CN116107276A - Logistics storage optimal coordination method based on distributed differential game - Google Patents
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Abstract
The invention relates to an optimal logistics storage coordination method based on distributed differential game, which comprises the following steps: step S1, establishing a communication topological structure between guide trolleys in a multi-automation guide trolley system based on a warehouse logistics scene by utilizing graph theory, wherein the communication topological structure comprises a game participant model and an obstacle environment model; step S2, designing an operation cost function of the automatic guided vehicle in a game participant model by using an artificial potential field method, and step S3, regarding the logistics storage coordination problem of the multi-automatic guided vehicle system limited by perception and communication as a distributed differential game problem, and establishing a distributed differential game model; and S4, analyzing the existence and uniqueness of the local optimal coordination strategy by utilizing the Pontrisia minimum value principle, solving the expression form of the local optimal coordination strategy, and giving a convergence condition from local optimal coordination to global Nash equilibrium to obtain an optimal coordination scheme. The invention can reduce the time for the agent to reach the target point and promote the expandability of the automatic guiding trolley.
Description
Technical Field
The invention relates to the technical field of coordinated control of a multi-automatic guided trolley system, in particular to an optimal logistics storage coordination method based on distributed differential game.
Background
Along with the development of economy, the automatic guiding trolley becomes a core component part of modern warehouse logistics, so that the transportation time can be shortened, and the labor burden is lightened. In recent years, research on effective coordination strategies for multiple automated guided vehicle systems has attracted attention from many researchers. The coordination strategy can effectively realize local target requirements while considering global targets, maximize economic benefits of the warehouse logistics, and improve transportation efficiency of the warehouse logistics when the automatic guiding trolley executes respective given tasks in the warehouse logistics. Namely, the transportation task is efficiently completed while collision is avoided. Considering that the perception and communication of the automatic guiding trolley in the warehouse logistics are limited, it is very practical to analyze the coordination problem of the automatic guiding trolley under limited communication.
In order to improve the transportation efficiency of warehouse logistics, the automatic guiding trolley should ensure that a given transportation package task is completed safely and efficiently. Therefore, a good coordination strategy needs to optimize the track, which is a key to improve the transportation efficiency of the automated guided vehicles. Currently, two main types of coordination strategies, negotiation-based strategies and planning-based strategies, are classified. The negotiation-based policy is a greedy algorithm, and the final policy cannot achieve optimal coordination. Planning-based strategies are generally optimal, but with increasing number of automated guided vehicles, the computational effort increases and scalability is poor.
The game theory can optimize the behavior of each automatic guided vehicle from the perspective of group performance so as to realize Nash equilibrium and further improve the group performance. In particular, differential gaming can quantify the dynamic interactions and collision processes between multiple automated guided vehicles, often used to solve coordination problems, such as chase problems, formation problems. The literature (Mylvaganam T, sassano M, astolfi A. Introduction game approachto multi-agent collision avoidance [ J ]. IEEE Transactions onAutomatic Control,2017,62 (8): 4229-4235) solves the problem of coordinating collision avoidance strategies by first utilizing differential gaming methods. Including literature (LinW, qu Z, siman MA. Nash strategies forpursuit-evasion differential games involving limited observations [ J ]. IEEE Transactions onAerospace and Electronic Systems,2015,51 (2): 1347-1356.) proposes a method of constructing a feedback chase strategy that does not rely on global state information of an agent. Literature (de la Cruz N, jimenez-lizarra m. Finish time robust feedbackNash equilibrium for linear quadratic games J. IFAC-paperson line,2017,50 (1): 11794-11799.) creates a centralized differential game model with external disturbances that are considered virtual players that maximize cost functions, but without considering limited communication capabilities of agents, literature (FuY, chai t. On solution of-player zero-sum games for continuous-time nonlinear systems with completely unknown dynamics J. IEEE transactions on neural networks and learning systems,2015,27 (12): 2577-2587.) creates a distributed uncertainty and differential game that yields local Lu Bangna assortment, but without strict theoretical assurance. To achieve coordination of multi-agent global tasks, global convergence guarantees with local Lu Bangna assorted balances are required. Although the problem of collision avoidance of multiple intelligent agents can be successfully solved, the method can not be directly applied to storage logistics to solve the problem of coordination collision avoidance of the automatic guided vehicle. Mainly because the obtained local optimal solution cannot improve the working efficiency of the automatic guiding trolley; second, the communication assumption of the automated guided vehicle is perfect and is not limited by communication.
Therefore, in order to solve the problem of low task completion efficiency caused by the introduction of the differential game method into the collision avoidance problem, the artificial potential field method can be considered to be introduced to design the collision avoidance rule in combination with the distributed optimization method. A distributed differential game coordination collision avoidance strategy method is designed. The solution of differential game proposed by the current prior art mainly focuses on the situation that global information is known, and for the distributed differential game method, the solution is still rarely applied to the problem of collision prevention of an automatic guiding trolley in logistics storage, and a proper solution cannot be provided.
Disclosure of Invention
Therefore, the present invention aims to provide an optimal logistics storage coordination method based on distributed differential game, which aims to solve the above problems.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a logistics storage optimal coordination method based on distributed differential game comprises the following steps:
step S1, establishing a communication topological structure between guide trolleys in a multi-automation guide trolley system based on a warehouse logistics scene by utilizing graph theory, wherein the communication topological structure comprises a game participant model and an obstacle environment model;
s2, designing an operation cost function of the automatic guiding trolley in a game participant model by using an artificial potential field method;
s3, regarding the logistics storage coordination problem of the multi-automation guiding trolley system limited by sensing and communication as a distributed differential game problem, and establishing a distributed differential game model;
and S4, analyzing the existence and uniqueness of the local optimal coordination strategy by utilizing the Pontrisia minimum value principle, solving the expression form of the local optimal coordination strategy, and giving a convergence condition from local optimal coordination to global Nash equilibrium to obtain an optimal coordination scheme.
Further, the warehouse logistics scene specifically includes
1) Task allocation: in the working environment, the staff assigns the command of transporting the package to the corresponding suitable automated guided vehicle;
2) And (3) parcel collection: after receiving the command, the automatic guiding trolley runs to a corresponding goods shelf from the charging station to pick up the package;
3) And (5) package transportation: after the automated guided vehicle picks up all the assigned packages, transporting the packages to the designated demand locations;
4) Returning to a charging station: after the automated guided vehicle performs the parcel transport task, it returns to the nearest charging station.
Further, the game participant model specifically comprises the following steps:
the specific form of the dynamic equation of the automatic guiding trolley is as follows:
wherein p is i (t) A method of producing a solid-state image sensor
Position and speed information of ith automated guided vehicle at time t, u i (t) is the control input of the ith automated guided vehicle at the moment t, B ii Is a corresponding constant matrix;
the automatic guiding trolley position error is specifically formed as follows:
in the method, in the process of the invention,
the position of the desired transport target point for the ith automated guided vehicle,/->
At tMarking a position error between the current transportation position of the ith automatic guiding trolley and a desired transportation target point;
the dynamic equation of the multi-automation guiding trolley system is specifically formed as follows:
in the method, in the process of the invention,
for the state of the automated guided vehicle system at time t, < >>
The state change rate of the automatic guiding trolley system at the time t is N, the number of the automatic guiding trolleys is B i Is a matrix of corresponding constants,
establishing directed interaction topological graphs G (v, epsilon) of N automated guided vehicles; wherein v= { v 1 ,...,v N And represents a collection of automated guided vehicles,
representing a collection of edges, e ij Indicating the connection relation between the automatic guiding trolley i and the automatic guiding trolley j, e ij Epsilon indicates that the automated guided vehicle i can receive the information of the automated guided vehicle j, and the neighbor set of the automated guided vehicle i is +.>
Defining a neighbor information matrix of the automated guided vehicle i as follows:
wherein I is 2 For a 2 x 2 matrix of units,
is Cronecker product, and is a kind of->
Information matrix for neighbor guided vehicles j other than automated guided vehicle i, wherein only matrix F i Row i and row j 1, the remainder being 0;
the local dynamic equation defining the automated guided vehicle i is:
in the method, in the process of the invention,
for the local status information of the automated guided vehicle i at time t,/>
Is a corresponding constant matrix.
Further, the obstacle environment model specifically includes:
expanding the outline of various shaped obstacles in logistics storage into an ellipse to define a collision prevention area S ik The method comprises the following steps:
wherein r is i For automating the safety radius of the guiding trolley i,
is the radius of obstacle k, c k (t) is the centroid position of obstacle k at time t, E k ＝I 2 Is a unit matrix;
defining a sensing region D ik The method comprises the following steps:
wherein R is i Is the induction range of the automated guided vehicle i;
definition of free region M ik The method comprises the following steps:
further, the step S2 specifically includes:
the following preset conditions are given:
(1): the automatic guiding trolley does not slip during running;
(2): the directed interaction topology graph G (v, epsilon) between the automated guided vehicles is fixed and strongly connected;
design the anti-collision rule based on the artificial potential field method:
in the formula, the constant χ i (0＜χ i < 1) and the like
Is constant (I)>
The obstacle penalty function for the automated guided vehicle i at time t is defined as follows:
wherein, gamma i For automatically guiding the deviation angle between the current track of the trolley i and the predefined reference track.
Further, the step S3 specifically includes:
the expression form of the cost function for establishing the distributed differential game is as follows:
wherein t is f For the end time of the game of automated guided vehicle i, u -i (t) is the control strategy set of the neighbor automatic guiding trolley except the automatic guiding trolley i at the moment t,
for the time t the operating cost function of the automated guided vehicle i is defined as +.>
u ij (t) is the control strategy of the neighbor automatic guiding trolley j of the automatic guiding trolley i at the moment t, U (t) is the moment t control cost, which is defined as
Wherein R is ii ,R ij The adjustable positive weight matrixes are respectively corresponding to the control strategies of the automatic guiding trolley i and the neighbor automatic guiding trolley j;
the objective of the distributed multi-automation guiding trolley system coordination control problem is to design an optimal coordination strategy for each automation guiding trolley, and the automation guiding trolley is required to safely reach a target point within a preset time, meanwhile, the automation guiding trolley i and the neighbor automation guiding trolley can be converged to local Nash equilibrium, namely a t moment strategy set
The method meets the following conditions:
in the method, in the process of the invention,
and (5) an optimal cost function for the automated guided vehicle i at the moment t.
Further, the step S4 specifically includes:
let t be the time additional state:
in the method, in the process of the invention,
for the t moment phase cost function, +.>
For the initial condition +.>
Cost for end time;
let t time expansion state be:
the corresponding dynamic equation is as follows:
in the method, in the process of the invention,
the distributed differential game problem is converted into an optimal control problem, and the expression form is as follows:
according to the Pontrisia minimum principle, a Hamiltonian is defined as
Wherein lambda is i (t) is the Lagrangian multiplier at time t;
the locally optimal coordination strategy satisfies the following differential equation set,
and boundary conditions thereof:
p * (0)＝p 0 ,
λ i (t f )＝0 (20)
wherein p is 0 For automatically guiding initial position of trolley system lambda i (t f ) The Lagrangian multiplier is the last moment;
the only existing condition of the local optimal coordination strategy is set: aiming at the distributed differential game problem of the automatic guided vehicle in a given warehouse logistics, the existing local optimal coordination strategy
The satisfied form of (c) is converted into the following matrix form: />
In the method, in the process of the invention,
for a given matrix, e.g.)>
If the matrix is positive, a unique local coordination strategy exists;
analyzing the convergence of the local optimal coordination strategy to the global optimal strategy, wherein the method is defined as follows: for differential gaming of N participants, the set of t-moment policies { u }, if the following inequality holds 1 (t),...,u i (t),...,u N (t) } converges to a global Nash equilibrium solution,
in the method, in the process of the invention,
strategy for all automated guided vehicles remaining at time t except automated guided vehicle i, furthermore strategy +.>
The following inequality is also satisfied:
Compared with the prior art, the invention has the following beneficial effects:
the invention aims at an automatic guiding trolley with a first-order linear model with limited perception and communication, and converts the coordination control problem of a multi-automatic guiding trolley system in a warehouse logistics into a distributed type differential game problem. Considering the existing differential game method only considering the obstacle avoidance target, introducing a track optimization target to punish the degree of the automatic guiding trolley deviating from the target point based on an artificial potential field method, weighing the distance between the automatic guiding trolley and the distance obstacle, and reducing the time for the automatic guiding trolley to reach the target point; based on the optimal control principle, giving out the expression form and the unique existence analysis of the local optimal strategy; under the assumption of a fixed strong communication topological graph, the global convergence of a local optimal strategy is ensured. The method can reduce the time for the automatic guiding trolley to reach the transportation point. In addition, a distributed architecture differential game model is introduced, compared with a centralized architecture, the distributed architecture differential game model has good expandability, and compared with the existing popular warehouse logistics coordination collision prevention method, the method reduces the task execution time by 16%.
Drawings
FIG. 1 is a block diagram of a method of an embodiment of the present invention;
FIG. 2 is a schematic view of a collision avoidance rule based on an artificial potential field method according to an embodiment of the present invention, wherein 1-automatic guided vehicle charging station, 2-shelf, 3-workbench, 4-obstacle, 5-automatic guided vehicle in operation, 6-package transportation point;
FIG. 3 is a graph of the positional deviation of the multi-homing car system in the abscissa axis in a simulation example of the practice of the present invention;
FIG. 4 is a graph of the positional deviation of the multiple automated guided vehicle system on the ordinate axis in a simulation example of the implementation of the present invention;
FIG. 5 is a communication topology of a multiple automated guided vehicle system employed in a simulation example of the present invention;
FIG. 6 is a diagram showing a transportation track of a multi-automated guided vehicle system in a simulation example of the implementation of the present invention;
FIG. 7 is a diagram showing algorithm transportation time versus time in a simulation example of an implementation of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
Referring to fig. 1, the present invention provides an optimal logistics storage coordination method based on distributed differential game, comprising the following steps:
describing a storage logistics scene, utilizing graph theory, establishing a communication topological structure among guide trolleys in a multi-automation guide trolley system, wherein in order to cope with obstacles possibly occurring in the work of the guide trolleys, taking the guide trolleys and neighbors thereof as game participants, establishing a first-order linear integrator as a model of the guide trolleys, considering the complex working environment of the guide trolleys, inevitably encountering obstacles, designing a collision area, a sensing area and a free area for the working environment of the guide trolleys, and expanding various obstacles with different shapes in logistics storage into an ellipse;
designing a collision avoidance rule by using an artificial potential field method as an operation cost function of the automatic guiding trolley in the game model;
the logistics storage coordination problem of the multi-automation guiding trolley system limited by sensing and communication is regarded as a distributed differential game problem; establishing a distributed differential game model, wherein the model comprises an operation cost function and a control cost;
analyzing the existence and uniqueness of the local optimal coordination strategy by utilizing the Pontrian Jin Jixiao value principle, and solving the expression form of the local optimal coordination strategy; and analyzing the convergence of the global Nash equilibrium of the local optimal coordination.
In this embodiment, the transportation package task executed by the automated guided vehicle is a corresponding transportation target point of the given multi-automated guided vehicle system, so that the automated guided vehicle can reach the target point without collision under the condition of limited sensing and communication, and the completion time of the transportation task of the automated guided vehicle is reduced. The position deviation of each motorized guiding trolley tends to zero, and the transportation task is completed.
In this embodiment, the information acquired by the automated guided vehicle includes the following categories: the method comprises the steps of calculating local state information of the automatic guiding trolley and a first-order linear model of the automatic guiding trolley according to position information and strategy information of the neighbor automatic guiding trolley:
wherein p is i (t) A method of producing a solid-state image sensor
Position and speed information of ith automated guided vehicle at time t, u i (t) is the control input of the ith automated guided vehicle at the moment t, B ii Is a corresponding constant matrix;
the automatic guiding trolley position error is specifically formed as follows:
in the method, in the process of the invention,
for the desired transport position of the ith automated guided vehicle,/or->
The position error between the current transportation position of the ith automatic guiding trolley at the t moment and the expected transportation target point is calculated;
the dynamic equation of the multi-automation guiding trolley system is specifically formed as follows:
in the method, in the process of the invention,
for the state of the automated guided vehicle system at time t, < >>
The state change rate of the automatic guiding trolley system at the time t is N, the number of the automatic guiding trolleys is B i Is a matrix of corresponding constants,
establishing a directed interaction topological graph G (v, epsilon) of N automated guided vehicles, wherein v= { v 1 ,...,v N And represents a collection of automated guided vehicles,
representing a collection of edges, e ij Indicating the connection relation between the automatic guiding trolley i and the automatic guiding trolley j, e ij Epsilon indicates that automated guided vehicle i can receive information of automated guided vehicle j, and neighbor set of automated guided vehicle i is +.>
Defining a neighbor information matrix of the automated guided vehicle i as follows:
wherein I is 2 For a 2 x 2 matrix of units,
information matrix for neighboring guided vehicles j other than automated guided vehicle i, wherein only matrix F i Row i and row j 1, the remainder being 0;
the local dynamic equation defining the automated guided vehicle i is:
in the method, in the process of the invention,
for the local status information of the automated guided vehicle i at time t,/>
Is a corresponding constant matrix;
establishing an obstacle environment model:
expanding obstacles with various shapes in warehouse logistics into an ellipse, and defining a collision prevention area S ik The method comprises the following steps:
wherein r is i For automating the safety radius of the guiding trolley i,
is the radius of obstacle k, c k (t) is the centroid position of obstacle k at time t, E k ＝I 2 Is a unit matrix;
defining a sensing regionDomain D ik The method comprises the following steps:
wherein R is i Is the induction range of the automated guided vehicle i;
definition of free region M ik The method comprises the following steps:
the following hypothetical conditions are given:
assume one: the automatic guiding trolley does not slip during running;
suppose two: the directed interaction topology graph G (v, ε) between automated guided vehicles is fixed and strongly connected;
design the anti-collision rule based on the artificial potential field method:
in the formula, the constant χ i (0＜χ i < 1) and the like
Is constant (I)>
Barrier penalty function for automated guided vehicle i at time t +.>
A distance penalty function of the automated guided vehicle i at the moment t; />
The distance penalty function is represented as follows:
in order to optimize the trajectory of the automated guided vehicle i, a distance penalty function is introduced, and the deviation of the penalty agent from the target point is expressed as follows:
wherein, gamma i A deviation angle for the running of the automated guided vehicle i, which is the angle between the current trajectory of the automated guided vehicle i and the predefined reference trajectory;
the expression form of the cost function for establishing the distributed differential game is as follows:
wherein t is f For the end time of the game of automated guided vehicle i, u -i (t) is the control strategy set of the neighbor automatic guiding trolley except the automatic guiding trolley i at the moment t,
for the time t the operating cost function of the automated guided vehicle i is defined as +.>
u ij (t) is the control strategy of the neighbor automatic guiding trolley j of the automatic guiding trolley i at the moment t, U (t) is the moment t control cost, which is defined as
Wherein R is ii ,R ij The adjustable positive weight matrixes are respectively corresponding to the control strategies of the automatic guiding trolley i and the neighbor automatic guiding trolley j;
the objective of the distributed multi-automation guided vehicle system coordination control problem is to design an optimal coordination strategy for each automation guided vehicle, and the automation guided vehicle needs to safely reach a target point in as little time as possible, meanwhile, the automation guided vehicle i and the neighbor automation guided vehicles can converge to local Nash equilibrium, namely, a t-moment strategy set
The method meets the following conditions:
in the method, in the process of the invention,
the optimal cost function of the automated guided vehicle i at the moment t;
the following relevant theorem and expression form are given for the locally optimal coordination strategy:
giving the additional state at time t:
in the method, in the process of the invention,
for the t moment phase cost function, +.>
For the initial state +.>
For the end cost, the expansion state at time t is given as:
the corresponding dynamic equation is as follows:
in the method, in the process of the invention,
the distributed differential game problem is converted into an optimal control problem, and the expression form is as follows:
according to the Pontriere principle, a Hamiltonian is defined as
Wherein lambda is i (t) is the Lagrangian multiplier at time t;
the locally optimal coordination strategy satisfies the following partial differential equation set:
boundary conditions:
p * (0)＝p 0 ,
λ i (t f )＝0 (20)
wherein p is 0 For automatically guiding initial position of trolley system lambda i (t f ) The Lagrangian multiplier is the last moment;
giving the condition that the locally optimal coordination strategy exists only: aiming at the distributed differential game problem of the automatic guided vehicle in a given warehouse logistics, the existing local optimal coordination strategy
The satisfied form of (c) is converted into the following matrix form:
giving the rule that the locally optimal coordination strategy exists only: for the distributed differential gaming problem of automated guided vehicles in a given warehouse logistics, the locally optimal coordination strategy can be converted into the following form
In the method, in the process of the invention,
for a given matrix, e.g.)>
If the matrix is positive, a unique local coordination strategy exists;
in order to achieve global optimal coordination of transportation tasks of a multi-automation guided off-board system, an analysis bureau is required
The convergence of the partially optimal coordination policy to the globally optimal policy is defined as follows: for differential gaming of N participants, the set of t-moment policies { u }, if the following inequality holds 1 (t),...,u i (t),...,u N (t) } converges to a global Nash equilibrium solution.
In the method, in the process of the invention,
strategy for all automatic guided vehicles except for automatic guided vehicle i, furthermore strategy +.>
So that the following formula is established;
giving the proposition of global convergence of a local optimal coordination strategy: order the
Is a locally optimal coordination strategy of the automatic guided vehicles relative to the neighbors, and if the topological graph among the automatic guided vehicles is strongly communicated, the method comprises the following steps: 1) For the automated guided vehicle i, each locally optimal coordination strategy is equal; 2) The local optimal coordination of the automated guided vehicles can converge to global nash equalization if and only if the communication topology of the automated guided vehicles is strongly connected.
In this embodiment, two specific examples are given to show the effectiveness and superiority of the proposed distributed differential gaming method in solving the problem of multi-homing dolly coordination and to verify the advantages of the method through experimentation.
In order to prove that the obtained local optimal coordination strategy can reduce the time for the automatic guided vehicle to complete the transportation task, the simulation experiment is carried out in the embodiment, and compared with the existing centralized differential game method only considering the obstacle punishment target. The specific model expression form of the multi-automatic guided vehicle system is given as follows:
wherein p is 1 (t) A method of producing a solid-state image sensor
Position and speed information of the 1 st automatic guiding trolley at t moment respectively, p 2 (t) and->
Position and speed information of the 2 nd automatic guiding trolley at the time t respectively, u 1 (t)，u 2 (t) represents the control strategy of the automated guided vehicles 1,2, respectively;
the initial position and the transport target point position of each Automatic Guided Vehicle (AGV) are: p is p 1 (0)＝[80,80] T ，p 2 (0)＝[360,360] T ，
The specific form of each automatic guiding trolley benefit function is as follows: />
As can be seen from fig. 3 to 4, the comparison method and the proposed method can both enable the deviation of the position of the agent to be 0, but the convergence time of the centralized differential game method introducing the trajectory optimization target is 105s and the convergence time of the centralized differential game method considering only the obstacle penalty is 125s, so the centralized differential game method introducing the trajectory optimization target can reduce the time for the agent to complete the task, and the transportation time is reduced by 16% compared with the comparison method.
To illustrate the distributed availability of the proposed method, this example provides a directed communication topology of 3 automated guided vehicles, as shown in fig. 5. The simulation experiment is carried out in the embodiment, and the specific model expression form of the multi-automatic guiding trolley is shown as follows:
wherein p is 1 (t) A method of producing a solid-state image sensor
Position and speed information of the 1 st automatic guiding trolley at t moment respectively, p 2 (t) and->
Position and speed information of the 2 nd automatic guiding trolley at the time t respectively, p 3 (t) and->
Position and speed information of the 3 rd automated guided vehicle at time t, u 1 (t)，u 2 (t)u 3 (t) represents automated guidance respectivelyControl strategy for the trolley 1,2, 3.
The initial position and the transport target point position of each automatic guiding trolley are as follows: p is p 1 (0)＝[30,30] T ，p 2 (0)＝[370,370] T ，p 3 (0)＝[370,30] T ，
p 3 (0)＝[30,370]T. Induction radius R 1 ＝R 2 ＝48。
The specific form of each automatic guiding trolley benefit function is as follows:
according to the method shown in fig. 6, the position deviation of each automatic guiding trolley can be made to be 0 by the proposed distributed differential game method, which indicates that the task is completed.
TO further illustrate the optimal coordination of the proposed distributed differential gaming method (DDG-TO), the negotiation-based method (FCFS) and the planning-based method (ETCEN-MCS) are compared TO the current more popular logistic warehousing methods.
Each automated guided vehicle was performed 10 times using the above three methods, respectively, and averaged. As can be seen from fig. 7, when the number of the automated guided vehicles is 4, the transportation time of the three methods is similar, the transportation time of the FCFS method is reduced and the transportation time of the ETCEN-MCS method is reduced as the number of the automated guided vehicles increases, and the transportation time of the proposed distributed differential game method (DDG-TO) method is the shortest, which is reduced by 15.7% and 9.2% compared with the former two methods, respectively. In summary, the distributed differential game method can enable each automatic guiding trolley to safely complete the transportation task, and can reduce the transportation time of each automatic guiding trolley.
The foregoing description is only of the preferred embodiments of the invention, and all changes and modifications that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Claims (7)
1. The logistics storage optimal coordination method based on the distributed differential game is characterized by comprising the following steps of:
step S1, establishing a communication topological structure between guide trolleys in a multi-automation guide trolley system based on a warehouse logistics scene by utilizing graph theory, wherein the communication topological structure comprises a game participant model and an obstacle environment model;
s2, designing an operation cost function of the automatic guiding trolley in a game participant model by using an artificial potential field method;
s3, regarding the logistics storage coordination problem of the multi-automation guiding trolley system limited by sensing and communication as a distributed differential game problem, and establishing a distributed differential game model;
and S4, analyzing the existence and uniqueness of the local optimal coordination strategy by utilizing the Pontrisia minimum value principle, solving the expression form of the local optimal coordination strategy, and giving a convergence condition from local optimal coordination to global Nash equilibrium to obtain an optimal coordination scheme.
2. The distributed differential game-based logistics storage optimal coordination method as claimed in claim 1, wherein the storage logistics scene specifically comprises the following steps
1) Task allocation: in the working environment, the staff assigns the command of transporting the package to the corresponding suitable automated guided vehicle;
2) And (3) parcel collection: after receiving the command, the automatic guiding trolley runs to a corresponding goods shelf from the charging station to pick up the package;
3) And (5) package transportation: after the automated guided vehicle picks up all the assigned packages, transporting the packages to the designated demand locations;
4) Returning to a charging station: after the automated guided vehicle performs the parcel transport task, it returns to the nearest charging station.
3. The distributed differential game-based logistics storage optimal coordination method of claim 1, wherein the game participant model is specifically:
the specific form of the dynamic equation of the automatic guiding trolley is as follows:
wherein p is i (t) A method of producing a solid-state image sensor
Position and speed information of ith automated guided vehicle at time t, u i (t) is the control input of the ith automated guided vehicle at the moment t, B ii Is a corresponding constant matrix;
the automatic guiding trolley position error is specifically formed as follows:
in the method, in the process of the invention,
the position of the desired transport target point for the ith automated guided vehicle,/->
The position error between the current transportation position of the ith automatic guiding trolley at the t moment and the expected transportation target point is calculated;
the dynamic equation of the multi-automation guiding trolley system is specifically formed as follows:
in the method, in the process of the invention,
for the state of the automated guided vehicle system at time t, < >>
The state change rate of the automatic guiding trolley system at the time t is N, the number of the automatic guiding trolleys is B i Is a matrix of corresponding constants,
establishing directed interaction topological graphs G (v, epsilon) of N automated guided vehicles; wherein v= { v 1 ,...,v N And represents a collection of automated guided vehicles,
representing a collection of edges, e ij Indicating the connection relation between the automatic guiding trolley i and the automatic guiding trolley j, e ij Epsilon indicates that the automated guided vehicle i can receive the information of the automated guided vehicle j, and the neighbor set of the automated guided vehicle i is +.>
Defining a neighbor information matrix of the automated guided vehicle i as follows:
wherein I is 2 For a 2 x 2 matrix of units,
is Cronecker product, and is a kind of->
Letter for neighbor guided vehicle j other than automated guided vehicle iInformation matrix, wherein only matrix F i Row i and row j 1, the remainder being 0;
the local dynamic equation defining the automated guided vehicle i is:
in the method, in the process of the invention,
for the local status information of the automated guided vehicle i at time t,/>
Is a corresponding constant matrix.
4. The logistic warehousing optimal coordination method based on the distributed differential game according to claim 1, wherein the obstacle environment model is specifically:
expanding the outline of various shaped obstacles in logistics storage into an ellipse to define a collision prevention area S ik The method comprises the following steps:
wherein r is i For automating the safety radius of the guiding trolley i,
is the radius of obstacle k, c k (t) is the centroid position of obstacle k at time t, E k ＝I 2 Is a unit matrix;
defining a sensing region D ik The method comprises the following steps:
wherein R is i Is an automated guided vehicle iIs a sensing range of (a);
definition of free region M ik The method comprises the following steps:
5. the logistic warehousing optimal coordination method based on the distributed differential game according to claim 1, wherein the step S2 is specifically:
the following preset conditions are given:
(1): the automatic guiding trolley does not slip during running;
(2): the directed interaction topology graph G (v, epsilon) between the automated guided vehicles is fixed and strongly connected;
design the anti-collision rule based on the artificial potential field method:
in the formula, the constant χ i (0＜χ i < 1) and the like
Is constant (I)>
The obstacle penalty function for the automated guided vehicle i at time t is defined as follows: />
wherein, gamma i For automatically guiding the deviation angle between the current track of the trolley i and the predefined reference track.
6. The logistic warehousing optimal coordination method based on the distributed differential game according to claim 1, wherein the step S3 is specifically:
the expression form of the cost function for establishing the distributed differential game is as follows:
wherein t is f For the end time of the game of automated guided vehicle i, u -i (t) is the control strategy set of the neighbor automatic guiding trolley except the automatic guiding trolley i at the moment t,
for the time t the operating cost function of the automated guided vehicle i is defined as +.>
u ij (t) is the control strategy of the neighbor automatic guiding trolley j of the automatic guiding trolley i at the moment t, U (t) is the moment t control cost, which is defined as
Wherein R is ii ,R ij The adjustable positive weight matrixes are respectively corresponding to the control strategies of the automatic guiding trolley i and the neighbor automatic guiding trolley j;
the objective of the distributed multi-automation guiding trolley system coordination control problem is to design an optimal coordination strategy for each automation guiding trolley, and the automation guiding trolley is required to safely reach a target point within a preset time, and meanwhile, the automation guiding trolley i and an adjacent guiding trolley i are required to safely reach the target pointThe automated guided vehicle can converge to local Nash equilibrium, i.e., the set of t-moment strategies
The method meets the following conditions:
in the method, in the process of the invention,
and (5) an optimal cost function for the automated guided vehicle i at the moment t.
7. The logistic warehousing optimal coordination method based on the distributed differential game according to claim 1, wherein the step S4 specifically includes:
let t be the time additional state:
in the method, in the process of the invention,
for the t moment phase cost function, +.>
For the initial condition +.>
Cost for end time;
let t time expansion state be:
the corresponding dynamic equation is as follows:
in the method, in the process of the invention,
the distributed differential game problem is converted into an optimal control problem, and the expression form is as follows:
according to the Pontrisia minimum principle, a Hamiltonian is defined as
Wherein lambda is i (t) is the Lagrangian multiplier at time t;
the locally optimal coordination strategy satisfies the following differential equation set,
and boundary conditions thereof:
p * (0)＝p 0 ,
λ i (t f )＝0 (20)
wherein p is 0 For automatically guiding initial position of trolley system lambda i (t f ) The Lagrangian multiplier is the last moment;
the only existing condition of the local optimal coordination strategy is set: aiming at the distributed differential game problem of the automatic guided vehicle in a given warehouse logistics, the existing local optimal coordination strategy
The satisfied form of (c) is converted into the following matrix form: />
In the method, in the process of the invention,
for a given matrix, e.g.)>
If the matrix is positive, a unique local coordination strategy exists;
analyzing the convergence of the local optimal coordination strategy to the global optimal strategy, wherein the method is defined as follows: for differential gaming of N participants, the set of t-moment policies { u }, if the following inequality holds 1 (t),...,u i (t),...,u N (t) } converges to a global Nash equilibrium solution,
in the method, in the process of the invention,
strategy for all automatic guided vehicles remaining at time t except for automatic guided vehicle i, and strategy
The following inequality is also satisfied:
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Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108171459A (en) * | 2017-12-29 | 2018-06-15 | 长春师范大学 | intelligent storage optimization method based on game theory |
| CN108829105A (en) * | 2018-06-21 | 2018-11-16 | 浙江工业大学 | It is a kind of to dispatch avoidance optimization method based on the warehouse logistics of KM algorithm and Artificial Potential Field Method |
| CN110751293A (en) * | 2019-09-29 | 2020-02-04 | 浙江财经大学 | Cloud manufacturing multi-task scheduling optimization method based on game theory |
| CN113159681A (en) * | 2021-04-20 | 2021-07-23 | 华南理工大学 | Multi-type intermodal dynamic path planning method based on game reinforcement learning |
| CN113393040A (en) * | 2021-06-18 | 2021-09-14 | 重庆邮电大学工业互联网研究院 | Industrial park logistics scheduling method and system based on game theory |
| WO2022133330A1 (en) * | 2020-12-18 | 2022-06-23 | Strong Force Vcn Portfolio 2019, Llc | Robot fleet management and additive manufacturing for value chain networks |
| CN114662381A (en) * | 2022-02-24 | 2022-06-24 | 上海交通大学 | Layered game-based fusion operation method and system for energy traffic system of port ship |
| CN115411728A (en) * | 2022-09-26 | 2022-11-29 | 南京理工大学 | Multi-microgrid system coordination control method integrating Q learning and potential game |
-
2022
- 2022-12-30 CN CN202211729139.0A patent/CN116107276A/en active Pending
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108171459A (en) * | 2017-12-29 | 2018-06-15 | 长春师范大学 | intelligent storage optimization method based on game theory |
| CN108829105A (en) * | 2018-06-21 | 2018-11-16 | 浙江工业大学 | It is a kind of to dispatch avoidance optimization method based on the warehouse logistics of KM algorithm and Artificial Potential Field Method |
| CN110751293A (en) * | 2019-09-29 | 2020-02-04 | 浙江财经大学 | Cloud manufacturing multi-task scheduling optimization method based on game theory |
| WO2022133330A1 (en) * | 2020-12-18 | 2022-06-23 | Strong Force Vcn Portfolio 2019, Llc | Robot fleet management and additive manufacturing for value chain networks |
| CN113159681A (en) * | 2021-04-20 | 2021-07-23 | 华南理工大学 | Multi-type intermodal dynamic path planning method based on game reinforcement learning |
| CN113393040A (en) * | 2021-06-18 | 2021-09-14 | 重庆邮电大学工业互联网研究院 | Industrial park logistics scheduling method and system based on game theory |
| CN114662381A (en) * | 2022-02-24 | 2022-06-24 | 上海交通大学 | Layered game-based fusion operation method and system for energy traffic system of port ship |
| CN115411728A (en) * | 2022-09-26 | 2022-11-29 | 南京理工大学 | Multi-microgrid system coordination control method integrating Q learning and potential game |
Non-Patent Citations (1)
| Title |
|---|
| 庞明宝, 魏连雨: "区域物流线路网络双层规划研究", 公路交通科技, no. 10, 15 October 2005 (2005-10-15), pages 162 - 166 * |
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