably, in step 3, the power of the vehicle is:

[0043]

[0044] Among them, P represents power, n represents motor speed;

[0045] The energy consumption / recovery E of a vehicle between two points on the topological map is:

[0046] When the route between two points on the topological map is flat or uphill, the energy consumption formula is:

[0047]

[0048] When the route between two points on the topological map is downhill, the vehicle charges the battery through energy recovery, and the energy consumption is positive. The formula is:

[0049] (1) Potential energy change

[0050] When the vehicle slides down the slope, the gravitational potential energy decreases, that is, the potential energy that can be recovered is:

[0051] ΔE potential =mgLsinθ

[0052] Among them, ΔE potential is the potential energy that can be recovered;

[0053] (2) Energy consumed by resistance

[0054] When the vehicle slides downhill, it overcomes the following resistance forces, which cannot be recovered:

[0055]

[0056] F r =f rmg cosθ

[0057] ΔE loss =(F a +F r )L

[0058] Where, ΔE loss Indicates the energy consumed by resistance;

[0059] (3) Recyclable energy

[0060] The regenerative braking system converts part of the kinetic energy into electrical energy, deducting the drag loss and considering the efficiency:

[0061] E regen =η(ΔE potential -ΔE loss )

[0062] Where η represents the comprehensive efficiency of regenerative braking, which is usually 50% to 70%, including the efficiency of the motor and battery; E rege n is the recoverable energy;

[0063] When the vehicle slides down at a constant speed, that is, the driving force and the resistance are balanced, the regenerative braking force E brake for:

[0064] F brake =mgsinθ-(F a +F r )

[0065] Energy recovery is:

[0066] E regen =ηF brake L

[0067]

[0068] When the slope θ≥0, the vehicle consumes energy E exhaust ; When the slope θ<0, the vehicle recovers energy E regen :

[0069]

[0070] As a preference: in step 4, when the vehicle speed is stabilized at V max When , the running time T between two points is:

[0071]

[0072] When the curvature k is small (straight road or gentle curve), the speed is close to the maximum running speed V max ;

[0073] When the curvature k is large (sharp bend), the speed is significantly reduced, and the vehicle running speed expression is as follows:

[0074]

[0075] Among them, k 0 is the curvature threshold, and α is the adjustment parameter.

[0076] Preferably, in step 5, the comprehensive weight algorithm expression is as follows:

[0077] w=w 1 *E+w 2 *T

[0078] Among them, w 1 is the weight of energy consumption, w 2 is the weight of efficiency.

[0079] Preferably, in step 7, the cost function f(N) is:

[0080] f(N)=g(N)+h(N)

[0081] Among them, f(N) is the comprehensive cost of node N, g(N) is the cost of node N from the starting point, and h(N) is the estimated cost of node N from the end point.

[0082] Preferably, in step 8, the heuristic function h(N) is Manhattan distance plus height difference information, expressed as:

[0083] h(N)=(|x 1 -x 2 |+|y 1 -y 2 |)+u(z 1 -z 2 )

[0084] Among them, u is the adjustment coefficient, which is related to the total mass of the vehicle.

[0085] The beneficial effects of the present invention are as follows: the present invention improves the heuristic function of the A* algorithm, taking into account altitude information; when calculating the energy cost, the influence of factors such as vehicle cargo mass, road slope, and curve curvature on energy consumption is taken into account; when calculating the efficiency, three-dimensional information is used to calculate the distance between the current point and the target point; users can select global path planning with energy consumption and efficiency parameter adjustments according to actual conditions, which effectively reduces the energy consumption of point-to-point transportation of vehicles, improves operating efficiency, and reduces corporate logistics costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 It is a schematic diagram of the process of the present invention;

[0087] Figure 2 Schematic diagram of a high-definition map and a topological map of a logistics park in an embodiment;

[0088] Figure 3 A schematic diagram of a topological road section in a topological map in an embodiment;

[0089] Figure 4 Schematic diagram of the chord length d and arc length L between two points in the embodiment;

[0090] Figure 5 Schematic diagram of the force on a vehicle going uphill in the embodiment. DETAILED DESCRIPTION

[0091] The present invention is further described in detail below in conjunction with the accompanying drawings and specific examples. The following examples or drawings are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0092] like Figure 1 As shown: A global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario includes the following steps:

[0093] Step 1: Obtain a high-definition map of the target logistics park and preprocess the high-definition map into a topological map, such as Figure 2 As shown;

[0094] Step 2: According to the three-dimensional spatial coordinates of each point on the topological map, calculate the distance L, curvature k and slope θ between any two adjacent points on the topological map;

[0095] According to the triangle principle, the slope θ between two adjacent points is calculated through the three-dimensional spatial coordinates of two adjacent points on the topological map:

[0096]

[0097] Among them, (x 1 ,y 1 ,z 1 ) and (x 2 ,y 2 ,z 2 ) are the three-dimensional spatial coordinates of two adjacent points on the topological map;

[0098] According to the high-precision map of the logistics park, the coordinates of each point on the topological map (x i ,y i ,z i ), the curvature of each road segment in the topological map can be calculated based on the coordinates, such as Figure 3 As shown, the curvature k is approximately calculated by the coordinates of three consecutive points, and the calculation formula is:

[0099]

[0100] Among them, d 12 ,d 13 ,d 23 They represent the length of the chord between the three points; S represents the area of ​​the triangle formed by the three points;

[0101] The area of ​​the triangle S is calculated according to Heron's formula, and the expression is as follows:

[0102]

[0103] like Figure 4 As shown, use the distance formula between two points in three-dimensional space to calculate the chord length d between the two points:

[0104]

[0105] According to the curvature k between two points, the radius of the arc is obtained

[0106] According to the calculation formula of chord length d and arc length L:

[0107]

[0108] L=Rα

[0109] The relationship between the chord length d and the arc length L is obtained as follows:

[0110]

[0111] Step 3: Calculate the energy consumption / recovery E between two adjacent points on the topological map according to the vehicle longitudinal dynamics model;

[0112] According to L, slope θ, and road curvature k between two points on the topological map, and combined with the vehicle's dynamic model, the vehicle operating energy consumption weight under different load conditions between the two points is obtained.

[0113] like Figure 5 As shown, the vehicle longitudinal dynamics model expression is as follows:

[0114] F t =ma+F r +F a +F g

[0115] F r =f r mg cosθ

[0116]

[0117] F g =mgsinθ

[0118]

[0119] Among them, F t represents driving force, m represents vehicle mass, a represents acceleration, F r Indicates rolling resistance, F a Indicates air resistance, F g represents the gravitational resistance, f r represents the rolling coefficient, θ represents the vehicle driving slope, g represents the acceleration of gravity, ρ represents the air density, C d represents the air resistance coefficient, A represents the frontal area, v represents the vehicle speed, T e Represents the driving motor torque, i g Indicates the gear ratio, i 0 Indicates the speed ratio of the reducer, n t represents efficiency, and r represents the rolling radius of the tire.

[0120] The power of the vehicle is:

[0121]

[0122] Among them, P represents power, n represents motor speed;

[0123] The energy consumption / recovery E of a vehicle between two points on the topological map is:

[0124] When the route between two points on the topological map is flat or uphill, the energy consumption formula is:

[0125]

[0126] When the route between two points on the topological map is downhill, the vehicle charges the battery through energy recovery, and the energy consumption is positive. The formula is:

[0127] (1) Potential energy change

[0128] When the vehicle slides down the slope, the gravitational potential energy decreases, that is, the potential energy that can be recovered is:

[0129] ΔE potential =mgLsinθ

[0130] Among them, ΔE potential is the potential energy that can be recovered;

[0131] (2) Energy consumed by resistance

[0132] When the vehicle slides downhill, it overcomes the following resistance forces, which cannot be recovered:

[0133]

[0134] F r =f r mgcosθ

[0135] ΔE loss =(F a +F r )L

[0136] Among them, ΔE loss Indicates the energy consumed by resistance;

[0137] (3) Recyclable energy

[0138] The regenerative braking system converts part of the kinetic energy into electrical energy, deducting the drag loss and considering the efficiency:

[0139] E regen =η(ΔE potential -ΔE loss )

[0140] Where η represents the comprehensive efficiency of regenerative braking, which is usually 50% to 70%, including the efficiency of the motor and battery; E regen For recoverable energy;

[0141] When the vehicle slides down at a constant speed, that is, the driving force and the resistance are balanced, the regenerative braking force F bracke for:

[0142] F brake =mgsinθ-(F a +F r )

[0143] Energy recovery is:

[0144] E regen =ηF brake L

[0145]

[0146] Assuming that the speed V is a fixed value of 40km / h, according to the longitudinal dynamics equation of the vehicle:

[0147] Assuming that the vehicle moves at a uniform speed, the torque T required under different loads can be obtained: e .

[0148] The energy consumption of each topology segment is calculated according to the formula:

[0149] When θ≥0, the vehicle consumes energy E exhaust ; When θ<0, the vehicle recovers energy E regen .

[0150]

[0151] Step 4: According to the vehicle running speed v, calculate the running time T between two adjacent points on the topological map;

[0152] When the vehicle speed is stable at V max When , the running time T between two points is:

[0153]

[0154] When the curvature k is small (straight road or gentle curve), the speed is close to the maximum running speed V max ;

[0155] When the curvature k is large (sharp bend), the speed is significantly reduced, and the vehicle running speed expression is as follows:

[0156]

[0157] Among them, k 0 is the curvature threshold, and α is the adjustment parameter.

[0158] Step 5: Based on the energy consumption / recovery E and running time T of the vehicle at two points on the topological map, a comprehensive weight algorithm for energy consumption and efficiency between two adjacent points on the topological map is constructed. The expression is as follows:

[0159] w=w 1 *E+w 2 *T

[0160] Among them, w 1 is the weight of energy consumption, w 2 is the weight of efficiency.

[0161] Step 6: Calculate the weight w of each path on the topological map according to the comprehensive weight algorithm;

[0162] Step 7: Use the A* algorithm to construct the cost function f(N), which is expressed as follows:

[0163] f(N)=g(N)+h(N)

[0164] Among them, f(N) is the comprehensive cost of node N, g(N) is the cost of node N from the starting point, and h(N) is the estimated cost of node N from the end point.

[0165] Step 8: According to the characteristics of the topological map, construct a heuristic function h(N), which is the Manhattan distance plus the height difference information, and the expression is:

[0166] h(N)=(|x 1 -x 2 |+|y 1 -y 2 |)+u(z 1-z 2 )

[0167] Among them, u is the adjustment coefficient, which is related to the total mass of the vehicle.

[0168] Step 9: Based on the starting and ending position information of the vehicle on the topological map, the improved A* algorithm is used to search for the optimal global path of the vehicle.

[0169] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario, characterized in that: The following steps are involved: Step 1: Obtain a high-definition map of the target logistics park, and preprocess the high-definition map into a topological map; Step 2: According to the three-dimensional spatial coordinates of each point on the topological map, calculate the distance L, curvature k and slope θ between any two adjacent points on the topological map; Step 3: Calculate the energy consumption / recovery E between two adjacent points on the topological map according to the longitudinal dynamics model of the vehicle; Step 4: According to the vehicle running speed v, calculate the running time T between two adjacent points on the topological map; Step 5: Based on the energy consumption / recovery E and running time T of the vehicle at two points on the topological map, a comprehensive weight algorithm for energy consumption and efficiency between two adjacent points on the topological map is constructed; Step 6: Calculate the weight w of each path on the topological map according to the comprehensive weight algorithm; Step 7: Use the A* algorithm to construct the cost function f(N); Step 8: Construct the heuristic function h(N) according to the characteristics of the topological map; Step 9: Based on the starting and ending position information of the vehicle on the topological map, the improved A* algorithm is used to search for the optimal global path of the vehicle.

2. The global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario according to claim 1 is characterized by: In step 2, according to the triangle principle, the slope θ between two adjacent points is calculated by the three-dimensional spatial coordinates of two adjacent points on the topological map: Among them, (x1, y1, z1) and (x2, y2, z2) are the three-dimensional spatial coordinates of two adjacent points on the topological map; The curvature k is approximately calculated by the coordinates of three consecutive points, and the calculation formula is: Among them, d 12 ,d 13 ,d 23 They represent the length of the chord between the three points; S represents the area of ​​the triangle formed by the three points; The area of ​​the triangle S is calculated according to Heron's formula, and the expression is as follows: Using the distance formula between two points in three-dimensional space, calculate the length of the chord d between the two points: According to the curvature k between two points, the radius of the arc is obtained According to the calculation formula of chord length d and arc length L: L=Rα The relationship between the chord length d and the arc length L is obtained as follows:

3. The global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario according to claim 1 is characterized by: In step 3, the vehicle longitudinal dynamics model expression is as follows: F t =ma+F r +F a +F g F r =f r mg cosθ F g =mgsinθ Among them, F t represents driving force, m represents vehicle mass, a represents acceleration, F r Indicates rolling resistance, F a Indicates air resistance, F g represents the gravitational resistance, f r represents the rolling coefficient, θ represents the vehicle driving slope, g represents the acceleration of gravity, ρ represents the air density, C d represents the air resistance coefficient, A represents the frontal area, v represents the vehicle speed, T e Represents the driving motor torque, i g represents the gear ratio, i0 represents the reducer ratio, n t represents efficiency, and r represents the rolling radius of the tire.

4. The global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario according to claim 1 is characterized by: In step 3, the power of the vehicle is: Among them, P represents power, n represents motor speed; The energy consumption / recovery E of a vehicle between two points on the topological map is: When the route between two points on the topological map is flat or uphill, the energy consumption formula is: When the route between two points on the topological map is downhill, the vehicle charges the battery through energy recovery, and the energy consumption is positive. The formula is: (1) Potential energy change When the vehicle slides down the slope, the gravitational potential energy decreases, that is, the potential energy that can be recovered is: ΔE potential =mgLsinθ Where, ΔE potential is the potential energy that can be recovered; (2) Energy consumed by resistance When the vehicle slides downhill, it overcomes the following resistance forces, which cannot be recovered: F r =f r mgcosθ ΔE loss =(F a +F r )L Where, ΔE loss Indicates the energy consumed by resistance; (3) Recyclable energy The regenerative braking system converts part of the kinetic energy into electrical energy, deducting the drag loss and considering the efficiency: E regen =η(ΔE potential -NO loss ) Where η represents the comprehensive efficiency of regenerative braking, E regen For recoverable energy; When the vehicle slides down at a constant speed, that is, the driving force and the resistance are balanced, the regenerative braking force F brake for: F brake =mgsinθ-(F a +F r ) Energy recovery is: E regen =ηF brake L When the slope θ≥0, the vehicle consumes energy E exhaust ; When the slope θ<0, the vehicle recovers energy E regen :

5. The global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario according to claim 1 is characterized by: In step 4, when the vehicle speed is stabilized at V max When , the running time T between two points is: When the curvature k is small, the speed is close to the maximum operating speed V max ; When the curvature k is large, the speed decreases, and the vehicle running speed expression is as follows: Among them, k0 is the curvature threshold and α is the adjustment parameter.

6. The global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario according to claim 1 is characterized by: In step 5, the comprehensive weight algorithm expression is as follows: w=w1*E+w2*T Among them, w1 is the weight of energy consumption and w2 is the weight of efficiency.

7. The global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario according to claim 1 is characterized by: In step 7, the cost function f(N) is: f(N)=g(N)+h(N) Among them, f(N) is the comprehensive cost of node N, h(N) is the cost of node N from the starting point, and h(N) is the estimated cost of node N from the end point.

8. The global path planning method for a pure electric self-driving commercial vehicle in a logistics park scenario according to claim 1 is characterized by: In step 8, the heuristic function h(N) is the Manhattan distance plus the height difference information, and the expression is: h(N)=(|x1-x2|+|y1-y2|)+u(z1-z2) Where u is the adjustment coefficient.

Citation Information

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