Quadrotor unmanned aerial vehicle safety tracking optimization control method under denial of service attack

Abstract

The invention discloses a safety tracking optimization control method for a quad-rotor unmanned aerial vehicle under denial of service attack in the field of safety control of the quad-rotor unmanned aerial vehicle. The method comprises the following steps: 1) firstly, establishing a position-based visual servo control framework of the quad-rotor unmanned aerial vehicle in discrete time; 2) constructing a denial of service attack model based on a signal interference plus noise ratio; 3) reconstructing system state information under the denial of service attack by alternately utilizing a small amount of input / output data and predictor enhanced data; 4) deducing a Riccati equation under denial of service attack, and designing an optimal controller by solving the Riccati equation; and 5) iteratively solving the Riccati equation by using an adaptive dynamic programming technology. Compared with the existing four-rotor unmanned aerial vehicle tracking control, the four-rotor unmanned aerial vehicle tracking control method not only can ensure that the four-rotor unmanned aerial vehicle has excellent tracking control performance, but also can ensure that the four-rotor unmanned aerial vehicle stably operates under the influence of denial of service attack.

Description

Technical Field

[0001] The present invention belongs to the technical field of safety control of quad-rotor unmanned aerial vehicles, and in particular relates to a safety tracking optimization control method for a quad-rotor unmanned aerial vehicle under a denial of service attack. Background Art

[0002] Quadrotors have been widely used in agriculture, logistics, surveillance, search and rescue, environmental monitoring and other fields due to their simple structure, flexibility and low cost. However, to achieve stable, accurate and efficient operation of drones, the improvement of control technology is crucial. The design of drone control systems faces multiple challenges, including flight attitude control, path planning, obstacle avoidance algorithms, task allocation and coordination, energy management, etc. One of the current research trends is to improve the autonomous flight capability of drones. To achieve this goal, it is necessary to effectively combine sensor data with control algorithms so that drones have the ability to autonomously perceive the environment, avoid obstacles, plan paths and complete complex tasks.

[0003] With the widespread use of drones in data collection, monitoring, logistics and transportation, the security of their network communications has become increasingly prominent. Drones usually rely on wireless networks to communicate with ground stations or other drones, but this also makes them easy targets for network attacks, such as signal interference, data theft, and false command injection. Since the communication system is crucial in the execution of drone missions, network attacks may cause drones to lose control or even cause serious safety accidents. To address these security challenges, researchers have proposed a variety of protection measures, including communication protocols based on encryption algorithms, security authentication mechanisms, and control strategies to defend against external attacks.

[0004] Although some achievements have been made in the research on the safety control methods of quadrotor drones, there is still much room for improvement. Denial of service (DoS) attack is a common network security threat, which prevents legitimate users from accessing the system or services normally by occupying a large amount of system resources. For drone systems that rely on network communication, the harm of DoS attacks is particularly serious, which may cause the paralysis of real-time control systems, servers or other critical infrastructures, and then cause mission failure, communication interruption, and even equipment loss of control. To solve this problem, this paper proposes a quadrotor drone safety tracking optimization control method to deal with DoS attacks. This method can ensure that the drone's tracking control system can still maintain stable control performance when it is attacked by DoS. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a method for optimizing the safe tracking of a quad-rotor drone under a denial of service attack, which solves the problem of poor tracking control effect of a quad-rotor drone under a denial of service attack and enhances the stability of the system.

[0006] The object of the present invention is achieved by: a method for optimizing the safe tracking of a quad-rotor drone under a denial of service attack, comprising the following steps:

[0007] Step 1) Considering the tracking control system of a quadrotor drone, a position-based visual servo control framework of a discrete-time quadrotor drone is established through the Newton-Euler formula and coordinate transformation;

[0008] Step 2) According to the energy ratio of the denial of service attack and the valid signal, a communication model based on signal interference plus noise ratio is introduced to describe the probability of a successful denial of service attack in the sensor-controller channel;

[0009] Step 3) reconstructing the system state information under the denial of service attack by alternately using the sensor output data that has not been attacked and the virtual output generated by the predictor, and designing a feedback controller;

[0010] Step 4) The value function is given, and the Riccati equation of the system is derived through the Bellman optimality principle and the expression of the controller gain is determined;

[0011] Step 5) Combine the adaptive dynamic programming algorithm to obtain the optimal controller gain.

[0012] Further, step 1) specifically includes:

[0013] Step 1.1) Consider a quadrotor tracking control system, which consists of a quadrotor equipped with a monocular camera and IMU and a ground vehicle with an ApirlTag posted on the top platform;

[0014] Step 1.2) The motion of the quadrotor is described using two coordinate systems: the inertial frame and body fixing frame The fuselage fixed frame The origin of is located at the center of mass of the quadrotor drone; definition as well as Four-rotor drones In this system, the quadcopter cannot collect information about the position vector p, and can only collect the relative position r between the quadcopter and AprilTag through the monocular camera. pt ;

[0015] Step 1.3) Set the relative position r pt With expected position Error and the relative speed error Augmentation as a new state Taking the X-axis as an example (the analysis of the Y and Z-axis is the same as that of the X-axis), and discretizing it with a sampling period of t = 0.01s, the system equation can be obtained:

[0016]

[0017] Among them, A=[1,0.01;0,1], B=[0.001;0.01], C=[1,0].

[0018] Further, step 2) specifically includes:

[0019] Step 2.1) Establish the relationship between the bit error rate SER and the signal-to-noise ratio SNR in the sensor-controller channel:

[0020]

[0021] Where Q(x) represents the Gaussian Q function, ξ is the network parameter;

[0022] Step 2.2) Considering that DoS attacks occur randomly in the sensor-controller channel, the signal-interference-plus-noise ratio replaces the signal-to-noise ratio:

[0023]

[0024] where p s is the energy of the signal emitted by the sensor, p a is the energy of the signal sent by the attacker, and ω is the additive Gaussian white noise in the channel; at this time:

[0025]

[0026] Step 2.3) To describe the impact of DoS attacks on the actuator, define the indicator function α k ; When α k =1, it means that an attack has occurred, blocking the transmission of data packets; otherwise, α k =0 means the data packet transmission is normal; at this time, the success rate of sensor-controller channel data transmission under denial of service attack is obtained Relationship with bit error rate SER:

[0027]

[0028] Further, step 3) specifically includes:

[0029] Step 3.1) For the quadrotor tracking control system, the expanded state equation using the input / output sequence on the time range [k-1, kN] can be written as

[0030]

[0031] in For mixed output,

[0032] V(N)=[B,AB,…,A N-1 B],U(N)=[(CA N-1 ) T ,…,(CA) T ,C T ] T ,

[0033] And N = max{ρ u ,ρ v}, ρ u is such that U(ρ u ) is the smallest integer with full column rank, ρ v is such that V(ρ v ) is the smallest integer with full row rank; therefore, there exists a left inverse of U(N) such that U + (N)=[U T (N)U(N)] -1 U T (N);

[0034] Step 3.2) The state of the quadrotor tracking control system can be uniquely obtained based on the measured input / output sequence:

[0035]

[0036] Among them, M y =A N U + (N), M u =V(N)-M y T(N) is a given parameter, Θ=[M u M y ],

[0037] Step 3.3) Build a predictor to generate virtual output to compensate for the impact of the denial of service attack on the system:

[0038]

[0039] in Dummy output generated for the predictor;

[0040] Step 3.4) Build the feedback controller:

[0041]

[0042] Where K represents the controller gain,

[0043] Further, step 4) specifically includes:

[0044] Step 4.1) The value function is defined as follows:

[0045]

[0046] Where Q and R are weight matrices;

[0047] Step 4.2) The controller gain is:

[0048]

[0049] The P is the unique solution of the Riccati equation as follows:

[0050]

[0051] Further, step 5) specifically includes:

[0052] Step 5.1) Use As control input, To make the system stable, the initial gain, e is the detection noise, and the parameter j=0 is set;

[0053] Step 5.2) Solve the Riccati equation using the least squares algorithm to obtain the solution P j And gain

[0054] Step 5.3) Set j←j+1. For j≥1, if ||P j -P j+1 ||>ε, repeat step 5.2; otherwise, let j * ←j, and execute step 5.4; where the parameter ε is the algorithm convergence criterion;

[0055] Step 5.4) As the optimal control gain output.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] (1) The present invention reconstructs the system status information under the denial of service attack by alternately utilizing a small amount of input / output data and predictor enhancement data, and more accurately estimates the real status of the system.

[0058] (2) In the case of a DoS attack on the sensor-controller channel, the Riccati equation with random variables is derived, and the optimal controller is designed by solving the Riccati equation.

[0059] (3) The present invention designs a set of safe tracking optimization control methods based on adaptive dynamic programming for the UAV tracking control system under DoS attack, which greatly improves the tracking control performance of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0061] Figure 1 Flow chart of the control method of the present invention.

[0062] Figure 2 It is a block diagram of the system and control system in the present invention.

[0063] Figure 3 The flowchart of the algorithm for solving the gain using the adaptive dynamic programming algorithm in the present invention. DETAILED DESCRIPTION

[0064] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] like Figure 1-3 As shown, a method for optimizing the safe tracking of a quad-rotor drone under a denial of service attack includes the following steps:

[0066] Step 1) Considering the tracking control system of a quadrotor drone, a discrete-time position-based visual servo control framework of the quadrotor drone is established through the Newton-Euler formula and coordinate transformation.

[0067] Step 1.1) considers a quadrotor tracking control system, which consists of a quadrotor equipped with a monocular camera and IMU and a ground vehicle with an ApirlTag posted on the top platform.

[0068] Step 1.2) The motion of a quadrotor can be described using two coordinate systems: the inertial frame and body fixing frame The fuselage fixed frame The origin of is located at the center of mass of the quadrotor drone. as well as Four-rotor drones The position and velocity vectors in . Using the Newton-Euler formula

[0069]

[0070] Where J is the inertia matrix of the quadcopter; g is the acceleration due to gravity; i3 =

[001] T is a unit vector. The thrust f and τ = [τ x τ y τ z ] T In the framework Upper limit mapping represents a skew-symmetric matrix, but for any x, there is Ω ^ x=Ω×x.

[0071] Fixed frame In the equation, φ, θ, ψ are defined as the roll angle, pitch angle, and yaw angle relative to the inertial coordinate system W. The rotation matrix from the fuselage coordinate system B to the inertial coordinate system W is

[0072]

[0073] Then the model of the position loop of the quadrotor can be rewritten as follows

[0074]

[0075] This patent does not consider the design of the attitude loop. In order to obtain a controller u that makes the system stable, x ,u y ,u z After that, the desired posture loop inverse solution is:

[0076]

[0077] Among them, φ d is the desired roll angle, θ d is the desired pitch angle, ψ d The desired yaw angle is set to 0 radians in this system.

[0078] By default, in this system, the quadcopter cannot collect information about the position vector p, and can only collect the relative position r between the quadcopter and AprilTag through the monocular camera. pt .

[0079] Step 1.3) Set the relative position r pt With expected position Error and the relative speed error Augmentation as a new state Taking the X-axis as an example (the analysis of the Y and Z-axis is the same as that of the X-axis), and discretizing it with a sampling period of t = 0.01s, the system equation can be obtained:

[0080]

[0081] Among them, A=[1,0.01;0,1], B=[0.001;0.01], C=[1,0].

[0082] Step 2) According to the energy ratio of the denial of service attack and the valid signal, a communication model based on signal interference plus noise ratio is introduced to describe the probability of a successful denial of service attack in the sensor-controller channel;

[0083] Step 2.1) Establish the relationship between the bit error rate SER and the signal-to-noise ratio SNR in the sensor-controller channel:

[0084]

[0085] Where Q(x) represents the Gaussian Q function and ξ is the network parameter.

[0086] Step 2.2) Considering that DoS attacks occur randomly in the sensor-controller channel, the signal-interference-plus-noise ratio replaces the signal-to-noise ratio:

[0087]

[0088] where p s is the energy of the signal emitted by the sensor, p a is the energy of the signal sent by the attacker, and ω is the additive Gaussian white noise in the channel. At this time, we have:

[0089]

[0090] Step 2.3) To describe the impact of DoS attacks on the actuator, define the indicator function α k When α k =1, it means that an attack has occurred, blocking the transmission of data packets. k =0 means the data packet transmission is normal. At this point, the success rate of sensor-controller channel data transmission under denial of service attack can be obtained. Relationship with bit error rate SER:

[0091]

[0092] Step 3) The system state information under the denial of service attack is reconstructed by alternately using the sensor output data that has not been attacked and the virtual output generated by the predictor, and a feedback controller is designed.

[0093] Step 3.1) For the quadrotor tracking control system, the expanded state equation using the input / output sequence on the time range [k-1, kN] can be written as

[0094]

[0095] in For mixed output,

[0096] V(N)=[B,AB,…,A N-1 B],U(N)=[(CA N-1 ) T ,…,(CA) T ,C T ] T ,

[0097] And N = max{ρ u ,ρ v}, ρ u is such that U(ρ u ) is the smallest integer with full column rank, ρ v is such that V(ρ v ) is the smallest integer with full row rank. Therefore, there exists a left inverse of U(N) such that U + (N)=[U T (N)U(N)] -1 U T (N).

[0098] Step 3.2) The state of the quadrotor tracking control system can be uniquely obtained based on the measured input / output sequence:

[0099]

[0100] The M y =A N U + (N), M u =V(N)-M y T(N) is a given parameter, Θ=[M u M y ],

[0101] Step 3.3) Build a predictor to generate virtual output to compensate for the impact of the denial of service attack on the system:

[0102]

[0103] Said Dummy output generated for the predictor.

[0104] Step 3.4) Build the feedback controller:

[0105]

[0106] Where K represents the controller gain,

[0107] Step 4) The value function is given, and the Riccati equation of the system is derived through the Bellman optimality principle and the expression of the controller gain is determined;

[0108] Step 4.1) The value function is defined as follows:

[0109]

[0110] Where Q and R are weight matrices.

[0111] Step 4.2) Based on the form of the value function and You can get:

[0112]

[0113] At this point, the Bellman optimal equation can be written as:

[0114]

[0115] Combined with V(x k ), the Hamiltonian function is defined as follows

[0116]

[0117] For the above Hamiltonian function u k Taking partial derivatives we get:

[0118]

[0119] Move back,

[0120] u k =-(R+B T PB) -1 B T PAΘz k

[0121] The controller gain is obtained as:

[0122]

[0123] Substituting the controller gain into the Bellman equation yields the following Riccati equation:

[0124]

[0125] Step 5) Combined with the adaptive dynamic programming algorithm, the optimal controller gain is obtained.

[0126] Step 5.1) Use As control input, To stabilize the initial gain of the system, e is the detection noise, and the parameter j=0 is set.

[0127] Step 5.2) Solve the Riccati equation using the least squares algorithm to obtain the solution P j And gain

[0128] Step 5.3) Set j←j+1. For j≥1, if ||P j -P j+1 ||>ε, repeat step 5.2; otherwise, let j * ←j, and execute step 5.4. The parameter ε is the convergence criterion of the algorithm.

[0129] Step 5.4) As the optimal control gain output.

[0130] The above embodiments are only used to help understand the method and core idea of ​​the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing the safe tracking of a quad-rotor drone under a denial of service attack, characterized in that: The following steps are involved: Step 1) Considering the tracking control system of a quadrotor drone, a position-based visual servo control framework of a discrete-time quadrotor drone is established through the Newton-Euler formula and coordinate transformation; Step 2) According to the energy ratio of the denial of service attack and the valid signal, a communication model based on signal interference plus noise ratio is introduced to describe the probability of a successful denial of service attack in the sensor-controller channel; Step 3) reconstructing the system state information under the denial of service attack by alternately using the sensor output data that has not been attacked and the virtual output generated by the predictor, and designing a feedback controller; Step 4) The value function is given, and the Riccati equation of the system is derived through the Bellman optimality principle and the expression of the controller gain is determined; Step 5) Combine the adaptive dynamic programming algorithm to obtain the optimal controller gain.

2. The method for optimizing the safe tracking of a quad-rotor drone under a denial of service attack according to claim 1 is characterized in that: Step 1) specifically includes: Step 1.1) Consider a quadrotor tracking control system, which consists of a quadrotor equipped with a monocular camera and IMU and a ground vehicle with an ApirlTag posted on the top platform; Step 1.2) The motion of the quadrotor is described using two coordinate systems: the inertial frame and body fixing frame The fuselage fixed frame The origin of is located at the center of mass of the quadrotor drone; definition as well as Four-rotor drones In this system, the quadcopter cannot collect information about the position vector p, and can only collect the relative position r between the quadcopter and AprilTag through the monocular camera. pt ; Step 1.3) Set the relative position r pt With expected position Error and the relative speed error Augmentation as a new state Taking the X-axis as an example (the analysis of the Y and Z-axis is the same as that of the X-axis), and discretizing it with a sampling period of t = 0.01s, the system equation can be obtained: Among them, A=[1,0.01;0,1], B=[0.001;0.01], C=[1,0].

3. The method for optimizing the safe tracking of a quad-rotor drone under a denial of service attack according to claim 2 is characterized in that: Step 2) specifically includes: Step 2.1) Establish the relationship between the bit error rate SER and the signal-to-noise ratio SNR in the sensor-controller channel: Where Q(x) represents the Gaussian Q function, ξ is the network parameter; Step 2.2) Considering that DoS attacks occur randomly in the sensor-controller channel, the signal-interference-plus-noise ratio replaces the signal-to-noise ratio: where p s is the energy of the signal emitted by the sensor, p a is the energy of the signal sent by the attacker, and ω is the additive Gaussian white noise in the channel; at this time: Step 2.3) To describe the impact of DoS attacks on the actuator, define the indicator function α k ; When α k =1, it means that an attack has occurred, blocking the transmission of data packets; otherwise, α k =0 means the data packet transmission is normal; at this time, the success rate of sensor-controller channel data transmission under denial of service attack is obtained Relationship with bit error rate SER:

4. The method for optimizing the safe tracking of a quad-rotor drone under a denial of service attack according to claim 3 is characterized in that: Step 3) specifically includes: Step 3.1) For the quadrotor tracking control system, the expanded state equation using the input / output sequence on the time range [k-1, kN] can be written as in For mixed output, V(N)=[B,AB,…,A N-1 B],U(N)=[(CA N-1 ) T ,…,(CA) T ,C T ] T , And N = max{ρ u ,ρ v }, ρ u is such that U(ρ u ) is the smallest integer with full column rank, ρ v is such that V(ρ v ) is the smallest integer with full row rank; therefore, there exists a left inverse of U(N) such that U + (N)=[U T (N)U(N)] -1 U T (N); Step 3.2) The state of the quadrotor tracking control system can be uniquely obtained based on the measured input / output sequence: Among them, M y =A N U + (N), M u =V(N)-M y T(N) is a given parameter, Θ=[M u M y ], Step 3.3) Build a predictor to generate virtual output to compensate for the impact of the denial of service attack on the system: in Dummy output generated for the predictor; Step 3.4) Build the feedback controller: Where K represents the controller gain, 5. The method for optimizing the safe tracking of a quad-rotor drone under a denial of service attack according to claim 4 is characterized in that: Step 4) specifically includes: Step 4.1) The value function is defined as follows: Where Q and R are weight matrices; Step 4.2) The controller gain is: The P is the unique solution of the Riccati equation as follows:

6. The method for optimizing the safe tracking of a quad-rotor drone under a denial of service attack according to claim 5 is characterized in that: Step 5) specifically includes: Step 5.1) Use As control input, To make the system stable, the initial gain, e is the detection noise, and the parameter j=0 is set; Step 5.2) Solve the Riccati equation using the least squares algorithm to obtain the solution P j And gain Step 5.3) Set j←j+1. For j≥1, if ||P j -P j+1 ||>ε, repeat step 5.2; otherwise, let j * ←j, and execute step 5.4; where the parameter ε is the algorithm convergence criterion; Step 5.4) As the optimal control gain output.

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