A fault-tolerant control method for mobile robot coupler failure

Abstract

This invention discloses a fault-tolerant control method for coupled actuator failures in mobile robots, belonging to the field of nonholonomic mobile robot control technology. It includes: establishing an actuator coupling failure model for nonholonomic mobile robots that better reflects actual production conditions; cleverly solving the controllability problem caused by actuator coupling failures in nonholonomic robots by introducing the Proj function to handle unknown actuator failure coefficients; and designing a filter system suitable for nonholonomic mobile robot systems when speed is unmeasurable, avoiding the use of high-precision sensors. This invention improves the robustness of the mobile robot system while reducing its hardware costs.

Description

Technical Field

[0001] This invention relates to the field of nonholonomic mobile robot control technology, and in particular to a fault-tolerant control method for mobile robot coupled actuator failure. Background Technology

[0002] Nonholonomic mobile robots are a common type of robot. These robots rely on the differential speed of their left and right wheels for steering. This means that in actual control, controllers for both wheels need to be designed simultaneously to track the target trajectory. When the transmission systems of both wheels experience varying degrees of wear, leading to power failures in the actuators on both sides, ignoring these failures can result in reduced control accuracy or even accidents. Therefore, researching the control problem of nonholonomic robot systems with actuator coupling failures is of great significance.

[0003] Nonholonomic mobile robots have broad application prospects in space exploration, environmental monitoring, and other fields, thus attracting increasing attention from scholars both domestically and internationally. Currently, coupled actuator faults exist in mobile robot system research, particularly in areas such as trajectory tracking and multi-robot formation. A review of publicly available information and other literature on mobile robot control reveals that when addressing coupled actuator problems in nonholonomic mobile robots, linear transformations are used to decouple the left and right wheel controllers before designing the decoupled controllers. However, when coupled actuator faults are considered, the existence of unknown fault parameters prevents the decoupling of the left and right wheel controllers, rendering previous mobile robot control schemes inapplicable. In fact, coupled actuator faults are a relatively unstudied type of fault, making related reports scarce in publicly available information and literature. Furthermore, in practical robot control, speed information is frequently used in controller design; however, high-precision speed sensors are expensive, and errors in these sensors can reduce control accuracy. Additionally, the requirement for complete knowledge of the controller in speed observer design makes general speed observers difficult to apply to systems with actuator errors.

[0004] Therefore, this invention aims to provide a definition of actuator coupling failure for nonholonomic mobile robots. Considering the cost and accuracy of speed sensors, a filter reconstruction system based on position information is designed, thereby providing a fault-tolerant control method for coupled actuator failure in mobile robots, filling the gap in research on coupled actuator failure in nonholonomic mobile robots. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a fault-tolerant control method for the failure of the coupled actuator of a mobile robot, which improves the robustness of the mobile robot system and reduces the hardware cost of the system.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A fault-tolerant control method for the failure of a mobile robot's coupled actuator includes the following steps:

[0008] S1. The computer collects the physical parameters of the robot system, and based on dynamics and kinematics analysis, considering the failure coupling of the left and right wheel actuators and the influence of ground slope, establishes a nonlinear system model of the mobile robot.

[0009] S2. Introduce the transformation of the center point of the mobile robot, redefine the nonholonomic mobile robot system model, and design the control target of the nonholonomic mobile robot.

[0010] S3. Combine filter design to reconstruct the robot system model;

[0011] S4. Combine the Proj function to handle the controllability issues caused by coupled executors;

[0012] S5. Based on the Lyapunov stability criterion, and combined with filter design, reconstruct the robot system model, and give the controller and parameter adaptive law to realize the controller design of the robot system.

[0013] A further improvement to the technical solution of this invention lies in: In S1, the nonlinear system model of the mobile robot is established as follows:

[0014]

[0015] In the formula, (x,y),θ,v,ω represent the position, velocity, angle, and angular velocity of the mobile robot, respectively; k is the drive gain coefficient; and u... l ,u r To control the actuator torque of the left and right wheels separately, the physical parameters a1, a2, b1, b2, and c in the nonlinear system of the mobile robot are defined as follows:

[0016]

[0017] Where M represents the mass of the robot, r represents the wheel radius, and I ω I represents the moment of inertia of a wheel. v Let represent the moment of inertia about the center of gravity, l represent the distance from the center to the side of the robot, f be the coefficient of viscous friction, g represent the acceleration due to gravity, and φ be the angle between the robot's plane and the horizontal plane. The dual-actuator coupling fault modeling is as follows:

[0018]

[0019] in, and It is an unknown positive constant used to represent the wear coefficient of the transmission component; Represents a digital controller.

[0020] A further improvement to the technical solution of the present invention is that, according to the incomplete mobile robot system described in S1, S2 specifically includes the following steps:

[0021] Introduce a distance constant between the center of gravity of the mobile robot and the axle of the drive wheel. Perform a change in the center point of the mobile robot:

[0022]

[0023] Then equation (1) can be rewritten as:

[0024]

[0025] Where η = [vw] T Indicates speed signal, To represent the effect of slope, R = diag{a1, a2}, B = diag{kb1, kb2} It is the system matrix after the state transformation. Indicates a coupled fault controller;

[0026] Define the nonholonomic mobile robot target trajectory as

[0027] A further improvement to the technical solution of the present invention lies in: designing a corresponding filter to reconstruct the system state based on the incomplete mobile robot system described in step S2, wherein step S3 specifically includes the following steps:

[0028] S31. For the nonholonomic mobile robot system redefined in S2, in order to achieve output feedback, the following nonlinear filter is constructed to reconstruct the system state:

[0029]

[0030] Where p represents the robot's current position; ξ = [ξ1,...,ξ4] T ψ = [ψ1, ..., ψ4] T , These are the state variables of the filter. The state matrices A, Q, C, F, and U in the filter are defined as follows:

[0031]

[0032]

[0033] Gain matrices Q1, Q2 ∈ R 2×2 The selection criteria are as follows:

[0034]

[0035] Among them, P1 and P2 are positive definite diagonal matrices used in auxiliary gain design, and δ1 > 0 is any positive constant;

[0036] Using equation (3), the reconstructed position and velocity signals are defined as follows:

[0037]

[0038] in, Represents the coupling fault coefficient; here The reconstructed velocity and position information are presented, and further, the reconstructed incomplete mobile robot system is given:

[0039]

[0040] in, It is the system matrix of equation (6);

[0041] S32. To ensure that the reconstructed system can accurately compensate for the unknown velocity signal, the compensation error is defined as follows:

[0042]

[0043] A further improvement to the technical solution of the present invention is that S4 specifically includes the following steps:

[0044] First, consider the following coupling relationship in the controller:

[0045]

[0046] Where u1(t) and u2(t) represent the controllers to be solved, and f1(t), f2(t), g1(t), and g2(t) represent time-varying functions that will be defined later. The above system of equations has a unique solution if and only if f1f2≠-1.

[0047]

[0048] Use the Proj function to restrict the values ​​of f1(t) and f2(t):

[0049]

[0050] definition x * ∈Ω x Let x be the domain of x; for the first-order differential equation x = Proj(x,y), the following properties hold:

[0051] 1) If x(0)∈Ωx Then x(t)∈Ω x ;

[0052] 2) ||Proj(x,y)||≤||y||;

[0053] 3)-(x * -x)Proj(x,y)≤-(x * -x)y.

[0054] A further improvement to the technical solution of this invention lies in: designing and reconstructing the robot system based on S3 combined with a filter, designing the final output feedback fault-tolerant controller, and providing the adaptive rate. S5 specifically includes the following steps:

[0055] S51: Adaptive output feedback controller design achieved through Lyapunov stability criterion;

[0056] First, define the Lyapunov function as follows:

[0057]

[0058] In the formula For system parameters, These represent the designable adaptive gain, The corresponding adaptive errors, tracking errors z1 and z2, are defined as follows:

[0059]

[0060] Further differentiate (10):

[0061]

[0062] Differentiate the Lyapunov function (9) and find the virtual controller that makes the Lyapunov function V1(t) approach zero as t approaches infinity. for:

[0063]

[0064] To ensure system controllability, the Porj function described in S4 is used to give the following failure coefficients. Adaptive rate:

[0065]

[0066] S52: To ensure z i,2 Convergence, define the second Lyapunov function:

[0067]

[0068] in, Let V2 represent the error between the virtual controller and the actual controller. Differentiating the Lyapunov function, we find the controller that makes V2 approach zero as t approaches infinity:

[0069]

[0070] In formula (15) The adaptive rate is defined as follows:

[0071]

[0072] The adaptive parameter τ in the above equation l1 ,τ r1 ,τ c1 ,τ l2 ,τ r2 ,τ c2 The definition is as follows:

[0073]

[0074] To solve for the controller in equation (15), firstly, according to the definition of S4... The condition for obtaining a unique solution to the equation given in S4 is used to define an adaptive rate through the Proj function. Therefore, we obtain f1 > 0 and f2 > 0. At this point, the system of equations has a unique solution, and the controllability of the system is guaranteed. Further, we define the intermediate variables g1 and g2 of the equations as follows:

[0075]

[0076]

[0077] The final controller is given based on the form of the solution described in S4:

[0078]

[0079] The technological advancements achieved by this invention due to the adoption of the above technical solutions are as follows:

[0080] This invention solves the controllability problem caused by coupling faults in nonholonomic robot actuators. Through theoretical analysis, a fault-tolerant control framework for nonholonomic mobile robots is established. At the same time, virtual filter technology is introduced to replace high-precision speed sensors, reducing hardware costs and providing a high-precision fault-tolerant control scheme for nonholonomic mobile robot control. Attached Figure Description

[0081] Figure 1 This is a schematic diagram of the trajectory tracking of a non-holoscopic mobile robot in this invention;

[0082] Figure 2 This is a flowchart illustrating the design of the output feedback fault-tolerant control in this invention.

[0083] Figure 3 This is a control block diagram of the incomplete mobile robot system in this invention;

[0084] Figure 4 This is the trajectory tracking response diagram of the incomplete mobile robot in this invention;

[0085] Figure 5 This is the position error response diagram of the incomplete mobile robot in this invention. Detailed Implementation

[0086] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0087] like Figure 1 As shown, this specific embodiment selects a two-wheeled mobile robot as the target.

[0088] The following details the principle and implementation of a design method for a preset time force observer in a robot system according to the present invention, so that those skilled in the art can clearly understand a fault-tolerant control method applicable to non-holonomic mobile robots with coupled actuator failures.

[0089] A fault-tolerant control method for coupled actuator failure in a mobile robot, the design process is as follows: Figure 2 As shown, firstly, based on the dynamics and kinematics model, considering ground slope and coupled actuator failure, a comprehensive model of the two-wheeled mobile robot is established; a filter based on position information is designed to reconstruct the system state, and a fault-tolerant controller is designed based on the filter using the backstepping method. The specific design method of the controller is as follows:

[0090] S1. The computer collects the physical parameters of the robot system. Based on dynamics and kinematics analysis, and considering factors such as the failure coupling of the left and right wheel actuators and the ground slope, the nonlinear system model of the mobile robot is established as follows:

[0091]

[0092] Where η = [vw] T Indicates speed signal, To represent the effect of slope, R = diag{a1, a2}, B = diag{kb1, kb2} This is the system matrix after state transformation. The physical parameters a1, a2, b1, b2, and c in the nonlinear system of the mobile robot are defined as follows:

[0093]

[0094] Where M represents the mass of the robot, r represents the wheel radius, and I ω I represents the moment of inertia of a wheel. v Let φ represent the moment of inertia about the center of gravity, l represent the distance from the center to the side of the robot, f is the coefficient of viscous friction, g represents the acceleration due to gravity, and φ is the angle between the robot's plane and the horizontal plane. Indicates a coupled fault controller;

[0095] Define the target trajectory of the two-wheeled mobile robot: This invention achieves precise tracking of the target trajectory through the design of a reasonable controller. The final control scheme is as follows: Figure 3 As shown.

[0096] S2. Considering the high cost of high-precision speed sensors for robot systems, this invention combines filter design to reconstruct the robot system model, constructing the following nonlinear filter to reconstruct the system state:

[0097]

[0098] Where p represents the robot's current position; ξ = [ξ1,...,ξ4] T ψ = [ψ1, ..., ψ4] T , These are the state variables of the filter. The state matrices A, Q, C, F, and U in the filter are defined as follows:

[0099]

[0100] Gain matrices Q1, Q2 ∈ R 2×2 The selection criteria are as follows:

[0101]

[0102] Among them, P1 and P2 are positive definite diagonal matrices used in auxiliary gain design, and δ1 > 0 is any positive constant;

[0103] Using the above filter (19), the reconstructed position and velocity signals are defined as follows:

[0104]

[0105] in, Represents the coupling fault coefficient; here The reconstructed velocity and position information are presented, and further, the reconstructed incomplete mobile robot system is given:

[0106]

[0107] in, It is the system matrix of equation (6).

[0108] S3. Introduce the use of the Proj function to address the controllability issues caused by coupled actuators; first consider the following coupling relationship of the controller. Here, u1(t) and u2(t) represent the controller to be solved, and f1(t), f2(t), g1(t), and g2(t) represent time-varying functions. The above system of equations has a unique solution if and only if f1f2≠-1. Therefore, when the unique solution condition of the system of equations is guaranteed, the controllability problem caused by the coupled actuator can be solved; the values ​​of f1(t) and f2(t) are controlled by the following Proj function;

[0109]

[0110] definition x * ∈Ω x Let x be the domain of the first-order differential equation; The following properties can be proven: 1) If x(0)∈Ω x Then x(t)∈Ω x ,2)‖Proj(x,y)‖≤||y||,3)-(x * -x)Proj(x,y)≤-(x * -x)y, by using the Proj function, can solve the controllability problem caused by coupled actuators.

[0111] S4. The adaptive output feedback controller design can be realized through the Lyapunov stability criterion; first, the following Lyapunov function is defined:

[0112]

[0113] In the formula These are system parameters, defined in equation (1). γ ρl ,γ ρr ,γ c These represent the designable adaptive gain, The corresponding adaptive errors, tracking errors z1 and z2, are defined as follows:

[0114]

[0115] Obviously, if a controller can be designed to make z i,1 If the value approaches 0, then the robot can track the target trajectory. Further differentiation is needed:

[0116]

[0117] Differentiating the Lyapunov function (24), the virtual controller and adaptive law that make V1(t) approach zero as t approaches infinity are:

[0118]

[0119] To ensure system controllability, the Porj function described in S4 is used to give the following failure coefficients. Adaptive rate:

[0120]

[0121] To ensure z i,2 Convergence, define the second Lyapunov function:

[0122]

[0123] in, Let V2 represent the error between the virtual controller and the actual controller. Differentiating the Lyapunov function, we find the controller that makes V2 approach zero as t approaches infinity:

[0124]

[0125] In formula (30) The adaptive rate is defined as follows:

[0126]

[0127] The adaptive parameter τ in the above equation l1 ,τ r1 ,τ c1 ,τ l2 ,τ r2 ,τ c2 The definition is as follows:

[0128]

[0129] To solve for the controller in equation (30), firstly, according to the definition of S4... The equation given in S4 provides a unique solution. Furthermore, to avoid meaningless oscillations caused by sign changes in the estimated value due to actuator failure, this invention defines an adaptive rate using the Proj function such that:

[0130]

[0131] This leads to f1 > 0 and f2 > 0, at which point the system of equations has a unique solution, thus ensuring the controllability of the system. Further, the intermediate variables g1 and g2 of the equations are defined as follows:

[0132]

[0133] The final controller can then be determined as follows:

[0134]

[0135] After applying the designed fault-tolerant controller, Figure 4-5 The response curves of a nonholonomic mobile robot system are given, from Figure 4 As can be seen, the fault-tolerant controller designed in this method enables the robot to quickly track the ideal trajectory. Figure 5 The error response curve shows that the system tracking error converges rapidly to zero, indicating that the robot can track the ideal trajectory in real time and achieve the expected control objective. Simulation parameters for the two-wheeled mobile robot system are shown in Table 1.

[0136] Table 1 Simulation Parameters of Two-Wheeled Mobile Robot System

[0137]

[0138] In summary, this invention provides a fault-tolerant control method for mobile robot coupler failures, which improves the robustness of the mobile robot system while reducing the system's hardware cost.

Claims

1. A fault-tolerant control method for a mobile robot coupled actuator failure, characterized in that: Includes the following steps: S1. The computer collects the physical parameters of the robot system, and based on dynamics and kinematics analysis, considering the failure coupling of the left and right wheel actuators and the influence of ground slope, establishes a nonlinear system model of the mobile robot. In S1, the nonlinear system model of the mobile robot is established as follows: In the formula, (x,y),θ,v,ω represent the position, angle, velocity, and angular velocity of the mobile robot, respectively; k is the driving gain coefficient; and u... l ,u r To control the actuator torque of the left and right wheels separately, the physical parameters a1, a2, b1, b2, and c in the nonlinear system of the mobile robot are defined as follows: Where M represents the mass of the robot, r represents the wheel radius, and I ω I represents the moment of inertia of a wheel. v Let represent the moment of inertia about the center of gravity, l represent the distance from the center to the side of the robot, f be the coefficient of viscous friction, g represent the acceleration due to gravity, and φ be the angle between the robot's plane and the horizontal plane. The dual-actuator coupling fault modeling is as follows: in, and It is an unknown positive constant used to represent the wear coefficient of the transmission component; Represents a digital controller; S2. Introduce the transformation of the center point of the mobile robot, redefine the nonholonomic mobile robot system model, and design the control target of the nonholonomic mobile robot. S2 specifically includes the following steps: Introduce a distance constant between the center of gravity of the mobile robot and the axle of the drive wheel. Perform a change in the center point of the mobile robot: Then equation (1) can be rewritten as: Where η = [vw] T Indicates speed signal, To represent the effect of slope, R = diag{a1, a2}, B = diag{kb1, kb2} It is the system matrix after the state transformation. Indicates a coupled fault controller; Define the nonholonomic mobile robot target trajectory as S3. Combine filter design to reconstruct the robot system model; Step S3 specifically includes the following steps: S31. For the nonholonomic mobile robot system redefined in S2, in order to achieve output feedback, the following nonlinear filter is constructed to reconstruct the system state: Where p represents the robot's current position; ξ = [ξ1,...,ξ4] T ψ = [ψ1, ..., ψ4] T , These are the state variables of the filter. The state matrices A, Q, C, F, and U in the filter are defined as follows: C=[I2 0 2×2 ], Gain matrices Q1, Q2 ∈ R 2×2 The selection criteria are as follows: Among them, P1 and P2 are positive definite diagonal matrices used in auxiliary gain design, and δ1 > 0 is any positive constant; Using equation (3), the reconstructed position and velocity signals are defined as follows: in, Represents the coupling fault coefficient; here The reconstructed velocity and position information are presented, and further, the reconstructed incomplete mobile robot system is given: in, It is the system matrix of equation (6); S32. To ensure that the reconstructed system can accurately compensate for the unknown velocity signal, the compensation error is defined as follows: S4. Combine the Proj function to handle the controllability issues caused by coupled executors; S5. Based on the Lyapunov stability criterion, and combined with filter design, reconstruct the robot system model, and give the controller and parameter adaptive law to realize the controller design of the robot system.

2. The fault-tolerant control method for mobile robot coupled actuator failure according to claim 1, characterized in that: S4 specifically includes the following steps: First, consider the following coupling relationship in the controller: Where u1(t) and u2(t) represent the controllers to be solved, and f1(t), f2(t), g1(t), and g2(t) represent time-varying functions that will be defined later. The above system of equations has a unique solution if and only if f1f2≠-1. Use the Proj function to restrict the values ​​of f1(t) and f2(t): definition x * ∈Ω x Let x be the domain of the first-order differential equation; The following properties hold true: 1) If x(0)∈Ω x Then x(t)∈Ω x ; 2) ||Proj(x,y)||≤||y||; 3)-(x * -x)Proj(x,y)≤-(x * -x)y。 3. The fault-tolerant control method for mobile robot coupler failures according to claim 2, characterized in that: Based on the design of the robot system using S3 combined with the filter, the final output feedback fault-tolerant controller is designed, and the adaptive rate is given. S5 specifically includes the following steps: S51: Adaptive output feedback controller design achieved through Lyapunov stability criterion; First, define the Lyapunov function as follows: In the formula, k, For system parameters, γ ρl ,γ ρr ,γ c These represent the designable adaptive gain, The corresponding adaptive errors, tracking errors z1 and z2, are defined as follows: Further differentiate (10): Differentiate the Lyapunov function (9) and find the virtual controller that makes the Lyapunov function V1(t) approach zero as t approaches infinity. for: To ensure system controllability, the Proj function described in S4 is used to give the following failure coefficients. Adaptive rate: S52: To ensure z i,2 Convergence, define the second Lyapunov function: in, Let V2 represent the error between the virtual controller and the actual controller. Differentiating the Lyapunov function, we find the controller that makes V2 approach zero as t approaches infinity: In formula (15) The adaptive rate is defined as follows: The adaptive parameter τ in the above equation l1 ,τ r1 ,τ c1 ,τ l2 ,τ r2 ,τ c2 The definition is as follows: To solve for the controller in equation (15), firstly, according to the definition of S4... The condition for obtaining a unique solution to the equation given in S4 is used to define an adaptive rate through the Proj function. Therefore, we obtain f1 > 0 and f2 > 0. At this point, the system of equations has a unique solution, and the controllability of the system is guaranteed. Further, we define the intermediate variables g1 and g2 of the equations as follows: The final controller is given based on the form of the solution described in S4:

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