CN110196588A - Method for planning path for mobile robot based on networks decomposition - Google Patents

Method for planning path for mobile robot based on networks decomposition Download PDF

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CN110196588A
CN110196588A CN201910244831.6A CN201910244831A CN110196588A CN 110196588 A CN110196588 A CN 110196588A CN 201910244831 A CN201910244831 A CN 201910244831A CN 110196588 A CN110196588 A CN 110196588A
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barrier
network
mobile robot
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formula
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张鹏超
李海婷
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Shaanxi University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0217—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with energy consumption, time reduction or distance reduction criteria

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  • Aviation & Aerospace Engineering (AREA)
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  • General Physics & Mathematics (AREA)
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  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention discloses the method for planning path for mobile robot based on networks decomposition, the basic line of line using starting point to target point as traveling, barrier network model is established using networks decomposition, and tear out sub-network, path and the minimum weight of time of mobile robot are calculated separately by Mathematical Fitting, it show that mobile robot reaches and bypass the optimum path planning of next barrier, basic line is adjusted.Method for planning path for mobile robot of the invention based on networks decomposition, simple clear, exploitativeness is strong；Movement routine can be effectively corrected according to barrier, and in time and path can be adjusted flexibly for newly-increased barrier, with the path planning being optimal；Mobile robot can effectively avoid colliding with barrier in the process of moving, improve the service life of mobile robot.

Description

Method for planning path for mobile robot based on networks decomposition
Technical field
The invention belongs to robotic technology fields, and in particular to the mobile robot path planning side based on networks decomposition Method.
Background technique
Currently, most typical robot global path planning method includes Grid Method, Visual Graph method, topological approach, freely sky Between method, artificial neural network method etc..A kind of Chinese patent " robot path planning method and system based on topological map " (Shen It please day: 2018.04.27；Application number: CN2018103933653；Publication date: 2018.10.16；The patent No.: CN108664022A) Robot path planning method and system based on topological map are disclosed, this method establishes the mistake of topological network by topological approach Journey is considerably complicated；Chinese patent " a kind of paths planning method in discontinuous grid division three-dimensional point cloud face " (applying date: 2018.03.09；Application number: CN2018101961343；Publication date: 2018.08.21；The patent No.: CN108422670A) it is open The paths planning method in discontinuous grid division three-dimensional point cloud face, the division of this method grid directly affect its program results, Path planning accuracy is poor.Chinese patent " paths planning method of the mobile robot " (applying date: 2015.01.20；Application Number: CN2015100282750；Publication date: 2015.04.29；The patent No.: CN104571113A) disclose the road of mobile robot Diameter planing method, this method uses artificial neural network method, but its overall applicability is not very successful, and the environment encountered is thousand changes Ten thousand is changing, random, and is difficult to describe with the formula of mathematics.
Summary of the invention
The object of the present invention is to provide the method for planning path for mobile robot based on networks decomposition, can be according to obstacle Object effectively corrects path.
The technical scheme adopted by the invention is that the method for planning path for mobile robot based on networks decomposition, to rise Initial point to target point line as traveling basic line, establish barrier network model using networks decomposition, and tear Sub-network out is calculated separately path and the minimum weight of time of mobile robot by Mathematical Fitting, obtains mobile robot The optimum path planning for reaching and bypassing next barrier, is adjusted basic line, specifically includes the following steps:
Step 1) finds out the geometric center of barrier, estimates the area S of barrier, and using barrier area S as class electricity Hinder Z, S=Z；
Step 2) establishes barrier network mould using each barrier as network node, according to Global obstacle object and its position Barrier position and its size total weight value are analogized to voltage by type, and the distance between network node analogizes to resistance, Oriented dependence between node analogizes to electric current, and barrier network model is torn out sub-network using networks decomposition；
Step 3) calculates the node class voltage U after tearinga, fitting quasi-resistance Z and node class voltage UaRelational expression；
Step 4) is according to quasi-resistance Z and node class voltage UaRelational expression calculate mobile robot cut-through object and pass by Arc length l0, then show that mobile robot reaches and bypasses the optimal path of next barrier and complete optimal path and taken Between, mobile robot is adjusted basic line according to the optimal path of planning, is travelled by starting point to target point.
The features of the present invention also characterized in that
The area S of estimation barrier is specifically, using the geometric center of barrier as origin, with the barrier in step 1) Geometric center to farthest boundary point distance as radius, do the circumscribed circle of the barrier, the area of circumscribed circle is the barrier Hinder the area S of object.
Barrier network model is torn out specifically, selected distance is mobile by sub-network using networks decomposition in step 2) The nearest point of the mobile starting point of robot is reference point, sub-network is torn out from boundary point, node total number contained by sub-network is not Less than the half of barrier network model node total number, sub-network is made of barrier network model by the branch of tear fracture, obstacle The part that object network model removes sub-network is to retain network.
Step 3) is specifically implemented according to the following steps:
Step 3.1) lists barrier network mould according to KCL Kirchhoff's current law (KCL) and KVL Kirchhoff's second law Type tearing before nodal voltage equation, be
YnUn=Jn (1)
In formula (1), JnFor the injection current matrix of n node, YnFor the admittance matrix of n node, UnFor n node Node voltage matrix, n are the node total numbers in barrier network model, and n is 0 natural number；
Step 3.2) is arranged according to the superposition theorem of circuit, KCL Kirchhoff's current law (KCL) and KVL Kirchhoff's second law Out barrier network model tearing after nodal voltage equation, be
YaUa=Ja+Jn (2)
In formula (2), subscript a indicates the reservation network portion for having common node with sub-network, which is to retain network G, YaFor the node class admittance for retaining network G, YaFor the block diagonal battle array for retaining network G, JaIt is injection caused by tear fracture branch Retain the unitary current of network G node, JaDirection be to be directed toward target point, U from mobile starting pointa=Un；
Step 3.3) is set by the electric current of tear fracture branch as unit electric current Is, then by the electric current of tear fracture branch and reservation network G Relationship is,
Ja=CasIs (3)
In formula (3), subscript s is indicated by the branch of tear fracture, CasIt is the negative submatrix of incidence matrix A, incidence matrix A is to retain The incidence matrix that all nodes of network G are constituted with all directed line segments by between tear fracture branch respectively, the column quilt of incidence matrix A Tear fracture branch, the row of incidence matrix A correspond to the node for retaining network G, and numerical value is respectively to be directed toward by tear fracture branch in incidence matrix A The node of network G is -1, by the node that tear fracture branch leaves network G be 1, is by tear fracture branch is uncorrelated to the node of network G 0, negative submatrix CasColumn it is corresponding by tear fracture branch, negative submatrix CasThe corresponding node for retaining network G of row；
Step 3.4) is set by tear fracture branch as pure resistance branch, then
ZsIs=Us (4)
In formula (4), ZsIt indicates by tear fracture branch impedance matrix, ZsFor by tear fracture branch diagonal matrix, UsIt indicates by tear fracture branch Road voltage,
It is with the voltage relationship for retaining network G by tear fracture branch,
US=-Cas TUa(5)；
Step 3.5) is brought formula (3) into formula (2) and is obtained,
YaUa-CasIs=Jn (6)
Formula (4) is brought into formula (5) to obtain,
Cas TUa+ZsIs=0 (7)
(6) formula is brought into (7) formula to obtain,
Is=(Zs+Cas TYa -1Cas)Cas TYa -1Jn (8)
IfIt brings (8) formula into (6) formula, calculates UaFor,
By the node class voltage U after tearingaAs the equipressure circle of robot path approach, i.e., mobile robot encounters obstacle The deceleration early warning value of object and avoidance；
Step 3.6) is according to the quasi-resistance z node class voltage U corresponding with its of nodes all in barrier network modela, Fitting its functional relation by least square method is,
Z=f (ua) (10)。
Step 4) is specifically implemented according to the following steps:
If particle center to geometric figure boundary maximum distance be r, then
S=π r2 (11)
If the region area that barrier is worn by robot is R, then
In formula (12), θ is central angle corresponding to the string for the barrier circumscribed circle that will be detoured, the barrier circumscribed circle String is the line segment that starting point passes through the barrier circumscribed circle that will be detoured to target point line；
It calculatesValue, ifThen mobile robot is turned left, ifThen mobile robot is turned right, ifThen mobile robot turns left or turns right and chooses any one kind of them, ifThen mobile robot presses former straight-line travelling without rotation；
The arc length l that the barrier that mobile robot will detour is passed by0For,
The barrier that mobile robot will detour is passed by arc length l0Time be,
In formula (14), v0For the detour speed of robot,
Mobile robot pass by clear space linear distance be l1, pass by clear space linear distance l1Time be,
In formula (15), v1For robot linear motion speed,
Then mobile robot reaches and bypasses the optimal path of next barrier and is,
L=l1+l0(16),
Completing optimal path required time is,
T=t1+t0(17),
From starting point, the line along starting point to target point travels mobile robot, in the equipressure circle of deceleration early warning Detour speed v along circular arc in region0Traveling, with point-to-point speed v behind the round region of the equipressure of deceleration early warning after being driven out to1Before straight line Row, according to this driving mode until reaching target point.
The beneficial effects of the present invention are:
The present invention is based on the method for planning path for mobile robot of networks decomposition, simple clear, exploitativeness is strong；It can Movement routine is effectively corrected according to barrier, and in time and path can be adjusted flexibly for newly-increased barrier, to reach most Excellent path planning；Mobile robot can effectively avoid colliding with barrier in the process of moving, improve mobile robot Service life.
Detailed description of the invention
Fig. 1 is the flow chart of the method for planning path for mobile robot the present invention is based on networks decomposition.
Specific embodiment
The present invention is described in detail With reference to embodiment.
The present invention is based on the method for planning path for mobile robot of networks decomposition, as shown in Figure 1, with starting point to target Basic line of the line of point as traveling, establishes barrier network model using networks decomposition, and tear out sub-network, leads to It crosses Mathematical Fitting and calculates separately the path of mobile robot and the minimum weight of time, show that mobile robot is reached and bypassed down The optimum path planning of one barrier, is adjusted basic line, specifically includes the following steps:
Step 1) finds out the geometric center of barrier, using the geometric center of barrier as origin, with the several of the barrier What center to farthest boundary point distance as radius, do the circumscribed circle of the barrier, the area of circumscribed circle is the barrier Area S, and using barrier area S as quasi-resistance Z, S=Z.
Step 2) establishes barrier network mould using each barrier as network node, according to Global obstacle object and its position Type tears out subnet specifically, it is reference point that selected distance mobile robot, which moves the nearest point of starting point, from boundary point Network, node total number contained by sub-network are no less than the half of barrier network model node total number, and sub-network is by barrier network mould Type is formed by the branch of tear fracture, and the part that barrier network model removes sub-network is to retain network, by barrier position And its size total weight value analogizes to voltage, the distance between network node analogizes to resistance, the oriented dependence between node Relationship analogizes to electric current, and barrier network model is torn out sub-network using networks decomposition.
Step 3) calculates the node class voltage U after tearinga, fitting quasi-resistance Z and node class voltage UaRelational expression；
Step 3.1) lists barrier network mould according to KCL Kirchhoff's current law (KCL) and KVL Kirchhoff's second law Type tearing before nodal voltage equation, be
YnUn=Jn (1)
In formula (1), JnFor the injection current matrix of n node, YnFor the admittance matrix of n node, UnFor n node Node voltage matrix, n are the node total numbers in barrier network model, and n is 0 natural number；
Step 3.2) is arranged according to the superposition theorem of circuit, KCL Kirchhoff's current law (KCL) and KVL Kirchhoff's second law Out barrier network model tearing after nodal voltage equation, be
YaUa=Ja+Jn (2)
In formula (2), subscript a indicates the reservation network portion for having common node with sub-network, which is to retain network G, YaFor the node class admittance for retaining network G, YaFor the block diagonal battle array for retaining network G, JaIt is injection caused by tear fracture branch Retain the unitary current of network G node, JaDirection be to be directed toward target point, U from mobile starting pointa=Un；
Step 3.3) is set by the electric current of tear fracture branch as unit electric current Is, then by the electric current of tear fracture branch and reservation network G Relationship is,
Ja=CasIs (3)
In formula (3), subscript s is indicated by the branch of tear fracture, CasIt is the negative submatrix of incidence matrix A, incidence matrix A is to retain The incidence matrix that all nodes of network G are constituted with all directed line segments by between tear fracture branch respectively, the column quilt of incidence matrix A Tear fracture branch, the row of incidence matrix A correspond to the node for retaining network G, and numerical value is respectively to be directed toward by tear fracture branch in incidence matrix A The node of network G is -1, by the node that tear fracture branch leaves network G be 1, is by tear fracture branch is uncorrelated to the node of network G 0, negative submatrix CasColumn it is corresponding by tear fracture branch, negative submatrix CasThe corresponding node for retaining network G of row；
Step 3.4) is set by tear fracture branch as pure resistance branch, then
ZsIs=Us (4)
In formula (4), ZsIt indicates by tear fracture branch impedance matrix, ZsFor by tear fracture branch diagonal matrix, UsIt indicates by tear fracture branch Road voltage,
It is with the voltage relationship for retaining network G by tear fracture branch,
US=-Cas TUa(5)；
Step 3.5) is brought formula (3) into formula (2) and is obtained,
YaUa-CasIs=Jn (6)
Formula (4) is brought into formula (5) to obtain,
Cas TUa+ZsIs=0 (7)
(6) formula is brought into (7) formula to obtain,
Is=(Zs+Cas TYa -1Cas)Cas TYa -1Jn (8)
IfIt brings (8) formula into (6) formula, calculates UaFor,
By the node class voltage U after tearingaAs the equipressure circle of robot path approach, i.e., mobile robot encounters obstacle The deceleration early warning value of object and avoidance；
Step 3.6) is according to the quasi-resistance z node class voltage U corresponding with its of nodes all in barrier network modela, Fitting its functional relation by least square method is,
Z=f (ua) (10)。
Step 4) is according to quasi-resistance Z and node class voltage UaRelational expression calculate mobile robot cut-through object and pass by Arc length l0, then show that mobile robot reaches and bypasses the optimal path of next barrier and complete optimal path and taken Between, mobile robot is adjusted basic line according to the optimal path of planning, is travelled by starting point to target point.
Step 4) is specifically implemented according to the following steps:
If particle center to geometric figure boundary maximum distance be r, then
S=π r2 (11)
If the region area that barrier is worn by robot is R, then
In formula (12), θ is central angle corresponding to the string for the barrier circumscribed circle that will be detoured, the barrier circumscribed circle String is the line segment that starting point passes through the barrier circumscribed circle that will be detoured to target point line；
It calculatesValue, ifThen mobile robot is turned left, ifThen mobile robot is turned right, ifThen mobile robot turns left or turns right and chooses any one kind of them, ifThen mobile robot presses former straight-line travelling without rotation；
The arc length l that the barrier that mobile robot will detour is passed by0For,
The barrier that mobile robot will detour is passed by arc length l0Time be,
In formula (14), v0For the detour speed of robot,
Mobile robot pass by clear space linear distance be l1, pass by clear space linear distance l1Time be,
In formula (15), v1For robot linear motion speed,
Then mobile robot reaches and bypasses the optimal path of next barrier and is,
L=l1+l0(16),
Completing optimal path required time is,
T=t1+t0(17),
From starting point, the line along starting point to target point travels mobile robot, in the equipressure circle of deceleration early warning Detour speed v along circular arc in region0Traveling, with point-to-point speed v behind the round region of the equipressure of deceleration early warning after being driven out to1Before straight line Row, according to this driving mode until reaching target point.

Claims (5)

1. the method for planning path for mobile robot based on networks decomposition, which is characterized in that with the company of starting point to target point Basic line of the line as traveling, establishes barrier network model using networks decomposition, and tear out sub-network, passes through mathematics Fitting calculates separately path and the minimum weight of time of mobile robot, show that mobile robot reaches and bypasses next obstacle The optimum path planning of object, is adjusted basic line, specifically includes the following steps:
Step 1) finds out the geometric center of barrier, estimates the area S of barrier, and using barrier area S as quasi-resistance Z, S =Z；
Step 2) establishes barrier network model using each barrier as network node, according to Global obstacle object and its position, will Barrier position and its size total weight value analogize to voltage, and the distance between network node analogizes to resistance, node Between oriented dependence analogize to electric current, barrier network model is torn out by sub-network using networks decomposition；
Step 3) calculates the node class voltage U after tearinga, fitting quasi-resistance Z and node class voltage UaRelational expression；
Step 4) is according to quasi-resistance Z and node class voltage UaRelational expression calculate the arc length passed by of mobile robot cut-through object l0, the time required to then showing that mobile robot reaches and bypasses the optimal path of next barrier and completes optimal path, move Mobile robot is adjusted basic line according to the optimal path of planning, is travelled by starting point to target point.
2. the method for planning path for mobile robot according to claim 1 based on networks decomposition, which is characterized in that institute The area S of estimation barrier in step 1) is stated specifically, using the geometric center of barrier as origin, with the geometry of the barrier Center to farthest boundary point distance as radius, do the circumscribed circle of the barrier, the area of circumscribed circle is the barrier Area S.
3. the method for planning path for mobile robot according to claim 1 based on networks decomposition, which is characterized in that institute It states in step 2) and barrier network model is torn out specifically, selected distance mobile robot by sub-network using networks decomposition The nearest point of mobile starting point is reference point, and sub-network is torn out from boundary point, and node total number contained by sub-network no less than hinders Hinder the half of object network model node total number, sub-network is made of barrier network model by the branch of tear fracture, barrier network The part that model removes sub-network is to retain network.
4. the method for planning path for mobile robot according to claim 1 based on networks decomposition, which is characterized in that institute Step 3) is stated to be specifically implemented according to the following steps:
Step 3.1) is listed barrier network model according to KCL Kirchhoff's current law (KCL) and KVL Kirchhoff's second law and is torn Nodal voltage equation before splitting is
YnUn=Jn (1)
In formula (1), JnFor the injection current matrix of n node, YnFor the admittance matrix of n node, UnFor the node of n node Voltage matrix, n are the node total numbers in barrier network model, and n is 0 natural number；
Step 3.2) lists barrier according to the superposition theorem of circuit, KCL Kirchhoff's current law (KCL) and KVL Kirchhoff's second law Hinder object network model tear after nodal voltage equation, be
YaUa=Ja+Jn (2)
In formula (2), subscript a indicates the reservation network portion for having common node with sub-network, which is to retain network G, YaFor Retain the node class admittance of network G, YaFor the block diagonal battle array for retaining network G, JaIt is that injection caused by tear fracture branch retains net The unitary current of network G node, JaDirection be to be directed toward target point, U from mobile starting pointa=Un；
Step 3.3) is set by the electric current of tear fracture branch as unit electric current Is, then by the current relationship of tear fracture branch and reservation network G For,
Ja=CasIs (3)
In formula (3), subscript s is indicated by the branch of tear fracture, CasIt is the negative submatrix of incidence matrix A, incidence matrix A is to retain network The incidence matrix that all nodes of G are constituted with all directed line segments by between tear fracture branch respectively, the column of incidence matrix A are by tear fracture Branch, the row of incidence matrix A correspond to the node for retaining network G, and numerical value is respectively to be directed toward network by tear fracture branch in incidence matrix A The node of G is -1, by the node that tear fracture branch leaves network G be 1, by tear fracture branch it is uncorrelated to the node of network G be 0, bear Submatrix CasColumn it is corresponding by tear fracture branch, negative submatrix CasThe corresponding node for retaining network G of row；
Step 3.4) is set by tear fracture branch as pure resistance branch, then
ZsIs=Us (4)
In formula (4), ZsIt indicates by tear fracture branch impedance matrix, ZsFor by tear fracture branch diagonal matrix, UsIt indicates by tear fracture branch electricity Pressure,
It is with the voltage relationship for retaining network G by tear fracture branch,
US=-Cas TUa(5)；
Step 3.5) is brought formula (3) into formula (2) and is obtained,
YaUa-CasIs=Jn (6)
Formula (4) is brought into formula (5) to obtain,
Cas TUa+ZsIs=0 (7)
(6) formula is brought into (7) formula to obtain,
Is=(Zs+Cas TYa -1Cas)Cas TYa -1Jn (8)
IfIt brings (8) formula into (6) formula, calculates UaFor,
By the node class voltage U after tearingaAs the equipressure circle of robot path approach, i.e., mobile robot encounters barrier simultaneously The deceleration early warning value of avoidance；
Step 3.6) is according to the quasi-resistance z node class voltage U corresponding with its of nodes all in barrier network modela, by most Small square law fits its functional relation,
Z=f (ua) (10)。
5. the method for planning path for mobile robot according to claim 1 based on networks decomposition, which is characterized in that institute Step 4) is stated to be specifically implemented according to the following steps:
If particle center to geometric figure boundary maximum distance be r, then
S=π r2 (11)
If the region area that barrier is worn by robot is R, then
In formula (12), θ is central angle corresponding to the string for the barrier circumscribed circle that will be detoured, and the string of the barrier circumscribed circle is Starting point passes through the line segment for the barrier circumscribed circle that will be detoured to target point line；
It calculatesValue, ifThen mobile robot is turned left, ifThen mobile robot is turned right, ifThen move Mobile robot, which turns left or turns right, chooses any one kind of them, ifThen mobile robot presses former straight-line travelling without rotation；
The arc length l that the barrier that mobile robot will detour is passed by0For,
The barrier that mobile robot will detour is passed by arc length l0Time be,
In formula (14), v0For the detour speed of robot,
Mobile robot pass by clear space linear distance be l1, pass by clear space linear distance l1Time be,
In formula (15), v1For robot linear motion speed,
Then mobile robot reaches and bypasses the optimal path of next barrier and is,
L=l1+l0(16),
Completing optimal path required time is,
T=t1+t0(17),
From starting point, the line along starting point to target point travels mobile robot, in the equipressure circle region of deceleration early warning Along circular arc with the speed v that detours0Traveling, with point-to-point speed v behind the round region of the equipressure of deceleration early warning after being driven out to1Going straight ahead, according to Driving mode is until reach target point like this.
CN201910244831.6A 2019-03-28 2019-03-28 Method for planning path for mobile robot based on networks decomposition Pending CN110196588A (en)

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