Mechanical arm neural network control method considering sensor failure

Abstract

The application relates to a mechanical arm neural network control method considering sensor faults, which establishes a single-joint mechanical arm mathematical model considering sensor faults to obtain joint angle positions and joint angular velocities under sensor measurement; according to the joint angle positions and joint angular velocities under sensor measurement, a filter with a neural network is constructed to obtain filtered joint angle positions and joint angular velocities; for the angle position error generated by the filtered joint angle positions, a nonlinear transformation with a performance constraint function is designed to limit the convergence trajectory of the angle position error, and an unconstrained error is obtained; according to the unconstrained error and a backstepping method, a command filter is designed; according to the filtered joint angular velocities and the output of the command filter, a neural network control law is designed, and the angle position error is required to converge according to the performance constraint function. The application can filter out the adverse effects introduced by sensor faults, avoid frequent oscillation of motor control torque, and has low calculation amount.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mechanical arm control, and particularly relates to a mechanical arm neural network control method considering sensor faults. BACKGROUND

[0002] Mechanical arms are widely used in national defense, medical treatment and industry, and improving the trajectory tracking accuracy and dynamic performance of the control system of the mechanical arm has become a key problem in current research. In the case that the model parameters of the mechanical arm are unknown, the universal approximation characteristics of a neural network can be used to effectively estimate the uncertain terms in the mathematical model, thereby assisting the design of a controller to achieve accurate trajectory tracking. In the process of designing the controller, the joint angle position and angular velocity information is usually required to be obtained, however, under the action of external disturbance, the sensor used to measure the information may fail, resulting in distorted measurement data, thereby adversely affecting the performance of the controller. The design of most current neural network controllers for mechanical arms does not fully consider the influence of sensor faults, which easily leads to the decline of the control performance of the system, and causes frequent oscillation of the motor control torque, thereby affecting the stability and execution accuracy of the system.

[0003] In the current neural network-based mechanical arm control method, in order to effectively approximate the uncertain terms in the mechanical arm system, a large number of neural network nodes are usually required to be set. With the increase in the number of nodes, the number of online adjustment parameters required also increases significantly, thereby increasing the computational burden of the control algorithm. In addition, most traditional control methods need to perform time derivative operation on the virtual control law in the design process, which not only increases the implementation complexity, but also to some extent limits the application feasibility and popularization value of the control strategy in engineering practice.

[0004] In summary, for a single-joint mechanical arm with sensor faults, designing a neural network control method based on a filter without relying on the model parameters of the mechanical arm has become a research difficulty in the field of mechanical arm control. SUMMARY

[0005] The present application provides a mechanical arm neural network control method considering sensor faults, which aims to solve the problem that the current control method cannot make the joint angle position error converge according to the requirements of the performance constraint function without relying on the model parameters of the mechanical arm, and cannot effectively filter the joint angle position and angular velocity, resulting in frequent oscillation of the motor control torque and high computational complexity of the control algorithm.

[0006] To achieve the above-mentioned purpose, the present application adopts the following technical scheme, comprising:

[0007] The mechanical arm neural network control method considering sensor faults comprises the following steps:

[0008] Step 1. Establish a single-joint robot mathematical model considering sensor failure, get joint angle position and joint angular velocity under sensor measurement;

[0009] Step 2. According to the joint angle position and joint angular velocity under sensor measurement, construct a filter with neural network to get filtered joint angle position and joint angular velocity;

[0010] Step 3. For the angular position error generated by the filtered joint angle position Design a nonlinear transformation with performance constraint function to limit the convergence trajectory of the angular position error, get the unconstrained error z1;

[0011] Step 4. According to the unconstrained error z1 and backstepping method, design the command filter;

[0012] Step 5. According to the filtered joint angular velocity and the output of the command filter, design the neural network control law, realize the convergence of the angular position error according to the requirements of the performance constraint function.

[0013] Further, the single-joint robot mathematical model considering sensor failure in step 1 is:

[0014]

[0015] Where, F p (p 1s , p 2s , u) = (u - V m p 2s - M m gl m sin(p 1s )) / J m - u, d m = -△ dis / J mm , p 1s is the actual joint angle position, p 2s is the actual joint angular velocity, J m is the rotational inertia of the motor, V m is the viscous friction coefficient, M m is the mass of the joint, l m is the distance from the joint axis to the center of mass, g is the acceleration of gravity, Δ dis is the disturbance, u is the control torque provided by the motor, and the sensor failure is represented as:

[0016]

[0017] Where, δ1 and δ2 represent the failure variables, p1 is the joint angle position under sensor measurement, and p2 is the joint angular velocity under sensor measurement.

[0018] Further, the filter with neural network in step 2 is:

[0019]

[0020] wherein, represents a compensation term of disturbance, represents an adjustment parameter of the compensation term, tanh(·) represents a hyperbolic tangent function, p1 is a joint angle position measured by a sensor, p2 is a joint angular velocity measured by a sensor, h1, h2, γ w , σ w , γ μ and σ μ are design parameters, and are positive numbers, represents a filtered joint angle position, represents a filtered joint angular velocity, represents an output of the neural network, represents an excitation function vector, represents an adjustment parameter of the neural network, represents a Gaussian basis function vector, n is a number of nodes of the neural network, and the Gaussian basis function is:

[0021]

[0022] wherein, represents a center vector of the Gaussian basis function, b N represents a width of the Gaussian basis function, and exp(·) represents an exponential function.

[0023] Further, the unconstrained error in step 3 is:

[0024]

[0025] wherein, z1 represents an unconstrained error, and β PP (0) are initial values of the angle position error and the performance constraint function β PP , respectively;

[0026] wherein, the angle position error is:

[0027]

[0028] wherein, represents a filtered joint angle position, p d represents a desired signal;

[0029] The performance constraint function is:

[0030]

[0031] Where, β P0 β Pf and R Pf The design parameter is a positive number, t represents time, and exp(·) represents the exponential function.

[0032] Furthermore, the instruction filter mentioned in step 4 is:

[0033]

[0034] Where, η f1 and η f2 s is a design parameter and is a positive number. f1 and s f2 y is the state variable of the instruction filter. fs express The estimated quantity, Let α1 be the time derivative of the virtual control law. The expression for the virtual control law α1 is:

[0035]

[0036] Where c1 is a design parameter and is a positive number. and The desired signal p is respectively d and performance constraint function β PP Time derivative, z1 represents the unconstrained error. This represents the angular position error.

[0037] Furthermore, the neural network control law described in step 5 is:

[0038]

[0039] Where c2 and h2 are design parameters, and are positive numbers. p1 is the filtered joint angular velocity, and p2 is the joint angular velocity measured by the sensor. α1 represents the virtual control law. β is the angular position error. PP Let z1 represent the performance constraint function, z1 represent the unconstrained error, and y represent the performance constraint function. fs express The estimated quantity, This represents the time derivative of the virtual control law α1. This represents the compensation term for the disturbance. This represents the adjustment parameter of the compensation term, and tanh(·) represents the hyperbolic tangent function. represents an output of a neural network, represents an excitation function vector, represents a filtered joint angle position, represents an adjusting parameter of a neural network, represents a Gaussian basis function vector, n is a node number of a neural network, and the Gaussian basis function is:

[0040]

[0041] wherein, represents a center vector of a Gaussian basis function, b N represents a width of a Gaussian basis function, and exp(·) represents an exponential function.

[0042] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0043] 1. The present application is directed to a single-joint robot arm considering sensor faults, and a filter with a neural network is constructed without relying on robot arm model parameters, so that the adverse effects caused by sensor faults are effectively filtered out, and frequent oscillation of motor control torque is avoided.

[0044] 2. The neural network constructed by the present application has fewer online adjusting parameters, and the time derivative operation on the virtual control law is avoided by designing an instruction filter, so that the calculation burden of the control algorithm is effectively reduced.

[0045] 3. The present application designs a nonlinear transformation with a performance constraint function to limit the convergence trajectory of the angle position error, so that the angle position error converges according to the requirements of the performance constraint function.

[0046] Based on the above reasons, the present application can be widely popularized in the field of robot arm control. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 is a control method flow chart of the present application;

[0048] Figure 2 is a joint angle position tracking effect diagram of the control method of the present application;

[0049] Figure 3 is a joint angle position comparison diagram under different conditions;

[0050] Figure 4 is a joint angular velocity comparison diagram under different conditions;

[0051] Figure 5 is a comparison diagram of actual angle position error using different control methods;

[0052] Figure 6 is a comparison diagram of control torque using different control methods;

[0053] Figure 7 Fig. 2 is a comparison chart of actual angular position error for different cases. DETAILED DESCRIPTION

[0054] The application will be described in greater detail in connection with the attached drawings.

[0055] The application is directed to the problem of trajectory tracking for a single-joint robot arm with sensor faults, a filter with a neural network is constructed to obtain filtered joint angular position and joint angular velocity; for the angular position error generated by the filtered joint angular position, a nonlinear transformation with a performance constraint function is designed to limit the convergence trajectory of the angular position error, to obtain an unconstrained error; according to the unconstrained error and the backstepping method, a command filter is designed; according to the filtered joint angular velocity and the output of the command filter, a neural network control law is designed to realize the convergence of the angular position error according to the requirements of the performance constraint function.

[0056] As shown in Figure 1 , the application provides a neural network control method for a robot arm considering sensor faults, comprising the following steps:

[0057] Step 1. Establish a mathematical model of a single-joint robot arm considering sensor faults to obtain joint angular position and joint angular velocity under sensor measurement;

[0058] The mathematical model of a single-joint robot arm considering sensor faults is:

[0059]

[0060] Where, F p (p 1s , p 2s , u) = (u - V m p 2s - M m gl m sin(p 1s )) / J m -u, d m = -Δ dis / J m , p 1s is the actual joint angular position, p 2s is the actual joint angular velocity, J m is the rotational inertia of the motor, V m is the viscous friction coefficient, M m is the mass of the joint, l m is the distance from the joint axis to the center of mass, g is the acceleration of gravity, Δ dis is the disturbance, u is the control torque provided by the motor, and the sensor fault is represented as:

[0061]

[0062] where δ1 and δ2 represent fault variables, p1 is the joint angle position measured by sensors, and p2 is the joint angular velocity measured by sensors.

[0063] Step 2. Construct a filter with a neural network according to the joint angle position and the joint angular velocity measured by sensors to obtain the filtered joint angle position and the filtered joint angular velocity;

[0064] The filter with the neural network is:

[0065]

[0066] where, represents the compensation term of the disturbance, represents the adjustment parameter of the compensation term, tanh(·) represents the hyperbolic tangent function, p1 is the joint angle position measured by sensors, p2 is the joint angular velocity measured by sensors, h1, h2, γ w , σ w , γ μ , and σ μ are design parameters and are positive numbers, is the filtered joint angle position, is the filtered joint angular velocity, represents the output of the neural network, represents the excitation function vector, represents the adjustment parameter of the neural network, represents the Gaussian basis function vector, n is the number of nodes of the neural network, and the Gaussian basis function is:

[0067]

[0068] where, represents the center vector of the Gaussian basis function, b N represents the width of the Gaussian basis function, and exp(·) represents the exponential function.

[0069] Step 3. The angular position error generated by the filtered joint angle position is designed to limit the convergence trajectory of the angular position error by a nonlinear transformation with a performance constraint function, to obtain an unconstrained error z1;

[0070] The unconstrained error is:

[0071]

[0072] where z1 represents the unconstrained error, and β PP (0) are the angular position error and the performance constraint function β, respectively.PP the initial value of the angle position error

[0073] wherein the angle position error is:

[0074]

[0075] wherein, is the filtered joint angle position, p d is the desired signal;

[0076] the performance constraint function is:

[0077]

[0078] wherein β P0 , β Pf and T Pf are design parameters, and are positive numbers, t represents time, and exp(·) represents the exponential function.

[0079] Step 4. Design the command filter according to the unconstrained error z1 and the backstepping method;

[0080] the command filter is:

[0081]

[0082] wherein η f1 and η f2 are design parameters, and are positive numbers, s f1 and S f2 are state variables of the command filter, y fs represents an estimate of p represents the time derivative of the virtual control law α1, and the expression of the virtual control law α1 is:

[0083]

[0084] wherein c1 is a design parameter, and is a positive number, and are the time derivatives of the desired signal p d and the performance constraint function β PP respectively, z1 represents the unconstrained error, is the angle position error.

[0085] Step 5. Design the neural network control law according to the filtered joint angular velocity and the output of the command filter, so that the angle position error converges according to the requirements of the performance constraint function;

[0086] the neural network control law is:

[0087]

[0088] where c2 and h2 are design parameters and positive, is the filtered joint angular velocity, p2 is the joint angular velocity measured by the sensor, α1 represents the virtual control law, is the angular position error, β PP represents the performance constraint function, z1 represents the unconstrained error, y fs represents the estimate of represents the time derivative of the virtual control law α1, represents the compensation term of the disturbance, represents the adjustment parameter of the compensation term, tanh(·) represents the hyperbolic tangent function, represents the output of the neural network, represents the excitation function vector, is the filtered joint angular position, represents the adjustment parameter of the neural network, represents the Gaussian basis function vector, n is the number of nodes of the neural network, and the Gaussian basis function is:

[0089]

[0090] where, represents the center vector of the Gaussian basis function, b N represents the width of the Gaussian basis function, exp(·) represents the exponential function.

[0091] The designed neural network control method for the manipulator considering sensor failure is simulated in a virtual environment to verify the feasibility of the proposed method. In the simulation experiment, the mathematical model of the single-joint manipulator considering sensor failure is:

[0092]

[0093] where F p (p 1s , p 2s , u) = (u - V m p 2s - M m gl m sin(p 1s )) / J m - u, d m = -Δ dis / J m , p 1sp is the actual joint angle position 2s J is the actual joint angular velocity m V is the moment of inertia of the motor m M is the viscous friction coefficient m m is the mass of the joint m l is the distance from the joint axis to the center of mass dis g is the gravitational acceleration m is the disturbance u is the control torque provided by the motor Sensor faults are represented as:

[0094]

[0095] where δ1 and δ2 represent the fault variables, p1 is the joint angle position measured by the sensor, and p2 is the joint angular velocity measured by the sensor.

[0096] The fault variables are: δ1 = 0.04 sin(30πt) rad, δ2 = 0.05 sin(30πt) rad / s. The model parameters of the robotic arm are: J m = 1 kg·m 2 , V m = 1 Nm·s / rad, M m gl m = 10 Nm, Δ dis = -0.3 sin(2πt) - 0.2 sin(3πt) Nm. The simulation time is set to 30 seconds.

[0097] The initial state of the robotic arm is p 1s (0) = 3 rad, p 2s (0) = 0 rad / s. The desired signal is set to p d = cos(t) rad. The actual angle position error θ 1s is defined as: θ 1s = p 1s - p d .

[0098] The control law-related parameters are set to h1 = 2, h2 = 2, γ w = 10, σ w = 0.01, γ μ = 1, σ μ = 0.15, β P0 = 3, β Pf = 0.1, T Pf = 5, η f1 = 50, η f2 = 20, c1 = 1, c2 = 10, and The initial values of h1 and h2 are and The center vectors of the Gauss kernel are uniformly distributed in the interval [-1.5, 1.5] x [-1.5, 1.5], b N = 2.5456.

[0099] To illustrate the superiority of the control method of the application, a comparative experiment is conducted with a conventional control method (a neural network control method for a mechanical arm without a filter).

[0100] Figure 2 The joint angle position tracking effect diagram of the control method of the application is shown in FIG. 6. Figure 2 It can be seen that the control method of the application can realize actual joint angle position tracking of the expected signal.

[0101] Figure 3 The joint angle position comparison diagram under different conditions is shown in FIG. 7. Figure 3 It can be seen that the filter designed in the application can effectively filter out the adverse effects introduced by sensor failure, so that the filtered joint angle position can better approximate the actual joint angle position.

[0102] Figure 4 The joint angle velocity comparison diagram under different conditions is shown in FIG. 8. Figure 4 It can be seen that the filter designed in the application can effectively filter out the adverse effects introduced by sensor failure, so that the filtered joint angle velocity can better approximate the actual joint angle velocity.

[0103] Figure 5 The actual angle position error comparison diagram using different control methods is shown in FIG. 9. Figure 5 It can be seen that the control method of the application and the conventional control method can both realize the convergence of the actual angle position error according to the requirements of the performance constraint function, but the convergence speed of the angle position error in the control method of the application is faster.

[0104] Figure 6 The control torque comparison diagram using different control methods is shown in FIG. 10. Figure 6 It can be seen that the control torque generated by the conventional control method has obvious high-frequency oscillation phenomenon, which shows that the filter designed in the application can avoid frequent oscillation of the control torque, which is helpful for practical engineering application.

[0105] To further illustrate the effectiveness of the control method of the application, the performance constraint function is set in two cases. Case 1: β P0 = 3, β Pf = 0.1, T Pf = 5. Case 2: β P0 = 3, β Pf = 0.02, T Pf= 2. From the above two cases, it can be seen that the actual angular position error in case 2 converges within 2 seconds and has higher steady-state accuracy.

[0106] Figure 7 The actual angular position error comparison chart in different cases is shown in Figure 6. Figure 7 It can be seen that the actual angular position error in case 2 converges faster and has higher steady-state accuracy.

[0107] The simulation results show that the single-joint robot considering sensor faults can converge the actual angular position error according to the performance constraint function without relying on the model parameters of the robot, and the filter with the neural network can effectively filter the joint angular position and angular velocity, thereby avoiding frequent oscillation of the control torque. In addition, the control method has low computational complexity.

[0108] It can be understood that the above specific description of the present application is only used to illustrate the present application and is not limited to the technical solutions described in the embodiments of the present application. Those skilled in the art should understand that the present application can still be modified or replaced equivalently to achieve the same technical effect; as long as the use needs are met, it is within the protection scope of the present application.

Claims

1. A method for neural network control of a robot arm considering sensor faults, characterized in that, The method comprises the following steps: Step 1. A single-joint robot mathematical model considering sensor failure is established to obtain joint angle position and joint angular velocity under sensor measurement; Step 2. According to the joint angle position and joint angular velocity under sensor measurement, a filter with a neural network is constructed to obtain filtered joint angle position and joint angular velocity; Step 3. Angular position error generated against filtered joint angle position , design nonlinear transformation with performance constraint function to limit the convergence trajectory of angular position error, get unconstrained error ; Step 4. Design the command filter according to the unconstrained error and backstepping Step 5. According to the filtered joint angular velocity and the output of the command filter, a neural network control law is designed to realize that the angle position error converges according to the performance constraint function; The single-joint robot mathematical model considering sensor failure in step 1 is as follows: ， wherein , , is the actual joint angle position, is the actual joint angular velocity, is the moment of inertia of the motor, is the viscous friction coefficient, is the mass of the joint, is the distance from the joint axis to the center of mass, is the gravitational acceleration, is the disturbance, is the control torque provided by the motor, the sensor fault is denoted by: ， wherein and denotes a fault variable, is the joint angle position under sensor measurement, is the joint angular velocity under sensor measurement.

2. The robot arm neural network control method considering sensor faults according to claim 1, characterized in that: The filter with a neural network in step 2 is as follows: ， wherein denotes a compensation term for disturbances, denotes an adjustment parameter for the compensation term, denotes a hyperbolic tangent function, is the joint angle position under sensor measurement, is the joint angular velocity under sensor measurement, and are design parameters and are positive, is the filtered joint angle position, is the filtered joint angular velocity, denotes the output of the neural network, denotes the activation function vector, denotes the adjustment parameter of the neural network, denotes the vector of Gaussian basis functions, is the number of nodes of the neural network, the Gaussian basis functions are:​​​​ ， wherein denotes a center vector of the Gaussian kernel, denotes a width of the Gaussian kernel, denotes an exponential function.

3. The robot arm neural network control method considering sensor faults according to claim 1, characterized in that: The unconstrained error in step 3 is as follows: ， wherein, represents the unconstrained error, and are the angular position errors and the performance constraint function the initial values; where the angular position error is: ， wherein, is the filtered joint angle position, is the desired signal; The performance constraint function is as follows: ， wherein , and are design parameters and are positive numbers, denotes time, denotes the exponential function.

4. The robot arm neural network control method considering sensor faults according to claim 1, wherein: The command filter in step 4 is as follows: ， wherein and are design parameters and positive, and are state variables of the command filter, denotes an estimate of denotes the time derivative of the virtual control law whose expression is ​ ， wherein is a design parameter and is positive, and are the desired signal and performance constraint functions time derivatives, , denotes the unconstrained error, , is the angular position error.

5. The robot arm neural network control method considering sensor faults according to claim 1, wherein: The neural network control law in step 5 is as follows: ， in, and These are design parameters, and they are positive numbers. , The filtered joint angular velocity. The joint angular velocity measured by the sensor. , Represents a virtual control law. , This is the angular position error. Represents the performance constraint function. This represents unconstrained error. express The estimated quantity, Representing virtual control law Time derivative, This represents the compensation term for the disturbance. This indicates the adjustment parameter of the compensation term. Represents the hyperbolic tangent function. This represents the output of the neural network. Represents the activation function vector. The filtered joint angle position. This represents the adjustment parameters of the neural network. Represents the Gaussian function vector. Given the number of nodes in the neural network, the Gaussian function is: ， wherein denotes a center vector of the Gaussian kernel, denotes a width of the Gaussian kernel, denotes an exponential function.

Images