CN110244759B - Underwater robot time optimal path planning method based on interval optimization - Google Patents

Underwater robot time optimal path planning method based on interval optimization Download PDF

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CN110244759B
CN110244759B CN201910483637.3A CN201910483637A CN110244759B CN 110244759 B CN110244759 B CN 110244759B CN 201910483637 A CN201910483637 A CN 201910483637A CN 110244759 B CN110244759 B CN 110244759B
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interval
ocean current
value
time
path
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CN110244759A (en
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姚绪梁
王峰
王景芳
赵继成
马赫
黄乘齐
关越铭
姜奕舒
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Harbin Engineering University
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Abstract

The invention discloses an underwater robot time optimal path planning method based on interval optimization, which comprises the following steps: step 1: determining a rectangular path search area according to the path and rasterizing, wherein the size of a grid is determined by the resolution of an ocean current prediction system, and an uncertain ocean current model is established based on a predicted value given by the ocean current prediction system; step 2: searching a candidate path from a starting point to an end point by using an ant colony system algorithm; and step 3: calculating the maximum value and the minimum value of the navigation time of the candidate path generated in the step 2 under the interval ocean current environment by using a vector analysis method; and 4, step 4: converting the response interval of the candidate path into an interval radius and an interval mean value; then, calculating the evaluation function value of the candidate path according to the section radius and the section mean value; and 5: and returning the evaluation function value to the ant colony system algorithm, and searching the optimal path according to an optimization mechanism. The method adopts an interval optimization algorithm to solve the problem of inaccuracy of ocean current prediction, and is simple, reliable, easy to implement, small in calculated amount and good in real-time performance.

Description

Underwater robot time optimal path planning method based on interval optimization
Technical Field
The invention relates to a novel time optimal path planning method in an uncertain ocean current environment, in particular to an underwater robot time optimal path planning method based on interval optimization, and belongs to the field of underwater robot control.
Background
In the marine environment, ocean currents, a widely existing phenomenon of seawater flow, have a non-negligible effect on the navigation of the AUV. How to reasonably utilize ocean current energy to pre-plan an AUV navigation path so that the AUV can efficiently and safely reach a target area becomes one of main research contents of AUV path planning in recent years. However, due to the inaccuracy of the ocean current prediction system, the predicted ocean current data is different from the real ocean current data in the ocean environment, and the utilization of the ocean current is the basis of the AUV time optimal and energy consumption optimal path planning, so that the processing of the ocean current uncertainty is very important and has practical significance, and the method becomes a hotspot for research of scholars at home and abroad gradually.
The path planning algorithm using ocean current energy mainly aims to find a path between a starting point and a terminal point which is as downstream as possible so as to save the navigation time and energy consumption of the AUV. The traditional path planner search method comprises: according to the ocean current data predicted by the ocean current prediction system, a minimum navigation time path or a minimum energy consumption path from a starting point to an end point is searched by using a graph search algorithm, a group optimization algorithm and the like. The traditional path planning algorithm does not consider uncertainty of ocean current, the obtained path has poor robustness, and even the planned path cannot reach the end point. Because the AUV mostly runs under an unsupervised state when executing tasks and only carries energy by the AUV, the performance of the path planner directly influences the AUV range and the safety. The method solves the problem of inaccuracy of ocean current prediction by adopting an interval optimization algorithm for the first time, and is simple, reliable, easy to realize, small in calculated amount and good in real-time performance.
Disclosure of Invention
Aiming at the prior art, the invention aims to solve the technical problem of providing the underwater robot time optimal path planning method based on interval optimization, which solves the problem of ocean current prediction inaccuracy, is simple and reliable, is easy to realize, has small calculated amount and good real-time performance.
In order to solve the technical problem, the invention provides an underwater robot time optimal path planning method based on interval optimization, which comprises the following steps:
step 1: determining a rectangular path search area according to the starting point and the end point of the underwater robot path, rasterizing the area, determining the grid size by the resolution of an ocean current prediction system, and establishing an uncertain ocean current model based on a predicted value given by the ocean current prediction system;
step 2: searching a candidate path from a starting point to an end point by using an ant colony system algorithm according to the pheromone concentration and heuristic information;
and step 3: calculating the maximum value and the minimum value of the navigation time of the candidate path generated in the step 2 in the interval ocean current environment by using a vector analysis method, namely a response interval;
and 4, step 4: converting the response interval of the candidate path obtained in the step 3 into an interval radius and an interval mean value through an interval order relation conversion model, namely converting the interval number into a real number; then, calculating the evaluation function value of the candidate path by using the interval radius and the interval mean value by using a linear weighting method;
and 5: and (4) taking the evaluation function value obtained in the step (4) as a fitness value of the candidate path, returning to the ant colony system algorithm, and searching the optimal path by the ant colony system algorithm according to the optimizing mechanism of the ant colony system algorithm.
The invention also includes:
1. the uncertain ocean current model comprises: [ lbcd,ubcd]And [ lb ]cm,ubcm]Wherein [ lb ]cd,ubcd]Is the interval of ocean current direction, [ lbcm,ubcm]Is the size interval of ocean current; wherein, lbcd,ubcd,lbcm,ubcmThe expression satisfies:
Figure BDA0002084641000000021
in the formula, cdNAnd cmNNominal values, c, representing direction and magnitude of the sea current, respectivelydNAnd cmNPredicting the predicted value of the system for the ocean current; upsilon and sigma respectively represent uncertainty levels of the direction and the size of the ocean current, and values are taken through errors of a predicted value and an actually measured value in historical data.
2. The step 2 comprises the following steps:
step 2.1: setting parameters and initializing ant colony;
step 2.2: the state transition equation of the ant k moving from the current grid i to the neighborhood satisfies:
Figure BDA0002084641000000022
where j represents the next grid to be accessed, h represents any neighborhood of grid i,
Figure BDA0002084641000000023
represents the neighborhood set of ant k on grid i, τihAnd ηihPheromone and heuristic information between grids i and h respectively, alpha and beta represent the importance of the pheromone and the heuristic information in the process of constructing the path by the ants respectively, and q is uniformly distributed in intervals [0,1 ]]A random variable of q0Is [0,1 ]]J is a random variable generated according to the probability distribution, and the probability distribution formula satisfies:
Figure BDA0002084641000000024
in the formula (I), the compound is shown in the specification,
Figure BDA0002084641000000025
representing the probability of an ant k transitioning from the current grid i to the adjacent grid h, and determining j by roulette wheel method, by adjusting the parameter q0Adjusting the exploration degree of the algorithm on the new path;
step 2.3: local pheromone updating: in the path construction process, each time an ant passes through one edge (i, j), the pheromone on the edge is updated, and the updating rule meets the following requirements:
τij＝(1-ξ)τij+ξτ0
where xi is local pheromone evaporation coefficient, its value satisfies 0 < xi < 1, tau0Is the initial value of the pheromone quantity, each time an ant passes the edge (i, j), the pheromone tau of the edgeijThe probability that other ants select the edge will be reduced;
step 2.4: if the ants arrive at the end point, inputting the constructed candidate path into an inner-layer algorithm; if the end point is not reached, the step 2.2 is returned to, and the path is continuously constructed.
3. The method for determining the maximum value and the minimum value of the navigation time comprises the following steps:
when AUV pre-sailing direction is in ocean current angle range [ lbcd,ubcd]Internal time:
minimum value of voyage time: when in use
Figure BDA0002084641000000031
Direction and
Figure BDA0002084641000000032
in the same direction, and
Figure BDA0002084641000000033
the time of flight is minimal, wherein,
Figure BDA0002084641000000034
the vector of the sea current is represented,
Figure BDA0002084641000000035
representing an AUV pre-voyage vector;
maximum value of navigation time: taking lbcdAnd ubcdNeutralization of
Figure BDA0002084641000000036
The one with larger included angle is used as
Figure BDA00020846410000000322
Direction, in the direction of the ocean current, the size of the ocean current is lbcmAnd ubcmThe greater of the two is the maximum navigation time in the ocean current interval;
when AUV pre-sailing direction is in ocean current angle range [ lbcd,ubcd]When the external force is applied:
minimum value of voyage time: taking lbcdAnd ubcdNeutralization of
Figure BDA0002084641000000037
The one with smaller angle is used as
Figure BDA0002084641000000038
Direction, if the included angle is greater than or equal to pi/2, let
Figure BDA0002084641000000039
If the included angle is less than pi/2, the size of the ocean current of the minimum navigation time meets the following requirements:
Figure BDA00020846410000000310
in the formula (I), the compound is shown in the specification,
Figure BDA00020846410000000311
the AUV is the propulsion speed; theta represents
Figure BDA00020846410000000312
And
Figure BDA00020846410000000313
the included angle is that the AUV navigation time is minimum under the ocean current condition;
maximum value of navigation time: taking lbcdAnd ubcdNeutralization of
Figure BDA00020846410000000314
The one with larger included angle is used as
Figure BDA00020846410000000315
Direction, in the direction of the ocean current, the size of the ocean current is lbcmAnd ubcmThe greater of the two is the maximum navigation time in the ocean current interval;
in the formula (I), the compound is shown in the specification,
Figure BDA00020846410000000316
representing an ocean current vector;
Figure BDA00020846410000000317
representing an AUV pre-voyage vector; theta represents
Figure BDA00020846410000000318
And
Figure BDA00020846410000000323
and (4) forming an included angle.
4. Step 4 comprises the following steps:
hypothesis candidate path ΓAThe navigation time interval of the ocean current in the corresponding interval is
Figure BDA00020846410000000319
Wherein
Figure BDA00020846410000000320
And
Figure BDA00020846410000000321
respectively representing a minimum flight time and a maximum flight time,
Figure BDA0002084641000000041
respectively, the midpoint and radius values are recorded as
Figure BDA0002084641000000042
And
Figure BDA0002084641000000043
satisfies the following conditions:
Figure BDA0002084641000000044
the invention adopts the method of less than or equal tocwThe sequence relation model and the linear weighting method convert the navigation time interval into a deterministic evaluation function:
Figure BDA0002084641000000045
wherein C is CI＝[CL,CR]
Converting the multi-objective optimization problem into a single-objective optimization problem by using a linear weighting method:
Figure BDA0002084641000000046
in the formula (f)dIs an evaluation function; c represents an uncertain ocean current vector; omega is more than or equal to 0 and less than or equal to 1, which is a multi-target weight coefficient and the value can be set according to the preference of a decision maker;
Figure BDA0002084641000000047
and
Figure BDA0002084641000000048
respectively representing the mean value and the radius of a navigation time interval of the path gamma in an uncertain ocean current environment; phi and
Figure BDA00020846410000000411
regularization factor, phi, and for multi-objective functions
Figure BDA00020846410000000412
Take values of the same order of magnitude as the respective targets.
4. The step 5 of searching the optimal path by the ant colony system algorithm according to the optimizing mechanism comprises the following steps:
the ant colony system algorithm updates the global pheromone according to the evaluation function value, if the ant colony system algorithm termination condition is met, the search is stopped, and the optimal path at present is output as a result path; if the termination condition is not met, returning to the step 2 to continue operation;
global pheromone update rule: only so far the optimal ants are allowed to release the pheromone after each iteration, the update rule is satisfied:
Figure BDA0002084641000000049
wherein, Δ τij＝1/E*，E*To the optimal path fitness value so far; rho is an evaporation coefficient, and rho is more than 0 and less than 1;
algorithm termination conditions are as follows: the ant colony system algorithm termination condition comprises a maximum iteration time condition and an additional termination condition, and when any one termination condition is met, the algorithm is ended;
wherein, the maximum iteration frequency condition is as follows: when the iteration times of the algorithm are equal to the maximum iteration times;
additional termination conditions were:
Figure BDA00020846410000000410
where r represents the current iteration number, Er-iRepresents the fitness value of the (r-i) th generation, and W is smaller than the set value.
The invention has the beneficial effects that: the invention fully considers the uncertainty problem caused by the inaccuracy of the ocean current prediction system, and converts the deterministic ocean current into the interval ocean current by increasing the uncertainty of the direction and the size of the ocean current so as to establish the uncertain ocean current model. And converting the interval optimization problem into a deterministic optimization problem through an interval sequence relation model based on an interval optimization theory. Meanwhile, a vector analysis method is used in the interval ocean current model to obtain the response interval of the candidate path, the problem of double-layer nesting in interval optimization is solved, the calculation efficiency of the algorithm is improved, and the robustness of the path planner is improved.
Drawings
Fig. 1 is a schematic view of an interval ocean current.
Fig. 2 is an interval ocean current environment model.
Fig. 3 is a flowchart of a time optimal path planning method based on interval optimization.
Fig. 4(a) is a schematic diagram illustrating a relationship between inter-zone ocean currents and the AUV pre-voyage direction in the ocean current angle range of the AUV pre-voyage direction.
FIG. 4(b) is a schematic diagram showing the relationship between the ocean currents and the AUV pre-sailing direction in the outer region of the AUV pre-sailing direction within the ocean current angle interval.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
a time optimal path planning algorithm based on interval optimization comprises the following steps:
step (1): as shown in fig. 1 and 2, an uncertain ocean current model is established based on a predicted value given by an ocean current prediction system;
and determining a rectangular path search area according to the starting point and the end point of the underwater robot path, and rasterizing the rectangular path search area, wherein the grid size is determined by the resolution of the ocean current prediction system. The direction and size of the interval ocean current are respectively expressed as [ lbcd,ubcd]And [ lbcm,ubcm]. Wherein, lbcd,ubcd,lbcm,ubcmThe expression is as follows:
Figure BDA0002084641000000051
in the formula, cdNAnd cmNRespectively representing nominal values of the direction and the magnitude of the ocean current, wherein the values are predicted values of an ocean current prediction system; upsilon and sigma respectively represent uncertainty levels of the direction and the size of the ocean current, and values can be obtained through errors of predicted values and measured values in historical data.
After the establishment of the environment model based on the interval ocean current is completed, as shown in fig. 3, the AUV path planning method designed by the present invention mainly comprises an outer layer algorithm and an inner layer algorithm, and the specific planning process comprises the following steps.
Step (2): and searching a candidate path from the starting point to the end point by using an ant colony system algorithm according to the pheromone concentration and heuristic information.
Step (2.1): setting parameters and initializing ant colony;
step (2.2): the state transition equation for ant k moving from current grid i to its neighborhood is as follows:
Figure BDA0002084641000000061
where j represents the next grid to be accessed, h represents any neighborhood of grid i,
Figure BDA0002084641000000062
representing the ant k in the neighborhood set of grid i. Tau.ihAnd ηihPheromone and heuristic information between grids i and h respectively, alpha and beta represent the importance of the pheromone and the heuristic information in the process of constructing the path by the ants respectively, and q is uniformly distributed in the interval [0,1 ]]A random variable of q0Is [0,1 ]]J is a random variable generated according to the probability distribution, which has the following formula:
Figure BDA0002084641000000063
in the formula (I), the compound is shown in the specification,
Figure BDA0002084641000000064
representing the probability of an ant k transitioning from the current grid i to the adjacent grid h and determining j by roulette wheel method. According to the above formula, the ant constructs the path channel in such a way that the probability of selecting the best possible moving mode currently is q0The optimal shifting pattern is obtained from the accumulated amount of the pheromones and the heuristic information value. Meanwhile, ants are represented by (1-q)0) The probability of (3) is biased to search other paths. By adjusting the parameter q0The degree of exploration of the algorithm for new paths may be adjusted.
Step (2.3): local pheromone update rules. In the path construction process, every time an ant passes through an edge (i, j), the rule is called immediately to update the pheromone on the edge:
τij＝(1-ξ)τij+ξτ0
where xi is local pheromone evaporation coefficient, its value satisfies 0 < xi < 1, tau0Is the initial value of the pheromone quantity. The effect of local renewal is that each time an ant passes the edge (i, j) the pheromone tau of which isijWill be reduced so that the probability of other ants selecting the edge is relatively reduced.
Step (2.4): and judging whether the ants reach the end point. If the destination is reached, inputting the constructed candidate path into an inner-layer algorithm; if the end point is not reached, the step 2.2 is returned to, and the path is continuously constructed.
And (3): and (3) calculating the maximum value and the minimum value of the navigation time of the candidate path generated in the step (2) in the interval ocean current environment by using a vector analysis method, namely, calculating a response interval.
As shown in fig. 4(a), when the AUV pre-voyage direction is within the ocean current angle interval:
minimum flight time: when in use
Figure BDA0002084641000000071
Direction and
Figure BDA0002084641000000072
in the same direction, and
Figure BDA0002084641000000073
the time of flight is minimal. Wherein the content of the first and second substances,
Figure BDA0002084641000000074
which is indicative of the vector of the sea current,
Figure BDA0002084641000000075
indicating the AUV pre-voyage vector.
Maximum time of flight: taking lbcdAnd ubcdNeutralization of
Figure BDA0002084641000000076
The one with larger included angle is used as
Figure BDA0002084641000000077
And (4) direction. In the direction of the ocean current, the size of the ocean current is respectively calculated as lbcmAnd ubcmThe greater of the two is the maximum voyage time in the current interval.
As shown in fig. 4(b), when the AUV pre-voyage direction is outside the ocean current angle interval:
minimum flight time: taking lbcdAnd ubcdNeutralization of
Figure BDA0002084641000000078
The one with smaller angle is used as
Figure BDA0002084641000000079
And (4) direction. If the included angle is greater than or equal to pi/2, let
Figure BDA00020846410000000710
If the included angle is less than pi/2, determining the size of the ocean current of the minimum navigation time according to the following expression,
Figure BDA00020846410000000711
in the formula (I), the compound is shown in the specification,
Figure BDA00020846410000000712
the AUV is the propulsion speed; theta represents
Figure BDA00020846410000000713
And
Figure BDA00020846410000000714
and (4) an included angle. The AUV navigation time is minimum under the ocean current condition obtained by the method.
Maximum voyage time: taking lbcdAnd ubcdNeutralization of
Figure BDA00020846410000000715
The one with larger included angle is used as
Figure BDA00020846410000000716
And (4) direction. In the direction of the ocean current, the size of the ocean current is respectively calculated as lbcmAnd ubcmThe greater of the two is the maximum voyage time in the current interval.
In the above description, the ocean current vectors at maximum and minimum voyages have been given, from which
Figure BDA00020846410000000717
And the AUV pre-voyage vector may be calculated by:
Figure BDA00020846410000000718
where t represents the time of flight of the AUV.
Figure BDA00020846410000000719
Wherein c isx，cyRespectively vector of ocean currents
Figure BDA00020846410000000720
Components in the x and y axes;
Figure BDA00020846410000000721
and
Figure BDA00020846410000000722
are respectively vectors
Figure BDA00020846410000000723
The components in the x and y axes.
And (4): converting the response interval of the candidate path obtained in the step (3) into an interval radius and an interval mean value through an interval order relation conversion model, namely converting the interval number into a real number; and then, calculating the evaluation function value of the candidate path by using the interval radius and the interval mean value by using a linear weighting method.
For any timeAnd selecting a path, wherein the value of the navigation time is an interval rather than a determined real value, so that in the optimization process, the advantages and the disadvantages of different candidate path navigation time intervals need to be compared, so that the advantages and the disadvantages of corresponding candidate paths are evaluated, and the optimal candidate path is searched. In interval optimization, interval order relationship can be used to determine whether an interval is better or worse than another interval. Hypothesis candidate path ΓAThe navigation time interval of the ocean current in the corresponding interval is
Figure BDA0002084641000000081
Wherein
Figure BDA0002084641000000082
And
Figure BDA0002084641000000083
respectively representing a minimum flight time and a maximum flight time,
Figure BDA0002084641000000084
respectively, the midpoint and radius values are recorded as
Figure BDA0002084641000000085
And
Figure BDA0002084641000000086
the expression is as follows:
Figure BDA0002084641000000087
the inter-sequence relationship is determined by the above four parameters, wherein
Figure BDA0002084641000000088
The method mainly embodies the average performance of the objective function under uncertainty; while
Figure BDA0002084641000000089
The minimization can reduce the sensitivity of the objective function to the uncertainty, thereby ensuring the design robustness. The invention adopts the following componentscwThe sequence relation model and the linear weighting method convert the navigation time interval into a deterministic evaluation function:
Figure BDA00020846410000000810
wherein C is CI＝[CL,CR]
In the formula, fdIs an evaluation function; c represents an uncertain ocean current vector; omega is more than or equal to 0 and less than or equal to 1, which is a multi-target weight coefficient and the value can be set according to the preference of a decision maker;
Figure BDA00020846410000000811
and
Figure BDA00020846410000000812
respectively representing the mean value and the radius of a navigation time interval of the path gamma in an uncertain ocean current environment; phi and
Figure BDA00020846410000000815
the regularization factor is a multi-objective function, and the value of the regularization factor can be approximately the same magnitude as that of each objective according to specific problems.
And (5): and (4) taking the evaluation function value obtained in the step (4) as a fitness value of the candidate path, returning to the ant colony system algorithm, and updating the global pheromone by the ant colony system algorithm according to the value. If the ant colony system algorithm termination condition is met, stopping searching, and outputting the current optimal path as a result path; and if the termination condition is not met, returning to the step 2 to continue the operation.
Global pheromone update rule: only the best ants to date are allowed to release pheromones after each iteration. The update rule is given by:
Figure BDA00020846410000000813
wherein, Δ τij＝1/E*，E*The optimal path fitness value is the optimal path fitness value up to now; rho is an evaporation coefficient, and rho is more than 0 and less than 1.
Algorithm termination conditions are as follows: the ant colony system algorithm has two termination conditions, namely maximum iteration times and an additional termination condition. And when the algorithm meets any one termination condition, the algorithm is ended.
1) When the iteration number of the algorithm is equal to the maximum iteration number, the termination condition is met;
2) additional termination criteria:
Figure BDA00020846410000000814
where r represents the current iteration number, Er-iRepresenting the fitness value of the (r-i) th generation. In the upper ant colony system algorithm, let λ be 20, when W is less than 1 × 10-7The termination criteria are satisfied.
The function of the above formula is to judge whether the fitness value tends to be flat in the calculation of the latest lambda generation, wherein
Figure BDA0002084641000000091
The item represents the variation degree of the fitness value of two adjacent generations; (0.5)i-1The term is coefficient term and represents the latest 20 generations
Figure BDA0002084641000000092
The importance of the value, the closer to the current generation,
Figure BDA0002084641000000093
the greater the impact of value of (c) on the above equation. When the value of W is smaller than the set value, the change of the fitness value is small, and the planning algorithm can be considered to be converged.
The specific implementation mode of the invention also comprises:
an underwater robot time optimal path planning method based on interval optimization comprises the steps of establishing an uncertain ocean current model, calculating a response interval under an uncertain ocean current environment, converting interval sequence relations and searching an optimal path based on an ant colony system algorithm. The method is characterized in that a path planning problem under an uncertain environment is converted into a deterministic planning problem through a section order relation conversion model, and the method mainly comprises the following steps:
step (1): and establishing an uncertain ocean current model based on a predicted value given by an ocean current prediction system.
The ocean current information is treated as a section parameter, and the ocean current direction and the size section are respectively expressed as [ lbcd,ubcd]And [ lbcm,ubcm]. Wherein, lbcd,ubcd,lbcm,ubcmThe expression is as follows:
Figure BDA0002084641000000094
in the formula, cdNAnd cmNRespectively representing nominal values of the direction and the magnitude of the ocean current, wherein the values are predicted values of an ocean current prediction system; υ and σ represent the uncertainty level of the direction and magnitude of the sea flow, respectively.
Step (2): and searching a candidate path from the starting point to the end point by using an ant colony system algorithm according to the pheromone concentration and heuristic information.
And (3): and (3) calculating the maximum value and the minimum value of the navigation time of the candidate path generated in the step (2) in the interval ocean current environment by using a vector analysis method, namely, calculating a response interval.
When the AUV pre-navigation direction is within the ocean current angle interval:
minimum flight time: when in use
Figure BDA0002084641000000095
Direction and
Figure BDA0002084641000000096
in the same direction, and
Figure BDA0002084641000000097
the time of flight is minimal. Wherein the content of the first and second substances,
Figure BDA0002084641000000098
the vector of the sea current is represented,
Figure BDA0002084641000000099
representing the AUV pre-voyage vector.
Maximum voyage time: taking lbcdAnd ubcdNeutralization of
Figure BDA00020846410000000910
The one with larger included angle is used as
Figure BDA00020846410000000911
And (4) direction. Respectively calculating the size of the ocean current as lb in the direction of the ocean currentcmAnd ubcmThe greater of the two is the maximum voyage time in the current interval.
When the AUV pre-navigation direction is outside the ocean current angle interval:
minimum flight time: taking lbcdAnd ubcdNeutralization of
Figure BDA0002084641000000101
With a smaller included angle as
Figure BDA0002084641000000102
And (4) direction. If the included angle is greater than or equal to pi/2, let
Figure BDA0002084641000000103
If the included angle is less than pi/2, determining the size of the ocean current of the minimum navigation time according to the following expression,
Figure BDA0002084641000000104
in the formula (I), the compound is shown in the specification,
Figure BDA0002084641000000105
the AUV is the propulsion speed; theta represents
Figure BDA0002084641000000106
And with
Figure BDA0002084641000000107
And (4) an included angle. The AUV navigation time is minimum under the ocean current condition obtained by the method.
Maximum voyage time: taking lbcdAnd ubcdNeutralization of
Figure BDA0002084641000000108
The one with larger included angle is used as
Figure BDA0002084641000000109
And (4) direction. In the direction of the ocean current, the size of the ocean current is respectively calculated as lbcmAnd ubcmThe greater of the two is the maximum voyage time in the current interval.
In the above description, the ocean current vectors at maximum and minimum voyages have been given, from which
Figure BDA00020846410000001010
And the AUV pre-voyage vector may be calculated by:
Figure BDA00020846410000001011
where t represents the time of flight of the AUV.
Figure BDA00020846410000001012
Wherein c isx，cyRespectively vector of ocean currents
Figure BDA00020846410000001013
Components in the x and y axes;
Figure BDA00020846410000001014
and
Figure BDA00020846410000001015
are respectively vectors
Figure BDA00020846410000001016
The components in the x and y axes.
And (4): converting the response interval of the candidate path obtained in the step (3) into an interval radius and an interval mean value through an interval order relation conversion model, namely converting the interval number into a real number; and then, calculating the evaluation function value of the candidate path by using the interval radius and the interval mean value by using a linear weighting method.
For any candidate path, the navigation time value is an interval instead of a determined real value, so in the optimization process, the advantages and the disadvantages of the navigation time intervals of different candidate paths need to be compared, so that the advantages and the disadvantages of the corresponding candidate paths are evaluated, and the optimal candidate path is searched. In interval optimization, interval order relationship can be used to determine whether an interval is better or worse than another interval. Hypothesis candidate path ΓAThe navigation time interval of the ocean current in the corresponding interval is
Figure BDA00020846410000001017
Wherein
Figure BDA00020846410000001018
And
Figure BDA00020846410000001019
respectively representing a minimum time of flight and a maximum time of flight,
Figure BDA00020846410000001020
respectively, the midpoint and radius values are recorded as
Figure BDA00020846410000001021
And
Figure BDA00020846410000001022
the expression is as follows:
Figure BDA0002084641000000111
the inter-sequence relationship is determined by the above four parameters, wherein
Figure BDA0002084641000000112
The method mainly embodies the average performance of the objective function under uncertainty; while
Figure BDA0002084641000000113
The minimization can reduce the sensitivity of the objective function to the uncertainty, thereby ensuring the design robustness. The invention adopts the method of less than or equal tocwThe sequence relation model and the linear weighting method convert the navigation time interval into a deterministic evaluation function:
Figure BDA0002084641000000114
wherein C is CI＝[CL,CR]
In the formula (f)dIs an evaluation function; c represents an uncertain ocean current vector; omega is more than or equal to 0 and less than or equal to 1, which is a multi-target weight coefficient and the value can be set according to the preference of a decision maker;
Figure BDA0002084641000000115
and
Figure BDA0002084641000000117
respectively representing the mean value and the radius of a navigation time interval of the path gamma in an uncertain ocean current environment; phi and
Figure BDA0002084641000000116
the regularization factor is a multi-objective function, and the value of the regularization factor can be approximately the same magnitude as that of each objective according to specific problems.
And (5): and (4) taking the evaluation function value obtained in the step (4) as a fitness value of the candidate path, returning to the ant colony system algorithm, and searching the optimal path by the ant colony system algorithm according to the optimizing mechanism of the ant colony system algorithm.
Compared with the prior art, the method fully considers the uncertainty problem caused by the inaccuracy of the ocean current prediction system, and converts the deterministic ocean current into the interval ocean current by increasing the uncertainty of the direction and the size of the ocean current so as to establish the uncertain ocean current model. And converting the uncertain optimization problem into the deterministic optimization problem by using an interval optimization theory. Meanwhile, a response interval of the candidate path is obtained in the interval ocean current model by using a vector analysis method, so that the problem of nested optimization in interval optimization is solved, and the calculation efficiency of the algorithm is improved.

Claims (6)

1. An underwater robot time optimal path planning method based on interval optimization is characterized by comprising the following steps:
step 1: determining a rectangular path search area according to the starting point and the end point of the underwater robot path, rasterizing the area, determining the grid size by the resolution of an ocean current prediction system, and establishing an uncertain ocean current model based on a predicted value given by the ocean current prediction system;
step 2: searching a candidate path from a starting point to an end point by using an ant colony system algorithm according to the pheromone concentration and heuristic information;
and step 3: calculating the maximum value and the minimum value of the navigation time of the candidate path generated in the step 2 in the interval ocean current environment by using a vector analysis method, namely a response interval;
and 4, step 4: converting the response interval of the candidate path obtained in the step 3 into an interval radius and an interval mean value through an interval order relation conversion model, namely converting the interval number into a real number; then, calculating an evaluation function value of the candidate path by using the interval radius and the interval mean value by using a linear weighting method;
and 5: and (4) taking the evaluation function value obtained in the step (4) as a fitness value of the candidate path, returning to the ant colony system algorithm, and searching the optimal path by the ant colony system algorithm according to the optimizing mechanism of the ant colony system algorithm.
2. The underwater robot time optimal path planning method based on interval optimization according to claim 1, characterized in that: the uncertain ocean current model comprises: [ lbcd,ubcd]And [ lbcm,ubcm]Wherein [ lb ]cd,ubcd]Is the interval of ocean current direction, [ lbcm,ubcm]Is the size interval of ocean current; wherein, lbcd,ubcd,lbcm,ubcmThe expression satisfies:
Figure FDA0003518895690000011
in the formula, cdNAnd cmNRespectively representing nominal values of the direction and the magnitude of the ocean current, wherein the values are predicted values of an ocean current prediction system; upsilon and sigma respectively represent uncertainty levels of the direction and the size of the ocean current, and values are taken through errors of predicted values and measured values in historical data.
3. The underwater robot time optimal path planning method based on interval optimization according to claim 1, characterized in that: the step 2 comprises the following steps:
step 2.1: setting parameters and initializing ant colony;
step 2.2: the state transition equation of the ant k moving from the current grid i to the neighborhood satisfies:
Figure FDA0003518895690000012
where j represents the next grid to be accessed, h represents any neighborhood of grid i,
Figure FDA0003518895690000013
represents the neighborhood set of ant k on grid i, τihAnd ηihPheromone and heuristic information between grids i and h respectively, alpha and beta represent the importance of the pheromone and the heuristic information in the process of constructing the path by the ants respectively, and q is uniformly distributed in intervals [0,1 ]]A random variable of q0Is [0,1 ]]J is a random variable generated according to the probability distribution, and the probability distribution formula satisfies:
Figure FDA0003518895690000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003518895690000022
representing the probability of an ant k transitioning from the current grid i to the adjacent grid h, and determining j by roulette wheel method, by adjusting the parameter q0Adjusting the exploration degree of the algorithm on the new path;
step 2.3: local pheromone updating: in the path construction process, each time an ant passes through one edge (i, j), the pheromone on the edge is updated, and the updating rule meets the following conditions:
τij＝(1-ξ)τij+ξτ0
where xi is local pheromone evaporation coefficient, its value satisfies 0 < xi < 1, tau0Is the initial value of the pheromone quantity, each time an ant passes the edge (i, j), the pheromone tau of the edgeijThe probability that other ants select the edge will be reduced;
step 2.4: if the ants arrive at the end point, inputting the constructed candidate path into an inner-layer algorithm; if the end point is not reached, the step 2.2 is returned to, and the path is continuously constructed.
4. The underwater robot time optimal path planning method based on interval optimization according to claim 1, characterized in that: the method for determining the maximum value and the minimum value of the navigation time comprises the following steps:
when AUV pre-sailing direction is in ocean current angle range [ lbcd,ubcd]Internal time:
minimum value of voyage time: when in use
Figure FDA0003518895690000023
Direction and
Figure FDA0003518895690000024
in the same direction, and
Figure FDA0003518895690000025
the time, the time of flight is minimal, wherein,
Figure FDA00035188956900000213
the vector of the sea current is represented,
Figure FDA0003518895690000026
representing an AUV pre-voyage vector;
maximum value of navigation time: taking lbcdAnd ubcdNeutralization of
Figure FDA0003518895690000027
The one with larger included angle is used as
Figure FDA0003518895690000028
Direction, in the direction of the ocean current, the size of the ocean current is lbcmAnd ubcmThe greater of the two is the maximum navigation time in the ocean current interval;
when AUV pre-sailing direction is in ocean current angle range [ lbcd,ubcd]When the external force is applied:
minimum value of voyage time: taking lbcdAnd ubcdNeutralization of
Figure FDA0003518895690000029
With a smaller included angle as
Figure FDA00035188956900000210
Direction, if the included angle is greater than or equal to pi/2, let
Figure FDA00035188956900000211
If the included angle is less than pi/2, the size of the ocean current of the minimum navigation time meets the following requirements:
Figure FDA00035188956900000212
in the formula (I), the compound is shown in the specification,
Figure FDA0003518895690000031
the propulsion speed of the AUV is obtained;theta represents
Figure FDA0003518895690000032
And
Figure FDA0003518895690000033
the included angle is that the AUV navigation time is minimum under the ocean current condition;
maximum value of navigation time: taking lbcdAnd ubcdNeutralization of
Figure FDA0003518895690000034
The one with larger included angle is used as
Figure FDA0003518895690000035
Direction, in the direction of the ocean current, the size of the ocean current is lbcmAnd ubcmThe larger of the two is the maximum voyage time in the current interval.
5. The underwater robot time optimal path planning method based on interval optimization according to claim 1, characterized in that: step 4 comprises the following steps:
hypothesis candidate path ΓAThe navigation time interval of the ocean current in the corresponding interval is
Figure FDA0003518895690000036
Wherein
Figure FDA0003518895690000037
And
Figure FDA0003518895690000038
respectively representing a minimum flight time and a maximum flight time,
Figure FDA0003518895690000039
respectively, the midpoint and radius values are recorded as
Figure FDA00035188956900000310
And
Figure FDA00035188956900000311
satisfies the following conditions:
Figure FDA00035188956900000312
converting the navigation time interval into a deterministic evaluation function by adopting an interval sequence relation conversion model and a linear weighting method:
Figure FDA00035188956900000313
wherein C ∈ CI＝[CL,CR]
Converting the multi-objective optimization problem into a single-objective optimization problem by using a linear weighting method:
Figure FDA00035188956900000314
in the formula (f)dIs an evaluation function; c represents an uncertain ocean current vector; omega is more than or equal to 0 and less than or equal to 1, which is a multi-target weight coefficient, and the value can be set according to the preference of a decision maker;
Figure FDA00035188956900000315
and
Figure FDA00035188956900000316
respectively representing the mean value and the radius of a navigation time interval of the path gamma in an uncertain ocean current environment; phi and
Figure FDA00035188956900000317
regularization factor, phi, and for multi-objective functions
Figure FDA00035188956900000318
Get the same as their respective targetsA value of an order of magnitude.
6. The underwater robot time optimal path planning method based on interval optimization according to claim 1, characterized in that: the step 5 of searching the optimal path by the ant colony system algorithm according to the optimizing mechanism comprises the following steps:
the ant colony system algorithm updates the global pheromone according to the evaluation function value, if the ant colony system algorithm termination condition is met, the search is stopped, and the optimal path at present is output as a result path; if the termination condition is not met, returning to the step 2 to continue operation;
global pheromone update rule: only so far the optimal ants are allowed to release the pheromone after each iteration, the update rule is satisfied:
Figure FDA0003518895690000041
wherein, Δ τij＝1/E*，E*The optimal path fitness value is the optimal path fitness value up to now; rho is an evaporation coefficient, and rho is more than 0 and less than 1;
algorithm termination conditions are as follows: the ant colony system algorithm termination condition comprises a maximum iteration time condition and an additional termination condition, and when any one termination condition is met, the algorithm is ended;
wherein, the maximum iteration number condition is as follows: when the iteration times of the algorithm are equal to the maximum iteration times;
additional termination conditions were:
Figure FDA0003518895690000042
where r represents the current iteration number, Er-iRepresents the fitness value of the (r-i) th generation, and W is smaller than the set value.
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