CN113821027A - Priority-based incomplete self-body deck coordinated dispatching path planning method - Google Patents

Priority-based incomplete self-body deck coordinated dispatching path planning method Download PDF

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CN113821027A
CN113821027A CN202110992146.9A CN202110992146A CN113821027A CN 113821027 A CN113821027 A CN 113821027A CN 202110992146 A CN202110992146 A CN 202110992146A CN 113821027 A CN113821027 A CN 113821027A
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dispatching
time
self
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CN113821027B (en
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刘洁
董献洲
刘纯
贾珺
徐浩
樊硕
彭超
乐剑
雷霆
邱凯
施展
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Research Institute of War of PLA Academy of Military Science
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0214—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with safety or protection criteria, e.g. avoiding hazardous areas
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0219—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory ensuring the processing of the whole working surface
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
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Abstract

A priority-based incomplete self-body deck coordinated dispatching path planning method belongs to the technical field of path planning. The method comprises the following steps: first, the dispatch start time of all the agents participating in the dispatch task is preset to 0 s. And then, sequentially calculating off-line paths of the dispatching of each self-body off-line by adopting an optimal control method. And finally, listing all priority ranking schemes by adopting an exhaustion method, optimizing the actual dispatching time of each subject and the total time consumed by all subjects to finish dispatching operation based on the offline path and the priority method of each subject aiming at each ranking scheme, selecting the scheme with the shortest total time consumption as the optimal scheme from all the ranking schemes, and dispatching along each offline path by each subject by taking the optimized actual sliding-out time in the optimal scheme as the starting time. The method can rapidly realize the collaborative path planning of the multi-isomorphic/heterogeneous autonomous body on the deck, and obtain a smooth path which meets various constraint relations.

Description

Priority-based incomplete self-body deck coordinated dispatching path planning method
Technical Field
The invention belongs to the technical field of the planning of the cooperative dispatching path of an incomplete autonomous body deck, and relates to a priority-based planning method of the cooperative dispatching path of the incomplete autonomous body deck.
Background
Since the advent of the aircraft carrier, the aircraft carrier becomes an important symbol of military strength and level of the country. Its combat power depends on one hand on its own performance and on the other hand on its output recovery power. As an important link throughout the process of movement recovery, the dispatching operation aims to enable dispatched objects to efficiently and safely reach positions such as a take-off station, a guarantee point, a parking station and the like to complete flight or guarantee tasks, and the targeted objects mainly comprise 4 types of carrier-borne special vehicles, self-bodies, rodless traction systems and rod traction systems. Although the 4 types of moving bodies have different structures, they are all systems which are not completely restricted, and therefore all moving bodies can be regarded as non-completely self-bodies. How to realize the effective coordinated dispatching among the incomplete multiple self bodies in a narrow deck space and a complex operation environment so as to ensure the coordination, safety and high efficiency of operation at each stage is a key problem for improving the output recovery capability of the aircraft carrier.
Compared with the trajectory planning problem of a single autonomous body, the collaborative trajectory planning problem of multiple autonomous bodies is more complex, and especially when nonlinear dynamics/kinematics, control and state constraints need to be considered, the planning becomes more difficult, and the narrow and complex deck environment further increases the solution difficulty and sometimes even is difficult to solve. When the autonomous bodies participating in the planning are isomorphic, the number is small, the quality requirement of solution is low, long-time offline calculation is allowed, the deck environment complexity is low, only static obstacles exist, the tail end time is fixed, the control constraint is ignored, and the nonlinear constraint can be linearized, the coordinated dispatching trajectory planning of the multiple autonomous bodies can be easily realized. However, in practical applications, these preconditions are difficult to be satisfied simultaneously, and it is often necessary to solve the multi-subject collaborative trajectory planning problem with high solution performance (including high computational efficiency and high solution accuracy). When the multi-isomerous autonomous cooperative operation exists, the cooperative trajectory planning problem is more complex than the multi-isomerous cooperative trajectory planning problem due to different kinematics/dynamics constraints of different structures.
At present, researches on the planning of the coordinated dispatching track of multiple autonomous bodies on a deck are few, the existing researches mainly adopt bionic algorithms such as particle swarm to realize the path planning of the coordinated sliding of multiple autonomous bodies, and although the research results can provide reference for the research of the project, the results are difficult to strictly meet the constraints of kinematics/dynamics, terminals, control and the like. And the collaborative trajectory planning problem in the fields of unmanned aerial vehicles, unmanned vehicles, robots and the like has been widely researched, so that the collaborative trajectory planning problem can be used for reference. Among these fields, the most commonly used methods at present are: an artificial potential field algorithm, a mathematical programming method, an artificial intelligence algorithm, an interactive collision avoidance strategy, a priority strategy and the like. The methods can solve the problem of multi-subject trajectory planning, but the calculation efficiency and the precision are difficult to be considered at the same time.
Collaborative trajectory planning methods for multiple agents can be classified into centralized and distributed. The centralized solution is to plan the trajectory from a global perspective, and the planning result is a global solution. In contrast, the distributed approach is to implement collaborative trajectory planning for multiple agents based on multiple agents.
In the centralized method, the top-level decision unit can receive the states of all the autonomous bodies, and regards all the autonomous bodies as an integral system, and the top-level decision unit performs integral planning and provides control input for a single autonomous body, and usually adopts mixed integer planning, sequential convex planning, pseudo-spectral method and the like.
In the distributed method, each autonomous body obtains the state information of other autonomous bodies through the autonomous body so as to make autonomous decision. Thus, each autonomous body can make decisions autonomously and provide control inputs to itself, regardless of the dynamics and control inputs of other autonomous bodies. However, the problem of multi-autonomous distributed local trajectory planning in complex dynamic environments still faces many challenges: first, the multi-subject trajectory obtained by assuming a stationary state cannot ensure safety in an actual dynamic environment; secondly, since each autonomous body individually uses one trajectory planner, an unreasonable movement of one autonomous body may cause a collision to confuse the entire system; finally, due to the lack of prior knowledge of the working space and other self-subjects, performance indexes such as terminal time and total distance are not easy to optimize.
While the allocation and transportation of a non-complete autonomous body on a deck often requires that the autonomous body accurately reaches a target position at a preset angle, that is, the motion trail of the autonomous body must strictly meet the end constraint, and most of the existing centralized/distributed methods cannot achieve the target with higher computational efficiency and precision. Therefore, an efficient and robust solving method needs to be designed for the characteristic of the planning of the coordinated dispatching track of the carrier-borne autonomous body to realize the solving.
In summary, at present, there is an urgent need for a non-complete autonomous coordination dispatching path planning algorithm with good applicability, which can give consideration to both calculation accuracy and efficiency.
Disclosure of Invention
In order to solve the technical problems, the invention provides a priority-based incomplete self-body deck coordinated dispatching path planning method which can give consideration to both calculation precision and efficiency and has good applicability.
The technical scheme adopted by the invention is as follows:
a method for planning a route of non-complete self-body deck cooperative allocation and transportation based on priority comprises the steps of firstly presetting the time of starting allocation and transportation of all self-bodies participating in allocation and transportation tasks to 0 s; then, for a certain self-body, according to the initial state and the end state formed by the position, the angle and the speed of the self-body, simultaneously, regarding the other self-bodies participating in the dispatching task as static obstacles always stopping at the initial position, adopting an optimal control method to calculate the offline path of the self-body dispatching in an offline manner, and adopting the method to calculate the offline path of each self-body in sequence; and finally, listing all priority ranking schemes by adopting an exhaustion method, optimizing the actual dispatching time of each subject and the total time consumed by all subjects to finish dispatching operation based on the offline path and the priority method of each subject aiming at each ranking scheme, selecting the scheme with the shortest total time consumption as the optimal scheme from all ranking schemes, and dispatching along each offline path by each subject by taking the optimized actual sliding-out time in the optimal scheme as the starting time. The method comprises the following steps:
step 1, determining the number N of incomplete autonomous bodies to be dispatched, and presetting the time for all autonomous bodies to slide out to be 0 s;
and 2, respectively calculating the off-line paths of the respective main bodies by adopting an optimal control method based on the initial state and the tail end state of the respective main bodies to obtain 4-dimensional path data consisting of the abscissa, the ordinate, the angle and the time of the respective main bodies. When an optimal control method is adopted to calculate an offline path of a self-body, the rest self-bodies are all regarded as static obstacles which are always stopped at the initial position. The specific steps of calculating the off-line path by adopting the optimal control method are as follows:
step 2-1: establishing kinematic equation of incomplete self-body transfer
Establishing a state space x describing the incomplete autonomous body dispatching, and determining a control variable u, thereby establishing the following kinematic equation of the incomplete autonomous body dispatching:
Figure BDA0003232686320000031
wherein t is a time variable;
step 2-2: determining state and control constraints in a non-complete autonomous dispatch process
The constraints applied to the state variables and the control variables in the incomplete self-body dispatching process are expressed in the form of inequalities as follows:
C(x,u,t)≤0 (2)
step 2-3: establishing obstacle avoidance constraint model
The collision avoidance constraints of the non-integral autonomous body and the obstacle are described by adopting the following continuous functions:
Figure BDA0003232686320000032
wherein (x)oh,yoh) Respectively representing the position coordinates of the geometric center of the h-th obstacle; d represents the distance between the center of the rear wheel of the airplane and the center of a characteristic circle describing the outline of the incomplete autonomous body; dist denotes the safety separation distance; a ish、bh、phRespectively is the long axis, short axis and outline parameters of the h barrier; r isiTo describe the radius of a non-complete self-body feature circle.
When p ishThe obstacle is rhombus when 1, when phWhen 2 the obstacle is circular, when phThe obstacle is approximately rectangular > 2. The collision avoidance constraint of the incomplete autonomous body with all obstacles can be expressed in the form of a matrix as follows:
H(x,t)≤0 (4)
step 2-4: determining boundary conditions for a single incomplete autonomous dispatch trajectory plan
Defining the incomplete starting dispatching time and the terminal time of the self-body as tsAnd tfThe states of the incomplete self-body at the initial moment and the terminal moment are x respectivelysAnd xfThen, the boundary conditions of the single incomplete self-body dispatching trajectory planning problem are as follows:
x(ts)＝xs,x(tf)＝xf (5)
step 2-5: establishing an optimal control model for single incomplete self-body dispatching
According to the formulas (1), (2), (3) and (4), the following time-energy optimal control problem is established:
Figure BDA0003232686320000041
wherein w is a terminal time weight factor;
step 2-6: solution of optimal control model
And (4) solving the data by adopting an optimal control algorithm according to a formula (6) to optimize the minimum tail end time and the corresponding 4-dimensional path data.
And 3, listing all priority ranking schemes by adopting an exhaustion method, optimizing the actual dispatching starting time of each subject and the total time consumed by all subjects to finish dispatching operation based on a priority method aiming at each ranking scheme, finally selecting the scheme with the shortest total time consumption from all the ranking schemes as an optimal scheme, and taking the actual dispatching starting time optimized in the optimal scheme as the starting time by each subject and dispatching along each off-line path.
The specific steps of optimizing the actual dispatching starting time of each main body and the total time consumed by all the main bodies to finish dispatching operation based on the priority method are as follows:
step 3-1: a prioritization scheme is generated. N self-service bodies to be dispatched are respectively numbered as 1,2, 3, … and N, the N numbers of 1,2, 3, … and N are arranged in a whole way, and M is generated (M is more than or equal to 1, and M belongs to N+) An ordering scheme that may constitute an ordering scheme set P ═ P1,P2,…,PN！In which P isi＝[Pi1,Pi2,…,PiN]，i＝1,2,…,M，Pij(j ═ 1,2, …, N) for ordering scheme PiThe jth element in (a).
Step 3-2: let i equal to 1, determine the ordering scheme PiThe priority of (2). For ordering scheme PiThe priority in the ranking is sequentially lowered from left to right,i.e. the first element Pi1For the N autonomous agents to be dispatched, P is the highest priorityi2Next, PiNAnd the lowest.
Step 3-3: computing an ordering scheme PiEach from the actual start of commissioning of the subject.
Step 3-3-1: from body Pi1The priority of (2) is highest, no delay is needed, and only the dispatching needs to be started from 0s along the track obtained in the step (2), meanwhile, the sequence number of the self body to be optimized of the actual dispatching starting time is initialized to j-2, and the delay time is initialized to calculate the step length delta T in an iterative manner.
Step 3-3-2: will be from body PijTo avoid high priority autonomous body Pik( k 1,2, …, j-1) and the set of times that the departure needs to be delayed
Figure BDA0003232686320000042
Is initialized to 0, wherein
Figure BDA0003232686320000043
Is shown from the body PijIn order to avoid autonomous body P with higher priorityikThe time of the delayed departure.
Step 3-3-3: let k equal to 1 and will be from the body PikConsidered as a dynamic barrier.
Step 3-3-4: will be from body PijAnd a self body PikPerforming collision detection if used to describe the self-body PijAnd a self body PikThe distance between the centers of the two characteristic circles is constantly greater than or equal to
Figure BDA0003232686320000051
And (4) if no collision occurs, switching to the step 3-3-5, otherwise, switching to the step 3-3-6.
Step 3-3-5: from body PijNeed not be for and from the body PikDelay departure from collision and record from subject PijTo interact with the self-body PikThe delayed departure time for collision avoidance is
Figure BDA0003232686320000052
And (4) transferring to the step 3-3-6.
Step 3-3-6: will be provided with
Figure BDA0003232686320000053
Repeating the superposition delay time step Delta T until the description of the self-body PijAnd a self body PikThe distance between the centers of the two characteristic circles is greater than or equal to at any moment
Figure BDA0003232686320000054
Up to now, update self-body PijTo avoid the self-body PikTime required to delay departure
Figure BDA0003232686320000055
Step 3-3-7: if k is less than j, k is equal to k +1, and the step 3-3-3 is carried out; otherwise, the step 3-3-8 is carried out.
Step 3-3-8: determination of self-body PijTo avoid all higher priority autonomous bodies PikSet of times required to delay roll-out
Figure BDA0003232686320000056
From body PijThe actual start-up time of
Figure BDA0003232686320000057
Namely from the body PijIn that
Figure BDA0003232686320000058
And (5) starting dispatching according to the track planned in the step 2.
Step 3-3-9: if j is less than N, making j equal to j +1, and then proceeding to step 3-3-2; otherwise, the step 3-4 is carried out.
Step 3-4: for ordering scheme PiTaking the sum of the actual starting dispatching time obtained in the step 3-3 and the minimum end time obtained in the step 2 as the actual arrival time of each subject, and taking the maximum value of the actual arrival time of all the subjects as a sequencing scheme PiInstitute for completing dispatching taskThe total time consumed.
Step 3-5: if i is less than M, i is i +1, and the step 3-2 is carried out; otherwise, taking the sorting scheme corresponding to the minimum value of the total time consumed by the dispatching tasks of all the sorting schemes as an optimal scheme, starting according to the actual dispatching starting time corresponding to the respective main body in the optimal scheme, and dispatching along the dispatching track obtained in the step 2.
Further, the optimal control algorithm comprises a pseudo spectrum method, a guaranty pseudo spectrum algorithm and the like.
Compared with the prior art, the invention has the beneficial effects that:
the invention can solve the problem of collaborative path planning of a plurality of incomplete autonomous bodies with higher precision and efficiency, can rapidly realize the collaborative path planning of a plurality of isomorphic/heterogeneous autonomous bodies on a deck, obtains a smooth path meeting various constraint relations, has strong operability and feasibility and is convenient for practical application.
Drawings
FIG. 1 is a flow chart of the calculation of the present invention.
Fig. 2 is a diagram of the transfer trajectories of the airplanes a1, a2 and A3 of the present invention.
FIG. 3 is a graph of the position and angle of aircraft A1 of the present invention as a function of time; fig. 3(a) is a graph showing a change with time in the abscissa of the center position of the rear wheel of the aircraft a1, fig. 3(b) is a graph showing a change with time in the ordinate of the center position of the rear wheel of the aircraft a1, and fig. 3(c) is a graph showing a change with time in the included angle between the ordinate and the abscissa of the aircraft a 1.
FIG. 4 is a graph of the position and angle of aircraft A2 of the present invention as a function of time; fig. 4(a) is a time-dependent change chart of the abscissa of the center position of the rear wheel of the aircraft a2, fig. 4(b) is a time-dependent change chart of the ordinate of the center position of the rear wheel of the aircraft a2, and fig. 4(c) is a time-dependent change chart of the included angle between the ordinate and the abscissa of the aircraft a 2.
FIG. 5 is a graph of the position and angle of aircraft A3 of the present invention as a function of time; fig. 5(a) is a time-dependent change chart of the abscissa of the center position of the rear wheel of the aircraft A3, fig. 5(b) is a time-dependent change chart of the ordinate of the center position of the rear wheel of the aircraft A3, and fig. 5(c) is a time-dependent change chart of the included angle between the ordinate and the abscissa of the aircraft A3.
Detailed Description
The present invention is further illustrated by the following specific examples.
In a certain task, 2 airplanes (A1 and A2) need to be launched preferentially, the two airplanes are guaranteed to be finished and can directly slide to corresponding positions to be ready to take off, and then one airplane (A3) is transported to a parking position near a certain guarantee point from an original parking position in a rod traction mode to be guaranteed. Wherein aircraft A1 taxis from (44m, 138m) at an initial angle of 90 °, an initial speed of 0m/s to (192m, 185m), a terminal angle of 0 °, a terminal speed of 0 m/s; airplane a2 taxied from (44m, 188m) at an initial angle of-90 °, an initial speed of 0m/s to (192m, 152m), a terminal angle of 0 °, a terminal speed of 0 m/s; the aircraft A3 was pulled from (155m, 138m) at an initial angle of 90 deg. at an initial velocity of 0m/s to (44m, 138m), at an end angle of 90 deg. at an end velocity of 0 m/s. In this environment, there is a static rectangular obstacle of length 34m and width 20m, with its geometric center at (102m, 138 m). The incomplete self-body deck coordinated dispatching path planning method based on the priority in the embodiment comprises the following steps:
according to the step 1, the number N of the incomplete self-bodies needing to be dispatched is determined to be 3, and the time for starting all the self-bodies to slide out is preset to be 0 s.
According to the step 2, based on the initial state and the end state of the 3 autonomous bodies, the off-line paths of the autonomous bodies are respectively calculated by adopting a pseudo-spectrum method in the optimal control method, and 4-dimensional path data consisting of the abscissa, the ordinate, the angle and the time of the 3 autonomous bodies are obtained. When a pseudo-spectrum method is adopted to calculate an off-line path of a certain self-body, the other self-bodies are regarded as static obstacles which are always stopped at an initial position, and the specific steps of calculating the off-line path by adopting the pseudo-spectrum method are as follows:
according to step 2-1, the following equations for the non-complete autonomous transfer kinematics for aircraft A1 or A2 are established:
Figure BDA0003232686320000061
whereinT is a time variable, marked (#)iRepresents the ith self-body, where i-1 corresponds to airplane a1 and i-2 corresponds to airplane a 2; the state variable is
Figure BDA0003232686320000062
Figure BDA0003232686320000063
Is the coordinate of the central position of the rear wheel of the airplane,
Figure BDA0003232686320000064
is the included angle between the longitudinal axis of the airplane and the abscissa,
Figure BDA0003232686320000071
is the aircraft speed; the control variable may be selected as the tangent of the aircraft nose wheel steering angle
Figure BDA0003232686320000072
And acceleration
Figure BDA0003232686320000073
The control variable of the self-body of the airplane is
Figure BDA0003232686320000074
For A3, the maneuvering kinematics equation for the aircraft A3 corresponding to the traction system is established as follows:
Figure BDA0003232686320000075
wherein the state variable is
Figure BDA0003232686320000076
Figure BDA0003232686320000077
Is the coordinate of the central position of the rear wheel of the airplane,
Figure BDA0003232686320000078
as an aircraftThe included angle between the longitudinal direction and the horizontal coordinate,
Figure BDA0003232686320000079
is the included angle between the longitudinal direction of the airplane and the draw bar,
Figure BDA00032326863200000710
is the angle between the draw bar and the longitudinal direction of the towing vehicle, alpha3Is the steering angle of the front wheel of the tractor,
Figure BDA00032326863200000711
is the aircraft speed; control variable U3Steering angular velocity from tractor front wheel
Figure BDA00032326863200000712
And aircraft acceleration
Figure BDA00032326863200000713
And (4) forming.
According to step 2-2, the state-control constraints during taxiing of the aircraft A1 and A2 are:
Figure BDA00032326863200000714
the state-control constraints for aircraft a3 corresponding to the towing aircraft system are:
Figure BDA00032326863200000715
according to the step 2-3, the collision avoidance constraint of the incomplete self-body and the obstacle is described by adopting the following continuous function:
Figure BDA00032326863200000716
wherein (x)oh,yoh) Respectively, the position coordinates of the geometric center of the h-th obstacle. D represents the center of the rear wheel of the airplane and a characteristic circle for describing the incomplete self-body contourThe distance between the centers of the circles is 3m when the incomplete self-body is an airplane A1 or A2; when the non-intact autonomous body is the traction system corresponding to aircraft a3, this value is taken to be 5 m. dist denotes the safety separation distance, which in this case is taken to be 1 m. a ish、bh、phRespectively is the major axis, the minor axis and the outline parameters of the h barrier. r isiTo describe the radius of the characteristic circle of the incomplete autonomous body i, r is given when the incomplete autonomous body is an airplane A1 or A2i7 m; when the non-integral autonomous body is an airplane A3, r39 m. When p ishThe obstacle is rhombus when 1, when phWhen 2 the obstacle is circular, when phThe obstacle is approximately rectangular at > 2, which in this case takes the value 10.
Then for aircraft a1 whose obstacles include a static rectangular obstacle, aircraft a2 at the starting or terminal position, and the traction system corresponding to A3 at the starting position, its collision avoidance constraints with all obstacles are represented in the form:
Figure BDA0003232686320000081
for aircraft a2, the obstacles of which include a static rectangular obstacle, aircraft a1 at the starting or terminal position, and a towed aircraft system corresponding to A3 at the starting position, the collision avoidance constraints with all the obstacles are expressed in the form:
Figure BDA0003232686320000082
for a traction system corresponding to aircraft A3, whose obstacles include a static rectangular obstacle, aircraft a2 located at the starting or terminal position, and a1 possibly at the terminal position, the collision avoidance constraints with all obstacles can be expressed in the form:
Figure BDA0003232686320000091
according to the steps 2-4, recording the incomplete starting dispatching time and the terminal time of the self-body as t respectivelysAnd tfThe states of the incomplete self-body at the initial moment and the terminal moment are x respectivelysAnd xf。
The boundary conditions for aircraft a1 are:
xs＝[44,138,90°,0]T,xf＝[192,185,0°,0]T
the boundary conditions for aircraft a2 are:
xs＝[44,188,-90°,0]T,xf＝[192,152,0°,0]T
the boundary conditions for aircraft a3 for the towing system are:
xs＝[155,138,90°,0°,0°,0°,0]T,xf＝[44,138,90°,0°,0°,0°,0]T
according to the steps 2-5, an optimal control model for the dispatching of the aircraft A1 can be established as follows:
Figure BDA0003232686320000101
the optimal control model for the dispatching and transportation of the airplane A2 is established as follows:
Figure BDA0003232686320000102
the optimal control model for dispatching and transportation of the corresponding traction system of the airplane A3 is established as follows:
Figure BDA0003232686320000111
according to the steps 2-6, the common pseudo-spectrum method in the optimal control algorithm is adopted to respectively solve the optimal control models of the dispatching and transportation of the traction systems corresponding to the airplane A1, the airplane A2 and the airplane A3, so that the minimum tail end time of the dispatching and transportation of the airplane A1, the airplane A2 and the airplane A3 is 169.71s, 164.96s and 165.36s respectively, and the corresponding 4-dimensional path data are shown in the attached figures 2, 3, 4 and 5 respectively.
And 3, listing all priority ranking schemes by adopting an exhaustion method, optimizing the actual dispatching starting time of each subject and the total time consumed by all subjects to finish dispatching operation based on a priority method aiming at each ranking scheme, finally selecting the scheme with the shortest total time consumption from all the ranking schemes as an optimal scheme, and dispatching each subject along each off-line path by taking the optimized actual dispatching starting time in the optimal scheme as the starting time.
Then, according to step 3-1, 3 self-dispatched bodies are numbered 1,2 and 3 respectively, and 3 numbers of 1,2 and 3 are arranged to generate 2 arrangement schemes, which may form an ordering scheme set P ═ P1,P2In which P is1＝[1,2,3]，P2＝[2,1,3]。
According to step 3-2, first, a sort plan P is determined1The priority of (2). For ordering scheme PiThe priority in the sorting is made to decrease from left to right in turn, i.e. the first element P11The highest priority among the 3 autonomous agents to be dispatched, P12Next, P13And the lowest.
According to step 3-3, an ordering scheme P is calculated1The actual starting time of each self-body is specifically as follows:
according to step 3-3-1, from subject P11The priority of (2) is highest, no delay is needed, and only the dispatching needs to be started from 0s along the track obtained in step 2, and meanwhile, the sequence number of the self body to be optimized of the actual dispatching starting time is initialized to be j-2, and the iterative calculation step length delta T of the initialized delay time is 0.01 s.
According to step 3-3-2, the host P is12To avoid high priority autonomous body P11But the set of times that the departure needs to be delayed
Figure BDA0003232686320000121
The initialization is 0.
According to step 3-3-3, the host P will be11Considered as a dynamic barrier.
According to step 3-3-4, the host P will be12And a self body P11Performing collision detection if used to describe the self-body P12And a self body P11The distance between the centers of the two characteristic circles is constantly greater than or equal to
Figure BDA0003232686320000122
If the collision does not occur, the step is shifted to the step 3-3-5, otherwise, the step is shifted to the step 3-3-6.
According to step 3-3-5, from subject P12Need not be for and from the body P11Delay departure from collision and record from subject P12To interact with the self-body P11The delayed departure time for collision avoidance is
Figure BDA0003232686320000123
And (4) transferring to the step 3-3-6.
According to step 3-3-6, the
Figure BDA0003232686320000124
Repeating the superposition delay time step of 0.01s until the description of the self-body P12And a self body P11The distance between the centers of the two characteristic circles is greater than or equal to at any moment
Figure BDA0003232686320000125
(i.e., 16m) up to the point of updating the self-body P12To avoid the self-body P11Time required to delay departure
Figure BDA0003232686320000126
And (5) switching to the step 3-3-8 according to the step 3-3-7.
From steps 3-3-8, the self-body P can be determined12To avoid all higher priority autonomous bodies P12Set of times required to delay roll-out
Figure BDA0003232686320000127
From body P12Has an actual start-up time of 21.28s, i.e. from the subject P12And starting the dispatching according to the track planned in the step 2 at the moment of 21.28 s.
According to steps 3-3-9: when j is equal to 3, the process proceeds to step 3-3-2 to obtain
Figure BDA0003232686320000128
From body P13Has an actual start-up time of 150.57s, i.e. from subject P13And starting the dispatching according to the track planned in the step 2 at the time 150.57 s.
According to steps 3-4, for the ordering scheme P1The sum of the actual starting dispatching time obtained in the step 3-3 and the minimum end time obtained in the step 2 is used as the actual arrival time of each subject, the finishing dispatching time of A1 in the scheme is obtained to be 169.71s, A2 is 186.24s, A3 is 315.93s, and the maximum value 315.93s of the actual arrival time of all subjects is used as a sorting scheme P1The total time it takes to complete the dispatch task.
According to step 3-5, since i < 2, i ═ i +1, and proceed to step 3-2, protocol P can be obtained2In, P12Needs to delay the departure for 13.82s, P13The start of max {129.29,13.41} is delayed, and the time for completing the dispatching task from the main body A1 in the scheme is 183.53s, A2 is 186.24s and A3 is 294.65s, so that the total time consumed for completing the dispatching task is 291.77 s. Comparing the two ordering schemes, since 315.93s is greater than 294.65s, scheme P2And taking the corresponding sorting scheme as an optimal scheme.
According to the optimal scheme, the dispatching is respectively carried out along the dispatching tracks obtained in the step 2 when the self-body A1 is at 13.82s, the self-body A2 is at 0.00s and the self-body A3 is at 129.29s, the dispatching time of the self-body A1 is 183.53s, the dispatching time of the A2 is 186.24s, and the dispatching time of the A3 is 294.65 s.
The above-mentioned embodiments only express the embodiments of the present invention, but not should be understood as the limitation of the scope of the invention patent, it should be noted that, for those skilled in the art, many variations and modifications can be made without departing from the concept of the present invention, and these all fall into the protection scope of the present invention.

Claims (2)

1. A priority-based incomplete self-body deck coordinated dispatching path planning method is characterized by comprising the following steps:
step 1, determining the number N of incomplete autonomous bodies to be dispatched, and presetting the time for all autonomous bodies to slide out to be 0 s;
step 2, respectively calculating the off-line paths of the respective main bodies by adopting an optimal control method based on the initial state and the tail end state of the respective main bodies to obtain 4-dimensional path data consisting of the abscissa, the ordinate, the angle and the time of the respective main bodies; when an optimal control method is adopted to calculate an autonomous body offline path, the rest autonomous bodies are all regarded as static obstacles which are always stopped at the initial position; the specific steps of calculating the off-line path by adopting the optimal control method are as follows:
step 2-1: establishing kinematic equation of incomplete self-body transfer
Establishing a state space x for describing the incomplete dispatching of the autonomous body, determining a control variable u, and establishing the following kinematic equation of the incomplete dispatching of the autonomous body:
Figure FDA0003232686310000011
wherein t is a time variable;
step 2-2: determining state and control constraints in a non-complete autonomous dispatch process
The constraints applied to the state variables and the control variables in the incomplete self-body dispatching process are expressed in the form of inequalities as follows:
C(x,u,t)≤0 (2)
step 2-3: establishing obstacle avoidance constraint model
The collision avoidance constraints of the non-integral autonomous body and the obstacle are described by adopting the following continuous functions:
Figure FDA0003232686310000012
wherein (x)oh,yoh) Respectively representing the position coordinates of the geometric center of the h-th obstacle; d represents the distance between the center of the rear wheel of the airplane and the center of a characteristic circle describing the outline of the incomplete autonomous body; dist denotes the safety separation distance; a ish、bh、phRespectively is the long axis, short axis and outline parameters of the h barrier; r isiTo describe the radius of the incomplete self-body feature circle;
when p ishThe obstacle is rhombus when 1, when phWhen 2 the obstacle is circular, when phThe obstacle is approximately rectangular when the distance is more than 2; the collision avoidance constraint of the incomplete autonomous body with all obstacles can be expressed in the form of a matrix as follows:
H(x,t)≤0 (4)
step 2-4: determining boundary conditions for a single incomplete autonomous dispatch trajectory plan
Recording the incomplete starting dispatching time and the terminal time of the self-body as t respectivelysAnd tfThe states of the incomplete self-body at the initial moment and the terminal moment are x respectivelysAnd xfThen, the boundary conditions of the single incomplete self-body dispatching trajectory planning problem are as follows:
x(ts)＝xs,x(tf)＝xf (5)
step 2-5: establishing an optimal control model for single incomplete self-body dispatching
According to the formulas (1), (2), (4) and (5), the following time-energy optimal control problem is established:
Figure FDA0003232686310000021
wherein w is a terminal time weight factor;
step 2-6: solution of optimal control model
According to a formula (6), solving the data by adopting an optimal control algorithm to optimize the minimum tail end time and the corresponding 4-dimensional path data;
step 3, listing all priority ranking schemes by adopting an exhaustion method, optimizing the actual dispatching starting time of each subject and the total time consumed by all subjects to finish dispatching operation based on a priority method aiming at each ranking scheme, selecting the scheme with the shortest total time consumption as an optimal scheme from all ranking schemes, taking the optimized actual dispatching starting time in the optimal scheme as the starting time by each subject, and dispatching along each off-line path;
the specific steps of optimizing the actual dispatching starting time of each main body and the total time consumed by all the main bodies to finish dispatching operation based on the priority method are as follows:
step 3-1: generating a priority ordering scheme; respectively numbering N self-service bodies to be dispatched as 1,2, 3, … and N, and fully arranging N numbers of 1,2, 3, … and N to generate M arrangement schemes, wherein M is more than or equal to 1, and M belongs to N+The set of ordering schemes P ═ { P ═ P can be formed1,P2,…,PN！In which P isi＝[Pi1,Pi2,…,PiN]，i＝1,2,…,M，Pij(j ═ 1,2, …, N) for ordering scheme PiThe jth element in (a);
step 3-2: let i equal to 1, determine the ordering scheme PiThe priority of (2); for ordering scheme PiThe priority in the sorting is made to decrease from left to right in turn, i.e. the first element Pi1For the N autonomous agents to be dispatched, P is the highest priorityi2Next, PiNThe lowest;
step 3-3: computing an ordering scheme PiThe actual start dispatching time of each self-body;
step 3-3-1: from body Pi1The priority of (2) is highest, delay is not needed, and only the dispatching needs to be started from 0s along the track obtained in the step (2), meanwhile, the sequence number of the self body to be optimized of the actual dispatching starting time is initialized to j-2, and the delay time is initialized to calculate the step length delta T in an iterative manner;
step 3-3-2: will be from body PijTo avoid high priority autonomous body Pik(k 1,2, …, j-1) and delay of departure timeCollection
Figure FDA0003232686310000022
Is initialized to 0, wherein
Figure FDA0003232686310000023
Is shown from the body PijIn order to avoid autonomous body P with higher priorityikThe time of the delayed departure;
step 3-3-3: let k equal to 1 and will be from the body PikAs a dynamic barrier;
step 3-3-4: will be from body PijAnd a self body PikPerforming collision detection if used to describe the self-body PijAnd a self body PikThe distance between the centers of the two characteristic circles is constantly greater than or equal to
Figure FDA0003232686310000031
If the collision does not occur, the step is shifted to the step 3-3-5, otherwise, the step is shifted to the step 3-3-6;
step 3-3-5: from body PijNeed not be for and from the body PikDelay departure from collision and record from subject PijTo interact with the self-body PikThe delayed departure time for collision avoidance is
Figure FDA0003232686310000032
Turning to the step 3-3-6;
step 3-3-6: will be provided with
Figure FDA0003232686310000033
Repeating the superposition delay time step Delta T until the description of the self-body PijAnd a self body PikThe distance between the centers of the two characteristic circles is greater than or equal to at any moment
Figure FDA0003232686310000034
Up to now, update self-body PijTo avoid the self-body PikTime required to delay departure
Figure FDA0003232686310000035
Step 3-3-7: if k is less than j, k is equal to k +1, and the step 3-3-3 is carried out; otherwise, turning to the step 3-3-8;
step 3-3-8: determination of self-body PijTo avoid all higher priority autonomous bodies PikSet of times required to delay roll-out
Figure FDA0003232686310000036
From body PijThe actual start-up time of
Figure FDA0003232686310000037
Namely from the body PijIn that
Figure FDA0003232686310000038
Starting dispatching according to the track planned in the step 2;
step 3-3-9: if j is less than N, making j equal to j +1, and then proceeding to step 3-3-2; otherwise, turning to the step 3-4;
step 3-4: for ordering scheme PiTaking the sum of the actual starting dispatching time obtained in the step 3-3 and the minimum end time obtained in the step 2 as the actual arrival time of each subject, and taking the maximum value of the actual arrival time of all the subjects as a sequencing scheme PiThe total time required to complete the dispatch task;
step 3-5: if i is less than M, i is i +1, and the step 3-2 is carried out; otherwise, taking the sorting scheme corresponding to the minimum value of the total time consumed by the dispatching tasks of all the sorting schemes as an optimal scheme, starting according to the actual dispatching starting time corresponding to the respective main body in the optimal scheme, and dispatching along the dispatching track obtained in the step 2.
2. The method as claimed in claim 1, wherein the optimal control algorithm includes pseudo-spectrum method and pseudo-spectrum algorithm for preserving simmering.
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