CN114610066A - Method for generating formation flight tracks of distributed cluster unmanned aerial vehicles in complex unknown environment - Google Patents
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Abstract
The invention discloses a method for generating a formation flight track of distributed cluster unmanned aerial vehicles in a complex unknown environment. Compared with other methods at present, the method disclosed by the invention is based on the idea of rough to fine track planning, generates the local flight track through multi-layer track planning, ensures the real-time performance, can also generate the high-quality local track, and can meet the flight requirements under the complex and unknown environment. The multi-layer track planning structure has high flexibility, simplifies track calculation amount by distributing the priority of formation flying tasks in different layers, is convenient for users to define cluster formation tasks, and has guiding significance for practical engineering application.
Description
Technical Field
The invention relates to the technical field of unmanned aerial vehicle cooperative control, in particular to a method for generating a formation flight trajectory of distributed cluster unmanned aerial vehicles in a complex unknown environment.
Background
In recent years, the autonomous navigation technology of the unmanned aerial vehicle is mature day by day, but the defects of small single-machine load, short endurance time, low system fault tolerance rate and the like still exist when a single unmanned aerial vehicle executes a task, and the clustered unmanned aerial vehicle enhances the task execution capacity through a multi-machine redundancy system and effectively makes up the defects, so that the development of the clustered unmanned aerial vehicle technology is urgent.
In the cluster unmanned aerial vehicle technology, a cluster unmanned aerial vehicle is called to form a flight, namely, the cluster unmanned aerial vehicle keeps a certain formation form to fly according to task requirements, so that the cooperation capability of the cluster unmanned aerial vehicle for executing specific tasks can be obviously improved, and the cluster unmanned aerial vehicle has a great number of applications in the military and civil fields, for example, the perception capability of the cluster on the same signal source can be improved by keeping a circular formation form, the coverage range of the cluster can be improved by keeping a linear formation form, and the like.
When the clustered unmanned aerial vehicle executes a formation navigation task in a complex unknown environment, at least the following three points are required to be ensured: a. keeping the formation of unmanned aerial vehicle clusters; b. flight safety is guaranteed under a complex and unknown environment; c. the capacity of switching formation forms in the flight process is provided. The cluster unmanned aerial vehicle knows the real-time state of the cluster unmanned aerial vehicle and the real-time state of the cluster unmanned aerial vehicle through mutual communication, adjusts the flight track of the cluster unmanned aerial vehicle according to the real-time state to keep the formation of the cluster unmanned aerial vehicle, considers that communication delay and insufficient airborne computing capability are insufficient, adopts rough to detailed guidance ideas for calculating the flight track, and emphasizes different flight requirements in different frames through a multi-layer track planning frame. Is subject to literature[1]Inspiring, the cluster unmanned aerial vehicle formation flight track of above-mentioned thought generates the frame, possesses the ability of nimble processing formation flight under the complicated unknown environment, simultaneously because the design of multilayer orbit planning frame, cluster unmanned aerial vehicleThe formation flight task with high quality, high precision and high flexibility can be completed on the premise of greatly reducing the consumption of computing resources.
At present, many methods are proposed in the field of cluster formation flight, such as a virtual structure method, a navigation function method, a reaction behavior method and a local feedback control method based on a consistency theory. But most of the above methods can only realize the formation flying of unmanned aerial vehicle clusters in an open scene without external obstacles.
In a complex environment, the difficulty of formation flight tasks is greatly improved, mainly because each unmanned aerial vehicle still satisfies the safety of cluster flight while keeping an expected formation. One method is to design a feedback control law to simultaneously realize obstacle avoidance and formation maintenance of the unmanned aerial vehicle. Literature reference[2]Han et al propose a formation flight controller with a complex laplace matrix as a feedback gain, the size of the formation during flight being determined by the pilot (long aircraft), who controls the size of the entire formation to make the cluster perform a specific flight mission, e.g. through a narrow slot. In the literature[3]Zhao proposes a control law based on a navigator-follower frame, and the control law can enable the formation of the unmanned aerial vehicle to perform affine transformation according to the change of the environment. Most feedback control methods adopt a pilot-follower framework, but the mode enables the parameters of the formation to be controlled only by a pilot, and once the pilot fails, the flight of the whole cluster fails.
Compared with the navigator-follower framework, the decentralization strategy can better deal with the condition that some unmanned aerial vehicles in the cluster have faults. Literature reference[4]Among them, Alonso-Mora et al divide the trajectory planning of a cluster drone into two phases, the first phase is to calculate the optimal formation parameters and the corresponding drone-target point assignment relationship according to the current map information, and the second phase is to arrive at the assigned target point by each drone independently performing local trajectory planning according to the calculation results of the first phase. The method can realize the obstacle avoidance of the unmanned aerial vehicle cluster, but in the second stageThe requirement of formation is not considered, so that the real-time performance of formation maintenance is poor. Literature reference[5]In the middle, Zhou et al adopts a virtual structure method and combines an artificial potential field method to generate a collision-free formation flight trajectory, but because local optimal points are easily generated in a superimposed artificial potential field, an unmanned aerial vehicle cluster using the method is easy to generate trajectory oscillation and deadlock in the flight process, and meanwhile, the optimality of the overall trajectory cannot be guaranteed. Literature reference[6]In Pary et al, a method using distributed model predictive control is proposed to achieve formation of a cluster for flight, which method maintains a geometric formation primarily by imposing relative position constraints on the drones. During the flight, once obstacles appear in the environment to make the requirement of the relative position of the unmanned aerial vehicle unable to be met, the framework gives up the requirement of formation cooperation to meet the safety of the flight. Although the passive mechanism can ensure obstacle avoidance, the synergy of the cluster system is greatly reduced.
Reference documents:
[1]X.Zhou，Z.Wang，X.Wen，J.Zhu，C.Xu，and F.Gao，“Decentralized spatial－temporal trajectory planning for multicopter swarms，”arXiv preprint arXiv：，2021
[2]Z.Han，L.Wang，and Z.Lin，“Local formation control strategies with undetermined and determined formation scales for co－leader vehicle networks，”in 52nd IEEE Conference on Decision and Control.IEEE，2013，pp.7339–7344.
[3]S.Zhao，“Affifine formation maneuver control of multiagent systems，”IEEE Transactions on Automatic Control，vol.63，no.12，pp.4140–4155，2018.
[4]J.Alonso－Mora，E.Montijano，M.Schwager，and D.Rus，“Distributed multi－robot formation control among obstacles：A geometric and optimization approach with consensus，”in 2016 IEEE international conference on robotics and automation(ICRA).IEEE，2016，pp.5356–5363.
[5]D.Zhou，Z.Wang，and M.Schwager，“Agile coordination and assistive collision avoidance for quadrotor swarms using virtual structures，”IEEE Transactions on Robotics，vol.34，no.4，pp.916–923，2018.
[6]R.Van Parys and G.Pipeleers，“Distributed model predictive formation control with inter－vehicle collision avoidance，”in 2017 11th Asian Control Conference(ASCC).IEEE，2017，pp.2399–2404.
disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method for generating a formation flight trajectory of distributed cluster unmanned aerial vehicles in a complex unknown environment.
In order to achieve the purpose, the invention adopts the following technical scheme:
the method for generating the formation flight trajectory of the distributed cluster unmanned aerial vehicle in the complex unknown environment comprises the following five steps:
(1) user requirement initialization: before the automatic navigation task starts, a user needs to define parameters of formation of cluster unmanned aerial vehicles according to task types, wherein the parameters comprise the number of the unmanned aerial vehicles, expected formation forms, target end points of a geometric center of a cluster and initial distribution of formation tasks; after the user finishes the definition, the cluster unmanned aerial vehicle starts in a distributed mode according to the definition of the user and executes subsequent tasks;
(2) global trajectory: firstly, generating a global track connecting the current position and the target position of the unmanned aerial vehicle under the condition of not considering the obstacle, and taking the global track as a guide track for formation flight of the cluster unmanned aerial vehicle under an ideal condition; on the basis of the global track, selecting a local terminal point which arrives after flying from the current position for a set time as the final state of the subsequent track planning; after a local end point set of the cluster unmanned aerial vehicle is obtained, whether the formation task allocation is optimal under the condition of the local end point set is judged, if so, the subsequent step is started by the task allocation corresponding to the current local end point set, and if not, the formation task re-allocation is carried out, and the subsequent step is started by the optimal task allocation corresponding to the calculated local end point set;
(3) front-end reference trajectory: firstly, searching a front-end multi-topology path by taking the current position and the local end point of an unmanned aerial vehicle as a first state and a last state, obtaining a topology path in a complex environment after sampling and pruning, then selecting the topology with the optimal formation form in the multi-topology path based on the index with the optimal formation form, and generating a high-order continuous front-end reference track on the basis of the optimal topology;
(4) performing a rear-end optimization track on the front-end reference track generated in the step (3): in order to generate a high-quality local track, constructing a multi-objective track optimization problem, considering similarity factors of obstacle avoidance and formation flight of the unmanned aerial vehicle, reducing the number of optimization variables in a discrete track mode to ensure the real-time performance of optimization solution, checking whether the track is safe again after the rear-end optimized track is obtained, executing the track if the track is safe, weakening the consideration of the similarity factors of formation flight if the track is unsafe, optimizing again until the safe track is obtained, and then executing the track;
(5) and (4) re-planning track inspection: because the effective field of view of the sensor of the unmanned aerial vehicle is limited, the flight track may collide with the obstacle which just enters the field of view of the sensor, so whether the track collides with the environmental obstacle is judged at the checking frequency of 1 millisecond/time, if so, the track is started and returned to the step (2) for re-planning, and meanwhile, an updated local terminal point is distributed according to the global track during re-planning based on a rolling optimization strategy.
Further, the specific process of the step (1) is as follows:
in a user requirement initialization step, the number N of cluster unmanned aerial vehicles needs to be defined, which represents that the cluster has N unmanned aerial vehicles, and the number i of each unmanned aerial vehicle is 1,2, …, N; describing the formation of the unmanned aerial vehicle by adopting a graph structure, and defining a non-directional full-connection graph G ═ V, E, wherein V: n represents a set of vertices,
a set of representative edges; in graph G, vertex i represents the position coordinate p of the ith droneiEdge ei,jRepresenting the correlation between the ith drone and the jth drone; it is also necessary to define the end point coordinates p of the geometric center of the clustergAnd the terminal coordinates of each unmanned aerial vehicle are solved by the position of each unmanned aerial vehicle in the formation, pi,g＝pg+Δpi.oWherein Δ pi.oRepresenting the displacement of the ith unmanned aerial vehicle in the ideal formation relative to the geometric center of the cluster; finally, defining initial allocation of formation tasks, wherein for the cluster of N unmanned aerial vehicles, the formation task set is A ═ A1,…,AN}，AiAnd representing the formation allocation of the ith unmanned aerial vehicle, namely the ith unmanned aerial vehicle corresponds to the relative position in the formation.
Further, the specific process of the step (2) is as follows:
firstly, under the condition of not considering the barrier, planning a track connecting the current state of the unmanned aerial vehicle and the global terminal; the track is expressed by a piecewise polynomial, and a three-dimensional track with M segments is defined as:
where t is the current time, tkThe track time of the kth track is;
wherein the kth segment of the segmented track is represented by a high-order polynomial as:
where c is the coefficient of the piecewise polynomial, T is the time distribution of the piecewise polynomial, TkIs the total time of the kth polynomial, and is the time element; when planning a global track, in order to provide more appropriate direction guidance and time distribution for subsequent track optimization, the global track considers the energy consumption and total flight time of the flight track of the unmanned aerial vehicle, and the following optimization problems are solved:
s.t.p(0)＝p0
p(T)＝pg
wherein p is0The current position coordinate of the unmanned aerial vehicle is used, and m is the order corresponding to the control input;
after the global track is obtained, different local planning areas are set according to an actual application scene and a sensing range of a sensor, and an intersection point of the global track and the local planning areas is solved to obtain a local terminal;
finding out the local end point position of each unmanned aerial vehicle in the cluster on the global track and storing the local end point position as a vector h, and storing the position of each unmanned aerial vehicle in the expected formation form as a vector s; before generating the local track, the local end point needs to be adjusted to a local target point according to h and s, and the task allocation is performed on each unmanned aerial vehicle according to the adjusted local target point, so that the calculation needs to be divided into two parts: aligning formation forms and distributing formation tasks;
when the local target point which accords with the expected formation form is regenerated according to the local end point, only the translation and the scaling of the expected formation form are considered, and the rotation of the formation form is not considered;
the coordinates of the desired formation after translation and size scaling transformation, i.e. the aligned coordinates, are denoted as q, then there are:
qj＝αsj+d
wherein s isjA coordinate point representing the jth position in the desired formation, j being 1,2, …, N, α being a scaling factor for size scaling, d being a translation vector; after alignment is given, the euclidean distance from the aligned coordinates to each local endpoint coordinate is recorded as a cost term:
constructing a cost function of the distribution problem according to the cost item, wherein the corresponding integer programming problem is as follows:
xij＝{0，1}，i，j＝1，...，N
wherein xijTo assign a variable, when xijWhen the number of the unmanned planes is 1, the ith unmanned plane is allocated to the jth coordinate in the formation; the specific process is as follows:
firstly, reconstructing an integer programming problem according to a local end point position h and an expected formation s:
then, solving the integer programming problem by using a distribution algorithm to obtain the optimal distribution X and the corresponding minimum cost function value K;
thereafter, parameters s and s are calculated as followssAnd d ands；
calculating the parameters alpha and d for optimal alignment:
then, the alignment parameters alpha, d and the optimal distribution X are obtained, and the optimal alignment coordinate is as follows:
q*＝α*s+d*
after the optimal alignment coordinate is obtained, the optimal alignment coordinate can be distributed to each unmanned aerial vehicle as a local target point according to X < o >; the local target point at the moment is obtained by optimizing the local end point position of each unmanned aerial vehicle inquired on the global track, so that the geometric distribution of the expected formation can be met.
Further, the specific process of the step (3) is as follows:
in the front-end reference track generation step, firstly, front-end multi-topology path searching is carried out based on the current position of the unmanned aerial vehicle and local target points, and a topology path in a complex environment is obtained after sampling and pruning.
Further, in step (3), the generation of the topological path specifically adopts a probabilistic roadmap method, which includes the following steps:
(1) initializing a sampling tree, setting a sampling space according to a sampling starting point and a sampling end point, and adding the sampling starting point and the sampling end point into the sampling tree;
(2) judging whether the total number of the sampling points is smaller than a set threshold value, if so, ending, otherwise, continuing; randomly sampling in a sampling space to obtain a sampling point, judging whether the sampling point is in the obstacle or not, if so, repeating the step (2), and if not, entering the step (3);
(3) judging whether the sampling point can be in collision-free connection with a node in the sampling tree, wherein the collision-free connection means that a connecting line of the sampling point and the node does not penetrate through an obstacle, if not, adding the sampling point into the sampling tree, repeating the step (2), and if so, entering the step (4);
(4) and (3) judging whether the sampling point which can be connected with the node in the sampling tree without collision can replace the node in the current sampling tree or not according to the judgment standard, wherein the judgment standard is that whether the path length formed by the sampling point and the neighbor node is smaller than the path length formed by the original node and the same neighbor node or not, if so, replacing the node in the current sampling tree by the sampling point, and repeating the step (2).
Further, in step (3), the specific steps of generating the topological path in the complex environment are as follows:
1) firstly, carrying out breadth-first search on a sampling tree, finding out all paths connecting a search starting point and a search end point, then carrying out topology judgment on the paths, classifying the paths belonging to the same topology into one class, and reserving one path with the shortest length;
2) pruning the reserved path, wherein the original path is obtained after limited sampling, the shortest path under the topology cannot be guaranteed to be obtained, in the pruning process, a ray is sent to the original path from the search starting point until the ray hits an obstacle, the previous ray is used as a part of the pruned path, and the path pruning can be completed after the ray end point reaches the search end point;
3) finally, a plurality of topological paths after pruning are obtained, whether the paths are in the same topological path is judged pairwise, and if the two paths are in the same topological path, the shortest path is reserved; judging whether the path is defined as a same-topology path or not as follows: given two paths xi1(r) and xi2(r), where r represents the parameterization of the path, and r ∈ [0,1 ]]If two paths satisfy xi1(0)＝ξ2(0)，ξ1(1)＝ξ2(1) I.e. with the same starting and ending points, and for
Connecting wire
If the two paths do not touch the barrier, the two paths are the same topological paths, otherwise, the two paths are different topological paths;
4) and (3) screening out the shortest path from the plurality of topological paths obtained in the step 3) as a reference track according to the flight distance.
Further, the specific process of the step (4) is as follows:
the rear-end track optimization is based on the front-end reference track, factors of safe obstacle avoidance and formation flight of the unmanned aerial vehicle are considered at the same time, a constraint-free optimization problem is formed, and a track with higher quality is obtained through optimization and solution; the unconstrained optimization problem form of the constructed back-end trajectory is as follows:
the piecewise polynomial coefficient c and the time distribution T are optimization variables, J with subscripts represents a certain objective function or a constraint penalty term, lambda represents a corresponding weight coefficient, and the subscripts { e, a, o, f, b and h } respectively represent an energy cost term, a total track time term, a safety obstacle avoidance constraint term, a formation similarity term, a mutual inter-cluster collision avoidance term and a dynamic feasibility term; and then, performing iterative optimization on the optimization problem based on the gradient information, and finally generating a safe and collision-free high-quality track capable of maintaining the formation for the current unmanned aerial vehicle.
The invention has the beneficial effects that: the invention provides a general track planning framework for formation flight of cluster unmanned aerial vehicles in a complex unknown environment, which adopts a multilayer track planning structure and generates high-quality formation flight tracks of the cluster unmanned aerial vehicles in a distributed manner through a multilayer framework such as user demand initialization, global track planning, front-end reference track planning, rear-end track optimization, re-planning state inspection and the like. Compared with other methods at present, the method disclosed by the invention is based on the idea of planning the track from rough to fine, and generates the local flight track through multi-layer track planning, so that the high quality of the local track is ensured, the real-time property is also ensured, and the method can cope with complex unknown environments. In addition, the structure of the multilayer track planning has high flexibility, the priority of formation flight is distributed at different levels, a user can define formation tasks conveniently, and the method has significance for practical engineering application.
Drawings
FIG. 1 is a schematic diagram of the method in example 1 of the present invention;
fig. 2 is a schematic diagram of full connection of formation forms of the clustered unmanned aerial vehicles in embodiment 1 of the present invention;
fig. 3 is a schematic diagram of a relationship between a global track and a local track in embodiment 1 of the present invention;
fig. 4 is a schematic diagram of local end-point formation alignment and formation allocation of an optimal cluster in embodiment 1 of the present invention;
fig. 5 is a schematic diagram of searching a topological path in embodiment 1 of the present invention;
fig. 6 is a schematic diagram illustrating a pruning effect of a topological path in embodiment 1 of the present invention;
fig. 7 is a schematic diagram of a flight simulation experiment result of the large-scale cluster heart-shaped formation in embodiment 2 of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, and it should be noted that the present embodiment is based on the technical solution, and the detailed implementation and the specific operation process are provided, but the protection scope of the present invention is not limited to the present embodiment.
Example 1
The embodiment provides a method for generating a formation flight track of a distributed cluster unmanned aerial vehicle in a complex unknown environment, which is used for generating a formation flight track of a cluster unmanned aerial vehicle in a complex environment by finally generating a high-quality local flight track through multi-layer track planning based on the idea of rough to fine track planning.
As shown in fig. 1, the method mainly includes the following five steps:
(1) user requirement initialization: before the automatic navigation task starts, a user needs to define parameters of formation of the cluster unmanned aerial vehicles according to task types, the parameter is only one user interaction in the whole task process, and after the user finishes the definition of the number of the unmanned aerial vehicles, the expected formation shape, the target end point of a cluster geometric center and the initial distribution of the formation tasks, the cluster unmanned aerial vehicles are started in a distributed mode according to the definition of the user to execute subsequent tasks;
(2) global trajectory: firstly, global trajectory planning is carried out, namely, a global trajectory connecting the current position and the target position of the unmanned aerial vehicle is quickly generated under the condition of not considering obstacles and is used as a guide trajectory for cluster formation flying under an ideal condition; on the basis of the global trajectory, selecting a local end point which arrives after the current position flies for a set time as the final state of subsequent trajectory planning, and after a local end point set of the cluster unmanned aerial vehicle is obtained, judging whether the allocation of the formation tasks is optimal under the condition of the local end point set, if so, starting the subsequent step by the task allocation corresponding to the current local end point set, and if not, re-allocating the formation tasks, and starting the subsequent step by the optimal task allocation corresponding to the calculated local end point set;
(3) front-end reference trajectory: firstly, searching a front-end multi-topology path by taking the current position and the local end point of an unmanned aerial vehicle as a first state and a last state, obtaining a topology path in a complex environment after sampling and pruning, then selecting the topology with the optimal formation form in the multi-topology path based on the index with the optimal formation form, and generating a high-order continuous front-end reference track on the basis of the optimal topology;
(4) performing a rear-end optimization track on the front-end reference track generated in the step (3): in order to generate a high-quality local track, constructing a multi-objective track optimization problem, considering similarity factors of obstacle avoidance and formation flight of the unmanned aerial vehicle, reducing the number of optimization variables in a discrete track mode to ensure the real-time performance of optimization solution, checking whether the track is safe again after the rear-end optimized track is obtained, executing the track if the track is safe, weakening the consideration of the similarity factors of formation flight if the track is unsafe, optimizing again until the safe track is obtained, and then executing the track;
(5) and (4) re-planning track inspection: because the effective field of view of the sensor of the unmanned aerial vehicle is limited, the flight track may collide with the obstacle which just enters the field of view of the sensor, so whether the track collides with the environmental obstacle is judged at the checking frequency of 1 millisecond/time, if so, the track is started and returned to the step (2) for re-planning, and meanwhile, an updated local terminal point is distributed according to the global track during re-planning based on a rolling optimization strategy.
Specifically, the specific process of step (1) is as follows:
in the initialization step of user requirement, defining cluster is requiredThe number of the unmanned aerial vehicles is N, which represents that the cluster is provided with N unmanned aerial vehicles, and the number of each unmanned aerial vehicle is 1,2, … and N; describing the formation of the unmanned aerial vehicles by using a graph structure, defining an undirected fully-connected graph G ═ (V, E), wherein V ═ 1, 2.. multidot.N } represents a set of vertexes,
a set of representative edges; in graph G, vertex i represents the position coordinate p of the ith droneiEdge ei,jRepresenting the correlation between the ith drone and the jth drone; it is also necessary to define the end point coordinates p of the geometric center of the clustergAnd the terminal coordinates of each unmanned plane are solved by the position of each unmanned plane in the formation, namely pi,g＝pg+Δpi.oWherein Δ pi.oRepresenting the displacement of the ith unmanned aerial vehicle in the expected formation relative to the geometric center of the cluster; finally, defining initial allocation of formation tasks, wherein for the cluster of N unmanned aerial vehicles, the formation task set is A ═ A1,…,AN}，AiAnd representing the formation allocation of the ith unmanned aerial vehicle, namely the relative position of the ith unmanned aerial vehicle in the formation.
Fig. 2 is an exemplary diagram of formation of drones when N is 5.
In this embodiment, the specific process of step (2) is as follows:
firstly, a track connecting the current state of the unmanned aerial vehicle and the global terminal point is planned without considering the obstacles. The track is expressed by a piecewise polynomial, and a three-dimensional track with M segments is defined as:
where t is the current time, tkThe track time of the kth track is;
wherein the k-th segment of the segmentation track is represented by a high-order polynomial as:
where c is the coefficient of the piecewise polynomial, T is the time distribution of the piecewise polynomial, TkIs the total time of the kth polynomial, and is the time element; when planning a global track, in order to provide more appropriate direction guidance and time distribution for subsequent track optimization, the global track considers the energy consumption and total flight time of the flight track of the unmanned aerial vehicle, and the following optimization problems are solved:
s.t.p(0)＝p0
p(T)＝pg
wherein p is0For the current position coordinates of the drone, m is the order to which the control input corresponds.
After the global track is obtained, different local planning areas are set according to the actual application scene and the sensing range of the sensor, and the intersection point of the global track and the local planning areas is solved, namely the local terminal.
Fig. 3 is a schematic diagram showing a relationship between a global track and a local track. In the method of this embodiment, the local end point is defined as an intersection point of the global trajectory and the local perception range, but when the trajectory is optimized at the back end, the local end point needs to be adjusted to obtain a local target point, which is an actual end point of the local trajectory.
And finding out the local end point position of each unmanned aerial vehicle in the cluster on the global track and storing the local end point position as a vector h, and storing the position of each unmanned aerial vehicle in the expected formation form as a vector s. Before generating the local track, the local end point needs to be adjusted to a local target point according to h and s, and the task allocation is performed on each unmanned aerial vehicle according to the adjusted local target point, so that the calculation needs to be divided into two parts: queuing form alignment (alignment) and queuing task allocation (alignment).
The method only considers the translation and the scaling of the expected formation shape and does not consider the rotation of the formation shape when regenerating the local target point which accords with the expected formation shape according to the local end point. In this case, the alignment problem and the assignment problem can be optimized simultaneously, wherein the optimal solution to the alignment problem can be resolved without the need to iterate the alignment-assignment process to approach the optimum.
The coordinates of the desired formation after translation and size scaling transformation, i.e. the aligned coordinates, are denoted as q, then there are:
qj＝αsj+d
wherein s isjA coordinate point representing the jth position in the desired formation, j being 1,2, …, N, α being the scaling factor for the size scaling, d being the translation vector. After alignment is given, in this embodiment, the euclidean distance from the aligned coordinates to each local end point coordinate is recorded as a cost term:
constructing a cost function of the distribution problem according to the cost item, wherein the corresponding integer programming problem is as follows:
xij＝{0，1}，i，j＝1，...，N
wherein xijTo assign a variable, when xijWhen 1, the ith drone is assigned to the jth coordinate in the formation. The specific process is as follows:
firstly, reconstructing an integer programming problem according to a local end point position h and an expected formation s:
and then solving the integer programming problem by using an allocation algorithm, such as Hungarian algorithm, to obtain the optimal allocation X and the corresponding minimum cost function value K.
Thereafter, parameters s and s are calculated as followssAnd d ands。
calculating the parameters alpha and d for optimal alignment:
then, the alignment parameters alpha, d and the optimal distribution X are obtained, and the optimal alignment coordinate is as follows:
q*＝α*s+d*
after the optimal alignment coordinate is obtained, the optimal alignment coordinate can be distributed to each unmanned aerial vehicle as a local target point according to X. The local target point at the moment is obtained by optimizing the local end point position of each unmanned aerial vehicle inquired on the global track, so that the geometric distribution of the expected formation can be met. Fig. 4 is a schematic diagram illustrating local end-point formation alignment and formation allocation of an optimal cluster.
Further, in this embodiment, the specific process of step (3) is as follows:
in the front-end reference track generation step, firstly, front-end multi-topology path searching is carried out based on the current position of the unmanned aerial vehicle and local target points, and a topology path in a complex environment is obtained after sampling and pruning.
Fig. 5 is a schematic diagram of the topological path search. The generation of the topological path specifically adopts a probability route map method, which comprises the following steps:
(1) initializing a sampling tree, setting a sampling space according to a sampling starting point and a sampling end point, and adding the sampling starting point and the sampling end point into the sampling tree;
(2) and judging whether the total number of the sampling points is smaller than a set threshold value, if so, ending, and otherwise, continuing. Randomly sampling in a sampling space to obtain a sampling point, judging whether the sampling point is in the obstacle or not, if so, repeating the step (2), and if not, entering the step (3);
(3) judging whether the sampling point can be in collision-free connection with a node in the sampling tree, wherein the collision-free connection means that a connecting line of the sampling point and the node does not penetrate through an obstacle, if not, adding the sampling point into the sampling tree, repeating the step (2), and if so, entering the step (4);
(4) and (3) judging whether the sampling point which can be connected with the node in the sampling tree without collision can replace the node in the current sampling tree or not according to the judgment standard, wherein the judgment standard is that whether the path length formed by the sampling point and the neighbor node is smaller than the path length formed by the original node and the same neighbor node or not, if so, replacing the node in the current sampling tree by the sampling point, and repeating the step (2).
And constructing an environment topological path connecting the starting point and the end point by the method of the probability route map. The specific steps for generating the topological path in the complex environment are as follows:
1) firstly, carrying out breadth-first search on a sampling tree, finding out all paths connecting a search starting point and a search end point, then carrying out topology judgment on the paths, classifying the paths belonging to the same topology into one class, and reserving one path with the shortest length;
2) pruning the reserved path, as shown in fig. 6, because the original path is obtained after limited sampling, the shortest path under the topology cannot be guaranteed to be obtained, in the pruning process, a ray is sent to the original path from the search starting point until the ray hits an obstacle, the previous ray is used as a part of the path after pruning, and the path pruning can be completed by circulating until the ray end point reaches the search end point;
3) finally, a plurality of topological paths after pruning are obtained, whether the paths are in the same topological path is judged pairwise, and if the two paths are in the same topological path, the shortest path is reserved; the definition of judging whether the two paths are in the same topology is as follows: given two paths xi1(r) and xi2(r), where r represents the parameterization of the path, and r ∈ [0,1 ]]If two paths satisfy xi1(0)＝ξ2(0)，ξ1(1)＝ξ2(1) I.e. with the same starting and ending points, and for
Connecting wire
If the two paths do not meet the obstacle, the two paths are the same topological paths, otherwise, the two paths are different topological paths.
4) And (3) screening out the shortest path from the plurality of topological paths obtained in the step 3) as a reference track according to the flight distance.
The rear-end track optimization is mainly based on the front-end reference track, factors such as safe obstacle avoidance of the unmanned aerial vehicle, formation flight and the like are considered at the same time, an unconstrained optimization problem is formed, and the track with higher quality is obtained through optimization and solution. The unconstrained optimization problem form of the rear-end trajectory constructed by the method of the embodiment is as follows:
the piecewise polynomial coefficient c and the time distribution T are optimization variables, J with subscripts represents a certain objective function or a constraint penalty term, lambda represents a corresponding weight coefficient, and the subscripts { e, a, o, f, b and h } respectively represent an energy cost term, a total track time term, a safety obstacle avoidance constraint term, a formation similarity term, a mutual collision avoidance term among clusters and a dynamic feasibility term. And then, performing iterative optimization on the optimization problem based on gradient information, and finally generating a safe and collision-free high-quality track capable of maintaining the formation for the current unmanned aerial vehicle.
Compared with other methods at present, the method of the embodiment is based on the idea of planning the track from rough to fine, generates the local flight track through multi-layer track planning, guarantees the high quality of the local track, also guarantees the real-time performance, and can cope with complex unknown environments. In addition, the structure of the multilayer track planning has high flexibility, the priority of formation flight is distributed at different levels, a user can define formation tasks conveniently, and the method has significance for practical engineering application.
Example 2
In order to verify the performance of the method described in example 1 in dealing with the large-scale cluster irregular formation flying task, the simulation environment experiment part designs a heart-shaped formation composed of ten unmanned aerial vehicles, and at the same time, 300 cylindrical obstacles and 80 annular obstacles are placed in a space of 80m × 20m, as shown in fig. 7, the unmanned aerial vehicle cluster flies from left to right in a heart shape, and passes through a very dense obstacle area, and captures images are taken in the flying process at an interval of 20m, so that it can be seen that the irregular heart shape is always kept good in the whole flying process, as can be seen from the flying trajectory of the unmanned aerial vehicle cluster, each unmanned aerial vehicle encounters many obstacles in the flying process, but under the control of the method of example 1, the unmanned aerial vehicle keeps the heart-shaped formation in the flying process while avoiding obstacles, which fully shows the universality and robustness of the method of example 1, the large-scale cluster irregular formation flight simulation experiment is remarkably completed.
Various corresponding changes and modifications can be made by those skilled in the art based on the above technical solutions and concepts, and all such changes and modifications should be included in the protection scope of the present invention.
Claims (7)
1. A method for generating a formation flight track of a distributed cluster unmanned aerial vehicle in a complex unknown environment is characterized by comprising the following five steps:
(1) user requirement initialization: before the automatic navigation task starts, a user needs to define parameters of formation of cluster unmanned aerial vehicles according to task types, wherein the parameters comprise the number of the unmanned aerial vehicles, expected formation forms, target end points of a geometric center of a cluster and initial distribution of formation tasks; after the user finishes the definition, the cluster unmanned aerial vehicle starts in a distributed mode according to the definition of the user and executes subsequent tasks;
(2) global trajectory: firstly, generating a global track connecting the current position and the target position of the unmanned aerial vehicle under the condition of not considering the obstacle, and taking the global track as a guide track for formation flight of the cluster unmanned aerial vehicle under an ideal condition; on the basis of the global track, selecting a local terminal point which arrives after flying from the current position for a set time as the final state of the subsequent track planning; after a local end point set of the cluster unmanned aerial vehicle is obtained, whether the formation task allocation is optimal under the condition of the local end point set is judged, if so, the subsequent step is started by the task allocation corresponding to the current local end point set, and if not, the formation task re-allocation is carried out, and the subsequent step is started by the optimal task allocation corresponding to the calculated local end point set;
(3) front-end reference trajectory: firstly, searching a front-end multi-topology path by taking the current position and the local end point of an unmanned aerial vehicle as a first state and a last state, obtaining a topology path in a complex environment after sampling and pruning, then selecting the topology with the optimal formation form in the multi-topology path based on the index with the optimal formation form, and generating a high-order continuous front-end reference track on the basis of the optimal topology;
(4) performing a rear-end optimization track on the front-end reference track generated in the step (3): in order to generate a high-quality local track, constructing a multi-objective track optimization problem, considering similarity factors of obstacle avoidance and formation flight of the unmanned aerial vehicle, reducing the number of optimization variables in a discrete track mode to ensure the real-time performance of optimization solution, checking whether the track is safe again after the rear-end optimized track is obtained, executing the track if the track is safe, weakening the consideration of the similarity factors of formation flight if the track is unsafe, optimizing again until the safe track is obtained, and then executing the track;
(5) and (4) re-planning track inspection: because the effective field of view of the sensor of the unmanned aerial vehicle is limited, the flight track may collide with the obstacle which just enters the field of view of the sensor, so whether the track collides with the environmental obstacle is judged at the checking frequency of 1 millisecond/time, if so, the track is started and returned to the step (2) for re-planning, and meanwhile, an updated local terminal point is distributed according to the global track during re-planning based on a rolling optimization strategy.
2. The method according to claim 1, wherein the specific process of step (1) is as follows:
in the user requirement initialization step, the number N of cluster unmanned aerial vehicles needs to be defined, N unmanned aerial vehicles represent the cluster, and the number i of each unmanned aerial vehicle is 1,2, …, N; describing the formation of the unmanned aerial vehicle by adopting a graph structure, and defining a non-directional full-connection graph G ═ V, E, wherein V: n represents a set of vertices,
a set of representative edges; in graph G, vertex i represents the position coordinate p of the ith droneiEdge ei，jRepresenting the correlation between the ith drone and the jth drone; it is also necessary to define the end point coordinates p of the geometric center of the clustergAnd the terminal coordinates of each unmanned aerial vehicle are solved by the position of each unmanned aerial vehicle in the formation, pi，g＝pg+Δpi.oWherein Δ pi.oRepresenting the displacement of the ith unmanned aerial vehicle in the ideal formation relative to the geometric center of the cluster; finally, defining initial allocation of formation tasks, wherein for the cluster of N unmanned aerial vehicles, the formation task set is A ═ A1，...，AN}，AiAnd representing the formation allocation of the ith unmanned aerial vehicle, namely the ith unmanned aerial vehicle corresponds to the relative position in the formation.
3. The method according to claim 1, wherein the specific process of step (2) is as follows:
firstly, under the condition of not considering the barrier, planning a track connecting the current state of the unmanned aerial vehicle and the global terminal; the track is expressed by a piecewise polynomial, and a three-dimensional track with M segments is defined as:
where t is the current time, tkThe track time of the kth track;
wherein the kth segment of the segmented track is represented by a high-order polynomial as:
where c is the coefficient of the piecewise polynomial, T is the time distribution of the piecewise polynomial, TkIs the total time of the kth polynomial, and is the time element; when planning a global track, in order to provide more appropriate direction guidance and time distribution for subsequent track optimization, the global track considers the energy consumption and total flight time of the flight track of the unmanned aerial vehicle, and the following optimization problems are solved:
s.t.p(0)＝p0
p(T)＝pg
wherein p is0The current position coordinate of the unmanned aerial vehicle is used, and m is the order corresponding to the control input;
after the global track is obtained, different local planning areas are set according to an actual application scene and a sensing range of a sensor, and an intersection point of the global track and the local planning areas is solved to obtain a local terminal;
finding out the local end point position of each unmanned aerial vehicle in the cluster on the global track and storing the local end point position as a vector h, and storing the position of each unmanned aerial vehicle in the expected formation form as a vector s; before generating the local track, the local end point needs to be adjusted to a local target point according to h and s, and the task allocation is performed on each unmanned aerial vehicle according to the adjusted local target point, so that the calculation needs to be divided into two parts: aligning formation forms and distributing formation tasks;
when the local target point which accords with the expected formation form is regenerated according to the local end point, only the translation and the scaling of the expected formation form are considered, and the rotation of the formation form is not considered;
the coordinates of the desired formation after translation and size scaling transformation, i.e. the aligned coordinates, are denoted as q, then there are:
qj＝αsj+d
wherein s isjA coordinate point representing the jth position in the desired formation, j being 1, 2.., N, α being a scaling factor for size scaling, d being a translation vector; after alignment is given, the euclidean distance from the aligned coordinates to each local endpoint coordinate is recorded as a cost term:
constructing a cost function of the distribution problem according to the cost item, wherein the corresponding integer programming problem is as follows:
xij＝{0，1}，i，j＝1，...，N
wherein xijTo assign a variable, when xijWhen the number of the unmanned planes is 1, the ith unmanned plane is allocated to the jth coordinate in the formation; the specific process is as follows:
firstly, reconstructing an integer programming problem according to a local end point position h and an expected formation s:
then, solving the integer programming problem by using an allocation algorithm to obtain optimal allocation X and a corresponding minimum cost function value K;
thereafter, parameters s and s are calculated as followssAnd d ands；
parameters α and d for calculating the optimal alignment:
then, the alignment parameters α, d and the optimal distribution X are obtained, and the optimal alignment coordinate is:
q*＝α*s+d*
after the optimal alignment coordinate is obtained, distributing the optimal alignment coordinate to each unmanned aerial vehicle as a local target point according to X; the local target point at the moment is obtained by optimizing the local end point position of each unmanned aerial vehicle inquired on the global track, so that the geometric distribution of the expected formation can be met.
4. The method according to claim 1, wherein the specific process of step (3) is as follows:
in the front-end reference track generation step, firstly, front-end multi-topology path searching is carried out based on the current position of the unmanned aerial vehicle and local target points, and a topology path in a complex environment is obtained after sampling and pruning.
5. The method according to claim 4, wherein in step (3), the generation of the topological path specifically employs a probabilistic roadmap method, and the steps are as follows:
(1) initializing a sampling tree, setting a sampling space according to a sampling starting point and a sampling end point, and adding the sampling starting point and the sampling end point into the sampling tree;
(2) judging whether the total number of the sampling points is smaller than a set threshold value, if so, ending, otherwise, continuing; randomly sampling in a sampling space to obtain a sampling point, judging whether the sampling point is in the barrier or not, if so, repeating the step (2), and if not, entering the step (3);
(3) judging whether the sampling point can be in collision-free connection with a node in the sampling tree, wherein the collision-free connection means that a connecting line of the sampling point and the node does not penetrate through an obstacle, if not, adding the sampling point into the sampling tree, repeating the step (2), and if so, entering the step (4);
(4) and (3) judging whether the sampling point which can be connected with the node in the sampling tree without collision can replace the node in the current sampling tree or not according to the judgment standard, wherein the judgment standard is that whether the path length formed by the sampling point and the neighbor node is smaller than the path length formed by the original node and the same neighbor node or not, if so, replacing the node in the current sampling tree by the sampling point, and repeating the step (2).
6. The method according to claim 5, wherein in step (3), the specific steps of generating the topological path in the complex environment are as follows:
1) firstly, carrying out breadth-first search on a sampling tree, finding out all paths connecting a search starting point and a search end point, then carrying out topology judgment on the paths, classifying the paths belonging to the same topology into one class, and reserving one path with the shortest length;
2) pruning the reserved path, wherein the original path is obtained after limited sampling, the shortest path under the topology cannot be guaranteed to be obtained, in the pruning process, a ray is sent to the original path from the search starting point until the ray hits an obstacle, the previous ray is used as a part of the pruned path, and the path pruning can be completed after the ray end point reaches the search end point;
3) finally, a plurality of topological paths after pruning are obtained, whether the paths are in the same topological path is judged pairwise, and if the two paths are in the same topological path, the shortest path is reserved; judging whether the path is defined as a same-topology path or not as follows: given two paths xi1(r) and xi2(r), where r represents the parameterization of the path, and r ∈ [0,1 ]]If two paths satisfy xi1(0)＝ξ2(0)，ξ1(1)＝ξ2(1) I.e. with the same starting and ending points, and for
Connecting wire
If the two paths do not touch the barrier, the two paths are the same topological paths, otherwise, the two paths are different topological paths;
4) and (3) screening out the shortest path from the plurality of topological paths obtained in the step 3) as a reference track according to the flight distance.
7. The method according to claim 1, wherein the specific process of step (4) is as follows:
the rear-end track optimization is based on the front-end reference track, factors of safe obstacle avoidance and formation flight of the unmanned aerial vehicle are considered at the same time, an unconstrained optimization problem is formed, and a track with higher quality is obtained through optimization and solution; the unconstrained optimization problem form of the constructed back-end trajectory is as follows:
the piecewise polynomial coefficient c and the time distribution T are optimization variables, J with subscripts represents a certain objective function or a constraint penalty term, lambda represents a corresponding weight coefficient, and the subscripts { e, a, o, f, b and h } respectively represent an energy cost term, a total track time term, a safety obstacle avoidance constraint term, a formation similarity term, a mutual inter-cluster collision avoidance term and a dynamic feasibility term; and then, performing iterative optimization on the optimization problem based on the gradient information, and finally generating a safe and collision-free high-quality track capable of maintaining the formation for the current unmanned aerial vehicle.
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