A method for integral sliding mode control of a robot arm based on a cascade neural network

Abstract

The application is a kind of mechanical arm integral sliding mode control method based on cascade neural network. It includes: 1. Based on n degree of freedom mechanical arm with unknown external disturbance, the dynamic model is established; 2. The set of uncertain items of the dynamic model is regarded as a set of uncertain items, and a cascade radial basis function neural network is designed for accurate compensation; 3. Based on the estimation error generated by the RBF neural network, a time-varying disturbance observer is designed to accurately compensate it; step 4, based on the dynamic model of the mechanical arm, the cascade radial basis function neural network and the time-varying disturbance observer, the mechanical arm integral sliding mode controller based on cascade neural network is designed. The application adopts the technical scheme of combining cascade neural network, sliding mode control and observer technology, designs the trajectory tracking controller, which ensures the tracking accuracy of the mechanical arm system, improves the convergence speed of the neural network, and solves the chattering phenomenon of the mechanical arm caused by linear sliding mode control.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of robots, and particularly relates to a mechanical arm integral sliding mode control method based on a cascade neural network. BACKGROUND

[0002] The tasks usually performed by the mechanical arm include motion planning, trajectory tracking and the like. These tasks require the mechanical arm controller to maintain excellent dynamic behavior in the presence of possible external environmental disturbances, unknown model uncertainties and sensor information loss. Sliding mode control has been widely applied in the field of mechanical arm control due to its strong robustness to external disturbances and uncertainties, simple structure and easy implementation. However, in the operation process, linear sliding mode control will cause the mechanical arm to have a chattering phenomenon, resulting in instability of the mechanical arm system. Therefore, integral sliding mode control is proposed to overcome the chattering phenomenon caused by the state switching of the controller.

[0003] In practice, the nonlinearity of dynamic robot systems is usually unknown or difficult to obtain. In order to solve this problem, different methods have been developed to compensate for unmodeled uncertainties. Model-free adaptive compensation control has been widely applied, such as neural networks and fuzzy logic. Although the adaptive controller is for nonlinear and uncertain dynamic systems, its slow convergence will lead to performance degradation and even affect the running safety. Neural networks are used as function approximators to relax the linear parameterization assumption and the requirement for system knowledge. In time series modeling, a radial basis function neural network (RBFNN) is commonly used for function approximation because its value is different from zero in an infinite space, and its approximation can avoid local minimum. The RBFNN uses a Gaussian function as the activation function. Generally speaking, compared with other NN controllers, the RBFNN controller wastes less computing resources. However, the update law usually increases the weight value until the output error is alleviated, and if there is no robust design, continuous training will lead to excessive control effort. In order to avoid this situation, adaptive control often updates the neural weight according to the robust adaptive law, which is calculated by the Lyapunov method. SUMMARY

[0004] The application provides a mechanical arm integral sliding mode control method based on a cascade neural network, which adopts a technical scheme combining a cascade neural network, sliding mode control and observer technology to design a trajectory tracking controller. The controller ensures the tracking accuracy of the mechanical arm system, improves the convergence speed of the neural network, effectively overcomes the chattering phenomenon of the linear sliding mode, and solves the problem that the linear sliding mode control will cause the mechanical arm to have a chattering phenomenon and result in instability of the mechanical arm system in the operation process.

[0005] The technical scheme of the application is described below in combination with the accompanying drawings:

[0006] A cascade neural network-based manipulator integral sliding mode control method, comprising the following steps:

[0007] Step one, based on an n-degree-of-freedom manipulator with unknown external disturbance, a dynamic model is established;

[0008] Step two, the set of uncertain terms of the dynamic model is regarded as a lumped uncertain term, and a cascade radial basis function neural network is designed for accurate compensation;

[0009] Step three, based on the estimation error generated by the RBF neural network, a time-varying disturbance observer is designed for accurate compensation;

[0010] Step four, based on the manipulator dynamic model established in step one, the cascade radial basis function neural network designed in step two, and the time-varying disturbance observer designed in step three, a cascade neural network-based manipulator integral sliding mode controller is designed.

[0011] Further, the specific method of step one is as follows:

[0012] 11) The dynamic model of the n-degree-of-freedom manipulator is as follows:

[0013]

[0014] In the formula, M(q) is the inertia matrix; is the Coriolis-centrifugal matrix; G(q) is the gravity vector; is the friction term; q, and are the position, velocity and acceleration of the joint respectively; τ is the control input; τ d is the disturbance;

[0015] 12) According to the dynamic model of the manipulator, the state space expression form of the manipulator subsystem is as follows:

[0016]

[0017] In the formula, is the state variable of the manipulator system S i ; y i is the output of the manipulator system S i ;

[0018]

[0019]

[0020]

[0021] Further, the specific method of step two is as follows:

[0022] 21) Define the tracking error function e of the system i and variable function s i :

[0023] e i = q i - q id

[0024]

[0025] where μ i , υ i are gain coefficients; α i , β i are design parameters, and 0 < α i < 1, β i > 1; q id is the joint desired position;

[0026] 22) Define the integral sliding mode surface function ω i :

[0027]

[0028] where ∑ i (q i ) = B i g i (q i ), Π i = B i g i (q i )τ d

[0029] Its derivative is:

[0030]

[0031] where q i is the actual joint position;

[0032] 23) Define the radial basis neural network function to estimate the uncertainty term and ∑ i (q i );

[0033]

[0034]

[0035] where the subscript "i" is the ith joint module; W iF and W iΣ are neural network weights, Φi (·) is the neural network basis function; ε iF and ε iΣ For approximation error; ε1and ε2are known constants; ε0is a positive constant.

[0036] Further, the specific method of step three is as follows:

[0037] 31) Based on the integral sliding mode function established in step two and its derivative, we have:

[0038]

[0039] where τ c is the compensation controller; Λ i = Π i is the external disturbance term; ρ i = ε iF + ε iΣ is the neural network estimation error.

[0040] The compensation controller is:

[0041]

[0042] where χ i , ε i are control parameters.

[0043] 32) The time-varying disturbance observer estimates the disturbance term Λ i :

[0044]

[0045]

[0046] where k i0 is the observer gain.

[0047] 33) The predicted value of the neural network estimation error is estimated by a cascaded neural network, as follows:

[0048]

[0049] where W ρ is the ideal weight; Φ ρ is the Gaussian basis function.

[0050] Further, the specific method of step four is as follows:

[0051] 41) Define the speed error function e i2 :

[0052]

[0053] In the formula, alpha 1 is a virtual control law, and the expression form is k1 is a gain coefficient;

[0054] 42) A mechanical arm integral sliding mode controller based on a cascade neural network is as follows:

[0055]

[0056] In the formula, u nom is a virtual control law;

[0057] Wherein, the adaptive update law is as follows:

[0058]

[0059]

[0060]

[0061] In the formula, eta iF , eta iΣ , gamma ρ is an adaptive law parameter, is a function of a compensation signal; is an adaptive update law of neural network weight W iF . is an adaptive update law of neural network weight W iΣ . is an adaptive update law of neural network estimation error p i .

[0062] The beneficial effects of the present application are:

[0063] 1) The present application adopts a technical scheme combining cascade neural networks, sliding mode control and observer technology to design a trajectory tracking controller. The controller ensures the tracking accuracy of the mechanical arm system, improves the convergence speed of the neural network, and effectively overcomes the chattering phenomenon of the linear sliding mode;

[0064] 2) The present application introduces an online error compensation function to improve the convergence of the neural network weight, designs a time-varying disturbance observer to quickly compensate for external disturbances, and improves the robustness of the system to external disturbances and unknown system parameters. BRIEF DESCRIPTION OF DRAWINGS

[0065] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. It should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as a limitation on the scope, and other related drawings can also be obtained by those of ordinary skill in the art without creative labor on the basis of these drawings.

[0066] Figure 1 The flowchart of the present application.

[0067] Figure 2 The position curve of joint 1 and joint 2;

[0068] Figure 3 The error curve of joint 1 and joint 2;

[0069] Figure 4 The torque curve of joint 1 and joint 2. DETAILED DESCRIPTION

[0070] The present application will be further described in detail below in combination with the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the present application, and not to limit the present application. In addition, it should be noted that, in order to facilitate the description, only the parts related to the present application are shown in the drawings, and not all the structures.

[0071] Referring to Figure 1 , the present application provides a kind of integral sliding mode control method of mechanical arm based on cascade neural network, comprising the following steps:

[0072] Step one, based on n degree of freedom mechanical arm with unknown external disturbance, the dynamics model is established, as follows:

[0073] 11) the dynamics model of the n degree of freedom mechanical arm is as follows:

[0074]

[0075] In the formula, M (q) is inertia matrix; It is coriolis-centrifugal matrix;G (q) is gravity vector; It is friction term;q, And Position, velocity and acceleration of joint respectively;τ is control input;τ d It is disturbance;

[0076] 12) according to the dynamics model of mechanical arm, the state space expression form of mechanical arm subsystem is as follows:

[0077]

[0078] In the formula, State variables of the manipulator system S i i Output variables of the manipulator system S i

[0079]

[0080]

[0081]

[0082] Step two, the set of dynamic model uncertainty terms is regarded as lumped uncertainty terms, and a cascade radial basis function neural network is designed for accurate compensation, as follows:

[0083] 21) Define the tracking error function e i of the system i :

[0084] e i = q i - q id

[0085]

[0086] In the formula, μ i , υ i are gain coefficients; α i , β i are design parameters, and 0 < α i < 1, β i > 1; q id is the joint desired position;

[0087] 22) Define the integral sliding mode surface function ω i :

[0088]

[0089] In the formula, Σ i (q i ) = B i g i (q i ), Π i = B i g i (q i ) τ d

[0090] Its derivative is:

[0091]

[0092] In the formula, q​​i for the actual joint position;

[0093] 23) define a radial basis function neural network to estimate the uncertainty term and∑ i (q i );

[0094]

[0095]

[0096] where subscript "i" is the ith joint module; W iF and W iΣ are neural network weights, Φ i (·) is a neural network basis function; ε iF and ε iΣ are approximation errors; ε1 and ε2 are known constants; ε0 is a positive constant.

[0097] Step three, based on the estimation error generated by the RBF neural network, a time-varying disturbance observer is designed to accurately compensate it, as follows:

[0098] 31) according to the integral sliding mode function established in step two and its derivative, we get:

[0099]

[0100] where τ c is the compensation controller; Λ i =Π i is the external disturbance term; p i =ε iF +ε iΣ is the neural network estimation error;

[0101] The compensation controller is:

[0102]

[0103] where χ i , ε i are control parameters;

[0104] 32) define a time-varying disturbance observer to estimate the disturbance term Λ i :

[0105]

[0106]

[0107] where k i0 is the observer gain;

[0108] 33) The predicted value of the neural network estimation error is estimated by a cascaded neural network as follows:

[0109]

[0110] where W ρ is the ideal weight; Φ ρ is the Gaussian kernel function.

[0111] Step four, based on the dynamic model of the robot arm established in step one, the cascaded radial basis function neural network designed in step two and the time-varying disturbance observer designed in step three, a cascaded neural network-based integral sliding mode controller for the robot arm is designed, which is as follows:

[0112] 41) Define the velocity error function e i2 :

[0113]

[0114] where a1 is the virtual control law, and its expression is k1 is the gain coefficient;

[0115] 42) The cascaded neural network-based integral sliding mode controller for the robot arm is as follows:

[0116]

[0117] where u nom is the virtual control law;

[0118] where the adaptive update law is as follows:

[0119]

[0120]

[0121]

[0122] where η iF , η iΣ , γ ρ are adaptive law parameters, is a function of the compensation signal; is the adaptive update law of the neural network weight W iF ; is the adaptive update law of the neural network weight W iΣ ; is the adaptive update law of the neural network estimation error p i .

[0123] Embodiment

[0124] The embodiment utilizes the method to control the control arm, Figure 2 For the position curves of joint 1 and joint 2, it can be seen that the proposed algorithm can follow the expected position instruction in real time and has excellent tracking performance.

[0125] Figure 3 For the error curves of joint 1 and joint 2, compared with the neural network linear sliding mode control, the cascaded neural network integral sliding mode algorithm proposed in the patent has higher tracking accuracy.

[0126] Figure 4 For the torque curves of joint 1 and joint 2, compared with the neural network linear sliding mode control, the cascaded neural network integral sliding mode algorithm proposed in the patent requires smaller torque, is relatively smoother, and effectively reduces the chattering phenomenon caused by the linear sliding mode surface.

[0127] In summary, the application adopts the technical scheme of combining cascaded neural networks, sliding mode control and observer technology to design a trajectory tracking controller, ensures the tracking accuracy of the robot arm system, improves the convergence speed of the neural network, and effectively overcomes the chattering phenomenon of the linear sliding mode.

[0128] Although the embodiments of the application have been shown and described, it can be understood by those skilled in the art that various changes, modifications, replacements and variations can be made to the embodiments without departing from the principles and spirits of the application, and the scope of the application is defined by the appended claims and their equivalents.

Claims

1. A method for integral sliding mode control of a robot arm based on a cascaded neural network, characterized in that, The method comprises the following steps: Step one, based on the n degree of freedom robot arm with unknown external disturbance, the dynamic model is established; Step two, the set of uncertain terms of the dynamic model is regarded as a lumped uncertain term, and a cascade radial basis function neural network is designed for accurate compensation; Step three, based on the estimation error generated by the cascade radial basis function neural network, a time-varying disturbance observer is designed for accurate compensation; Step four, based on the robot arm dynamic model established in step one, the cascade neural network designed in step two and the time-varying disturbance observer designed in step three, a robot arm integral sliding mode controller based on cascade neural network is designed; The specific method of step two is as follows: 21) define a tracking error function e of the system i and a variable function s i : e i = q i - q id where μ i , υ i are gain coefficients; α i , β i are design parameters, and 0 < α i < 1, β i > 1; q id is the joint desired position; 22) Defining the integral sliding surface function ω i : wherein ∑ i (q i ) = B i g i (q i ), Π i = B i g i (q i )τ d The derivative thereof is: wherein q i is the actual joint position; 23) defining a radial basis neural network function to estimate the uncertainty term and∑ i (q i ); where the subscript "i" is the i-th joint module; W iF and W iΣ are neural network weights, Φ i (·) is a neural network basis function; ε iF and ε iΣ are approximation errors; ε1and ε2are known constants; ε0is a positive constant.

2. The integral sliding mode control method for a robot arm based on a cascade neural network according to claim 1, wherein, The specific method of step one is as follows: 11) The dynamic model of the n degree of freedom robot arm is as follows: where M(q) is the inertia matrix; is the Coriolis-centrifugal matrix; G(q) is the gravity vector; is the friction term; q, and are the joint position, velocity and acceleration, respectively; τ is the control input; τ d is the disturbance; 12) According to the dynamic model of the robot arm, the state space expression form of the robot arm subsystem is as follows: wherein is a state variable of the robot system S i , i = 1, 2,..., n; y i is an output quantity of the robot system S i ; 3. The integral sliding mode control method for a robot arm based on a cascade neural network according to claim 1, wherein, The specific method of step three is as follows: 31) According to the integral sliding mode surface function established in step two and its derivative, the following is obtained: where τ c is the compensating controller; Λ i = Π i is the external disturbance term; ρ i = ε iF + ε iΣ is the neural network estimation error; The compensation controller is: where χ i , ε i are control parameters; 32) Define a time-varying disturbance observer to estimate the disturbance term Λ i : where k i0 is the observer gain; 33) The prediction value of the neural network estimation error is estimated by the cascade neural network, as follows: In the formula, W ρ is an ideal weight; Φ ρ is a Gaussian-based function.

4. The integral sliding mode control method for a robot arm based on a cascade neural network according to claim 1, wherein, The specific method of step four is as follows: 41) define the velocity error function e i2 : In the formula, a1 is a virtual control law, expressed as k1 is a gain coefficient; 42) The robot arm integral sliding mode controller based on cascade neural network is as follows: In the formula, u nom is a virtual control law; Wherein, the adaptive update law is as follows: where η iF , η iΣ , γ ρ are adaptive law parameters, is a function of the compensation signal; is an adaptive update law for the neural network weights W iF ; is an adaptive update law for the neural network weights W iΣ ; is an adaptive update law for the neural network estimation error ρ i .

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