An unmanned aerial vehicle trajectory optimization method based on circumscribed circle steiner minimum tree

Abstract

The application discloses a kind of based on circumscribed circle Steiner minimum tree unmanned aerial vehicle trajectory optimization method, it is related to wireless sensor network and unmanned aerial vehicle path planning field.For unmanned aerial vehicle when carrying out data collection task to wireless sensor network, the path of existing trajectory planning method is long, and the problem that sensing node geometry relationship and perception neighborhood constraint are not fully utilized, the application proposes circumscribed circle Steiner minimum tree problem (CSMTPN) model with neighborhood.For N sensing nodes, three nodes are randomly taken to form triangle, and equilateral triangle is constructed outside each side of triangle and circumscribed circle, and the common intersection point of three circumscribed circles is Steiner point;All candidate Steiner points are sequentially connected to form the shortest flight trajectory covering the perception neighborhood of all sensing nodes.The application establishes the optimization model with the object of minimizing maximum collection completion time, jointly optimizes flight trajectory, hovering time and enhanced power, and proves the NP difficulty of the problem, and obtains suboptimal solution by approximation algorithm.When perception neighborhood is reduced to zero, CSMTPN naturally degenerates into standard SMTPN, with good theoretical generality.Simulation results verify the effectiveness of the proposed method in shortening flight path, reducing task completion time and improving data collection efficiency.

Description

Technical Field

[0001] This invention relates to the fields of wireless sensor networks and UAV path planning, specifically to a UAV trajectory optimization method based on a circumcircle Steiner minimum tree, used to solve the shortest flight trajectory of a UAV when performing data acquisition tasks on a wireless sensor network, minimizing task completion time and energy consumption. Background Technology

[0002] The efficiency of data acquisition in wireless sensor networks (WSNs) largely depends on the quality of flight trajectory planning for unmanned aerial vehicles (UAVs). Proper trajectory planning not only shortens mission completion time but also significantly reduces UAV flight energy consumption and extends endurance.

[0003] Existing UAV trajectory optimization schemes can be mainly divided into the following categories: First, circular trajectory-based methods, which design a circular flight path with a fixed radius and speed centered on the ground terminal. The theoretical analysis is simple, but the adaptability is poor. Second, path discretization-based methods, such as Flexible Path Discretization (FPD) and Path Compression (PD), which plan trajectories by setting an arbitrary number of designable waypoints, but the computational complexity is high. Third, methods based on variations of the Traveling Salesman Problem (TSP), such as the k-times non-uniform traveling salesman zone neighborhood problem (k-ITSPN), which provides optimization for the UAV's visit order, but lacks the utilization of Steiner intermediate points. Fourth, reinforcement learning-based methods, which have strong adaptability but high training costs and poor interpretability.

[0004] None of the methods mentioned above fully utilize the geometric relationships between sensor nodes to generate optimal intermediate waypoints (Steiner points), resulting in lengthy UAV flight paths, long mission completion times, and high energy consumption. Furthermore, most existing methods treat sensor nodes as point targets, neglecting the fact that each sensor node has a certain perceptual neighborhood, leaving room for improvement in trajectory planning.

[0005] The Steiner Minimum Tree (SMT) problem is a classic problem in combinatorial optimization. Its core idea is to minimize the total path length connecting all target nodes by introducing additional Steiner points. However, when directly applying SMT to UAV trajectory optimization, the practical constraint of each sensor node having a sensing neighborhood must be considered, making the standard SMT model unsuitable. Therefore, there is an urgent need to design an improved Steiner tree trajectory optimization method that incorporates the sensor node neighborhood constraint. Summary of the Invention

[0006] To overcome the shortcomings of the existing technology, this invention provides a UAV trajectory optimization method based on circumcircle Steiner minimum tree. It proposes the circumcircle Steiner minimum tree problem with neighborhood (CSMTPN), and accurately generates Steiner points through geometric methods to plan the shortest flight trajectory for the UAV that covers the perception neighborhood of all sensor nodes, thereby minimizing the data acquisition task completion time.

[0007] The technical solution adopted in this invention is as follows: For N sensing nodes in a wireless sensor network, three nodes are randomly selected to form a triangle. An equilateral triangle is constructed outward from each side of the triangle and a circumcircle is drawn. The common intersection of the three circumcircles is the Steiner point. All generated Steiner points are connected in sequence to obtain the shortest flight trajectory for the UAV to perform the data acquisition task. At the same time, an optimization model is established with the goal of minimizing the maximum acquisition completion time, and it is proven that the problem is NP-hard. Then, an approximation algorithm is used to solve it.

[0008] Compared with existing technologies, the beneficial effects of this invention include: First, it introduces the circumcircle Steiner minimum tree method into the field of UAV trajectory optimization for the first time, proposing the CSMTPN model, which can effectively shorten the total flight distance of the UAV compared with traditional TSP-type methods; Second, the generation of Steiner points is based on strict geometric theorems, and the construction process can be accurately calculated without random search, exhibiting good repeatability and interpretability; Third, CSMTPN incorporates the sensing neighborhood of sensor nodes into the constraints, enabling the UAV to complete data acquisition without flying directly above each sensor node, further shortening the flight path; Fourth, when the sensing neighborhood shrinks to zero, CSMTPN naturally degenerates into standard SMTPN, exhibiting good theoretical generality; Fifth, the method works in conjunction with the power enhancement mechanism, minimizing energy consumption while completing data acquisition in the shortest possible time. Attached Figure Description

[0009] Figure 1 This is a two-dimensional schematic diagram of the Steiner point in this invention, showing the geometric construction process of a triangle formed by three sensing nodes, an equilateral triangle drawn outwards, and the common intersection point (Steiner point) of the three circumscribed circles.

[0010] Figure 2 A schematic diagram of a collaborative design framework for UAV-assisted wireless sensor network data acquisition illustrates the overall relationship between ground-level sensor nodes, UAV flight paths in the air, and Steiner points. Detailed Implementation

[0011] (1) Network Models and Graph Theory Foundations

[0012] This invention utilizes N sensing nodes in a wireless sensor network. Model as a connected undirected graph target vertex set in Where M is the total number of target vertices. Each edge Represents vertices and The connection between them can be represented by a line segment.

[0013] For each vertex Define the range of the perceived neighborhood :by Let be the center of a circle with a perceptual radius d. The perceptual neighborhoods of two vertices are said to be tangent when their boundaries are adjacent. (Subgraph) The total side length is defined as The side lengths satisfy symmetry. .

[0014] Based on this, the present invention introduces the following key definitions:

[0015] Definition 1 (Tree): Given a graph G, a tree It is a connected subgraph in G that does not contain loops.

[0016] Definition 2 (Steiner Tree): Given a graph G and a Steiner set, For a Steiner tree in G that covers all Steiner points, This is the edge set of a Steiner tree.

[0017] Definition 3 (Steiner Minimum Tree, SMT): Given a graph G, a Steiner vertex set, and an edge length function Len, the Steiner minimum tree is defined as follows: It is to make the total side length The minimum Steiner tree reduces the total connection length by introducing additional intermediate nodes.

[0018] Definition 4 (SMT problem in graph): Given a graph G, a Steiner set of vertices and an edge length function Len, the SMT problem in graph is to find the SMT.

[0019] Definition 5 (Steiner Minimum Tree Problem with Neighborhood, SMTPN): Given a set of sensor nodes SMTPN requires finding path P such that for each All have a certain vertex lie in Inside or on the boundary; path P from Departure and termination Len(P) is the smallest.

[0020] (2) CSMTPN model definition

[0021] Definition 6 (CSMTPN: Steiner Minimum Tree Problem with Circumcircle of Neighborhood): Given a set of sensor nodes Given any three sensor nodes connected to form a triangle, construct equilateral triangles outward from each side of the triangle. The circumcircles of the three equilateral triangles intersect at a Steiner point. CSMTPN requires finding several paths. , so that;

[0022] For each All have a certain vertex , making lie in On the interior or boundary;

[0023] path from Departure and termination ;

[0024] The shortest flight path of the drone is obtained by sequentially connecting all Steiner points.

[0025] The relationship between CSMTPN and SMTPN: When the maximum acquisition range of a sensor node is reduced to zero, CSMTPN is equivalent to SMTPN; conversely, SMTPN can be considered a special case of CSMTPN when the neighborhood radius is zero. SMTPN can be extended to CSMTPN by adding neighborhood constraints, the latter being a more generalized form.

[0026] (3) Geometric construction method of Steiner point

[0027] The generation of Steiner points is the core step of this invention, such as... Figure 1 As shown, the specific construction process is as follows.

[0028] Step 1: Select any three nodes A, B, and C from the N sensor nodes, and connect them in pairs to form a triangle △ABC.

[0029] Step 2: Using side AB as the basis, construct an equilateral triangle △ABB' outward from △ABC, where B' is the newly constructed vertex; using side BC as the basis, construct an equilateral triangle △BCC' outward from △ABC; using side CA as the basis, construct an equilateral triangle △CAA' outward from △ABC.

[0030] Step 3: Construct the circumcircles O1, O2, and O3 of the three equilateral triangles △ABB', △BCC', and △CAA' respectively.

[0031] Step 4: The three circumcircles O1, O2, and O3 have a common intersection point, which is the Steiner point SP of the corresponding sensor node triple {A,B,C}.

[0032] Step 5: Repeat the above steps for all possible triples in the sensor node set to generate the complete set of candidate Steiner points.

[0033] Step 6: Select several Steiner points from the candidate Steiner point set and connect them in order so that the sensing neighborhood of each sensing node is covered by the path and the total path length is minimized.

[0034] The Steiner point mentioned above has important geometric significance: according to Fermat's point theorem, the intersection of the circumcircles of an equilateral triangle minimizes the sum of the total distances from the three sensor nodes to that point. Therefore, using this point as the intermediate waypoint of the UAV can effectively shorten the total flight path.

[0035] (4) Modeling of flight time and hovering time

[0036] The drone followed the trajectory planned by CSMTPN at maximum speed. Fly to each Steiner point in sequence The total flight time is:

[0037] The drone hovered at each Steiner point to collect data, and was positioned at the location. The hovering time at that location is The total hovering time is:

[0038] Sensor Node Communication rate at the location satisfy: ,in This is the interruption probability threshold.

[0039] At the optimal solution, the hovering time constraint The equality holds, that is / Therefore, the hovering time is determined by both the amount of target data and the communication rate; the higher the communication rate, the shorter the hovering time.

[0040] (5) Optimize problem modeling

[0041] By jointly optimizing the UAV's flight trajectory, hovering time, and power enhancement, an optimization problem P12 is established with the objective of minimizing the maximum data acquisition completion time.

[0042] Objective function: ;

[0043] Constraint (a): Enhanced power constraint ;

[0044] Constraint (b): Sensor Node Set Constraint ;

[0045] Constraint (c): Perception radius constraint ;

[0046] Constraint (d): Hover time acquisition constraint .

[0047] make For the new target variable, P12 is equivalently transformed into P13:

[0048] Objective function P13: ;

[0049] Constraint (d'): ;

[0050] Other constraints: Same as constraints (a)-(c) in P12.

[0051] (6) Proof of NP difficulty

[0052] Theorem 2: The optimization problem P13 is an NP-hard problem.

[0053] Proof: When the UAV flies directly above the Steiner point, the Steiner point coincides with the sensing position of the sensor node, and the total hovering time of the UAV is a fixed value. The problem is further simplified to optimizing the total flight time, and its analysis process is the same as that of SMTPN. Since SMTPN has been proven to be an NP-hard problem, CSMTPN, as a generalized extension of SMTPN, is also an NP-hard problem. If SMTPN is not NP-hard, then CSMTPN is also not NP-hard, which leads to a contradiction. Therefore, P13 is an NP-hard problem, and there is no polynomial-time exact solution algorithm. A satisfactory suboptimal solution needs to be obtained by using an approximation algorithm.

[0054] Based on the aforementioned NP-hardness, this invention designs an approximation algorithm to solve P13 in order to obtain the UAV flight trajectory. Hovering time and enhanced power The near-optimal combination minimizes the data acquisition completion time within a reasonable computation time.

[0055] (7) Working in conjunction with power enhancement mechanisms

[0056] The trajectory optimization method of this invention can work in conjunction with the power enhancement mechanism to jointly improve the overall performance of UAV data acquisition. During the flight of the UAV according to the CSMTPN planned trajectory, the system dynamically determines whether to trigger the power enhancement mechanism based on its positional relationship with the circular acquisition range of each sensor node: when the UAV is within the circular acquisition range R of the sensor node, the power enhancement is zero, saving energy; when the UAV exceeds the acquisition range, the onboard battery power enhancement is activated to ensure that the channel quality does not degrade with distance.

[0057] By jointly optimizing the flight trajectory (determined by CSMTPN) and enhancing power (determined by the BCD-SCA algorithm), data acquisition from all sensor nodes can be completed in the shortest possible time while minimizing total energy consumption. Compared to single schemes that optimize only the trajectory or only the power, the collaborative optimization scheme significantly improves both data acquisition rate and energy efficiency.

[0058] (8) Application scenario description

[0059] This invention is applicable to the following typical scenarios: In large-scale environmental monitoring in remote areas, sensor nodes are randomly distributed across a vast area, and drones need to collect data from each node sequentially before returning to the base station. By using CSMTPN to plan the optimal trajectory for the drone, it flies along the shortest path through the sensing neighborhood of each sensor node, hovers within the sensing neighborhood to collect data, and then flies to the next Steiner point until all nodes have been collected. Compared to a direct flight approach that flies directly above each sensor node, this invention significantly shortens the total flight distance, saving flight time and energy.

Claims

1. A method for optimizing UAV trajectory based on a Steiner minimum tree with circumcircle, characterized in that: (1.1) Network Graph Construction (1.1.1) N sensor nodes in a wireless sensor network Abstracted as a connected undirected graph target vertex set in ; (1.1.2) for each vertex Define the range of the perceived neighborhood , that is to A circular region with center at a given radius d; (1.1.3) Define a subgraph The total side length is ,in As vertices and The length of the side between; (1.2) Steiner point generation (1.2.1) Select any three nodes from the N sensing nodes to form a triangle; (1.2.2) Construct equilateral triangles on the outside of each side of the triangle to obtain three equilateral triangles on the outside; draw the circumcircles of the three equilateral triangles on the outside, and the common intersection of the three circumcircles is a Steiner point; (1.2.3) Repeat the above operation for all possible sensor node triples to generate a set of Steiner points; (1.3) CSMTPN path construction Based on the Steiner points generated above, solve the circumcircle Steiner minimum tree problem with neighborhood (CSMTPN): for each target vertex... In the vertex set There exists a vertex in , making lie in Within or at the boundary of the sensor; starting from the initial Steiner point, connect each Steiner point sequentially to form a path covering the sensing neighborhood of all sensor nodes. This path is the flight trajectory of the drone performing the data collection task; (1.4) Time-of-flight modeling The drone at maximum speed Fly sequentially to each Steiner point and calculate the total flight time; hover at each Steiner point to collect data and calculate the total hover time. ,in For drones in location Hovering time at the location; (1.5) Optimization Problem Modeling Establish an optimization problem P12 with the objective of minimizing the maximum acquisition completion time: Constraints include: enhanced power constraints. Sensor node set constraints The sensing radius constraint r = d ≥ 0, and the hovering time acquisition constraint. ,in This refers to the amount of target data that the drone needs to collect from the corresponding sensor nodes. For sensing nodes Communication rate at that location This is the interruption probability threshold; (1.6) Equivalent transformation and solution make For the new objective function, the optimization problem P12 is equivalently transformed into P13: under constraints Minimize By designing an approximation algorithm to solve this NP-hard problem, the flight trajectory of the UAV can be obtained. }, Hovering time { } and enhanced power { The approximate optimal solution of}; (1.7) Trajectory Output Connect each Steiner point in the order determined in step (1.3) to output the complete flight trajectory of the UAV, so that the UAV can complete the data acquisition task of all sensor nodes in the shortest possible time.

2. The UAV trajectory optimization method based on the circumcircle Steiner minimum tree according to claim 1, characterized in that, The specific geometric construction process of the Steiner point in step (1.2) is as follows: Let any three sensing nodes be A, B, and C. Construct an equilateral triangle △AB' with side AB to the outside of triangle ABC, construct an equilateral triangle △BC' with side BC to the outside, and construct an equilateral triangle △CA' with side CA to the outside. Construct the circumcircles O1, O2, and O3 of △AB', △BC', and △CA' respectively; the common intersection of the three circles O1, O2, and O3 is the Steiner point corresponding to the triplet {A,B,C} of the sensor nodes; the obtained Steiner point satisfies the property that the total connection length is the shortest when it is connected to all three sensor nodes, providing the optimal intermediate parking candidate position for the UAV.

3. The UAV trajectory optimization method based on the circumcircle Steiner minimum tree according to claim 1, characterized in that, The complete definition of CSMTPN in step (1.3) is: given a set of sensor nodes CSMTPN requires finding several paths. , so that: (3.1) For each All have a certain vertex , making lie in On the interior or boundary; (3.2) Path from Departure and termination ; (3.3) The total path length obtained by sequentially connecting all Steiner points is the shortest; when the maximum acquisition range of the sensor node is reduced to zero, CSMTPN degenerates into the standard Steiner minimum tree problem with neighborhood (SMTPN).

4. The UAV trajectory optimization method based on the circumcircle Steiner minimum tree according to claim 1, characterized in that, The optimization problem P12 described in step (1.5) is an NP-hard problem. The proof is as follows: When the UAV flies directly above the Steiner point, the Steiner point coincides with the sensing node, and the total hovering time of the UAV is fixed. The problem is simplified to the analysis of the total flight time. This simplified problem is equivalent to SMTPN. Since SMTPN has been proven to be an NP-hard problem, CSMTPN, as a generalized extension of SMTPN, is also an NP-hard problem. Therefore, there is no polynomial-time algorithm to solve its exact optimal solution. An approximate algorithm is needed to obtain a suboptimal solution.

5. The UAV trajectory optimization method based on the circumcircle Steiner minimum tree according to claim 1, characterized in that, Figure in step (1.3) The relevant definitions of Steiner trees are as follows: (5.1) A tree is a connected subgraph of graph G that does not contain cycles; (5.2) A Steiner tree is a tree in graph G that covers all Steiner points. ; (5.3) Steiner Minimum Tree (SMT) is the tree that minimizes the total edge length. The minimum Steiner tree, which reduces the total connection length by introducing additional Steiner nodes; (5.4) The SMT problem in the figure is to find the SMT given the graph G, the Steiner point set and the edge length function Len.

6. The UAV trajectory optimization method based on the circumcircle Steiner minimum tree according to claim 1, characterized in that, The hovering time of the UAV at each Steiner point in step (1.4) Determined by data acquisition constraints: Among them, sensor nodes Communication rate at the location It is given by the following formula: ,in for The exponential distribution parameters of the link channel power gain. For noise power, The threshold is the interruption probability threshold; the hovering time is inversely proportional to the communication rate. The higher the rate, the shorter the required hovering time, thereby shortening the total acquisition completion time.

7. The UAV trajectory optimization method based on the circumcircle Steiner minimum tree according to claim 1, characterized in that, Working in conjunction with the power enhancement mechanism described in Patent 1: In steps (1.4) and (1.5), as the UAV flies to each Steiner point, it dynamically adjusts the power enhancement based on its positional relationship with the sensor nodes. ; When the drone is within the circular acquisition range of the sensor node, the enhanced power is zero; when the drone goes beyond the acquisition range, the enhanced power is activated; by jointly optimizing the flight trajectory and the enhanced power, the data acquisition task can be completed in the shortest time while minimizing the total energy consumption.

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