Aircraft performance constraint compliance control method for contact type nondestructive testing

Abstract

The invention discloses an aircraft performance constraint compliance control method for contact type nondestructive testing, and belongs to the field of aircraft control. The implementation method comprises the following steps: introducing a saturated contact force controller into a position ring, and dynamically adjusting a confidence factor based on a position error to adaptively adjust normal rigidity and tangential flexibility; a zero-order control barrier function ZOCBF restrains the force controller, a three-dimensional dynamic safety boundary is established by using a sampling data mechanism, and the position, speed and contact force of the unmanned aerial vehicle are optimized and limited through quadratic programming; designing a hybrid torque controller in the attitude ring, and dynamically selecting a balance point through a binary logic switching strategy; the controller performs safety limitation on the attitude and angular velocity of the unmanned aerial vehicle in combination with zero-order control obstacle function constraint; monitoring a quaternion scalar component symbol in real time by defining a manifold switching set and a jump set; by fusing position loop and attitude loop control logic, compliance control during contact-type nondestructive testing of the unmanned aerial vehicle is realized.

Description

Technical Field

[0001] This invention relates to a compliant control method for aircraft performance constraints oriented towards contact-based non-destructive testing, belonging to the field of aircraft control technology. Background Technology

[0002] With the increasing aging of modern infrastructure, the demand for non-destructive testing (NDT) of large structures such as bridges and buildings is becoming increasingly urgent. Traditional manual inspection methods rely on aerial work platforms or scaffolding to achieve contact testing, which suffers from long operation cycles, high costs, and significant personnel safety risks. Unmanned aerial vehicles (UAVs), due to their high maneuverability and flexibility, offer a new solution for inspection in high-altitude, enclosed, and hazardous areas. However, when performing NDT tasks such as ultrasonic testing that require continuous sensor contact, the UAV must maintain stable contact pressure and achieve a certain level of positioning accuracy, which places high demands on the compliance, robustness, and safety of the control system. When encountering wind disturbances or sudden changes in contact force, existing control strategies lack a systematic mechanism to adaptively adjust the contact impedance, which may not only cause distortion of the ultrasonic detection signal but also induce body oscillations or even collision damage between the sensor and the inspected surface. Furthermore, traditional control architectures, such as centralized methods based on PID, sliding mode control, or nonlinear model predictive control, suffer from insufficient robustness and fail to consider the dual constraints of constant contact force required by the ultrasonic sensor and stable flight attitude during dynamic contact, which can easily lead to a decrease in force and torque adjustment accuracy due to unmodeled coupling effects. Therefore, how to construct a control architecture with active compliance characteristics and ensure the safety and reliability of implementing contact non-destructive testing has become a technical bottleneck that urgently needs to be overcome in the field of aircraft control.

[0003] Existing control technologies still face the following key technical bottlenecks in achieving precise contact operation:

[0004] (1) Unmanned aerial vehicle systems equipped with robotic arms have unmodeled dynamic coupling problems. The interaction between the inertial motion of the robotic arm and the aerodynamic characteristics of the unmanned aerial vehicle will significantly affect the accuracy of contact force adjustment, and the computational complexity of real-time dynamic interaction increases exponentially with the increase of the robotic arm's degrees of freedom.

[0005] (2) Although attitude control based on quaternions can avoid singularities, it is prone to attitude unwinding phenomenon (UP) when performing large-angle maneuvers. When the initial error quaternion scalar component has the opposite sign to the equilibrium point, it will lead to unnecessary rotational motion, resulting in energy loss and prolonging operation time.

[0006] (3) Existing safety barrier controls mostly employ first-order control barrier functions (CBFs), which have limited adaptability to safety conditions. While higher-order control barrier functions can expand the dimensions of safety constraints, their computational load and parameter sensitivity are difficult to meet the requirements of resource-constrained platforms. Furthermore, existing methods lack a systematic safety enforcement mechanism, making it difficult to effectively prevent structural overload during dynamic interactions. Summary of the Invention

[0007] To address the robustness and safety issues encountered in contact nondestructive testing (NDT) of unmanned aerial vehicles (UAVs), this invention provides a performance-constrained compliance control method for UAVs in contact NDT. This method utilizes a two-layer cascaded control approach to achieve precise control of contact force and contact torque, and dynamic assurance of safety margins. This invention offers comprehensive advantages in dynamic adaptability, effective safety constraints, and energy consumption optimization for contact NDT of UAVs, preventing surface damage caused by sudden contact during testing and ensuring the safety of both the tested object and the UAV.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] This invention discloses a performance-constrained compliant control method for aircraft in contact-based nondestructive testing. A saturated contact force controller is introduced into the position loop. Based on the position error, the confidence factor is dynamically adjusted to adaptively regulate the normal stiffness and tangential compliance. Contact force feedback signals are acquired in real time through an onboard force sensor. A zero-order control barrier function (ZOCBF) constrains this force controller. A three-dimensional dynamic safety boundary is established using a sampling data mechanism. Without relying on continuous derivative calculations, quadratic programming is used to optimize and limit the position, velocity, and contact force of the unmanned aerial vehicle (UAV), ensuring that the UAV remains within a preset safety threshold during contact tasks. A hybrid torque controller is designed in the attitude loop. To address the backtracking phenomenon in attitude control, a binary logic switching strategy dynamically selects the equilibrium point. The controller, combined with the zero-order control barrier function constraint, safely limits the attitude and angular velocity of the UAV. By defining manifold switching sets and jump sets, the quaternion scalar component signs are monitored in real time, and the equilibrium point is switched when necessary to eliminate redundant rotations and reduce energy consumption. By fusing the control logic of the position loop and attitude loop, compliant control of the UAV during contact-based nondestructive testing is achieved. Therefore, this invention has comprehensive advantages in dynamic adaptability, effective safety constraints and energy consumption optimization in contact non-destructive testing of unmanned aerial vehicles, preventing surface damage caused by sudden contact during the testing process and ensuring the safety of the tested object and the unmanned aerial vehicle body.

[0010] This invention discloses a performance constraint compliance control method for aircraft oriented towards contact-based nondestructive testing, comprising the following steps:

[0011] Step 1: Construct a global coordinate system and a quaternion rotation matrix mapping to achieve precise attitude mapping between the two systems, which will be used for position loop and attitude loop control in subsequent steps.

[0012] Based on the dual definitions of the global coordinate system G and the body coordinate system B, a kinematic model of the center of mass of the unmanned aerial vehicle (UAV) is constructed. The position vector of the UAV's center of mass in the global coordinate system is defined as p = [p x ,p y ,p z ] T The position vector in the body coordinate system is Rotational transformations between two coordinate systems are performed using unit quaternions. Realize, where σ is the quaternion scalar part, This is the vector part. The rotation matrix R(Q) based on this quaternion representation is specifically expanded as follows:

[0013] R(Q)=(σ 2 -q T q)I3+2qq T +2σq × ,

[0014] In the formula q × The rotation matrix is ​​a skew-symmetric matrix constructed from vector q, which is used to convert quaternions into rotation operations in three-dimensional space. The rotation matrix describes the attitude mapping from the body coordinate system B to the global coordinate system G, and is used for subsequent position control and attitude decoupling.

[0015] Step 2: Establish kinematic and dynamic models of the unmanned aerial vehicle's position and position error to achieve high-precision position tracking and dynamic compensation.

[0016] The position model of the unmanned aerial vehicle is

[0017]

[0018] in Let be the velocity vector of the unmanned aerial vehicle, g be the acceleration due to gravity, and e3 = [0, 0, 1]. T It is a unit vector in the vertical direction. This represents the thrust scalar in the body coordinate system, where m is the mass of the unmanned aerial vehicle. The force disturbance is unknown but bounded. The position tracking error and velocity tracking error are defined as follows: and p d Given the desired trajectory position, the position error model is derived as follows:

[0019]

[0020] In the formula, u = F B R(Q d )e3 / m=[u x ,u y ,u z ] T Q is the output vector of the force controller. d Let R(Q) be the desired attitude quaternion. The attitude convergence is achieved when R(Q) → R(Q) d And the thrust satisfies At that time, the disturbance term F B (R(Q)-R(Q d e3 / m approaches zero. The thrust constraint relationship satisfies F B =m||u|| and the rotation matrix property ||R(Q) d e3||=1.

[0021] Step 3: Construct a composite error variable and an auxiliary dynamic system using a saturation force control strategy to achieve disturbance estimation and position closed-loop control.

[0022] Based on the dynamic disturbance estimation method, an auxiliary observation system is constructed to compensate for unmodeled force disturbances. A composite error variable is defined. where k p =diag(k) px ,k py ,k pz Let be the diagonal matrix of the position error gain. Construct two auxiliary dynamic systems.

[0023]

[0024] The initial conditions are χ1(0) = 0 and χ2(0) = 0, where η x >0 represents the filtering parameter. By applying a low-pass filter η... x / (χ+η x )operate

[0025]

[0026] Derive the expression for the perturbation estimator

[0027]

[0028] Constructing a saturation force controller

[0029]

[0030] In the formula k ξ =diag(k) ξx ,k ξy ,k ξz) is the robust gain matrix, and the tanh(·) function is used to smooth control commands and avoid high-frequency chattering; As a saturation function, the disturbance estimate is limited to a preset threshold. Internally, to prevent overshoot. The closed-loop position subsystem is...

[0031]

[0032] in This represents the disturbance estimation residual. This design, by fusing dynamic estimation and nonlinear damping terms, improves the robustness of the closed-loop position subsystem to external disturbances while ensuring contact force tracking accuracy.

[0033] Step 4: Establish a three-dimensional position-velocity-force safety constraint based on the zero-order barrier function, and use quadratic programming to design a conical corridor, velocity barrier and contact force smooth control to ensure the stability and safety of the position loop.

[0034] To ensure the motion safety of the unmanned aerial vehicle (UAV) during contact operations, multidimensional safety constraints are designed based on a zero-order control barrier function. An end effector position model is established: a two-degree-of-freedom force-sensing robotic arm is installed below the UAV's center of mass. The fixed offset of the end effector position relative to the UAV's center of mass is the robotic arm length d. c Construct the constraint function for the cone-shaped safety corridor.

[0035]

[0036] In the formula, r and h represent the radial width and axial height parameters of the safety corridor, respectively. A velocity barrier function is also designed.

[0037] h v =v max (1-exp(-κ p ||p d -p‖))-v,

[0038] The maximum tracking speed is dynamically limited by an exponential decay function, where κ p The attenuation coefficient is introduced. A confidence factor Λ is introduced to achieve smooth transition adjustment of the contact force. The confidence factor is determined by two key factors, the first of which is...

[0039]

[0040] Among them, Λ d The contact distance between the force sensor carried at the end of the unmanned aerial vehicle's robotic arm and the surface being measured is related to d. t d represents the displacement of the force sensor. min and d max It depends on the range of the force sensor itself; the second key factor is

[0041]

[0042] Among them, Λ d Related to the positional error of the unmanned aerial vehicle. Based on the end position error in the reference contact force direction F r The projection dynamic calculation is performed using a coefficient of c. Λ The first-order filter provides a smooth transition to avoid step inputs at the beginning or end of non-zero expectation forces. The expression for this filter in the discretized state at time step k is:

[0043]

[0044] Wherein, coefficient 0 <c Λ <1. Apply the confidence factor to the contact force control loop, treating it as an external disturbance, and modify the force control command to u = [u x ,u y -ΛF r ,u z [and restrict it to a maximum constraint force of F] max and minimum contact force F min Apply contact force amplitude constraints between them.

[0045]

[0046] Based on the zero-order control barrier function theory, a safe set is defined. By predicting the barrier function value at the next time step using a sampling data mechanism, a quadratic programming problem with robust terms is constructed.

[0047]

[0048] Where γ * ∈(0,1) are the coefficients of the Class-K function. For robust parameters, it is ensured that the system state does not violate the safety boundary within the sampling period T. The position loop input is obtained by discretizing the prediction to avoid the calculation of continuous derivatives, thereby reducing the real-time calculation load and ensuring the coordinated safety limit of position, velocity and contact force.

[0049] Step 5: Establish a quaternion-based kinematic and dynamic model of the unmanned aerial vehicle's attitude and attitude error to achieve high-precision attitude tracking and dynamic compensation.

[0050] An attitude model of the unmanned aerial vehicle is constructed based on quaternion representation.

[0051]

[0052] in It is a quaternion kinematic matrix. Let J be the angular velocity of the aircraft, J be the inertial matrix of the unmanned aerial vehicle, and τ = [τ x ,τ y ,τ z ] T For torque control input, ζ τ This is the torque disturbance term. The error quaternion is defined. in The reference attitude quaternion is given. The error rotation matrix is... Error angular velocity is defined as ω d Given the desired angular velocity, the attitude error model is derived as follows:

[0053]

[0054]

[0055] When posture convergence is satisfied And the angular velocity satisfies and At that time, the disturbance term Approaching zero.

[0056] Step 6: Construct a composite error variable and auxiliary dynamic system with binary logic switching using a hybrid torque control strategy to avoid attitude backtracking and achieve disturbance estimation and attitude closed-loop control.

[0057] To eliminate attitude backtracking caused by quaternion dual equilibrium points, a hybrid control strategy based on manifold switching is proposed. Binary logic variables are defined. Constructing the state space of a hybrid system And divide manifold sets and jump sets.

[0058]

[0059] In the formula To switch the threshold parameter, k q =diag(k) qx ,k qy ,k qz () is the quaternion error gain matrix. Define the composite error variable. The derivative is obtained by combining the attitude error model.

[0060]

[0061] in Given the dynamic terms, design a torque perturbation estimator. The dynamic equations of the auxiliary systems Y1 and Y2 are as follows:

[0062]

[0063] Its initial state satisfies Y1(0) = 0 and Y2(0) = 0. A hybrid torque controller is constructed.

[0064]

[0065] where k z >0 represents the damping gain, κ b To switch sensitivity parameters, the adaptive law for logical variable b is:

[0066]

[0067] In manifold set Within, the closed-loop system dynamics are

[0068]

[0069] When the state enters the skip set At that time, a binary logic switch is triggered.

[0070]

[0071] Forced Quaternion Scalar Components The sign of the rotation is consistent with the current equilibrium point, thus avoiding redundant rotation paths. By jointly designing a hybrid logic of disturbance compensation, nonlinear damping, and energy triggering, this controller ensures attitude tracking accuracy while avoiding attitude backtracking and reducing energy loss.

[0072] Step 7: Establish a quadratic programming model based on the attitude-angular velocity safety constraints of the zero-order barrier function to ensure attitude stability and safety.

[0073] To ensure the attitude safety of the unmanned aerial vehicle during contact operations, a multidimensional safety constraint based on a zero-order control barrier function is constructed. First, attitude quaternion direction constraints and angular velocity amplitude constraints are defined.

[0074] Q T M c Q≥cos(θ c ),

[0075] ω T ω≤ω max 2 ,

[0076] Where M c The matrix representing the target attitude direction, θ c For the allowable attitude deviation angle, ω max The maximum permissible angular velocity is given. To address the non-convexity problem under quaternion constraints, a convexity matrix M is introduced. Q =M c -νI4 satisfies ν>1, transforming the original constraint into a convex form.

[0077] Q T M Q Q+νI4-cos(θ c )≥0,

[0078] Define attitude safety set Ensure the UAV's attitude consistently satisfies joint constraints during dynamic interactions. Design attitude and angular velocity barrier functions.

[0079] h Q =Q T M Q Q+νI4-cos(θ c ),

[0080] h ω =ω max 2 -ω T ω.

[0081] For the torque control loop, a quadratic programming problem with robust terms is constructed by predicting the barrier function value at the next sampling time using the second-order Runge-Kutta integral.

[0082]

[0083]

[0084] Where γ * ∈(0,1) are the coefficients of the Class-K function. For robustness parameters, ensure that the system state does not violate the safety boundary within the sampling period T. A quadratic programming problem is solved using a discretized prediction mechanism to obtain the attitude control input. While avoiding continuous derivative calculations, ensure that the attitude angle deviation and angular velocity amplitude are within predetermined ranges to prevent attitude instability and structural overload during dynamic contact.

[0085] Step 8: By integrating the position loop and attitude loop control logic, compliant control is achieved during UAV contact non-destructive testing.

[0086] In the two-layer cascaded control architecture, the saturation force control command output by the position loop is organically combined with the torque control of the attitude loop to form a cooperative closed loop: the position loop dynamically adjusts the virtual stiffness and damping to generate force commands based on real-time position error and contact force sensing feedback, and projects the commands as the reference torque of the attitude loop; the attitude loop uses quaternion error feedback to correct the force distribution ratio of the position loop, and implements joint constraints on position, velocity, attitude and angular velocity through zero-order control barrier function and quadratic programming, thereby realizing compliant control during UAV contact non-destructive testing.

[0087] Beneficial effects:

[0088] 1. This invention discloses a compliant control method for aircraft performance constraints in contact-based nondestructive testing. It employs a saturated force controller and a dynamic disturbance estimator to construct a compensation mechanism for unmodeled aerodynamic coupling effects and environmental disturbances, improving robustness under complex operating conditions and effectively adapting to the compliant contact requirements of complex contact-based nondestructive testing tasks. The design of the contact force during contact incorporates confidence factors based on the contact distance and positional error between the force sensor and the measured surface, ensuring a smooth transition of the contact force within a preset safety threshold and avoiding surface damage problems caused by rigid contact in traditional methods.

[0089] 2. This invention discloses a performance-constrained compliant control method for aircraft oriented towards contact-based non-destructive testing. The hybrid torque controller avoids attitude regression through a binary logic switching strategy and an energy triggering mechanism. When the sign of the initial error quaternion scalar component is opposite to the equilibrium point, the attitude stabilization time is reduced, improving the attitude stability and structural safety of the unmanned aerial vehicle during maneuvers.

[0090] 3. This invention discloses a performance-constrained compliant control method for aircraft in contact-based nondestructive testing. Based on a unified safety framework using a zero-order control barrier function, it embeds a sampled data constraint mechanism into the position and attitude loops. Through discretization prediction and quadratic programming optimization, it dynamically limits contact force, position error, velocity, attitude, and angular velocity in multiple dimensions, ensuring that the system state remains strictly within preset safety boundaries without relying on continuous derivative calculations. This design overcomes the coupling limitations of safety constraints and tracking performance in traditional methods, providing systematic safety assurance for nondestructive testing tasks of unmanned aerial vehicles in confined spaces, high altitudes, and hazardous environments. Attached Figure Description

[0091] Figure 1 A schematic diagram for setting the coordinate system of a quadcopter unmanned aerial vehicle.

[0092] Figure 2 This is a simulation diagram of a performance-constrained compliance control method for aircraft oriented towards contact-based non-destructive testing.

[0093] Figure 3 This is a flowchart of a performance-constrained compliance control method for aircraft oriented towards contact-based non-destructive testing. Detailed Implementation

[0094] To overcome the shortcomings of existing technologies, this invention aims to propose a performance-constrained compliant control method for aircraft oriented to contact nondestructive testing, thereby optimizing and improving the control of unmanned aerial vehicles in contact nondestructive testing.

[0095] like Figure 3 As shown in the figure, this embodiment discloses a performance constraint compliance control method for aircraft oriented to contact non-destructive testing. The specific implementation steps are as follows:

[0096] Step 1: Construct a global coordinate system and a quaternion rotation matrix mapping to achieve precise attitude mapping between the two systems, which will be used for position loop and attitude loop control in subsequent steps.

[0097] Based on the dual definitions of the global coordinate system G and the body coordinate system B, a kinematic model of the UAV's center of mass is constructed. The position vector of the UAV's center of mass in the global coordinate system is defined as follows: The position vector in the body coordinate system is And let the initial position be Rotational transformations between two coordinate systems are performed using unit quaternions. Realize, where σ is the quaternion scalar part, This is the vector part. The rotation matrix R(Q) based on this quaternion representation is specifically expanded as follows:

[0098]

[0099] In the formula q × Let be a skew-symmetric matrix constructed from vector q.

[0100] Step 2: Establish kinematic and dynamic models of the unmanned aerial vehicle's position and position error to achieve high-precision position tracking and dynamic compensation.

[0101] The position model of the unmanned aerial vehicle is

[0102]

[0103] in Let be the velocity vector of the unmanned aerial vehicle, with an initial velocity of . g = 9.81 m / s 2 It is the acceleration due to gravity. It is a unit vector in the vertical direction. This represents the thrust scalar in the body coordinate system, where m = 1.0 kg is the mass of the unmanned aerial vehicle. The force disturbance is unknown but bounded. The position tracking error and velocity tracking error are defined as follows: and For the desired trajectory, the position error model is derived as follows:

[0104]

[0105] In the formula, u = F B R(Q d )e3 / m=[u x ,u y ,u z ] T Q is the output vector of the force controller. dLet R(Q) be the desired attitude quaternion. The attitude convergence is achieved when R(Q) → R(Q) d And the thrust satisfies At that time, the disturbance term F B (R(Q)-R(Q d e3 / m approaches zero. The thrust constraint relationship satisfies F B =m||u|| and the rotation matrix property ||R(Q) d e3||=1.

[0106] Step 3: Construct a composite error variable and an auxiliary dynamic system using a saturation force control strategy to achieve disturbance estimation and position closed-loop control.

[0107] Based on the dynamic disturbance estimation method, an auxiliary observation system is constructed to compensate for unmodeled force disturbances. A composite error variable is defined. where k p =diag(k) px ,k py ,k pz Let [3.4, 3.4, 3.4] be the diagonal matrix of position error gain. Construct two auxiliary dynamic systems.

[0108]

[0109] The initial conditions are χ1(0) = 0 and χ2(0) = 0, where η x =0.2 is the filtering parameter. By applying a low-pass filter η... x / (χ+η x )operate

[0110]

[0111] Derive the expression for the perturbation estimator

[0112]

[0113] Constructing a saturation force controller

[0114]

[0115] In the formula k ξ =diag(k) ξx ,k ξy ,k ξz = [2.4, 2.4, 2.4] is the robust gain matrix, and the tanh(·) function is used to smooth control commands; It is a saturation function. The closed-loop position subsystem is

[0116]

[0117] in This represents the residual from the disturbance estimation.

[0118] Step 4: Establish a three-dimensional position-velocity-force safety constraint based on the zero-order barrier function, and use quadratic programming to design a conical corridor, velocity barrier and contact force smooth control to ensure the stability and safety of the position loop.

[0119] To ensure the motion safety of the unmanned aerial vehicle (UAV) during contact operations, multidimensional safety constraints are designed based on a zero-order control barrier function. An end effector position model is established: a two-degree-of-freedom force-sensing robotic arm is installed below the UAV's center of mass. The fixed offset of the end effector position relative to the UAV's center of mass is the robotic arm length d. c =0.2m. Construct the constraint function for the cone-shaped safety corridor.

[0120]

[0121] In the formula, r = 4.239 and h = 1.36 represent the radial width and axial height parameters of the safety corridor, respectively. A velocity barrier function is also designed.

[0122] h v =v max (1-exp(-κ p ||p d -p‖))-v,

[0123] The maximum tracking speed is dynamically limited by an exponential decay function, where κ p =0.8 is the attenuation coefficient, v max =5.0. A confidence factor Λ is introduced to achieve smooth transition adjustment of the contact force. This confidence factor is determined by two key factors, the first of which is...

[0124]

[0125] Among them, Λ d The contact distance between the force sensor carried at the end of the unmanned aerial vehicle's robotic arm and the surface being measured is related to d. t The displacement of the force sensor is represented by d. min =0.002, d max =0.01 depends on the force sensor's own measurement range; the second key factor is

[0126]

[0127] Among them, Λ d Related to the positional error of the unmanned aerial vehicle. Based on the end position error in the reference contact force direction F r The projection dynamic calculation, where F r =4.0N, Through coefficient c Λ The first-order filter provides a smooth transition to avoid step inputs at the beginning or end of non-zero expectation forces. The expression for this filter in the discretized state at time step k is:

[0128]

[0129] Wherein, coefficient c Λ =0.2. Applying the confidence factor to the contact force control loop, treating it as an external disturbance, the corrected force control command is u = [u x ,u y -ΛF r ,u z [and restrict it to a maximum constraint force of F] max =5.0N and minimum contact force F min Apply contact force amplitude constraints between 3.0N and 3.0N.

[0130]

[0131] Based on the zero-order control barrier function theory, a safe set is defined. By predicting the barrier function value at the next time step using a sampling data mechanism, a quadratic programming problem with robust terms is constructed.

[0132]

[0133] Where γ * =0.9 is the Class-K function coefficient, and δ=0.5 is the robustness parameter, ensuring that the system state does not violate the safety boundary within the sampling period T=0.005.

[0134] Step 5: Establish a quaternion-based kinematic and dynamic model of the unmanned aerial vehicle's attitude and attitude error to achieve high-precision attitude tracking and dynamic compensation.

[0135] An attitude model of the unmanned aerial vehicle is constructed based on quaternion representation.

[0136]

[0137] in It is a quaternion kinematic matrix. Let J = [0.02, 0.02, 0.04] be the angular velocity of the aircraft, and τ = [τ_0, ... x ,τ y ,τ z ] T For torque control input, ζ τ This is the torque disturbance term. The error quaternion is defined. in The reference attitude quaternion is given. The error rotation matrix is... Error angular velocity is defined as ω d To determine the desired angular velocity, derive the attitude error equation.

[0138]

[0139] When posture convergence is satisfied And the angular velocity satisfies and At that time, the disturbance term Approaching zero.

[0140] Step 6: Construct a composite error variable and auxiliary dynamic system with binary logic switching using a hybrid torque control strategy to avoid attitude backtracking and achieve disturbance estimation and attitude closed-loop control.

[0141] To eliminate attitude backtracking caused by quaternion dual equilibrium points, a hybrid control strategy based on manifold switching is proposed. Binary logic variables are defined. Constructing the state space of a hybrid system And divide manifold sets and jump sets.

[0142]

[0143] In the formula To switch the threshold parameter, k q =diag(k) qx ,k qy ,k qz Let [2.8, 2.8, 2.8] be the quaternion error gain matrix. Define the composite error variable. The derivative is obtained by combining the attitude error model.

[0144]

[0145] in Given the dynamic terms, design a torque perturbation estimator. The dynamic equations of the auxiliary systems Y1 and Y2 are as follows:

[0146]

[0147] Its initial state satisfies Υ1(0) = 0 and Υ2(0) = 0. Based on this, a hybrid torque controller is constructed.

[0148]

[0149] Where k z =3.8 is the damping gain, κ b =0.01 is the switching sensitivity parameter. The adaptive law of the logic variable b is:

[0150]

[0151] In manifold set Within, the closed-loop system dynamics are

[0152]

[0153] When the state enters the skip set At that time, a binary logic switch is triggered.

[0154]

[0155] Forced Quaternion Scalar Components The sign of the rotation is consistent with the current equilibrium point, thus avoiding redundant rotation paths. By jointly designing a hybrid logic of disturbance compensation, nonlinear damping, and energy triggering, this controller avoids backtracking and reduces energy loss while ensuring attitude tracking accuracy.

[0156] Step 7: Establish a quadratic programming model based on the attitude-angular velocity safety constraints of the zero-order barrier function to ensure attitude stability and safety.

[0157] To ensure the attitude safety of the unmanned aerial vehicle during contact operations, a multidimensional safety constraint based on a zero-order control barrier function is constructed. First, attitude quaternion direction constraints and angular velocity amplitude constraints are defined.

[0158] Q T M c Q≥cos(θ c ),

[0159]

[0160] Where M c The matrix representing the target attitude direction, θ c =30° is the allowable attitude deviation angle, ω max =1 rad / s is the maximum permissible angular velocity. To address the non-convexity problem of quaternion constraints, a convexity matrix M is introduced. Q =M c -νI4 satisfies ν>1, transforming the original constraint into a convex form.

[0161] Q T M Q Q+νI4-cos(θ c )≥0,

[0162] Based on this definition, the attitude safety set Ensure the system state consistently satisfies joint constraints during dynamic interactions. Design attitude and angular velocity barrier functions.

[0163] hQ =Q T M Q Q+νI4-cos(θ c ),

[0164]

[0165] For the torque control loop, a quadratic programming problem with robust terms is constructed by predicting the barrier function value at the next sampling time using the second-order Runge-Kutta integral.

[0166]

[0167] Where γ * =0.9 represents the Class-K function coefficients, and δ=0.5 represents the robustness parameter, ensuring that the system state does not violate the safety boundary within the sampling period T=0.005. This design, through a discretization prediction mechanism, avoids continuous derivative calculations while ensuring that attitude angle deviations and angular velocity amplitudes are limited to a certain range, effectively preventing attitude instability and structural overload during dynamic contact.

[0168] Step 8: By integrating the position loop and attitude loop control logic, compliant control is achieved during UAV contact non-destructive testing.

[0169] In the two-layer cascaded control architecture, the saturation force control command output by the position loop is organically combined with the torque control of the attitude loop to form a cooperative closed loop: the position loop dynamically adjusts the virtual stiffness and damping to generate force commands based on real-time position error and contact force sensing feedback, and projects the commands as the reference torque of the attitude loop; the attitude loop uses quaternion error feedback to correct the force distribution ratio of the position loop, and implements joint constraints on position, velocity, attitude and angular velocity through zero-order control barrier function and quadratic programming, thereby realizing compliant control during UAV contact non-destructive testing.

Claims

1. A performance-constrained compliance control method for aircraft oriented to contact-based nondestructive testing, characterized in that: A saturated contact force controller is introduced into the position loop. Based on the position error, the confidence factor is dynamically adjusted to adaptively adjust the normal stiffness and tangential compliance. The contact force feedback signal is obtained in real time through the airborne force sensor. The zero-order control barrier function (ZOCBF) constrains the force controller, establishing a three-dimensional dynamic safety boundary using a sampling data mechanism. Without relying on continuous derivative calculations, quadratic programming optimizes and limits the UAV's position, velocity, and contact force, ensuring the UAV remains within a preset safety threshold during contact tasks. A hybrid torque controller is designed in the attitude loop to dynamically select the equilibrium point using a binary logic switching strategy to address backtracking issues in attitude control. The controller, combined with the zero-order control barrier function constraint, safely limits the UAV's attitude and angular velocity. By defining manifold switching and jump sets, the quaternion scalar component signs are monitored in real time, and the equilibrium point is switched when necessary to eliminate redundant rotations and reduce energy consumption. By fusing the position and attitude loop control logic, compliant control is achieved for UAV contact-based non-destructive testing.

2. The aircraft performance constraint compliance control method for contact-based nondestructive testing as described in claim 1, characterized in that: Includes the following steps: Step 1: Construct a global coordinate system and a quaternion rotation matrix mapping to achieve accurate attitude mapping between the two systems, which will be used for position loop and attitude loop control in subsequent steps; Step 2: Establish kinematic and dynamic models of the unmanned aerial vehicle's position and position error to achieve high-precision position tracking and dynamic compensation; Step 3: Construct a composite error variable and auxiliary dynamic system using a saturation force control strategy to achieve disturbance estimation and position closed-loop control; Step 4: Establish a three-dimensional position-velocity-force safety constraint based on the zero-order barrier function, and use quadratic programming to design a conical corridor, velocity barrier and contact force smooth control to ensure the stability and safety of the position loop; Step 5: Establish a quaternion-based kinematic and dynamic model of the unmanned aerial vehicle's attitude and attitude error to achieve high-precision attitude tracking and dynamic compensation; Step 6: Construct a composite error variable and auxiliary dynamic system with binary logic switching using a hybrid torque control strategy to avoid attitude backtracking and achieve disturbance estimation and attitude closed-loop control. Step 7: Establish a quadratic programming model based on the attitude-angular velocity safety constraints of the zero-order barrier function to ensure attitude stability and safety; Step 8: By integrating the position loop and attitude loop control logic, compliant control is achieved during UAV contact non-destructive testing.

3. The aircraft performance constraint compliance control method for contact-based nondestructive testing as described in claim 2, characterized in that: The implementation method for step one is as follows: Based on the dual definition of global coordinate system G and body coordinate system B, a kinematic model of the center of mass of the unmanned aerial vehicle is constructed. The position vector of the center of mass of an unmanned aerial vehicle in the global coordinate system is defined as follows: The position vector in the body coordinate system is Rotational transformations between two coordinate systems are performed using unit quaternions. Implementation, where σ is the quaternion scalar part. For the vector part; the rotation matrix R(Q) based on this quaternion representation is specifically expanded as follows: In the formula q × The skew-symmetric matrix is ​​constructed from the vector q. Its function is to convert quaternions into three-dimensional rotation operations. This rotation matrix is ​​used to describe the attitude mapping relationship from the body coordinate system B to the global coordinate system G, and is used for subsequent position control and attitude decoupling.

4. The aircraft performance constraint compliance control method for contact-based nondestructive testing as described in claim 3, characterized in that: In step two, The position model of the unmanned aerial vehicle is in Let g be the velocity vector of the unmanned aerial vehicle, and g be the acceleration due to gravity. It is a unit vector in the vertical direction. This represents the thrust scalar in the body coordinate system, where m is the mass of the unmanned aerial vehicle. For unknown but bounded force disturbances; define position tracking error and velocity tracking error as follows: and p d Given the desired trajectory position, the position error model is derived as follows: In the formula Q is the output vector of the force controller. d Let R(Q) be the desired attitude quaternion; when the attitude converges, R(Q) → R(Q) d And the thrust satisfies At that time, the disturbance term F B (R(Q)-R(Q d ))e3 / m approaches zero.

5. The aircraft performance constraint compliance control method for contact-based nondestructive testing as described in claim 4, characterized in that: The method for implementing step three is as follows: Based on the dynamic disturbance estimation method, an auxiliary observation system is constructed to compensate for unmodeled force disturbances; a composite error variable is defined. Where k p =diag(k) px ,k py ,k pz Let be the diagonal matrix of position error gain; construct two auxiliary dynamic systems. The initial conditions are χ1(0) = 0 and χ2(0) = 0, where η x >0 represents the filtering parameter; a low-pass filter η is applied to the nominal error dynamic equation. x / (χ+η x )operate Derive the expression for the perturbation estimator Constructing a saturation force controller In the formula k ξ =diag(k) ξx ,k ξy ,k ξz ) is the robust gain matrix, and the tanh(·) function is used to smooth control commands and avoid high-frequency chattering; As a saturation function, the disturbance estimate is limited to a preset threshold. Internally to prevent overshoot; the closed-loop position subsystem is in This represents the disturbance estimation residual; by integrating dynamic estimation and nonlinear damping terms, this design improves the robustness of the closed-loop position subsystem to external disturbances while ensuring the accuracy of contact force tracking.

6. The aircraft performance constraint compliance control method for contact-based nondestructive testing as described in claim 5, characterized in that: Step four is implemented as follows: To ensure the motion safety of the unmanned aerial vehicle (UAV) during contact operations, multidimensional safety constraints are designed based on a zero-order control barrier function. An end effector position model is established: a two-degree-of-freedom force-sensing robotic arm is installed below the UAV's center of mass, with the end effector's position fixedly offset from the UAV's center of mass by the robotic arm length d. c Construct the constraint function for the cone-shaped safety corridor. In the formula, r and h represent the radial width and axial height parameters of the safety corridor, respectively; a velocity barrier function is also designed. h v =in max (1-exp(-κ p ‖p d -p‖))-v, The maximum tracking speed is dynamically limited by an exponential decay function, where κ p The attenuation coefficient is used; a confidence factor Λ is introduced to achieve smooth transition adjustment of the contact force. This confidence factor is determined by two key factors, the first of which is... Among them, Λ d The contact distance between the force sensor carried at the end of the unmanned aerial vehicle's robotic arm and the surface being measured is related to d. t d represents the displacement of the force sensor. min and d max It depends on the range of the force sensor itself; the second key factor is Among them, Λ d Related to the positional error of the unmanned aerial vehicle. Based on the end position error in the reference contact force direction F r The projection is dynamically calculated; this value is obtained through a coefficient of c. Λ The first-order filter provides a smooth transition to avoid step inputs at the beginning or end of non-zero expectation forces; the expression for the discretized state at time step k is... Where, coefficient 0 < c Λ <1; Apply the confidence factor to the contact force control loop, treating it as an external disturbance, and correct the force control command to u = [u x ,u y -ΛF r ,u z [and restrict it to a maximum constraint force of F] max and minimum contact force F min Apply contact force amplitude constraints between them. Based on the zero-order control barrier function theory, a safe set is defined. By predicting the barrier function value at the next time step using a sampling data mechanism, a quadratic programming problem with robust terms is constructed. Where γ * ∈(0,1) are the coefficients of the Class-K function. As a robust parameter, it ensures that the system state does not violate the safety boundary within the sampling period T; the position loop input is obtained by discretization prediction to avoid continuous derivative calculation, thereby reducing the real-time calculation load, while ensuring the coordinated safety limit of position, velocity and contact force.

7. The aircraft performance constraint compliance control method for contact-based nondestructive testing as described in claim 6, characterized in that: In step five, An attitude model of the unmanned aerial vehicle is constructed based on quaternion representation. in It is a quaternion kinematic matrix. Let J be the angular velocity of the aircraft and J be the inertial matrix of the unmanned aerial vehicle. For torque control input, ζ τ For torque disturbance terms; define error quaternions. in The reference attitude quaternion is; the error rotation matrix is... Error angular velocity is defined as ω d Given the desired angular velocity, the attitude error model is derived as follows: When posture convergence is satisfied And the angular velocity satisfies and At that time, the disturbance term Approaching zero.

8. The aircraft performance constraint compliance control method for contact-based nondestructive testing as described in claim 7, characterized in that: Step six is ​​implemented as follows: To eliminate the attitude regression phenomenon caused by quaternion double equilibrium points, a hybrid control strategy based on manifold switching is proposed; binary logic variables are defined. Constructing the state space of a hybrid system And divide manifold sets and jump sets. In the formula To switch the threshold parameter, k q =diag(k) qx ,k qy ,k qz Let ω be the quaternion error gain matrix; define the composite error variable z = ω + k q bq, the derivative is obtained by combining the attitude error model. in Given the dynamic terms, design a torque disturbance estimator. The dynamic equations of the auxiliary systems Y1 and Y2 are as follows: Its initial state satisfies Y1(0)=0 and Y2(0)=0; construct a hybrid torque controller. Where k z >0 represents the damping gain, κ b To switch sensitivity parameters; the adaptive law for logic variable b is: In manifold set Within, the closed-loop system dynamics are When the state enters the skip set At that time, a binary logic switch is triggered. Forced Quaternion Scalar Components The sign of the rotation is consistent with the current equilibrium point, thus avoiding redundant rotation paths. By jointly designing a hybrid logic of disturbance compensation, nonlinear damping and energy triggering, the controller can ensure attitude tracking accuracy while avoiding attitude backtracking and reducing energy loss.

9. The aircraft performance constraint compliance control method for contact-based nondestructive testing as described in claim 8, characterized in that: Step seven is implemented as follows: To ensure the attitude safety of unmanned aerial vehicles during contact operations, a multidimensional safety constraint based on a zero-order control barrier function is constructed. First, attitude quaternion direction constraints and angular velocity amplitude constraints are defined. Where M c The matrix representing the target attitude direction, θ c For the allowable attitude deviation angle, ω max To determine the maximum permissible angular velocity, and to address the non-convexity issue caused by quaternion constraints, a convexity matrix M is introduced. Q =M c -νI4 satisfies ν>1, transforming the original constraint into a convex form. Define attitude safety set Ensure that the UAV attitude always satisfies joint constraints during dynamic interactions; design attitude and angular velocity barrier functions. For the torque control loop, a quadratic programming problem with robust terms is constructed by predicting the barrier function value at the next sampling time using the second-order Runge-Kutta integral. Where γ * ∈(0,1) are the coefficients of the Class-K function. As robust parameters, it ensures that the system state does not violate the safety boundary within the sampling period T; the attitude control input is obtained by solving the quadratic programming problem through a discretization prediction mechanism; while avoiding the calculation of continuous derivatives, it ensures that the attitude angle deviation and angular velocity amplitude are within the predetermined range to prevent attitude instability and structural overload during dynamic contact.

10. The aircraft performance constraint compliance control method for contact-based nondestructive testing as described in claim 9, characterized in that: Step eight is implemented as follows: In the two-layer cascaded control architecture, the saturation force control command output by the position loop is organically combined with the torque control of the attitude loop to form a cooperative closed loop: the position loop dynamically adjusts the virtual stiffness and damping force command based on the real-time position error and contact force sensing feedback, and projects the command as the reference torque of the attitude loop. The attitude loop uses quaternion error feedback to correct the force distribution ratio of the position loop, and implements joint constraints on position, velocity, attitude and angular velocity through zero-order control barrier function and quadratic programming, thereby achieving compliant control during UAV contact non-destructive testing.

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