A propeller drive unmanned vehicle formation control method based on amplitude and rate saturation resistance

Abstract

The application discloses a kind of based on anti-amplitude and rate saturation paddle drive unmanned vehicle formation control method, belong to unmanned vehicle formation control technical field.The existing paddle drive unmanned platform executor is aimed at solving the problem of control failure and system oscillation caused by amplitude and rate saturation constraint in physical level, including: paddle drive unmanned vehicle dynamics model is established integrated executor dynamic characteristics;Based on the dynamics model, the control constraint model for paddle drive unmanned vehicle is constructed;Design anti-saturation formation cooperative control law under combined connected topology.The method offsets saturation deviation by auxiliary compensation system, and combines neural network to estimate system disturbance online.The amplitude and rate saturation problem of paddle drive unmanned vehicle under the vertical plane working condition is solved, the formation stability is maintained under the topology switching environment, and the control accuracy and safety of the system are improved.

Description

Technical Field

[0001] This invention belongs to the field of unmanned vehicle formation control technology, specifically relating to a propeller-driven unmanned vehicle formation control method based on anti-amplitude and rate saturation. Background Technology

[0002] With the rapid development of unmanned systems technology, drones and unmanned vehicles are increasingly used in complex urban environments, becoming important equipment for carrying out covert reconnaissance, precision detection, and emergency response tasks. To address the obstacles posed by broken roads and building barriers to the movement of single-modal platforms, multimodal unmanned platforms with terrain-crossing capabilities have become a research focus. Among them, propeller-driven unmanned vehicles achieve vertical attachment and movement by integrating propeller thrust, balancing aerial maneuverability with ground operation stability, significantly improving the robot's task adaptability in unstructured scenarios.

[0003] Among the various challenges faced by propeller-driven unmanned platforms in high-intensity missions, particularly the limited payload and endurance of individual units, swarm coordination control technology has become a key approach to optimizing system efficiency. By coordinating the operation of multiple unmanned platforms, the performance dependence on individual nodes can be effectively reduced, enabling large-scale area search and information collection while ensuring long-term operation. In actual swarm control, the control system needs to adjust the output state of each actuator in real time according to a preset topology to ensure the overall motion synchronization and mission reliability of the swarm. However, existing technologies for swarm control of propeller-driven unmanned vehicles often fail to fully consider the physical constraints of actuators in engineering practice. Traditional control schemes primarily focus on solving the amplitude saturation problem of control input signals, but generally ignore the rate saturation phenomenon in the mechanical or electrical drive links of actuators, leading to significant command tracking deviations during the rapid response phase. Furthermore, existing compensation mechanisms lack the comprehensive processing capability for both input rate saturation and amplitude saturation, making it difficult to accurately compensate for actuator output errors in complex dynamic environments. Furthermore, ignoring rate constraints can lead to a mismatch between control commands and the physical characteristics of actuators, which in turn can cause oscillations or even instability in the formation system, severely limiting the collaborative operation efficiency of propeller-driven unmanned vehicles in complex real-world scenarios.

[0004] Based on this, the present invention proposes a paddle-driven unmanned vehicle formation control method based on anti-amplitude and rate saturation to solve the problems existing in the prior art. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a propeller-driven unmanned vehicle formation control method based on anti-amplitude and rate saturation, which solves the problems of control failure and system oscillation caused by the physical-level amplitude and rate saturation constraints of existing propeller-driven unmanned platform actuators.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for formation control of propeller-driven unmanned vehicles based on resistance to amplitude and rate saturation includes the following steps:

[0008] Step 1: Establish a dynamic model of the paddle-driven unmanned vehicle with integrated actuator dynamic characteristics;

[0009] Step 2: Based on the dynamic model, construct a control constraint model for the propeller-driven unmanned vehicle;

[0010] Step 2.1: Analyze the force balance state of the propeller-driven unmanned vehicle during vertical driving and establish an input saturation model for control constraints;

[0011] Step 2.2: Use the Gaussian integral function to handle control input saturation and establish a transformation strategy from actuator rate saturation to command amplitude saturation;

[0012] Step 2.3: Establish an actuator rate saturation constraint strategy;

[0013] Step 2.4: Based on steps 2.1-2.3, establish a dynamic model that considers input saturation and velocity constraints;

[0014] Step 3: Design anti-saturation formation cooperative control law under combined connected topology.

[0015] In a preferred embodiment of the present invention, step 1, the process of establishing the dynamic model of the paddle-driven unmanned vehicle integrating the dynamic characteristics of the actuator, includes:

[0016] Step 1.1: Establish a dynamic model of the paddle-driven unmanned vehicle with integrated actuator dynamic characteristics;

[0017] Step 1.2: Based on the dynamic model of the propeller-driven unmanned vehicle, the motor thrust response is simplified to a first-order inertial element;

[0018] Step 1.3: Based on the dynamic model of the propeller-driven unmanned vehicle, the servo motor rotation is described as a second-order dynamic model;

[0019] Step 1.4: Combine the position and velocity variables of the unmanned vehicle in the ground inertial coordinate system to construct a third-order hierarchical dynamic model.

[0020] In a preferred embodiment of the present invention, the dynamic model of the paddle-driven unmanned vehicle for the dynamic characteristics of the actuator in step 1 is as follows:

[0021] ;

[0022] ;

[0023] ;

[0024] Among them, X i U represents the position vector. i Represents the velocity vector. This represents the control input that the actuator actually outputs. Represents the dynamic parameter matrix, Indicates the unknown dynamic part. Indicates control input, Indicates that the command controls the input; This represents the control input coefficient matrix. Instructions control the input coefficient matrix; This represents the unknown dynamic part of the model generated by the dynamic modeling of the actuator, including the uncertain dynamic model in motor dynamics and the uncertain dynamic model in servo dynamics.

[0025] In a preferred embodiment of the present invention, when establishing the input saturation model of control constraints in step 2.1, an active gravity offset strategy is adopted: the total propeller thrust is decomposed into a balancing force located in the plane and equal in magnitude and opposite in direction to gravity, and a control force located in the longitudinal plane of the vehicle body; wherein the control force is further decomposed into positive pressure and driving force, and the upper and lower boundaries of the driving force are dynamically determined according to the vehicle speed and support force.

[0026] In a preferred embodiment of the present invention, the lower and upper bounds of the driving force control input are respectively:

[0027] ;

[0028] ;

[0029] in, Indicates the quality of the driverless car. and These represent the thrust control inputs. The lower and upper bounds, Indicates balanced forces. Indicates controllable force. Indicates propeller thrust The upper boundary.

[0030] In a preferred embodiment of the present invention, the specific method for establishing the actuator rate saturation constraint strategy in step 2.3 is as follows: set the upper and lower boundaries of the actuator input rate, and use the actuator dynamic equation in step 1 to reverse map the physical rate limit into an amplitude constraint on the command control input, so as to ensure that the command generated by the controller is within the frequency domain of the actuator physical response.

[0031] In a preferred embodiment of the present invention, step 3, designing the anti-saturation formation cooperative control law under the combined connected topology, includes:

[0032] Step 3.1: Based on the preset formation topology, define the cooperative error variables of each unmanned vehicle node using the adjacency matrix and the navigator association matrix, and establish a formation error system that considers the error variables;

[0033] Step 3.2: Combine the formation error of the integrated formation error system, auxiliary compensation variables, and neural network estimates to synthesize an anti-saturation adaptive formation control law.

[0034] In a preferred embodiment of the present invention, the cooperative error variable defined in step 3.1 includes the position loop error variable. Speed ​​loop error variable Control loop error variables They are respectively:

[0035] ;

[0036] ;

[0037] ;

[0038] in, and Both represent virtual control variables. Represents auxiliary variables. U represents the formation error. i Represents the velocity vector. This indicates a control input.

[0039] In a preferred embodiment of the present invention, in step 3.2, the first virtual control quantity It integrates an adaptive term to compensate for transient impacts caused by topology switching; a second virtual control variable. Unknown disturbances in the system are estimated and counteracted online using a radial basis function neural network. .

[0040] In a preferred embodiment of the present invention, the instruction control input The design incorporates the principles of constructing auxiliary systems, using auxiliary variables. The dynamic evolution is used to mitigate the impact of actuator amplitude and rate saturation on the stability of the closed-loop system, and its auxiliary dynamic equation is related to the saturation approximation error.

[0041] Compared with existing technologies, this invention provides a propeller-driven unmanned vehicle formation control method based on resistance to amplitude and rate saturation, which has the following beneficial effects:

[0042] 1. This invention overcomes the response lag problem caused by treating the actuator as an ideal proportional element in traditional control methods through deep integration of the actuator's dynamic characteristics. By establishing a third-order model that includes the first-order characteristics of the motor and the second-order characteristics of the servo motor, the generation process of control commands fully predicts the physical response process of the actuator, thereby improving the transient accuracy of trajectory tracking when the unmanned vehicle is performing high-speed obstacle avoidance or sharp turns.

[0043] 2. This invention proposes a strategy for transforming rate saturation into amplitude saturation, solving the system oscillation problem caused by the limited response speed of the actuator. By mapping the rate of change constraint to the value range of the command in real time, and combining it with the smoothing processing of the Gaussian integral function, the jump phenomenon of the control signal at the saturation boundary is eliminated. This approach enables the actuator to switch states smoothly and physically achievably when the autonomous vehicle faces large changes in commands due to sudden task demands, avoiding mechanical fatigue and control failure caused by command overshoot.

[0044] 3. This invention achieves highly reliable driving of a propeller-driven unmanned vehicle in vertical conditions by actively counteracting gravity and setting a dynamic saturation boundary. By decoupling the propeller thrust distribution, the lift component required to counteract gravity is prioritized, and the upper limit of the driving force is adjusted in real time according to the movement speed. This technique ensures that the unmanned vehicle maintains sufficient adhesion when driving on a vertical wall, whether climbing, descending, or laterally translating, preventing the risk of falling due to improper thrust distribution.

[0045] 4. This invention combines an auxiliary compensation system with an adaptive RBF neural network to enhance the system's robustness in complex environments. The auxiliary compensation system prevents integral saturation by absorbing saturation errors, while the neural network accurately mitigates disturbances from unknown environments. During the dynamic process of communication topology switching, the adaptive mechanism adjusts the control gain to eliminate transient shocks caused by changes in information links, ensuring the consistency and stability of the overall formation configuration.

[0046] 5. The smooth approximation function and mean value theorem transformation method adopted in this invention theoretically guarantees the global stability of the control system. By transforming nonlinear saturation constraints into a computable linearized form, the complex nonlinear control problem is transformed into an easily implementable adaptive adjustment problem. This implementation not only reduces the computational burden on the onboard computing unit but also proves the uniform eventual boundedness of the closed-loop system state through Lyapunov analysis, providing a solid theoretical guarantee for propeller-driven unmanned vehicles to perform high-value, high-risk tasks. Attached Figure Description

[0047] Figure 1 This is a flowchart of the paddle-driven unmanned vehicle formation control method of the present invention.

[0048] Figure 2 This is a diagram showing the convoy trajectory of the propeller-driven unmanned vehicles of the present invention.

[0049] Figure 3 This is a curve showing the position error of the propeller-driven unmanned vehicle platooning in this invention.

[0050] Figure 4 This is a diagram showing the formation error curve for the propeller-driven unmanned vehicle platooning of the present invention.

[0051] Figure 5 This is a graph showing the vertical driving control input curves for the propeller-driven unmanned vehicle of the present invention.

[0052] Among them: Figure 2 middle, Figure 2 (a) is a plan view of the platooning trajectory of the unmanned vehicles; Figure 2 (b) is an isometric view of the unmanned vehicle platoon trajectory.

[0053] exist Figure 3 middle, Figure 3 (a) is Time curve; Figure 3 (b) is Time curve;

[0054] exist Figure 4 middle, Figure 4 (a) Formation error for follower 1 Line graph; Figure 4 (b) Formation error for follower 1 Line graph; Figure 4 (c) is the formation error of follower 2. Line graph; Figure 4 (d) represents the formation error of follower 2. Line graph; Figure 4 (e) is the formation error of follower 3. Line graph; Figure 4 (f) represents the formation error of follower 3. Curve graph; and in the above Figure 4 (a)- Figure 4 In (f), and They are The first and second elements.

[0055] exist Figure 5 middle, Figure 5 (a) is a velocity-time curve of follower 1; Figure 5 (b) Thrust input time curve for follower 1; Figure 5 (c) is the velocity-time curve of follower 2; Figure 5(d) is the thrust input time curve for follower 2; Figure 5 (e) is the velocity-time curve of follower 3; Figure 5 (f) is the thrust input time curve of follower 3. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] As per the instruction manual Figure 1 -Appendix Figure 5 As shown, to address the control failures and system oscillations caused by amplitude and rate saturation constraints at the physical level in existing propeller-driven unmanned platform actuators, this invention proposes a propeller-driven unmanned vehicle formation control method based on resistance to amplitude and rate saturation, comprising the following steps:

[0058] Step 1: Establish a dynamic model of the paddle-driven unmanned vehicle with integrated actuator dynamic characteristics;

[0059] The propeller-driven unmanned vehicle (UAV) relies on motor thrust for longitudinal motion and front wheel steering for lateral motion. Therefore, the precise control of this platform is closely related to the actuator dynamics of the motors and servos. Based on this analysis, to achieve precise control of the propeller-driven UAV, the actuator dynamics of the motors and servos are incorporated into the dynamic modeling, completing the construction of the UAV's dynamic model and control method. The specific steps include:

[0060] Step 1.1: First, construct the dynamic model of the propeller-driven unmanned vehicle in the ground inertial coordinate system;

[0061] The dynamic model of the propeller-driven unmanned vehicle includes the position vector X. i Velocity vector U i and the actual control input of the actuator output The details are as follows:

[0062] ;

[0063] ;

[0064] ;

[0065] in:( , This indicates the position of the propeller-driven unmanned vehicle in the ground coordinate system. This represents the linear velocity along the shaft system of the propeller-driven unmanned vehicle. Indicates the orientation angle of the machine system relative to the ground system; This indicates the linear velocity of the propeller-driven unmanned vehicle body along the lower edge of the ground coordinate system. The velocity component, therefore Similarly, This indicates the linear velocity of the vehicle body at the lower edge of the ground coordinate system. Similarly, the velocity components ; Indicates the axle spacing between the front and rear wheels. Indicates the front wheel steering angle, satisfying ; This represents the unknown dynamic components and external disturbances; The axle spacing between the front and rear wheels is represented by the following distance in the ground coordinate system: The distance component, The axle spacing between the front and rear wheels is represented by the following distance in the ground coordinate system: The distance component.

[0066] Step 1.2: Based on the dynamic model of the propeller-driven unmanned vehicle, the motor thrust response is simplified to a first-order inertial element, and the motor inertial time constant is introduced. This describes the process of the motor's actual speed tracking the desired speed, and establishes the propeller thrust u of the propeller-driven unmanned vehicle. i and motor dynamic model as follows:

[0067] ;

[0068] ;

[0069] in, Indicates the propeller thrust coefficient. The propeller speed is represented by s, which represents the complex variable used in the Laplace transform and is the equivalent variable after the time domain is transformed to the frequency domain. It can be identified through thrust test data parameters; and These represent the actual speed of the motor and the desired speed of the motor, respectively.

[0070] The desired speed of the actuator dynamic motor Substitute propeller thrust In the middle, there are:

[0071] ;

[0072] Where, m i Indicates the mass of the driverless car;

[0073] set up , Substituting these values, we get:

[0074] ;

[0075] ;

[0076] in: This indicates the thrust command after considering the dynamic model; This represents an uncertain dynamic model in motor dynamics. This indicates the tracking error of the motor speed command.

[0077] Step 1.3: Based on the dynamic model of the propeller-driven unmanned vehicle, the servo motor rotation is described as a second-order dynamic model, and the damping ratio of the servo motor system is introduced. With servo system time constant To reflect the inertia and damping characteristics of the servo motor during rotation, a servo motor dynamic model was constructed. The settings are as follows:

[0078] ;

[0079] in, and These represent the actual turning angle and the commanded turning angle, respectively.

[0080] Following the same derivation process as for motor dynamics, the dynamic model of the servo motor can be obtained as follows:

[0081] ;

[0082] in, and These represent the actual servo rotation angle and the desired servo rotation angle, respectively. and It can be identified through experimental data parameters; This indicates the tracking error of the servo motor's angle command.

[0083] Step 1.4: Combining Steps 1.1-1.3 above, and taking into account the position and velocity variables of the unmanned vehicle in the ground inertial coordinate system, a dynamic model of the propeller-driven unmanned vehicle integrating the dynamic characteristics of the actuators is established (a third-order hierarchical dynamic model).

[0084] Considering that the motor speed has an upper limit, an uncertain dynamic model of the motor can be derived. It must be bounded, denoted as Similarly, the uncertain dynamic model in servo motor dynamics Includes rotational acceleration determined by servo torque. ,so, It must also be bounded, denoted as .

[0085] Based on this, the dynamic model of the paddle-driven unmanned vehicle with integrated actuator dynamic characteristics is established as follows:

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] in, Indicates the orientation angle of the machine system relative to the ground system; This indicates the linear velocity of the propeller-driven unmanned vehicle body along the lower edge of the ground coordinate system. The velocity component, therefore Similarly, This indicates the linear velocity of the vehicle body at the lower edge of the ground coordinate system. Similarly, the velocity components ; Indicates the axle spacing between the front and rear wheels. Indicates the front wheel steering angle, satisfying ; The axle spacing between the front and rear wheels is represented by the following distance in the ground coordinate system: The distance component, The axle spacing between the front and rear wheels is represented by the following distance in the ground coordinate system: The distance component, This represents the unknown dynamic components and external disturbances. The time constant represents the inertial element of the motor. and These represent the time constant and damping of the second-order system, respectively. Represents the dynamic parameter matrix, Indicates the unknown dynamic part. Indicates control input, Indicates that the command controls the input; This represents the control input coefficient matrix. Instructions control the input coefficient matrix; This represents the unknown dynamic part of the model generated by the dynamic modeling of the actuator, including the uncertain dynamic model in motor dynamics and the uncertain dynamic model in servo dynamics.

[0096] The modeling method used in this step constructs a third-order hierarchical dynamic model that not only includes the kinematic relationship between position and velocity but also covers the evolution of the actuator's internal state variables. Among these, the unknown dynamic part D... i This integrated model is used to characterize uncertainties such as external wind field disturbances and fluctuations in ground friction. It provides a more physically accurate reference for the design of subsequent control laws, ensuring that the commands generated by the controller are within the frequency range that the actuator can respond to.

[0097] Step 2: Based on the dynamic model established in Step 1, construct a control constraint model for the propeller-driven unmanned vehicle;

[0098] This step is crucial for resolving the saturation problem at the physical level. Since the propeller thrust and steering mechanism of a paddle-driven autonomous vehicle are limited by motor power, power supply voltage, and mechanical structure limits, corresponding mathematical constraints must be established at the algorithm level. Therefore, in this step, by analyzing the force state during vertical driving, an input saturation model incorporating both driving force saturation and steering angle saturation is established, and a Gaussian integral function is used to transform the actuator rate saturation constraint into a command amplitude saturation constraint. The specific steps include:

[0099] Step 2.1: Analyze the force balance state of the propeller-driven unmanned vehicle during vertical driving and establish an input saturation model for control constraints;

[0100] In vertical driving mode, propeller-driven unmanned vehicles (UAVs) must overcome gravity to avoid falling. Existing solutions use thrust directed towards the contact surface to generate friction and overcome gravity. Force analysis shows that this approach relies on the friction coefficient of the contact surface and is energy-intensive. Therefore, this embodiment proposes a strategy of directly balancing gravity with thrust, i.e., an active gravity-counteracting strategy. Specific steps include:

[0101] Based on the active gravity-counteracting strategy, the force analysis of the propeller-driven unmanned vehicle traveling in the vertical plane is shown in the attached figure. Figure 1 As shown, the total propeller thrust It can be divided into two parts: balancing forces. and control force Among them, balanced forces Located opposite to gravity, in In the plane, with the car body The included angle is Control force It is located in the longitudinal plane of the vehicle body. Internally, it can be further decomposed into positive pressure. and driving force Controlling force and The included angle is .

[0102] Under the aforementioned body axis system, the balancing forces and control force The unit vector in the body axis system is written as:

[0103] ;

[0104] ;

[0105] and spatial vector angle Written as:

[0106] ;

[0107] According to the law of cosines, the total propeller thrust is:

[0108] ;

[0109] Considering that when traveling in a vertical plane, the propeller-driven unmanned vehicle will mostly travel close to a horizontal plane, and the vector angle... It can be approximated as Then it can be further simplified:

[0110] ;

[0111] in, Indicates propeller thrust The upper boundary.

[0112] Then driving force It can be further written as:

[0113] ;

[0114] in, This is equivalent to the supporting force. However, in the absence of vehicle slippage, the supporting force depends on the centripetal force. Therefore, it can be concluded that... It is related to the speed of movement, in other words, The upper and lower boundaries are also related to the speed of motion, that is, the driving force boundary is speed-related.

[0115] Based on the above analysis, the input saturation form can be obtained as follows:

[0116] ;

[0117] in, and These represent the thrust control inputs. The lower and upper bounds are expressed as:

[0118] ;

[0119] ;

[0120] in, This indicates the quality of the driverless car.

[0121] Besides the saturation of driving force, considering the spatial constraints of the mechanical structure, the front wheel steering angle will also inevitably have a saturation problem. Since this is due to the limitations of the mechanical mechanism, in this embodiment, the front wheel steering angle is a constant constraint, that is:

[0122] ;

[0123] in, and These represent the thrust control inputs. The lower and upper bounds.

[0124] Control input in the dynamic model Using saturation function Instead, the input saturation model becomes:

[0125] ;

[0126] ;

[0127] ;

[0128] ;

[0129] in, and These are the thrust control inputs. The lower and upper bounds.

[0130] This force analysis model allows the controller to prioritize the allocation of balancing forces for survival when generating commands, and then allocate driving forces for maneuvering based on the remaining power.

[0131] Step 2.2: Use the Gaussian integral function to handle control input saturation and establish a transformation strategy from actuator rate saturation to command amplitude saturation;

[0132] Traditional saturation handling methods typically employ hard-limiting functions, but this leads to the control law becoming non-differentiable at the saturation boundary, causing high-frequency oscillations in the system. This embodiment introduces a Gaussian integral function to smoothly approximate the saturation characteristics, transforming the nonlinear hard-limiting characteristics into a continuously differentiable mathematical expression. By adjusting the variance parameter of the Gaussian distribution, the approximate curve remains linear in the unsaturated region and smoothly transitions in the saturated region. Furthermore, utilizing the mean value theorem, the saturated input term is transformed into the product of a linear gain term and the control variable. This allows for the parameterization of complex saturation constraints from the control law in subsequent backstepping design, reducing the nonlinear coupling of the algorithm. The specific steps include:

[0133] Using Gaussian integral function Addressing the control input saturation problem. Based on the form of the Gaussian integral function, the saturation function can be rewritten as:

[0134] ;

[0135] ;

[0136] ;

[0137] ;

[0138] The saturation function is approximated by the Gaussian integral function, and is ultimately rewritten as follows: ; express Bounded variables obtained after processing by the sign function; similarly... express Bounded variables obtained after processing by the sign function.

[0139] According to the mean value theorem, the saturated input is transformed into the product of a linear gain term and a control variable. This allows the control variable to be separated from the saturation constraints in the control law design, resulting in... It can be written as:

[0140] ;

[0141] in, express The partial derivatives in The derivative value at point is given by the expression:

[0142] , ;

[0143] According to the Mean Value Theorem, the derivative function must take values ​​within the range of its derivative. express The value points, express The initial value to be taken. express The value points, express The initial value to be taken. When When it varies within the range of 0 to 1 The value is between and Between these two values, the requirements of the Mean Value Theorem are satisfied. Similarly.

[0144] ;

[0145] ;

[0146] The derivative is:

[0147] ;

[0148] ;

[0149] Ultimately, if we assume If the value is 0, then the saturation control input strategy can be obtained as follows:

[0150] ;

[0151] By introducing the Gaussian integral function and utilizing its derivative properties, the control variables were separated from the saturation function.

[0152] Step 2.3: Establish an actuator rate saturation constraint strategy;

[0153] In engineering practice, most control system actuators are driven by mechanical mechanisms or electronic devices. The actuator dynamics conform to first- or second-order dynamic characteristics. Therefore, not only does the actuator amplitude exhibit saturation, but the actuator rate also suffers from saturation. This embodiment utilizes the actuator dynamic equations to inversely map this physical rate limitation into an amplitude constraint on the controller's output command. By calculating the maximum allowable change in the actuator within the current sampling period, the search range of the control command is corrected in real time. This technical solution ensures that every command generated by the controller is within the actuator's physical response capability, eliminating the risk of actuator runaway due to excessively rapid command changes. The specific steps include:

[0154] The actuator of the propeller-driven unmanned vehicle exhibits the following input rate saturation:

[0155] ;

[0156] in, and These represent the control input rates of the unmanned vehicle with the corresponding number i. Upper and lower boundaries.

[0157] Since the actuator dynamically satisfies the kinetic equations, the rate saturation problem can be transformed using command control input. The command control input result is:

[0158] ;

[0159] ;

[0160] ;

[0161] in, , , , . and These represent the command control inputs corresponding to the unmanned vehicle numbered i. Upper and lower boundaries; and Indicates the upper and lower boundaries of the instruction control input; This represents the control input coefficient matrix. This indicates that the instruction controls the input coefficient matrix.

[0162] Command control input and Substituting back into the actuator dynamics equations, it is easy to see that they satisfy... This means that the input rate saturation is satisfied.

[0163] Step 2.4: Based on steps 2.1-2.3, establish a dynamic model that considers input saturation and velocity constraints;

[0164] Based on the above, the dynamic model considering input saturation and velocity constraints established in this embodiment is as follows:

[0165] ;

[0166] ;

[0167] in, Represents the dynamic parameter matrix, This represents the unknown dynamic part. Indicates control input, This indicates that the command controls the input. This represents the control input coefficient matrix. The instruction controls the input coefficient matrix. This represents the unknown dynamic part of the model generated by the dynamic modeling of the actuator.

[0168] The system contains control input assignment constraints and input rate constraints. The input rate constraints are converted into instruction control input constraints, as shown below:

[0169] ;

[0170] ;

[0171] The above model integrates amplitude saturation, rate saturation, and dynamic boundaries under vertical conditions, forming the basis of the controlled object in the closed-loop control system.

[0172] Step 3: Design anti-saturation formation cooperative control laws under combined connected topologies;

[0173] In actual formation missions, the communication links between unmanned vehicles may fail intermittently due to building obstruction or electromagnetic interference, resulting in a combined interconnected topology.

[0174] Step 3.1: Establish a formation error system that considers error variables;

[0175] Based on the preset formation topology, the cooperative error variables of each autonomous vehicle node are defined using the adjacency matrix and the navigator correlation matrix. These cooperative error variables combine the relative positional deviation between the current node and its neighboring nodes, as well as the tracking deviation between the current node and the navigator.

[0176] In the formation error system, the following position errors are set. and formation error :

[0177] ;

[0178] ;

[0179] in, Indicates the navigator's position. This represents the expected grouping distance between i and j. This represents the expected formation distance between i and the navigator; and Determined by the preset formation, satisfying ; The adjacency matrix represents the formation topology. This means that individual followers can obtain information about neighboring nodes; conversely, they cannot. ; The diagonal elements of the navigator matrix represent the formation topology. This means that individual followers can obtain information from the leader, and vice versa. .

[0180] The backstepping control method itself requires setting a virtual control quantity. This embodiment uses the aforementioned error... Incorporating virtual control quantities and This enables formation control. Furthermore, considering actuator dynamics, the controlled dynamics model is a third-order system; therefore, a third virtual control variable is also included. .

[0181] In summary, based on the backstepping control method, the following error variables are set:

[0182] ;

[0183] ;

[0184] ;

[0185] in, This represents the position loop error variable. Represents the velocity loop error variable. This represents the control loop error variable. and Both represent virtual control variables. This represents an auxiliary variable used to achieve rate saturation, which will be introduced in the following steps.

[0186] Step 3.2: Synthesize an anti-saturation adaptive formation control law;

[0187] Combining the above formation error and the estimated values ​​of auxiliary compensation variables, an adaptive term is generated to compensate for the transient impact caused by topology switching, and the first virtual control quantity is calculated. for:

[0188] ;

[0189] ;

[0190] in, , , , , All represent design parameters; Indicates adaptive parameters, Indicates to The estimated value, the estimation error is denoted as . .

[0191] Second virtual control quantity Unknown disturbances in the system are estimated and counteracted online using a radial basis function (RBF) neural network. The second virtual control quantity is obtained. for:

[0192] ;

[0193] ;

[0194] ;

[0195] in, and Both represent adaptive parameters. and All represent estimated values, and the estimation error is denoted as . as well as ; , , , , , , , All represent design parameters. , .

[0196] Based on the aforementioned first virtual control quantity Second virtual control quantity Based on the principle of constructing an auxiliary system, the command control input can be obtained. and auxiliary variables for:

[0197] ;

[0198] ;

[0199] ;

[0200] in, Represents auxiliary variables. This represents the saturation approximation error. , , , Indicates design parameters. Represents a symbolic function. This indicates the degree of the exponential function.

[0201] The control law is designed based on an adaptive backstepping control architecture. In the position control loop, a first virtual control variable is designed to eliminate position tracking errors. This virtual control variable integrates an adaptive term for online compensation of transient shocks caused by topology switching. In the velocity control loop, a second virtual control variable is designed, and a radial basis function neural network is introduced. This neural network utilizes its nonlinear mapping characteristics, taking the real-time state of the autonomous vehicle as input, to estimate and cancel unknown disturbances and model parameter perturbations in the system online. The weight update law of the neural network is derived based on Lyapunov stability theory, ensuring the convergence of the estimation error.

[0202] Example: To verify the effectiveness of the above-mentioned propeller-driven unmanned vehicle formation control method based on anti-amplitude and rate saturation of the present invention, this example applies it to a specific unmanned vehicle dynamic model for verification and explanation.

[0203] 1. The dynamic parameters and control parameters of the unmanned vehicle are shown in the table below.

[0204] Table 1: Dynamic Parameters of Propeller-Driven Unmanned Vehicles

[0205]

[0206] Table 2: Control Parameter Table

[0207]

[0208] 2. Based on the parameters described in Table 1 and Table 2 above, the simulation experiment follows... Figure 1 Demonstrate the simulation process. Figure 2 The motion trajectory diagram of the unmanned vehicle traveling in the vertical plane is given, and the numerical simulation results of the control algorithm are as follows: Figures 3-5 As shown.

[0209] Reference Appendix Figure 2 Three propeller-driven unmanned vehicles (UAVs) perform formation maneuvers in a vertical environment. The image shows the process of the UAVs starting from a random initial position and gradually forming and maintaining a preset formation configuration under the control law. The formation achieves high synchronization when the vehicles reach a position of approximately 6 meters. (Attached) Figure 2 (b) The isometric view shown clearly presents the trajectory of the unmanned vehicle in the vertical plane, verifying the reliability of the active gravity countermeasure strategy in maintaining vertical adhesion. Figure 2In the diagram, the markers on the trajectory represent the real-time position of the autonomous vehicle at 0.5-second intervals. Due to the influence of the combined connected topology, taking follower number 3 as an example, it can be seen from the trajectory that within each 1.5-second cycle, there are instances where the trajectory of the unfollowed leader is discontinuous. For instance, in the first 1.5-second cycle, follower number 3 does not turn in the first second due to the presence of lateral position error. This is because, in the first second, due to the disconnected topology, follower number 3 cannot receive the leader's position information and cannot generate a position error to drive steering. Therefore, even with the presence of lateral error, follower number 3 fails to obtain the leader's position information to generate a control signal due to the combined connected topology, thus failing to turn the vehicle and eliminate the error. However, in the third 0.5-second interval within the 1.5-second cycle, follower number 3 can receive the leader's information and therefore can obtain the leader's information to drive steering and eliminate the error.

[0210] The time curves for position error and formation error are as follows: Figure 3 and Figure 4 As shown in the diagram. Because a desired speed was set in the simulation and the autonomous vehicle itself had no initial speed, the error initially increased and then decreased. After approximately 2 seconds, the position error curve gradually decreased and approached 0. However, due to the influence of the combined connected topology, during the process of approaching 0, when the navigator information could not be received, a fluctuating convergence pattern occurred where the error increased and then decreased. The same applies to the formation error. Taking followers 1 and 3 as examples, follower 1 could receive information from the navigator and neighboring nodes at the initial moment, thus acquiring error information (-1.5m) at the initial moment. However, due to the influence of the combined connected topology, it could only intermittently acquire position information in subsequent operations, causing a fluctuating convergence pattern where the error increased and then decreased. Furthermore, follower 3 failed to acquire information about the navigator and neighboring nodes at the initial moment. As a result, the initial formation error was 0, and the error value (-1.76m) appeared only after acquiring information at 1 second. Similarly, due to the influence of the combined connected topology, follower 3 could only acquire position information intermittently in subsequent operation, resulting in a fluctuating convergence situation where the error increased and then decreased.

[0211] As attached Figure 3 The diagram illustrates the positional error variations of the autonomous vehicle in the longitudinal (x) and lateral (y) directions. In the initial stage, due to the significant displacement difference between the vehicle and the target configuration, the error curve exhibits a peak. At this point, the actuator is in a saturated state. Thanks to the smoothing and auxiliary compensation system based on the Gaussian integral function, the control command does not experience drastic changes; instead, the drive error rapidly decays within 2 seconds. The auxiliary variable plays a crucial role at this stage, ensuring the consistent boundedness of the closed-loop system by absorbing the saturation deviation. (See attached diagram) Figure 4As shown, the formation error curves of the three follower nodes are displayed in detail. Due to the influence of the combined connected topology, the communication link may be interrupted at some times. For example, follower 3 cannot obtain the navigator information at the initial moment, and its formation error is zero. When communication is restored at 1 second, the error signal suddenly increases, and the control law immediately responds. The fluctuating convergence characteristics shown by the curves in the figure are a manifestation of the adaptive algorithm continuously adjusting weights and approximating disturbances online in the topology switching environment. The online estimation capability of the neural network compensates for the transient impact caused by topology changes and maintains the stability of the formation configuration.

[0212] Thrust input curve as shown Figure 5 As shown, the correlation between actuator input and autonomous vehicle speed is illustrated. As the autonomous vehicle speed increases, the centripetal force increases, resulting in a decrease in the propeller thrust margin used for propulsion.

[0213] Figure 5 (b) Figure 5 (d) Figure 5 (f) clearly shows the limiting process of thrust command under dynamic boundary constraints. When the speed reaches its peak, the saturation boundary contracts, and the control law automatically limits the thrust output to prevent motor overload. This dynamic limiting mechanism achieves deep coupling between the algorithm layer and the physical layer, ensuring the safety of the system under extreme conditions.

[0214] This embodiment mathematically proves that all error signals converge to the neighborhood of the origin within a finite time. The introduction of the neural network eliminates the dependence on an accurate dynamic model, enabling it to generate compensating torques through autonomous learning when faced with sudden changes in friction caused by broken roads. The introduction of the auxiliary compensation system resolves the contradiction between "computational expansion" and "saturation instability" commonly found in the backstepping method, achieving a balance between control accuracy and physical constraints by dynamically correcting the error trajectory.

[0215] In practical applications, such as covert reconnaissance missions on urban building surfaces, propeller-driven unmanned vehicle platoons need to move rapidly across vertical walls. When a vehicle's driving force reaches its limit due to slippery walls, the anti-saturation mechanism described in this invention will immediately activate. The auxiliary system automatically reduces the desired speed of the affected vehicle by sensing the deviation between the actual output and the command, and notifies other members of the platoon to decelerate accordingly. This adaptive adjustment capability of the group ensures that the platoon will not disintegrate due to the physical limitations of a single node. Simultaneously, the conversion strategy for actuator rate saturation ensures that the servo steering commands remain within the mechanically tolerable frequency range, avoiding damage to the hardware from high-frequency oscillations.

[0216] In summary, this invention overcomes the shortcomings of traditional control methods that neglect physical layer constraints by integrating the modeling of actuator dynamic characteristics. It solves the differentiability problem in nonlinear control by utilizing a Gaussian integral function to smooth saturation. Through the collaborative work of an auxiliary compensation system and a neural network, it achieves multiple defenses against amplitude saturation, rate saturation, environmental disturbances, and topology switching. This method significantly improves the system's control accuracy and mission adaptability while ensuring the stability of propeller-driven unmanned vehicle platoons, providing reliable technical support for the collaborative operation of multimodal unmanned platforms.

[0217] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for formation control of propeller-driven unmanned vehicles based on resistance to amplitude and rate saturation, characterized in that, Including the following steps: Step 1: Establish a dynamic model of the paddle-driven unmanned vehicle with integrated actuator dynamic characteristics; Step 2: Based on the dynamic model, construct a control constraint model for the propeller-driven unmanned vehicle; Step 2.1: Analyze the force balance state of the propeller-driven unmanned vehicle during vertical driving and establish an input saturation model for control constraints; Step 2.2: Use the Gaussian integral function to handle control input saturation and establish a transformation strategy from actuator rate saturation to command amplitude saturation; Step 2.3: Establish an actuator rate saturation constraint strategy; Step 2.4: Based on steps 2.1-2.3, establish a dynamic model that considers input saturation and velocity constraints; Step 3: Design anti-saturation formation cooperative control law under combined connected topology.

2. The method for formation control of propeller-driven unmanned vehicles based on anti-amplitude and rate saturation as described in claim 1, characterized in that, Step 1, the process of establishing the dynamic model of the propeller-driven unmanned vehicle integrating the dynamic characteristics of the actuator, includes: Step 1.1: Establish a dynamic model of the paddle-driven unmanned vehicle with integrated actuator dynamic characteristics; Step 1.2: Based on the dynamic model of the propeller-driven unmanned vehicle, the motor thrust response is simplified to a first-order inertial element; Step 1.3: Based on the dynamic model of the propeller-driven unmanned vehicle, the servo motor rotation is described as a second-order dynamic model; Step 1.4: Combine the position and velocity variables of the unmanned vehicle in the ground inertial coordinate system to construct a third-order hierarchical dynamic model.

3. The method for formation control of propeller-driven unmanned vehicles based on anti-amplitude and rate saturation as described in claim 1, characterized in that, The dynamic model of the propeller-driven unmanned vehicle based on the actuator dynamic characteristics in step 1 is as follows: ； ； ； Among them, X i U represents the position vector. i Represents the velocity vector. This represents the control input that the actuator actually outputs. Represents the dynamic parameter matrix, Indicates the unknown dynamic part. Indicates control input, Indicates that the command controls the input; This represents the control input coefficient matrix. Instructions control the input coefficient matrix; This represents the unknown dynamic part of the model generated by the dynamic modeling of the actuator, including the uncertain dynamic model in motor dynamics and the uncertain dynamic model in servo motor dynamics.

4. The method for formation control of propeller-driven unmanned vehicles based on anti-amplitude and rate saturation as described in claim 1, characterized in that, Step 2.1 When establishing the input saturation model of control constraints, an active gravity countermeasure strategy is adopted: the total propeller thrust is decomposed into a balancing force located in the plane and equal in magnitude and opposite in direction to gravity, and a steering force located in the longitudinal plane of the vehicle body; The control force is further decomposed into positive pressure and driving force. The upper and lower boundaries of the driving force are determined dynamically based on the vehicle's speed and support force.

5. The method for formation control of propeller-driven unmanned vehicles based on anti-amplitude and rate saturation as described in claim 4, characterized in that, The lower and upper bounds of the drive force control input are as follows: ； ； in, Indicates the quality of the driverless car. and These represent the thrust control inputs. The lower and upper bounds, Indicates balanced forces. Indicates controllable force. Indicates propeller thrust The upper boundary.

6. The method for formation control of propeller-driven unmanned vehicles based on anti-amplitude and rate saturation as described in claim 1, characterized in that, The specific method for establishing the actuator rate saturation constraint strategy in step 2.3 is as follows: set the upper and lower boundaries of the actuator input rate, and use the actuator dynamic equation in step 1 to reverse map the physical rate limit into an amplitude constraint on the command control input, so as to ensure that the command generated by the controller is within the frequency domain of the actuator physical response.

7. The method for formation control of propeller-driven unmanned vehicles based on anti-amplitude and rate saturation according to claim 1, characterized in that, Step 3, designing the anti-saturation formation cooperative control law under combined connected topologies, includes: Step 3.1: Based on the preset formation topology, define the cooperative error variables of each unmanned vehicle node using the adjacency matrix and the navigator association matrix, and establish a formation error system that considers the error variables; Step 3.2: Combine the formation error of the integrated formation error system, auxiliary compensation variables, and neural network estimates to synthesize an anti-saturation adaptive formation control law.

8. The method for formation control of propeller-driven unmanned vehicles based on anti-amplitude and rate saturation according to claim 7, characterized in that, The cooperative error variables defined in step 3.1 include the position loop error variables. Speed ​​loop error variable Control loop error variables They are respectively: ； ； ； in, and Both represent virtual control variables. Represents auxiliary variables. U represents the formation error. i Represents the velocity vector. This indicates a control input.

9. A method for formation control of propeller-driven unmanned vehicles based on anti-amplitude and rate saturation according to claim 7, characterized in that, In step 3.2, the first virtual control quantity It integrates an adaptive term to compensate for transient impacts caused by topology switching; a second virtual control variable. Unknown disturbances in the system are estimated and counteracted online using a radial basis function neural network. .

10. The method for formation control of propeller-driven unmanned vehicles based on anti-amplitude and rate saturation according to claim 7, characterized in that, The command control input The design incorporates the principles of constructing auxiliary systems, using auxiliary variables. The dynamic evolution is used to mitigate the impact of actuator amplitude and rate saturation on the stability of the closed-loop system, and its auxiliary dynamic equation is related to the saturation approximation error.

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