CN113159417A - Heat conduction topology optimization mobile robot path planning method based on dichotomy solution - Google Patents

Heat conduction topology optimization mobile robot path planning method based on dichotomy solution Download PDF

Info

Publication number
CN113159417A
CN113159417A CN202110420876.1A CN202110420876A CN113159417A CN 113159417 A CN113159417 A CN 113159417A CN 202110420876 A CN202110420876 A CN 202110420876A CN 113159417 A CN113159417 A CN 113159417A
Authority
CN
China
Prior art keywords
heat
cooling channel
heat dissipation
domain
mobile robot
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110420876.1A
Other languages
Chinese (zh)
Other versions
CN113159417B (en
Inventor
李小虎
方远洋
李宝童
祁朋园
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xian Jiaotong University
Original Assignee
Xian Jiaotong University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xian Jiaotong University filed Critical Xian Jiaotong University
Priority to CN202110420876.1A priority Critical patent/CN113159417B/en
Publication of CN113159417A publication Critical patent/CN113159417A/en
Application granted granted Critical
Publication of CN113159417B publication Critical patent/CN113159417B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation

Landscapes

  • Engineering & Computer Science (AREA)
  • Business, Economics & Management (AREA)
  • Physics & Mathematics (AREA)
  • Human Resources & Organizations (AREA)
  • Theoretical Computer Science (AREA)
  • Economics (AREA)
  • Strategic Management (AREA)
  • General Physics & Mathematics (AREA)
  • Game Theory and Decision Science (AREA)
  • Development Economics (AREA)
  • Quality & Reliability (AREA)
  • Tourism & Hospitality (AREA)
  • Marketing (AREA)
  • General Business, Economics & Management (AREA)
  • Entrepreneurship & Innovation (AREA)
  • Operations Research (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Investigating Or Analyzing Materials Using Thermal Means (AREA)

Abstract

The invention discloses a path planning method of a heat conduction topology optimization mobile robot based on dichotomy solution, which comprises the steps of mapping a global path planning problem in a two-dimensional environment into a heat dissipation topological structure problem, and establishing a finite element model of heat conduction of the heat dissipation topological structure; according to the finite element model and the growth simulation calculation theory of the heat conduction of the heat dissipation topological structure, taking the heat dissipation weakness J as an evaluation function to obtain a single-step growth optimization model of a cooling channel in the heat dissipation topological structure; constructing the optimal growth direction of the cooling channel according to a single-step growth model and the principle of minimizing the heat dissipation weakness of the whole heat conduction domain in each growth step; defining 8 search directions of robot motion, and constructing a cooling channel material library in the corresponding direction; quickly solving by adopting a dichotomy under a finite element frame to obtain a final moving path of the robot; the dichotomy solution can be adopted, the calculation efficiency can be obviously improved, the planned path efficiency is higher, and the path is more stable.

Description

Heat conduction topology optimization mobile robot path planning method based on dichotomy solution
Technical Field
The invention belongs to the field of mobile robot path planning, and particularly relates to a heat conduction topology optimization mobile robot path planning method based on dichotomy solution.
Background
The path planning is one of key technologies for realizing the autonomous motion of the mobile robot, and how to plan a path meeting the performance requirement from a starting point to a terminal point is a research hotspot problem of the current path planning of the mobile robot. The existing path planning method such as the RRT algorithm is widely applied, but due to the random search characteristic, the convergence speed is low and the path effect is poor in a complex environment. Inspired by a heat transfer path under a steady state, the Chinese patent CN 110207709A-a mobile robot path planning method based on a parameterized level set adopts a method based on heat conduction topology optimization, and the method can solve the problem of local deadlock, but involves large-scale calculation, has long solving time and unstable calculation, and is easy to touch an obstacle under some conditions. As can be seen, although the research on the robot path planning has been advanced, there are problems such as weak ability to deal with complex environmental problems and complex calculation.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a heat conduction topology optimization mobile robot path planning method based on dichotomy solution, the algorithm considers that the topology optimization problem is a nonlinear optimization problem, the solution efficiency is low, the result is unstable, the path planning problem of the mobile robot is converted into the problem of designing the optimal heat dissipation topology structure under the stable state, and the dichotomy search-based mobile robot path planning method is provided based on the growth bionic heat conduction topology optimization idea, so that the instantaneity and the calculation efficiency of the mobile robot path planning algorithm are improved, the mobile robot path planning method can adapt to path planning in different complex environments, and has better search and calculation performances.
In order to achieve the purpose, the invention adopts the technical scheme that: a heat conduction topology optimization mobile robot path planning method based on dichotomy solution comprises the following steps:
mapping a global path planning problem in a two-dimensional environment into a heat dissipation topological structure problem, and establishing a finite element model of heat conduction of the heat dissipation topological structure;
according to the finite element model and the growth simulation calculation theory of the heat conduction of the heat dissipation topological structure, taking the heat dissipation weakness J as an evaluation function to obtain a single-step growth optimization model of a cooling channel in the heat dissipation topological structure;
setting a searching direction of the movement of the mobile robot, constructing a finite element model of a cooling channel material according to the searching direction in a thermal analysis domain, and constructing a cooling channel material library according to the finite element model of the cooling channel material; solving the single-step growth optimization model by adopting a dichotomy method based on the principle of optimal heat dissipation performance, and solving the optimal search direction theta in a cooling channel material library*；
Will solve to obtain theta*And adding the corresponding cooling channel into the thermal analysis domain, taking the end point of the cooling channel as a new iteration starting point of the cooling channel, stopping growing when the distance from the end of the new cooling channel to the heat sink is less than the length of the cooling channel, namely reaching the end point, and connecting the end points of each step to obtain a planned path.
The mapping of the global path planning problem in the two-dimensional environment to the heat dissipation topological structure problem is specifically realized as follows:
the robot's configuration space C includes a starting point CSTarget point CGAnd a barrier COAnd free space CFFour parts:
C＝CS+CG+CF+CO
mapping the bitmap space C into the thermal analysis domain H according to the following correspondence:
Figure BDA0003027792170000021
H＝HS+HG+HF+HO
wherein HS、HGHeat sink for heat source; hOMiddle is a non-design domain；HFA domain is designed.
When establishing a finite element model of heat conduction: the two-dimensional four-node quadrilateral units are adopted to disperse the whole thermal analysis domain, the units occupied by the non-design domain are regarded as thermal insulators, and the thermal conductivity k of the thermal insulators is00; heat transfer phenomena exist within the design domain, which have higher thermal conductivity than non-design domains.
During the growth process, the cooling channel is gradually increased in the design domain by a rectangular outline, the optimal growth direction is to minimize the heat dissipation weakness of the whole thermal analysis domain in each growth step, and the optimization function of the ith growth step is shown as the following formula:
min J(αi)＝TTK(αi)T
Figure BDA0003027792170000031
T＝TS on ST
Figure BDA0003027792170000032
0≤αi≤2π
in the formula: j is the heat dissipation weakness; alpha is alphaiThe growth angle in the step i is shown; t is the temperature field of the analysis domain; (.)TRepresenting a transpose; k (alpha)i) Is an integral heat conductivity coefficient matrix of the thermal analysis domain in the ith step,
Figure BDA0003027792170000035
is a gradient operator, k is the material heat conductivity coefficient, q is the heat source, and H is the thermal analysis domain; the first constraint is the steady state heat transfer equation in the thermal analysis domain and the second constraint is expressed as the boundary STWith constant temperature TSAnd the third constraint represents along the boundary SQThe heat flux of the outer unit normal vector of (a) is qN。
Solving the temperature field of the thermal analysis domain using a finite element method:
K·T＝F
in the formula: t is a thermal analysis domain temperature field; k is an integral heat conductivity coefficient matrix of thermal analysis; f is the heat load;
the cooling channel has a definite geometric boundary, the part covered by the cooling channel in the limited unit of the bottom layer design domain is regarded as an intermediate unit, the intermediate unit is processed by adopting a density method, the heat conductivity coefficient of the intermediate unit is between the high heat conductivity material and the design domain, and the heat conductivity coefficient matrix is as follows:
Ke＝KE·ρ
in the formula: ke is a heat conductivity coefficient matrix of the middle unit; kEA thermal conductivity coefficient matrix of a high thermal conductivity material; ρ is the pseudo density, which has the value:
Figure BDA0003027792170000033
in the formula, neIs the number of unit nodes, ne4; n is the number of nodes covered by the high thermal conductivity material for the limited unit of the underlying design domain.
Based on the finite element model, the heat dissipation weakness calculation form is as follows:
Figure BDA0003027792170000034
wherein, K (alpha)i) The integral heat conductivity coefficient matrix of the thermal analysis domain in the ith step is obtained; t is the temperature field of the thermal analysis domain (.)TRepresenting transpose, n is the number of nodes covered by high thermal conductivity material in the finite element of the underlying design domain, neIs the number of unit nodes, KEIs the cell stiffness matrix and N is the number of cells.
When the single-step growth optimization model is solved by adopting a bisection method, a cooling channel starts from a heat source, the starting end of the cooling channel is arranged at the heat source during initial growth, the optimal growth direction is selected from a material library according to the principle of optimal heat dissipation performance, the cooling channel corresponding to the optimal growth direction is laid in a thermal analysis domain, after the position of the high-heat-conductivity material in the design domain in the previous step is determined, the starting end of the current cooling channel is fixed at the tail end of the cooling channel in the previous step, then the growth direction in the current step is determined according to the searching principle of the optimal heat dissipation performance, and the growth is continuously carried out until the heat sink is reached, namely the distance from the tail end of the new cooling channel to the heat sink is smaller than the length of the cooling channel.
Solving for an optimal search direction θ in a cooling channel materials library*When the mobile robot moves, the searching directions of the mobile robot, namely 8 searching directions, are set along the axial direction of a certain unit, the direction perpendicular to the axial direction, the included angle of 45 degrees with the axial line and the included angle of minus 45 degrees with the axial line, the searching direction in the cooling channel material library corresponding to the movement of the mobile robot is represented by theta, the heat dissipation function of the searching direction is J (theta), and the optimal growth angle theta is*Expressed as:
J(θ*)＝min{J(θ)}
Figure BDA0003027792170000041
a computer device comprises a processor and a memory, wherein the memory is used for storing a computer executable program, the processor reads part or all of the computer executable program from the memory and executes the computer executable program, and when the processor executes part or all of the computer executable program, the dichotomy solution-based heat conduction topology optimization mobile robot path planning method can be realized.
A computer readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for planning a path of a heat conduction topology optimization mobile robot based on dichotomy solution according to the invention can be realized.
Compared with the prior art, the invention has at least the following beneficial effects:
1) the algorithm generates a final path through dynamic growth, path points obtained by each step of iteration can be immediately executed, the method is strong in real-time performance, and the path planning requirement of the mobile robot is better met;
2) the method has strong adaptability, can be applied to various complex environments, has no relation between the convergence speed of the algorithm and the complexity of the environment, and has more advantages in the complex environments;
3) compared with the traditional topological optimization method, the nonlinear constraint optimization problem can be converted into a discrete optimization problem by adopting the method for constructing the cooling channel, the dichotomy can be adopted for solving, the calculation efficiency can be obviously improved, the planned path efficiency is higher, and the path is more stable.
Furthermore, part of the limited units of the bottom layer design domain can be covered by the cooling channels, the number of the units covered by the cooling channels in different directions is different, errors can be brought to the calculation of the objective function, the intermediate units are processed by adopting a density method, the errors can be effectively eliminated, and the high-heat-conductivity material projected to the bottom layer finite element grid can have clear geometric boundaries.
Drawings
FIG. 1 is a flow chart of one possible method of the present invention.
FIG. 2 is a schematic diagram of a density process intermediate unit.
FIG. 3a is a schematic view of a robot moving direction, FIG. 3b is a schematic view of a diagonal cooling channel material finite element model, and FIG. 3c is a schematic view of a horizontal cooling channel material finite element model.
FIG. 4 is a test map using the method of the present invention.
Fig. 5 is a diagram of a path planning result in a complex environment.
Fig. 6 shows the result of the mobile robot path planning method based on the parameterized level set.
Fig. 7 shows a plan map based on a comparison of the methods described in the present invention and the prior art.
Fig. 8 shows the final result of the path planning based on the map shown in fig. 7.
Fig. 9 is a final result of path planning based on the map shown in fig. 7 in the related art.
Detailed Description
The technical scheme in the embodiment of the invention is further explained in detail as follows:
the parameters used in the simulation of the present invention are shown in table 2 below.
TABLE 2 simulation parameters Table
Figure BDA0003027792170000061
The flow of the path planning method for the heat conduction topology optimization mobile robot based on the dichotomy solution is shown in figure 1, and the method specifically comprises the following steps:
step 1: the correspondence between the heat conduction topology optimization and the robot path planning is shown in table 3, and the path planning problem of the mobile robot can be converted into an equivalent heat conduction topology optimization problem.
TABLE 3 Path planning and topology optimization analogy
Figure BDA0003027792170000062
The robot's configuration space C includes a starting point CSTarget point CGAnd a barrier COAnd free space CFFour parts:
C＝CS+CG+CF+CO
mapping the bitmap space C into the thermal analysis domain H according to the following correspondence:
Figure BDA0003027792170000063
H＝HS+HG+HF+HO
wherein HS、HGHeat sink for heat source; hOIs a non-design domain; hFA domain is designed.
When solving the heat conduction topological optimization problem, a corresponding heat conduction finite element model needs to be constructed, a two-dimensional four-node quadrilateral unit is adopted to disperse the whole thermal analysis domain, the unit occupied by the non-design domain is taken as a heat insulator, and the heat conductivity coefficient k of the heat insulator is00; heat transfer phenomena exist within the design domain, which have higher thermal conductivity than non-design domains.
Step 2: equivalent heat transfer paths are achieved by a continuously growing process. The cooling channels start from the heat source, grow gradually in the design domain, and finally reach the heat sink. In the growth process, the optimal growth direction of each growth step is determined according to the optimal heat dissipation performance, an evaluation function is required to be designed to evaluate the heat dissipation performance of a thermal analysis domain, the importance degree of each search direction is determined, the heat dissipation weakness is a commonly used excellent evaluation index, and the heat dissipation weakness is selected as the evaluation function of single-step growth. Therefore, the principle of the optimal growth direction is to minimize the heat dissipation weakness of the whole thermal analysis domain in each growth step, and the optimization function of the ith growth step is shown as the following formula:
min J(αi)＝TTK(αi)T
Figure BDA0003027792170000071
T＝TS on ST
Figure BDA0003027792170000072
0≤αi≤2π
in the formula: j is the heat dissipation weakness; alpha is alphaiThe growth angle in the step i is shown; t is the temperature field of the thermal analysis domain; k (alpha)i) The integral heat conductivity coefficient matrix of the thermal analysis domain in the ith step is obtained;
Figure BDA0003027792170000073
is a gradient operator, and k is the coefficient of thermal conductivity of the material; q is the heat source and H is the thermal analysis domain. The first constraint is the steady state heat transfer equation in the thermal analysis domain and the second constraint is expressed as the boundary STWith constant temperature TSAnd the third constraint represents along the boundary SQThe heat flux of the outer unit normal vector of (a) is qN。
And step 3: according to the heat dissipation weakness function, the temperature field T is one of conditions for calculating and optimizing the heat dissipation weakness of the objective function, and the finite element method is used for solving the temperature field of the heat analysis domain:
K·T＝F
in the formula: t is a thermal analysis domain temperature field; k is an integral heat conductivity coefficient matrix of thermal analysis; f is the heat load.
The cooling channels have well-defined geometric boundaries, and only a portion of the area of the limited unit where the underlying design domain exists is covered by the cooling channels. As shown in fig. 2, the partially covered elements are treated as intermediate materials, and the density processing of these intermediate elements can provide clear geometric boundaries for the high thermal conductivity material projected onto the underlying finite element mesh. The thermal conductivity of the intermediate material is between the high thermal conductivity material and the design domain, and the thermal conductivity matrix is:
Ke＝KE·ρ
wherein, Ke is a heat conductivity coefficient matrix of the intermediate material; kEA thermal conductivity coefficient matrix of a high thermal conductivity material; ρ is the pseudo density, which has the value:
Figure BDA0003027792170000081
wherein n iseIs the number of unit nodes, ne4; n is the number of nodes covered by the high thermal conductivity material of the cell.
In the thermal analysis domain, different levels of heat conduction performance are allocated to different area units, the heat conduction coefficient matrixes of all the units are assembled through a finite element method in the path growing process, and after analysis and calculation, the temperature field T in the analysis domain can be obtained. Under the finite element frame, the heat dissipation weakness is in the form of:
Figure BDA0003027792170000082
K(αi) The integral heat conductivity coefficient matrix of the thermal analysis domain in the ith step is obtained; t is the temperature field of the thermal analysis domain (.)TRepresenting transpose, n is the number of nodes covered by high thermal conductivity material in the finite element of the underlying design domain, neIs the number of unit nodes, KEIs the cell stiffness matrix and N is the number of cells.
The nodes of the finite element mesh covered by the cooling channels at different angles are different, the linear direction and the diagonal direction are the motion directions of the mobile robot, 8 directions shown in fig. 3a are selected as the search directions of the growth angles, rectangular cooling channel materials in the linear direction and the diagonal direction are added into a material library, and corresponding finite element models are shown in fig. 3b and 3 c. During each iteration of the growth process, cooling channels are selected from the material library that maximize the thermal dissipation performance of the thermal analysis domain.
The 8 search directions of the cooling channel material library are represented by theta, the heat dissipation function is J (theta), and the optimal growth angle theta is*Can be expressed as:
J(θ*)＝min{J(θ)}
Figure BDA0003027792170000091
and solving the minimum value of the heat dissipation weakness in the 8 search directions by using a dichotomy. Solving the problems of the initial point and the intermediate point:
1) starting point
Taking out 4 cooling channel assemblies in the linear direction in the material library, calculating the heat dissipation degrees of the cooling channel assemblies, and selecting the angle with the minimum heat dissipation degree as theta':
Figure BDA0003027792170000092
taking out the cooling channel assembly in the 45-degree angle direction adjacent to the theta' and calculating the heat dissipation weakness of the cooling channel assembly, wherein the angle with the minimum heat dissipation weakness is the optimal growth angle of the starting point:
Figure BDA0003027792170000093
2) intermediate point
The initial end of the new high heat conduction material is fixed at the tail end of the material in the previous step, and the growth angle in the nth step is the same as that in the (n-1) th step, namely:
θn＝θn-1
calculating thetanWeak heat dissipation corresponding to adjacent 45 degree components if thetanMinimum weakness of heat dissipation, i.e. thetanFor the optimal angle of growth for this step:
Figure BDA0003027792170000094
θ*＝θn
if not, then theta needs to be calculatednSelecting the angle with the minimum heat dissipation degree from the heat dissipation degrees of the adjacent 90-degree assemblies:
Figure BDA0003027792170000095
as an example: the minimum value of the heat dissipation weakness in the cooling channel material in the optimal search direction is solved by a dichotomy, the solution is divided into two conditions of a starting point and a middle point,
for the starting point: taking out the cooling channel materials in the central axis direction and the direction vertical to the central axis direction of the material library, calculating the heat dissipation weakness of the cooling channel materials, and selecting the angle with the minimum heat dissipation weakness as theta':
Figure BDA0003027792170000101
taking out the cooling channel materials in the 45-degree angle direction and the-45-degree angle direction adjacent to the theta', and calculating the heat dissipation weakness of the cooling channel materials, wherein the angle with the minimum heat dissipation weakness is the optimal growth angle of the starting point:
Figure BDA0003027792170000102
for the intermediate point: the starting end of the current heat conduction material is set as the tail end of the material in the previous step, and the growth angle in the nth step is the same as that in the (n-1) th step, namely:
θn＝θn-1
calculating thetanThe heat dissipation degree corresponding to the 45 degree angle direction and the-45 degree angle direction adjacent to the current direction is equal to the heat dissipation degreenOf minimum heat dissipation, i.e. thetanFor the optimal angle of growth for this step:
Figure BDA0003027792170000103
θ*＝θn
if not, then theta needs to be calculatednSelecting the angle with the minimum heat dissipation degree from the heat dissipation degrees of the adjacent 90-degree assemblies:
Figure BDA0003027792170000104
and 4, step 4: solving the solution in the step 3 to obtain theta*The corresponding cooling channel is added to the thermal analysis domain and the end point of the cooling channel is taken as a new iteration starting point, and the growth is stopped when the end of the cooling channel is less than the length L of the cooling channel from the heat sink.
Test map as shown in fig. 4, the obstacles are set to be distributed in a global static 88 × 88 grid map, with the red point as the starting point and the blue point as the target point. The final result of the path planning is shown in fig. 5, the total zero length is 68.93m, the search time is 8.69s, and compared with the mobile robot path planning method based on the parameterized level set in the prior art, the planning result is shown in fig. 6, the total zero length is 69.91m, and the search time is 44.67s, it can be seen that the path planning method based on the parameterized level set is slow in solving speed, the planned path is not good in effect, and difficulty is brought to the following trajectory tracking. The path planning method for the heat conduction topology optimization mobile robot based on the dichotomy solution has the advantages of high solution speed, no oscillation of the path and good effect in a complex environment.
The test map is shown in fig. 7, and the obstacles are distributed in a global static 80 × 80 grid map, with a red point as a starting point and a blue point as a target point. The final result of the path planning is shown in fig. 8, where the total length of zero is 98.04m and the search time is 11.81 s. Compared with the existing mobile robot path planning method based on the parameterized level set, the planning result is shown in fig. 9, and it can be seen that the path planning method based on the parameterized level set fails to plan for the map.
As an alternative embodiment, the present invention further provides a computer device, which includes a processor and a memory, where the memory is used to store a computer-executable program, the processor reads part or all of the computer-executable program from the memory and executes the computer-executable program, and when the processor executes part or all of the computer-executable program, the processor can implement part or all of the steps of the heat conduction topology optimization mobile robot path planning method of the present invention, and the memory is further used to store a history of a user.
A computer-readable storage medium, in which a computer program is stored, and when the computer program is executed by a processor, the method for planning a path of a heat conduction topology optimized mobile robot according to the present invention can be implemented.
The computer equipment can adopt a notebook computer, a tablet computer, a desktop computer, a mobile phone or a workstation.
The invention also provides an output device for outputting the prediction result, wherein the output device is linked with the output end of the processor, and the output device is a display or a printer.
The processor of the present invention may be a Central Processing Unit (CPU), a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC) or a ready-made programmable gate array (FPGA).
The memory of the present invention may be an internal storage unit of a laptop, a tablet computer, a desktop computer, a mobile phone, or a workstation, such as a memory, a hard disk: external memory units such as removable hard disks, flash memory cards may also be used.
Computer-readable storage media may include computer storage media and communication media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. The computer-readable storage medium may include: read Only Memory (ROM), Random Access Memory (RAM), solid State drive (ssd), or optical disc, etc. The Random Access Memory may include a resistive Random Access Memory (ReRAM) and a dynamic Random Access Memory (dram).

Claims (10)

1. A heat conduction topology optimization mobile robot path planning method based on dichotomy solution is characterized by comprising the following steps:
mapping a global path planning problem in a two-dimensional environment into a heat dissipation topological structure problem, and establishing a finite element model of heat conduction of the heat dissipation topological structure;
according to the finite element model and the growth simulation calculation theory of the heat conduction of the heat dissipation topological structure, taking the heat dissipation weakness J as an evaluation function to obtain a single-step growth optimization model of a cooling channel in the heat dissipation topological structure;
setting a searching direction of the movement of the mobile robot, constructing a finite element model of a cooling channel material according to the searching direction in a thermal analysis domain, and constructing a cooling channel material library according to the finite element model of the cooling channel material; solving the single-step growth optimization model by adopting a dichotomy method based on the principle of optimal heat dissipation performance, and solving the optimal search direction theta in a cooling channel material library*；
Will solve to obtain theta*Adding corresponding cooling channels into the thermal analysis domain, taking the end points of the cooling channels as new cooling channel iteration starting points, stopping growing when the distance from the new cooling channel end to the heat sink is less than the length of the cooling channel, namely reaching the end points, and taking the end points of each stepAnd connecting to obtain a planned path.
2. The method for planning a path of a heat conduction topology optimization mobile robot based on bisection solution of claim 1, wherein mapping a global path planning problem in a two-dimensional environment to a heat dissipation topology problem is implemented as follows:
the robot's configuration space C includes a starting point CSTarget point CGAnd a barrier COAnd free space CFFour parts:
C＝CS+CG+CF+CO
mapping the bitmap space C into the thermal analysis domain H according to the following correspondence:
Figure FDA0003027792160000011
H＝HS+HG+HF+HO
wherein HS、HGHeat sink for heat source; hOIs a non-design domain; hFA domain is designed.
3. The method for planning a path of a heat conduction topology optimized mobile robot based on bisection solution of claim 2, wherein when establishing the finite element model of heat conduction: the two-dimensional four-node quadrilateral units are adopted to disperse the whole thermal analysis domain, the units occupied by the non-design domain are regarded as thermal insulators, and the thermal conductivity k of the thermal insulators is00; heat transfer phenomena exist within the design domain, which have higher thermal conductivity than non-design domains.
4. The method for planning a path of a mobile robot based on the thermal conduction topology optimization of the bisection method solution of claim 1, wherein during the growing process, the cooling channel is gradually increased in the design domain by a rectangular outline, the optimal growing direction is to minimize the heat dissipation weakness of the whole thermal analysis domain in each growing step, and the optimization function of the ith growing step is as follows:
min J(αi)＝TTK(αi)T
Figure FDA0003027792160000021
T＝TS on ST
Figure FDA0003027792160000022
0≤αi≤2π
in the formula: j is the heat dissipation weakness; alpha is alphaiThe growth angle in the step i is shown; t is the temperature field of the analysis domain; (.)TRepresenting a transpose; k (alpha)i) Is an integral heat conductivity coefficient matrix of the thermal analysis domain in the ith step,
Figure FDA0003027792160000023
is a gradient operator, k is the material heat conductivity coefficient, q is the heat source, and H is the thermal analysis domain; the first constraint is the steady state heat transfer equation in the thermal analysis domain and the second constraint is expressed as the boundary STWith constant temperature TSAnd the third constraint represents along the boundary SQThe heat flux of the outer unit normal vector of (a) is qN。
5. The method of claim 3, wherein the finite element method is used to solve the temperature field of the thermal analysis domain:
K·T＝F
in the formula: t is a thermal analysis domain temperature field; k is an integral heat conductivity coefficient matrix of thermal analysis; f is the heat load;
the cooling channel has a definite geometric boundary, the part covered by the cooling channel in the limited unit of the bottom layer design domain is regarded as an intermediate unit, the intermediate unit is processed by adopting a density method, the heat conductivity coefficient of the intermediate unit is between the high heat conductivity material and the design domain, and the heat conductivity coefficient matrix is as follows:
Ke＝KE·ρ
in the formula: ke is a heat conductivity coefficient matrix of the middle unit; kEA thermal conductivity coefficient matrix of a high thermal conductivity material; ρ is the pseudo density, which has the value:
Figure FDA0003027792160000031
in the formula, neIs the number of unit nodes, ne4; n is the number of nodes covered by the high thermal conductivity material for the limited unit of the underlying design domain.
6. The method for planning a path of a heat conduction topology optimization mobile robot based on bisection solution of claim 1, wherein based on the finite element model, the heat dissipation weakness is calculated as follows:
Figure FDA0003027792160000032
wherein, K (alpha)i) The integral heat conductivity coefficient matrix of the thermal analysis domain in the ith step is obtained; t is the temperature field of the thermal analysis domain (.)TRepresenting transpose, n is the number of nodes covered by high thermal conductivity material in the finite element of the underlying design domain, neIs the number of unit nodes, KEIs the cell stiffness matrix and N is the number of cells.
7. The thermal conduction topology optimization mobile robot path planning method based on dichotomy solution of claim 1, it is characterized in that when the single-step growth optimization model is solved by adopting a dichotomy method, the cooling channel starts from a heat source, the initial end of the cooling channel is arranged at the heat source during initial growth, selecting an optimal growth direction from a material library according to the principle of optimal heat dissipation performance, laying a cooling channel corresponding to the optimal growth direction into a thermal analysis domain, after the position of the high thermal conductivity material of the previous step in the design domain is determined, the starting end of the current cooling channel is fixed at the end of the previous cooling channel, and then, determining the growth direction of the current step according to the searching principle of the optimal heat dissipation performance, and continuously growing until the heat sink is reached, namely the distance from the tail end of the new cooling channel to the heat sink is less than the length of the cooling channel.
8. The method of claim 1, wherein the optimal search direction θ is solved in a cooling channel materials library*When the mobile robot moves, the searching directions of the mobile robot, namely 8 searching directions, are set along the axial direction of a certain unit, the direction perpendicular to the axial direction, the included angle of 45 degrees with the axial line and the included angle of minus 45 degrees with the axial line, the searching direction in the cooling channel material library corresponding to the movement of the mobile robot is represented by theta, the heat dissipation function of the searching direction is J (theta), and the optimal growth angle theta is*Expressed as:
J(θ*)＝min{J(θ)}
Figure FDA0003027792160000041
9. a computer device, comprising a processor and a memory, wherein the memory is used for storing a computer executable program, the processor reads part or all of the computer executable program from the memory and executes the computer executable program, and the processor can realize the method for planning the path of the heat conduction topology optimization mobile robot based on the dichotomy solution according to the claims 1-8 when executing the part or all of the computer executable program.
10. A computer-readable storage medium, wherein a computer program is stored in the computer-readable storage medium, and when the computer program is executed by a processor, the method for planning a path of a heat conduction topology optimized mobile robot based on dichotomy solution as recited in claims 1-8 is implemented.
CN202110420876.1A 2021-04-19 2021-04-19 Heat conduction topology optimization mobile robot path planning method based on dichotomy solution Active CN113159417B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110420876.1A CN113159417B (en) 2021-04-19 2021-04-19 Heat conduction topology optimization mobile robot path planning method based on dichotomy solution

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110420876.1A CN113159417B (en) 2021-04-19 2021-04-19 Heat conduction topology optimization mobile robot path planning method based on dichotomy solution

Publications (2)

Publication Number Publication Date
CN113159417A true CN113159417A (en) 2021-07-23
CN113159417B CN113159417B (en) 2022-12-09

Family

ID=76868751

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110420876.1A Active CN113159417B (en) 2021-04-19 2021-04-19 Heat conduction topology optimization mobile robot path planning method based on dichotomy solution

Country Status (1)

Country Link
CN (1) CN113159417B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112800558A (en) * 2021-02-01 2021-05-14 西安交通大学 Design method for phase change temperature control assembly fin structure of high-heat-flow short-time working platform

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105912763A (en) * 2016-04-06 2016-08-31 西安交通大学 Heat conduction path topological optimization based underwater glider cruise path planning method
CN110207709A (en) * 2019-06-25 2019-09-06 西安交通大学 Method for planning path for mobile robot based on parametrization level set
CN111709171A (en) * 2020-06-08 2020-09-25 西安交通大学 Isogeometric solving and heat dissipation topology generation method for heat flow strong coupling problem

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105912763A (en) * 2016-04-06 2016-08-31 西安交通大学 Heat conduction path topological optimization based underwater glider cruise path planning method
CN110207709A (en) * 2019-06-25 2019-09-06 西安交通大学 Method for planning path for mobile robot based on parametrization level set
CN111709171A (en) * 2020-06-08 2020-09-25 西安交通大学 Isogeometric solving and heat dissipation topology generation method for heat flow strong coupling problem

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112800558A (en) * 2021-02-01 2021-05-14 西安交通大学 Design method for phase change temperature control assembly fin structure of high-heat-flow short-time working platform
CN112800558B (en) * 2021-02-01 2022-10-28 西安交通大学 Design method for phase change temperature control assembly fin structure of high-heat-flow short-time working platform

Also Published As

Publication number Publication date
CN113159417B (en) 2022-12-09

Similar Documents

Publication Publication Date Title
Agarwal et al. Indexing moving points
Nakatake et al. Module packing based on the BSG-structure and IC layout applications
Hong et al. Corner block list: An effective and efficient topological representation of non-slicing floorplan
CN105630968A (en) Distributed expandable quadtree indexing mechanism oriented to Cassandra and query method based on mechanism
CN113962030B (en) Method for updating disturbance domain of overlapped grids of multi-body separation simulation of aircraft
WO2019085709A1 (en) Pooling method and system applied to convolutional neural network
Chai et al. Fast ${\cal H} $-Matrix-Based Direct Integral Equation Solver With Reduced Computational Cost for Large-Scale Interconnect Extraction
CN113159417B (en) Heat conduction topology optimization mobile robot path planning method based on dichotomy solution
Ryu et al. Mobile robot path planning algorithm by equivalent conduction heat flow topology optimization
Leonardi et al. Realistic nano-polycrystalline microstructures: beyond the classical Voronoi tessellation
Gopalakrishnan et al. Architecture-aware FPGA placement using metric embedding
CN110207709B (en) Mobile robot path planning method based on parameterized level set
CN111695281A (en) Particle rapid positioning method for tetrahedral mesh division finite element particle simulation
Li et al. A novel thermal optimization flow using incremental floorplanning for 3D ICs
Ding et al. Resolution of unknown heat source inverse heat conduction problems using particle swarm optimization
Xu et al. Computing the map of geometric minimal cuts
Zhu et al. Distributed processing of continuous range queries over moving objects
Provatidis Coons-patch macroelements in two-dimensional parabolic problems
Moukalled et al. The discretization process
Lin et al. A new directional query method for polygon dataset in spatial database
Wang et al. Efficient spatial big data storage and query in HBase
Bastos et al. Two accelerated isogeometric boundary element method formulations: fast multipole method and hierarchical matrices method
Xiang et al. An Efficient Element-Free Galerkin Method Based on Adaptive TR-AB2 Scheme for Transient Heat Conduction Problems
Yan et al. Ultra-fast fpga implementation of graph cut algorithm with ripple push and early termination
Fang et al. Path planning algorithm of mobile robot based on dichotomy of thermal conduction topology optimization

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant