An unmanned aerial vehicle distributed optimization method based on a distributed security controller
By constructing a distributed safety controller, the distributed optimization problem of UAVs within a safety-constrained area is solved, achieving a balance between the common optimal output of the UAV output vector and safety control, thus ensuring the stable operation of the UAV within the safety-constrained area.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2026-01-22
- Publication Date
- 2026-07-31
AI Technical Summary
Existing drone distributed optimization and safety control are inadequate and cannot simultaneously achieve both. In particular, when the optimal output is located at the boundary of the safety constraint region, distributed optimization is often sacrificed to ensure safety.
A distributed safety controller is constructed to ensure that the UAV output always lies within the safety constraint region through the first to third control equations and the safety reference control equations. Furthermore, the common optimal output of the UAV is achieved by expanding the safety constraint set and the safety constraint projection set.
Distributed optimization of UAV output within a safe constraint region is achieved, ensuring that the UAV output vector is always within the safe constraint set, and preventing it from leaving when near the boundary through an appropriate expansion rate, thus achieving a common optimal output.
Smart Images
Figure CN121900140B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control, specifically to a distributed optimization method for UAVs based on a distributed safety controller. Background Technology
[0002] In recent years, UAVs have become reliable and cost-effective aerospace platforms due to their rapid response capabilities and excellent maneuverability, and have broad application prospects in the aerospace field. Therefore, the distributed optimization problem of UAVs has become a hot research direction. The goal of distributed optimization of UAVs is to design a distributed controller so that the output of each UAV can reach the common optimal output of the average objective function through its own information calculation and local communication with its neighbors.
[0003] Researchers have proposed a distributed containment control protocol based on neural network learning for switching event-triggered communication in drone swarms consisting of some leaders and some followers. For the distributed optimization control problem of drone swarm systems, researchers have proposed a novel event-triggered mechanism and feedback linearization method. Furthermore, researchers have designed a distributed two-layer framework, consisting of a distributed optimization algorithm in the decision layer and a tracking control law in the control layer, to solve the distributed optimization problem of linear multi-agent systems.
[0004] However, in practice, the distributed optimization problem of UAVs must be considered simultaneously with the safety control problem. The safety control problem requires that the UAV output always remain within a given safety constraint region to avoid dangerous areas. However, when the optimal output of the UAV lies on the boundary of the safety constraint region, current research prioritizes safety control, potentially sacrificing the distributed optimization objective to ensure the UAV does not violate safety constraints. This makes it impossible to simultaneously achieve distributed optimization and safety control of the UAV. In summary, current research on the distributed optimization and safety control problems of UAVs still has limitations. Summary of the Invention
[0005] To address the aforementioned problems and shortcomings, and the lack of balance between distributed optimization and safety control in existing UAVs, this invention provides a distributed optimization method for UAVs based on a distributed safety controller. This method constructs a distributed safety controller, which enables all UAVs to achieve a common optimal output, while ensuring that the output of each UAV always remains within a safety constraint area.
[0006] To achieve the above objectives, the following technical solution is adopted:
[0007] A distributed optimization method for unmanned aerial vehicles (UAVs) based on a distributed safety controller includes the following steps:
[0008] Step 1: Define the first auxiliary variable for the i-th UAV at time t. Second auxiliary variable and reference signal A distributed security controller is constructed, which includes the first to third control equations and the security reference control equation.
[0009] The construction of the first to third governing equations and the safety reference governing equations specifically includes:
[0010] Considering N drones, the dynamic equation of the i-th (i=1,…,N) drone is:
[0011] (t);
[0012] (t);
[0013] ;
[0014] in, Let be the x-position of the i-th UAV in the rotating coordinate system at time t. Let be the y-position of the i-th UAV in the rotating coordinate system at time t. Let be the x-direction velocity of the i-th UAV at time t. Let be the y-direction velocity of the i-th UAV at time t. Let be the x-direction acceleration of the i-th UAV at time t. Let be the y-direction acceleration of the i-th UAV at time t. Let be the thrust in the x-direction of the i-th UAV at time t. Let be the thrust in the y-direction of the i-th UAV at time t. Let be the angular velocity of the i-th UAV. Let be the output vector of the i-th UAV at time t.
[0015] Distributed optimization problem under the safe control of drones:
[0016] The output vector of the i-th UAV satisfies when t At 0 o'clock, And the output vectors of each of the N drones exist All reached And make Established.
[0017] in, For the safety constraint set of drones, It is a closed region. This is the common output vector for all drones. Let i be the local objective function of the i-th UAV. , Let i be the target vector of the i-th UAV. express The Euclidean norm.
[0018] To solve the distributed optimization problem under the safe control of UAVs, the dynamic equations of the (i=1,…,N)th UAV are rewritten in another form as follows:
[0019] ;
[0020] ;
[0021]
[0022] ;
[0023] in, Let be the state vector of the i-th UAV at time t. Let be the control input vector of the i-th UAV at time t. Let be the state coefficient matrix of the i-th UAV. Let be the control input coefficient matrix for the i-th UAV. Let be the output coefficient matrix of the i-th UAV.
[0024] For the first auxiliary variable of the i-th drone at time t Second auxiliary variable and reference signal have:
[0025] (1) Used for estimation ,in Let i be the local objective function of the i-th UAV. Position-related gradient values; to make For it to be established, it depends on Meanwhile, in order to make the output vectors of each of the N drones... When all reach a common output vector , that is to say Established, among which Let j be the output vector of the j-th UAV at time t. This needs to be implemented. The consensus, that is Established, among which Design the first control equation for the j-th UAV at time t as the first auxiliary variable:
[0026] ;
[0027] in, , for The first derivative with respect to time, Let be the neighbor parameters of the j-th drone to the i-th drone. This indicates that the i-th drone can receive information from the j-th drone, and the j-th drone is called the neighbor drone of the i-th drone. This indicates that the i-th drone cannot receive information from the j-th drone. for Differentiating with respect to time, As the first parameter, For the second parameter, .
[0028] In the first governing equation, Xiang Shi Capable of tracking , Item guarantee Established; and The value of determines The priority of terms in the first governing equation. The larger, the more The faster the consensus is reached, The smaller, the more effective The slower the rate of consensus.
[0029] (2) To ensure that the output vector of the i-th UAV satisfies when t At 0 o'clock, The security objective and the output vectors of each of the N drones exist All reached And make The established optimization objectives.
[0030] First, in order to Able to achieve optimization goals, utilizing Will and Connecting; in order to and Connecting these, design the third governing equation:
[0031] ;
[0032] in, for The first derivative with respect to time, Let j be the second auxiliary variable for the j-th UAV at time t. As the third parameter, The fourth parameter, To make the output vectors of N drones each When all reach a common output vector , that is to say Once established, it needs to be realized. The consensus, that is .
[0033] In the third governing equation, Item guarantee Established, Term used for estimation and Error between, introduce Xiang Yijiang and Connect with; and The value of determines The priority of the term in the third governing equation. The larger, the more The faster the consensus is reached, The smaller, the more effective The slower the rate of consensus; The value of determines Item pair The extent of the impact The larger, Item pair The greater the degree of influence, The smaller, Item pair The smaller the degree of impact; and The value of determines right The extent of the impact The larger, right The greater the degree of influence, The smaller, right The smaller the impact.
[0034] Secondly, in order to Able to achieve security goals and and By linking these together, an extended set of security constraints is introduced. and safety constraint projection set Design the second governing equation:
[0035] ;
[0036] in, ; The range expands as time t increases. The range gradually approached The range, which indicates Satisfy the condition at time t2 t1 At 0 o'clock, ,and Safety constraint projection set Is Inner selection and The distance is the smallest This ensures that when t At 0 o'clock, .
[0037] Furthermore, in order to make Satisfy when t2 t1 At 0 o'clock, ,and Extend the set of security constraints The expression is:
[0038] ;
[0039] in, For the selected location Inside and not The boundary point, Decide exist The initial position in Represents the extended set of security constraints The time-varying function, The value of is determined The rate of expansion of the range, The larger, The faster the rate of expansion, The smaller, The slower the rate of expansion, The expression is:
[0040] ;
[0041] in, The fifth parameter, , The value of is determined The size of the initial value, The larger, The larger the initial value, The smaller, The smaller the initial value; The sixth parameter, , The value of is determined The range of change, The larger, The greater the change, the better. The smaller, The smaller the range of change; The seventh parameter, ,in, It is a positive integer. , Indicates the real part of the item within the curly braces. The matrix within the brackets represents the first... 1 eigenvalue, The value of is determined The range of change, The larger, The smaller the change, the better. The smaller, The greater the range of change; It is a time constant. , The value of is determined The expansion frequency, The larger, The slower the expansion frequency, The smaller, The faster the expansion frequency.
[0042] (3) Due to To simultaneously achieve both optimization and safety objectives, and therefore, to solve the distributed optimization problem under the safe control of UAVs, the output vector of the i-th UAV is driven... track Design the safety reference control equations:
[0043] ;
[0044] in, Let be the first gain matrix of the i-th UAV. Let be the second gain matrix of the i-th UAV; Satisfaction The conditions for being a Hurwitz matrix. ,in, Let be the first constant matrix of the i-th UAV. Let be the second constant matrix of the i-th UAV. and Satisfaction and The conditions for its establishment, among which, It is the identity matrix. Substitution We can obtain:
[0045] ;
[0046] Substituting the above equation, we can obtain... We can obtain:
[0047] ;
[0048] because From the above formula, we can obtain:
[0049] ;
[0050] When the drone's dynamic system is in a stable state, ,because It is a Hurwitz matrix, therefore Established; because and ,so Therefore, we can obtain The output vector of the UAV is driven by the safety reference control equation. track This makes the output vector of the i-th UAV... Satisfy when t At 0 o'clock, And the output vectors of each of the N drones exist All reached And make Established.
[0051] Thus, the distributed security controller of this invention is constructed, comprising the first to third control equations and the security reference control equation, the specific expressions of which are:
[0052] First governing equation: ;
[0053] Second governing equation: ;
[0054] Third governing equation: ;
[0055] Safety reference control equations: .
[0056] Step 2, Obtain , and neighbor's drone Calculated using the first governing equation Thus, the next time step t can be calculated. next The first auxiliary variable of the i-th drone .
[0057] Step 3, Obtain Calculated using the second governing equation .
[0058] Step 4: Obtain information about neighboring drones Calculated using the third governing equation Thus, the next time step t can be calculated. next The second auxiliary variable of the i-th drone .
[0059] Step 5, Obtain and Calculated through safety reference control equations .
[0060] Step 6: Calculate the control input vector based on the safety reference control equation. Then, according to the calculated control input vector and state vector Perform drone control, and make the output vectors of all drones... All achieve a common optimal output vector Make The output vector of the drone reaches its minimum value. Always located in the set of safety constraints Inside.
[0061] In summary, this invention constructs a distributed safety controller comprising first to third control equations and a safety reference control equation, wherein the first to third control equations introduce... , , Safety constraint projection set and extended security constraint set In the first governing equation Used for estimation In the third governing equation As an intermediate variable and Connecting these, the second governing equation guarantees that when t At 0 o'clock, , satisfy and Thus ensuring that when t At 0 o'clock, The first to third governing equations guarantee In the set of security constraints Intra-reaching common optimal output vector The safety reference control equation drives the UAV's output vector. track When the optimal output vector lie in At the boundary, Limited by extended constraint set Suitable The expansion rate can prevent Approaching too quickly The boundary, thereby preventing Leaving the set of security constraints This allows each drone to achieve its own output vector. All achieve a common optimal output vector Meanwhile, the drone's output vector Always located in the set of safety constraints This invention effectively solves the problem of insufficient balance between distributed optimization and safety control in existing drones. Attached Figure Description
[0062] Figure 1 This is a flowchart illustrating the construction process of the distributed security controller of the present invention.
[0063] Figure 2 This is a schematic diagram of the trajectory curves of the output vectors and reference signals of the five UAVs in Example 1;
[0064] Figure 3 This is a schematic diagram showing the change of tracking error of the five drones over time in Example 1. Detailed Implementation
[0065] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.
[0066] A distributed optimization method for unmanned aerial vehicles (UAVs) based on a distributed safety controller is disclosed to ensure that the output of each UAV remains within a safety constraint region and that the outputs of all UAVs reach a common optimal output. Specifically, in this embodiment, a distributed safety controller is first constructed, comprising first to third control equations and a safety reference control equation. Then, a reference signal is calculated using the first to third control equations. Finally, based on the reference signal and the UAV's state vector, and using the safety reference control equation, the control input is calculated. The UAVs are then controlled according to the calculated control input and the UAV's state vector, ensuring that the outputs of all UAVs reach a common optimal output while remaining within the safety constraint set, thereby achieving distributed optimization and safe control of the UAVs.
[0067] Step 1: Construct a distributed security controller, including the first to third control equations and the security reference control equations. See [link to detailed process] for more information. Figure 1 .
[0068] To solve the distributed optimization problem under the safe control of UAVs, the dynamic equations of the (i=1,…,N)th UAV are rewritten in another form as follows:
[0069] ;
[0070] ;
[0071]
[0072] ;
[0073] Define the first auxiliary variable for the i-th UAV at time t. Second auxiliary variable and reference signal .
[0074] (1) Used for estimation ,in Let i be the local objective function of the i-th UAV. Position-related gradient values; if you want to make To be established, one must rely on Meanwhile, in order to make the output vectors of each of the N drones... When all reach a common output vector , that is to say Established, among which Let j be the output vector of the j-th UAV at time t. This needs to be implemented. The consensus, that is Established, among which Design the first control equation for the j-th UAV at time t as the first auxiliary variable:
[0075] ;
[0076] (2) To ensure that the output vector of the i-th UAV satisfies when t At 0 o'clock, The security objective and the output vectors of each of the N drones exist All reached And make The established optimization objectives.
[0077] First, in order to Able to achieve optimization goals, utilizing Will and Connecting; in order to and Connecting these, design the third governing equation:
[0078] .
[0079] Secondly, in order to Able to achieve security goals and and By linking these together, an extended set of security constraints is introduced. and safety constraint projection set Design the second governing equation:
[0080] .
[0081] (3) Due to To simultaneously achieve both optimization and safety objectives, and therefore, in order to solve the distributed optimization problem under the safe control of UAVs, the output vector driving the i-th UAV is... track Design the safety reference control equations:
[0082] .
[0083] Step 2: Calculate the reference signal using the first to third control equations.
[0084] First step, obtain , and neighbor's drone Calculated using the first governing equation Thus, the next time step t can be calculated. next The first auxiliary variable of the i-th drone .
[0085] The second step is to obtain... Calculated using the second governing equation .
[0086] The third step is to obtain information about the neighbor's drone. Calculated using the third governing equation Thus, the next time step t can be calculated. next The second auxiliary variable of the i-th drone .
[0087] Step 4, obtain and Calculated through safety reference control equations .
[0088] Step 3: Finally, based on the reference signal and the UAV's state vector, calculate the control input vector using the safety reference control equation. Then, according to the calculated control input vector and state vector Perform drone control, and make the output vectors of all drones... All achieve a common optimal output vector Make The output vector of the drone reaches its minimum value. Always located in the set of safety constraints Inside.
[0089] To verify the effectiveness of the preset control method for turbojet engines based on random output adjustment in this embodiment, the dynamic equations of the UAV were constructed in MatLab.
[0090] In this embodiment, we consider N drones, where N=5. When t=0:
[0091] , , , , , ;
[0092] It is a regular hexagon centered at (0, 0) with a radius of 2. , ,remove In addition, the rest All are 0. , The first gain matrix of the unmanned aerial vehicle system:
[0093] , ,
[0094] , ,
[0095] ;
[0096] Second gain matrix:
[0097] , , ,
[0098] , ;
[0099] , , , , , , , , Let be the tracking error of the i-th UAV, and its expression is: .
[0100] In this embodiment, the trajectory curves of the output vectors and reference signals of the five UAVs are shown in the diagram below. Figure 2 As shown, The x-position of the i-th drone. Let y be the position of the output vector of the i-th UAV in the y-direction. The following is a schematic diagram showing the time-varying curves of the tracking error of the five UAVs: Figure 3 As shown.
[0101] like Figure 2 , Figure 3 As shown, after 150 seconds, the output vectors of the five drones reached the common optimal output. Optimal output Located in the set of security constraints On the boundary, and during the process of the output vectors of the five drones reaching the common optimal output, the outputs of all drones and the common optimal output. All remain within the set of safety constraints Inside.
Claims
1. A distributed optimization method for unmanned aerial vehicles (UAVs) based on a distributed safety controller, characterized in that, Includes the following steps: Step 1: Define the first auxiliary variable for the i-th UAV at time t. Second auxiliary variable and reference signal Construct a distributed security controller, which includes the first to third control equations and a security reference control equation; First governing equation: ; in, , for The first derivative with respect to time, Let be the neighbor parameters of the j-th drone to the i-th drone. This indicates that the i-th drone can receive information from the j-th drone, and the j-th drone is called the neighbor drone of the i-th drone. This indicates that the i-th drone cannot receive information from the j-th drone. for Differentiating with respect to time, As the first parameter, For the second parameter, ; In the first governing equation, Xiang Shi Capable of tracking , Item guarantee Established; and The value of determines The priority of terms in the first governing equation. The larger, the more The faster the consensus is reached, The smaller, the more effective The slower the rate of consensus; Second governing equation: ; in, ; The range expands as time t increases. The range gradually approached The range, which indicates Satisfy the condition at time t2 t1 At 0 o'clock, ,and Safety constraint projection set Is Inner selection and The distance is the smallest This ensures that when t At 0 o'clock, ; In the second governing equation, an extended set of safety constraints is introduced. and safety constraint projection set ,make Able to achieve security objectives, and will and Connect with each other; Third governing equation: ; in, for The first derivative with respect to time, Let j be the second auxiliary variable for the j-th UAV at time t. As the third parameter, The fourth parameter, To make the output vectors of N drones each When all reach a common output vector , that is to say Once established, it needs to be realized. The consensus, that is ; In the third governing equation, Item guarantee Established, Term used for estimation and Error between, introduce Xiang Yijiang and Connect with each other; and The value of determines The priority of the term in the third governing equation. The larger, the more The faster the consensus is reached, The smaller, the more effective The slower the rate of consensus; The value of determines Item pair The extent of the impact The larger, Item pair The greater the degree of influence, The smaller, Item pair The smaller the degree of impact; and The value of determines right The extent of the impact The larger, right The greater the degree of influence, The smaller, right The smaller the degree of impact; Safety reference control equations: ; in, Let be the first gain matrix of the i-th UAV. Let be the second gain matrix of the i-th UAV; Satisfy The conditions for being a Hurwitz matrix. ,in, Let be the first constant matrix of the i-th UAV. Let be the second constant matrix of the i-th UAV. and Satisfy and The conditions for its establishment, among which, It is the identity matrix; Let be the state coefficient matrix of the i-th UAV. Let be the control input coefficient matrix for the i-th UAV; Step 2, Obtain , and neighbor's drone Calculated using the first governing equation Thus, the next time step t can be calculated. next The first auxiliary variable of the i-th drone ; Step 3, Obtain Calculated using the second governing equation ; Step 4: Obtain information about neighboring drones Calculated using the third governing equation Thus, the next time step t can be calculated. next The second auxiliary variable of the i-th drone ; Step 5, Obtain and Calculated through the safety reference control equation ; Step 6: Calculate the control input vector based on the safety reference control equation. Then, according to the calculated control input vector and state vector Perform drone control, and make the output vectors of all drones... All achieve a common optimal output vector Make The output vector of the drone reaches its minimum value. Always located in the set of safety constraints Inside.
2. The distributed optimization method for UAVs based on a distributed safety controller as described in claim 1, characterized in that, The first governing equation is constructed as follows: Consider N drones, i=1,…,N. The dynamic equation of the i-th drone is: (t)； (t)； ； in, Let be the x-position of the i-th UAV in the rotating coordinate system at time t. Let be the y-position of the i-th UAV in the rotating coordinate system at time t. Let be the x-direction velocity of the i-th UAV at time t. Let be the y-direction velocity of the i-th UAV at time t. Let be the x-direction acceleration of the i-th UAV at time t. Let be the y-direction acceleration of the i-th UAV at time t. Let be the thrust in the x-direction of the i-th UAV at time t. Let be the thrust in the y-direction of the i-th UAV at time t. Let be the angular velocity of the i-th UAV. Let be the output vector of the i-th UAV at time t; Distributed optimization problem under the safe control of drones: The output vector of the i-th UAV satisfies when t At 0 o'clock, And the output vectors of each of the N drones exist All reached And make Established; in, For the safety constraint set of drones, It is a closed region. This is the common output vector for all drones. Let i be the local objective function of the i-th UAV. , Let i be the target vector of the i-th UAV. express The Euclidean norm; To solve the distributed optimization problem under the safe control of UAVs, the dynamic equations of the i-th UAV are rewritten in another form as follows: ； ； ； in, Let be the state vector of the i-th UAV at time t. Let be the control input vector of the i-th UAV at time t. Let be the state coefficient matrix of the i-th UAV. Let be the control input coefficient matrix for the i-th UAV. Let be the output coefficient matrix of the i-th UAV; Define the first auxiliary variable for the i-th UAV at time t. Second auxiliary variable and reference signal ; Used for estimation ,in Let i be the local objective function of the i-th UAV. Position-related gradient values; to make For it to be established, it depends on Meanwhile, in order to make the output vectors of each of the N drones... When all reach a common output vector , that is to say Established, among which Let j be the output vector of the j-th UAV at time t. This needs to be implemented. The consensus, that is Established, among which Design the first control equation for the j-th UAV at time t as the first auxiliary variable: 。 3. The distributed optimization method for UAVs based on a distributed safety controller as described in claim 2, characterized in that, The construction of the third governing equation specifically includes: To ensure that the output vector of the i-th UAV satisfies when t At 0 o'clock, The security objective and the output vectors of each of the N drones exist All reached And make The established optimization objective; In order to Able to achieve optimization goals, utilizing Will and Connecting; in order to and Connecting these, design the third governing equation: 。 4. The distributed optimization method for UAVs based on a distributed safety controller as described in claim 3, characterized in that, The construction of the second governing equation specifically includes: In order to make Able to achieve security goals and and By linking these together, an extended set of security constraints is introduced. and safety constraint projection set Design the second governing equation: ； In order to make Satisfy when t2 t1 At 0 o'clock, ,and Extend the set of security constraints The expression is: ； in, For the selected location Inside and not The boundary point, Decide exist The initial position in Represents the extended set of security constraints The time-varying function, The value of is determined The rate of expansion of the range, The larger, The faster the rate of expansion, The smaller, The slower the rate of expansion, The expression is: ； in, The fifth parameter, , The value of is determined The size of the initial value, The larger, The larger the initial value, The smaller, The smaller the initial value; The sixth parameter, , The value of is determined The range of change, The larger, The greater the change, the better. The smaller, The smaller the range of change; The seventh parameter, ,in, It is a positive integer. , Indicates the real part of the item within the curly braces. The matrix within the brackets represents the first... 1 eigenvalue, The value of is determined The range of change, The larger, The smaller the change, the better. The smaller, The greater the change; It is a time constant. , The value of is determined The expansion frequency, The larger, The slower the expansion frequency, The smaller, The faster the expansion frequency.
5. The distributed optimization method for UAVs based on a distributed safety controller as described in claim 4, characterized in that, The construction of the safety reference control equations specifically includes: because To simultaneously achieve both optimization and safety objectives, and therefore, to solve the distributed optimization problem under the safe control of UAVs, the output vector of the i-th UAV is driven... track Design the safety reference control equations: ； Will Substitution We can obtain: ； Substituting the above equation, we can obtain... We can obtain: ； because From the above formula, we can obtain: ； When the drone's dynamic system is in a stable state, ,because It is a Hurwitz matrix, therefore Established; because and ,so Therefore, we can obtain The output vector of the UAV is driven by the safety reference control equation. track This makes the output vector of the i-th UAV... Satisfy when t At 0 o'clock, And the output vectors of each of the N drones exist All reached And make Established.