Fault-tolerant control method for coupling actuator fault of mobile robot

Abstract

The invention discloses a fault-tolerant control method for coupling actuator faults of a mobile robot, which belongs to the technical field of incomplete mobile robot control, and comprises the following steps of: establishing an actuator coupling fault model of the incomplete mobile robot more conforming to actual production, and processing an unknown actuator fault coefficient by introducing a Proj function to obtain a fault-tolerant fault model of the incomplete mobile robot; the problem of controllability caused by coupling faults of an incomplete robot actuator is ingeniously solved, meanwhile, under the condition that the speed cannot be measured, a filter system suitable for an incomplete mobile robot system is designed, and use of a high-precision sensor is avoided. The robustness of the mobile robot system is improved, and meanwhile the hardware cost of the system is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of non-holonomic mobile robot control, and in particular to a fault-tolerant control method for a coupled actuator failure of a mobile robot. Background Art

[0002] A non-holonomic mobile robot is a common type of robot. The robot relies on the differential speed of the left and right wheels to control the steering. This means that in actual control, it is necessary to design left and right wheel controllers to track the target trajectory. When the transmission system of the two wheels is worn to different degrees, causing the left and right actuator power failure, ignoring the fault problem may lead to reduced control accuracy or even accidents. Therefore, it is of great significance to study the control problem of non-holonomic robot systems with actuator coupling failures.

[0003] Non-holonomic mobile robots have broad application prospects in space exploration, environmental monitoring and other fields, and therefore have attracted more and more domestic and foreign scholars to pay attention to this field. At present, in the research of mobile robot systems, such as trajectory tracking, multi-robot formation and other directions, coupled actuator failures exist. By searching public materials and other literature based on mobile robot control, the relevant literature decouples the left and right wheel controllers through linear transformation when dealing with the coupled actuator problem of non-holonomic mobile robots, and then designs the decoupled controllers. However, when the coupled actuator failure is considered, the system has unknown fault parameters, which makes the left and right wheel controllers unable to be decoupled, so the previous mobile robot control scheme will no longer be applicable. In fact, since coupled actuator failure is a type of failure that has not been widely studied, it is difficult to find such related reports in relevant public materials and literature. On the other hand, in the actual robot control process, speed information is often used in controller design, but high-precision speed sensors are expensive, so that in actual control, due to the error of the speed sensor, the control accuracy may be reduced. At the same time, since the speed observer design requires the controller to be completely known, it is difficult for general speed observers to be applied to systems with actuator errors.

[0004] Therefore, the present invention aims to provide relevant definitions for actuator coupling failures of incomplete mobile robots. At the same time, 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 failures of mobile robots, filling the gap in research on coupled actuator failures of incomplete 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 a mobile robot coupled actuator failure, thereby improving the robustness of the mobile robot system and reducing the hardware cost of the system.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

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

[0008] S1. The computer collects the physical parameters of the robot system, and establishes a nonlinear system model of the mobile robot based on dynamic and kinematic analysis, taking into account the influence of the left and right wheel actuator fault coupling and the ground slope;

[0009] S2, introduce the mobile robot center point transformation, redefine the non-holonomic mobile robot system model and design the non-holonomic mobile robot control target;

[0010] S3, reconstruct the robot system model in combination with filter design;

[0011] S4, combined with Proj function to deal with the controllability problems caused by coupled actuators;

[0012] S5. Based on the Lyapunov stability criterion and combined with the filter design, the robot system model is reconstructed, the controller and parameter adaptation law are given, and the controller design of the robot system is realized.

[0013] The further improvement of the technical solution of the present invention is that in S1, the nonlinear system model of the mobile robot is established as:

[0014]

[0015] Where (x, y), θ, v, ω are the position, speed, angle, and angular velocity of the mobile robot, k is the drive gain coefficient, and u l ,u r To control the actuator torque of the left and right wheels respectively; the physical parameters a in the nonlinear system of the mobile robot 1 、a 2 、b 1 、b 2 , c is defined as follows:

[0016]

[0017] Where M is the mass of the robot, r is the wheel radius, and I ω represents the wheel moment of inertia, I v represents the moment of inertia around the center of gravity, l represents the distance from the center to the side of the robot, f is the coefficient of viscous friction, g represents the acceleration of gravity, φ is the angle between the robot plane and the horizontal plane, and the dual actuator coupling fault is modeled as follows:

[0018]

[0019] in, and is an unknown positive constant used to represent the wear coefficient of the transmission component; Stands for Digital Controller.

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

[0021] Introduce the distance constant between the center of gravity of the mobile robot and the axle of the power wheel Transform the center point of the mobile robot:

[0022]

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

[0024]

[0025] Where η = [vw] T Indicates the speed signal, Represents the influence of slope, R = diag{a 1 ,a 2}, B = diag{kb 1 ,kb 2} is the system matrix after state transformation, represents the coupled fault controller;

[0026] Define the target trajectory of the non-holonomic mobile robot as

[0027] A further improvement of the technical solution of the present invention is that: according to the non-holonomic mobile robot system in step S2, a corresponding filter is designed to reconstruct the system state, and step S3 specifically includes the following steps:

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

[0029]

[0030] Where p represents the current position of the robot; ξ=[ξ 1 ,...,ξ 4 ] T , ψ=[ψ 1 ,...,ψ 4 ] T , It is the state variable of the filter. The state matrix A, Q, C, F, U in the filter is defined as follows:

[0031]

[0032]

[0033] Gain matrix Q 1 ,Q 2 ∈R 2×2 The selection conditions are as follows:

[0034]

[0035] Among them, P 1 and P 2 is a positive definite diagonal matrix used in auxiliary gain design, δ 1 >0 is any normal number;

[0036] Through formula (3), the reconstructed position and velocity signals are defined as:

[0037]

[0038] in, represents the coupling fault coefficient; here Represents the reconstructed speed and position information. Furthermore, the reconstructed non-holonomic mobile robot system is given:

[0039]

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

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

[0042]

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

[0044] First, consider the following coupling relationship between controllers:

[0045]

[0046] Among them, u 1 (t),u 2 (t) represents the controller to be solved, f 1 (t), f 2 (t), g 1 (t), g 2 (t) indicates that the time-varying function will be defined later if and only if f 1 f 2≠-1, the above system of equations has a unique solution:

[0047]

[0048] Limit f through Proj function 1 (t), f 2 The value of (t):

[0049]

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

[0051] 1) If x(0)∈Ω x , then x(t)∈Ω x ;

[0052] 2) ‖Proj(x,y)‖≤||y||;

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

[0054] The further improvement of the technical solution of the present invention is: according to S3 combined with the filter design to rebuild the robot system, design the final output feedback fault-tolerant controller, and give the adaptive rate, S5 specifically includes the following steps:

[0055] S51: Adaptive output feedback controller design based on Lyapunov stability criterion;

[0056] First, define the following Lyapunov function:

[0057]

[0058] In the formula is the system parameter, They represent the designable adaptive gain, are the corresponding adaptive error and tracking error z 1 ,z 2 The definition is as follows:

[0059]

[0060] Further derive (10):

[0061]

[0062] Deriving the Lyapunov function (9), we find the solution for the Lyapunov function V when t approaches infinity. 1 (t) Virtual controller tends to zero for:

[0063]

[0064] In order to ensure the controllability of the system, the Porj function described in S4 is used to give the following fault coefficient Adaptation rate:

[0065]

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

[0067]

[0068] in, Represents the error between the virtual controller and the actual controller. Derivative the Lyapunov function and find the solution when t tends to infinity so that V 2 The controller that tends to zero is:

[0069]

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

[0071]

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

[0073]

[0074] To solve the controller in equation (15), first, according to S4 definition

[0075] The condition for obtaining a unique solution of the equation given in S4 is to define the adaptive rate through the Proj function so that Then we get f 1 >0,f 2 >0At this time, the system of equations has a unique solution, and the controllability of the system is guaranteed; further define the intermediate variable g of the equation 1 ,g 2 as follows:

[0076]

[0077]

[0078] The final controller is given by using the solution form described in S4:

[0079]

[0080] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0081] The present invention solves the controllability problem caused by the coupling failure of the actuator of the incomplete robot. Through theoretical analysis, a fault-tolerant control framework of the incomplete mobile robot is established. At the same time, virtual filter technology is introduced to replace the high-precision speed sensor, which reduces the hardware cost and provides a high-precision fault-tolerant control solution for the control of the incomplete mobile robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a schematic diagram of trajectory tracking of a non-holonomic mobile robot in the present invention;

[0083] Figure 2 It is a design flow chart of output feedback fault-tolerant control in the present invention;

[0084] Figure 3 is a control block diagram of the non-holonomic mobile robot system of the present invention;

[0085] Figure 4 is the trajectory tracking response graph of the nonholonomic mobile robot in the present invention;

[0086] Figure 5 It is the position error response diagram of the non-holonomic mobile robot in the present invention. DETAILED DESCRIPTION

[0087] The present invention is further described in detail below with reference to the accompanying drawings and embodiments:

[0088] like Figure 1 As shown, this specific embodiment selects a two-wheeled mobile robot as the object of action.

[0089] The following describes in detail the principles and implementation methods of a design method for a preset time force observer for a robot system of the present invention, so that technicians in this field can clearly understand a fault-tolerant control method suitable for a non-complete mobile robot with coupled actuator failures.

[0090] A fault-tolerant control method for coupled actuator failures in mobile robots. The design process is as follows: Figure 2As shown in the figure, firstly, according to the dynamic and kinematic models, the comprehensive model of the two-wheeled mobile robot is established by considering the ground slope and the coupled actuator failure; a filter based on position information is designed to reconstruct the system state, and the backstepping method is used to design a fault-tolerant controller based on the filter. The specific design method of the controller is as follows:

[0091] S1. The computer collects the physical parameters of the robot system. Based on the dynamics and kinematics analysis, the nonlinear system model of the mobile robot is established by considering the coupling of the left and right wheel actuator faults and the ground slope and other influencing factors as follows:

[0092]

[0093] Where η = [vw] T Indicates the speed signal, Represents the influence of slope, R = diag{a 1 ,a 2}, B = diag{kb 1 ,kb 2} is the system matrix after state transformation, and the physical parameter a in the nonlinear system of the mobile robot 1 、a 2 、b 1 、b 2 , c is defined as follows:

[0094]

[0095] Where M is the mass of the robot, r is the wheel radius, and I ω represents the wheel moment of inertia, I v represents the moment of inertia around the center of gravity, l represents 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, φ is the angle between the robot plane and the horizontal plane, represents the coupled fault controller;

[0096] Define the target trajectory of the two-wheeled mobile robot: The present invention realizes accurate tracking of the target trajectory by designing a reasonable controller. The final control scheme is as follows: Figure 3 shown.

[0097] S2. Considering the high price of high-precision speed sensors for robot systems, the present invention combines filter design to reconstruct the robot system model and constructs the following nonlinear filter to reconstruct the system state:

[0098]

[0099] Where p represents the current position of the robot; ξ=[ξ 1 ,...,ξ4 ] T , ψ=[ψ 1 ,...,ψ 4 ] T , It is the state variable of the filter. The state matrix A, Q, C, F, U in the filter is defined as follows:

[0100]

[0101] Gain matrix Q 1 ,Q 2 ∈R 2×2 The selection conditions are as follows:

[0102]

[0103] Among them, P 1 and P 2 is a positive definite diagonal matrix used in auxiliary gain design, δ 1 >0 is any normal number;

[0104] Through the above filter (19), the reconstructed position and velocity signals are defined as:

[0105]

[0106] in, represents the coupling fault coefficient; here Represents the reconstructed speed and position information. Furthermore, the reconstructed non-holonomic mobile robot system is given:

[0107]

[0108] in, is the system matrix of equation (6).

[0109] S3. Introduce the Proj function to deal with the controllability problem caused by the coupled actuator; first consider the following coupling relationship between the controller Here you 1 (t),u 2 (t) represents the controller to be solved, f 1 (t), f 2 (t), g 1 (t), g 2 (t) represents a time-varying function if and only if f 1 f 2 ≠-1, the above system of equations has a unique solution Therefore, when the unique solution condition of the equation system is guaranteed, the controllability problem caused by the coupled actuator can be solved; the following Proj function is used to control f 1(t), f 2 The value of (t);

[0110]

[0111] definition x * ∈Ω x is the domain of x; for the first-order differential equation The following properties can be proved: 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, the controllability problem caused by the coupled actuator can be solved.

[0112] S4. Adaptive output feedback controller design can be realized through Lyapunov stability criterion. First, define the following Lyapunov function:

[0113]

[0114] In the formula is the system parameter, defined in formula (1), γ ρl ,γ ρr ,γ c They represent the designable adaptive gain, are the corresponding adaptive error and tracking error z 1 ,z 2 The definition is as follows:

[0115]

[0116] Obviously, if the controller can be designed so that z i,1 Approaching 0, the robot can track the target trajectory and further derive:

[0117]

[0118] Derivate the Lyapunov function (24) and find the solution when t approaches infinity so that V 1 The virtual controller and adaptive law when (t) tends to zero are:

[0119]

[0120] In order to ensure the controllability of the system, the Porj function described in S4 is used to give the following fault coefficient Adaptation rate:

[0121]

[0122] To ensure z i,2 Convergence, define the second Lyapunov function:

[0123]

[0124] in, Represents the error between the virtual controller and the actual controller. Derivative the Lyapunov function and find the solution when t tends to infinity so that V 2 The controller that tends to zero is:

[0125]

[0126] In formula (30), The adaptation rate is defined as follows:

[0127]

[0128] The adaptive parameter τ in the above formula l1 ,τ r1 ,τ c1 ,τ l2 ,τ r2 ,τ c2 The definition is as follows:

[0129]

[0130] To solve the controller in equation (30), first, according to S4 definition

[0131] The condition for obtaining a unique solution of the equation given in S4 and in order to avoid meaningless oscillation caused by the change of sign of the estimated value due to actuator failure, the present invention defines the adaptive rate through the Proj function so that:

[0132]

[0133] Then we get f 1 >0,f 2 > 0, then the system of equations has a unique solution, and the controllability of the system is guaranteed; further define the intermediate variable g of the equation 1 ,g 2 as follows:

[0134]

[0135] Then the final controller can be solved as:

[0136]

[0137] By applying the designed fault-tolerant controller, Figure 4-5 The response curve of the non-holonomic mobile robot system is given. Figure 4 It can be seen that the fault-tolerant controller designed by this method can enable the robot to quickly track the ideal trajectory. Figure 5 The error response curve shows that the system tracking error converges to zero quickly, which indicates that the robot can track the ideal trajectory in real time and achieve the expected control goal. The simulation parameters of the two-wheeled mobile robot system refer to Table 1.

[0138] Table 1 Simulation parameters of two-wheeled mobile robot system

[0139]

[0140] In summary, the present invention provides a fault-tolerant control method for a mobile robot coupled actuator failure, which improves the robustness of the mobile robot system and reduces the hardware cost of the system.

Claims

1. A fault-tolerant control method for coupled actuator failure of a mobile robot, characterized in that: The following steps are involved: S1. The computer collects the physical parameters of the robot system, and establishes a nonlinear system model of the mobile robot based on dynamic and kinematic analysis, taking into account the influence of the left and right wheel actuator fault coupling and the ground slope; S2, introduce the mobile robot center point transformation, redefine the non-holonomic mobile robot system model and design the non-holonomic mobile robot control target; S3, reconstruct the robot system model in combination with filter design; S4, combined with Proj function to deal with the controllability problems caused by coupled actuators; S5. Based on the Lyapunov stability criterion and combined with the filter design, the robot system model is reconstructed, the controller and parameter adaptation law are given, and the controller design of the robot system is realized.

2. The fault-tolerant control method for coupling actuator failure of a mobile robot according to claim 1, characterized in that: In S1, the nonlinear system model of the mobile robot is established as: Where (x, y), θ, v, ω are the position, speed, angle, and angular velocity of the mobile robot, k is the drive gain coefficient, and u l ,u r To control the actuator torque of the left and right wheels respectively; the physical parameters a1, a2, b1, b2, c in the nonlinear system of the mobile robot are defined as follows: Where M is the mass of the robot, r is the wheel radius, and I ω represents the wheel moment of inertia, I v represents the moment of inertia around the center of gravity, l represents the distance from the center to the side of the robot, f is the coefficient of viscous friction, g represents the acceleration of gravity, φ is the angle between the robot plane and the horizontal plane, and the dual actuator coupling fault is modeled as follows: in, and is an unknown positive constant used to represent the wear coefficient of the transmission component; Stands for Digital Controller.

3. The fault-tolerant control method for coupling actuator failure of a mobile robot according to claim 2, characterized in that: According to the non-holonomic mobile robot system described in S1, S2 specifically includes the following steps: Introduce the distance constant between the center of gravity of the mobile robot and the axle of the power wheel Transform the center point of the mobile robot: Then formula (1) can be rewritten as: Where η = [vw] T Indicates the speed signal, Represents the influence of slope, R = diag{a1,a2}, B = diag{kb1,kb2} is the system matrix after state transformation, represents the coupled fault controller; Define the target trajectory of the non-holonomic mobile robot as 4. The fault-tolerant control method for coupling actuator failure of a mobile robot according to claim 3, characterized in that: According to the non-holonomic mobile robot system in step S2, a corresponding filter is designed to reconstruct the system state, and step S3 specifically includes the following steps: S31. For the nonholonomic mobile robot system redefined in S2, in order to realize output feedback, the following nonlinear filter is constructed to reconstruct the system state: Where p represents the current position of the robot; ξ=[ξ1,...,ξ4] T , ψ=[ψ1,...,ψ4] T , It is the state variable of the filter. The state matrix A, Q, C, F, U in the filter is defined as follows: Gain matrix Q1,Q2∈R 2×2 The selection conditions are as follows: Where P1 and P2 are positive definite diagonal matrices used in auxiliary gain design, and δ1>0 is any positive constant; Through formula (3), the reconstructed position and velocity signals are defined as: in, represents the coupling fault coefficient; here Represents the reconstructed speed and position information. Furthermore, the reconstructed non-holonomic mobile robot system is given: in, is the system matrix of equation (6); S32. In order to ensure that the reconstructed system can accurately compensate for the unknown speed signal, the compensation error is defined as follows:

5. The fault-tolerant control method for coupling actuator failure of a mobile robot according to claim 1, characterized in that: S4 specifically includes the following steps: First, consider the following coupling relationship between the controllers: Among them, u1(t), u2(t) represent the controllers that need to be solved, f1(t), f2(t), g1(t), g2(t) represent the time-varying functions that will be defined later. The above equations have a unique solution if and only if f1f2≠-1: Use the Proj function to limit the values ​​of f1(t) and f2(t): definition x * ∈Ω x is the domain of x; for the first-order differential equation The following properties hold: 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。 6. The fault-tolerant control method for coupling actuator failure of a mobile robot according to claim 5, characterized in that: According to S3 combined with filter design, the robot system is rebuilt, 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 based on Lyapunov stability criterion; First, define the following Lyapunov function: Where k, is the system parameter, γ ρl ,γ ρr ,γ c They represent the designable adaptive gain, The corresponding adaptive errors and tracking errors z1 and z2 are defined as follows: Further derive (10): Deriving the Lyapunov function (9), we can find the virtual controller that makes the Lyapunov function V1(t) approach zero when t approaches infinity. for: In order to ensure the controllability of the system, the Porj function described in S4 is used to give the following fault coefficient Adaptation rate: S52: To ensure z i,2 Convergence, define the second Lyapunov function: in, Represents the error between the virtual controller and the actual controller. Derivative of the Lyapunov function is used to solve the controller that makes V2 approach zero when t approaches infinity: In formula (15), The adaptation rate is defined as follows: The adaptive parameter τ in the above formula l1 ,τ r1 ,τ c1 ,τ l2 ,τ r2 ,τ c2 The definition is as follows: To solve the controller in equation (15), first, according to S4 definition The condition for obtaining a unique solution of the equation given in S4 is to define the adaptive rate through the Proj function so that Then we get f1>0, f2>0. At this time, the system of equations has a unique solution, and the controllability of the system is guaranteed. The intermediate variables g1 and g2 of the equation are further defined as follows: The final controller is given by using the solution form described in S4:

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