CN109352656A - A multi-joint manipulator control method with time-varying output constraints - Google Patents

Abstract

The invention discloses a multi-joint mechanical arm control method with time-varying output constraints. The specific steps include: (1) establishing a multi-joint mechanical arm dynamics model and a desired tracking trajectory under the time-varying output constraints; (2) establishing Convert the system with time-varying output constraints to the transfer function of the new system without constraints; (3) Convert the original manipulator system to the new manipulator system according to the transfer function obtained in step (2); (4) Define the conversion The tracking error signal of the rear manipulator system; (5) Design a stable adaptive neural network controller for the converted manipulator system. The present invention can realize the accurate trajectory tracking of the manipulator under the condition that the system parameters are completely unknown and have time-varying output constraints, and ensure the satisfaction of the time-varying output constraints.

Description

A multi-joint manipulator control method with time-varying output constraints

technical field

The invention relates to the field of automation, in particular to a multi-joint mechanical arm control method with time-varying output constraints.

Background technique

The rapid development of science and technology has provided assistance for the further application and promotion of robotic arms. Multi-joint robotic arms are the most widely used automated mechanical equipment, and are widely used in industrial manufacturing, military, medical, entertainment and even space exploration. In practical applications, various constraints exist in the robotic arm control system, such as input saturation, limited task space, and limited speed. Once these constraints are violated, the performance of the robotic arm system may be degraded, or even lead to damage to the system and threaten the safety of the staff related to the robotic arm system. With the further development of science and technology, the concept of human-computer interaction is proposed, and more and more robots will work around humans in the future. Therefore, designing controllers for robotic arm systems with specified constraints has important theoretical significance and practical application value. However, most of the current researches mainly focus on the stability and control accuracy of the robot system, which are insufficient in the controller design considering the output constraints. With the existing recursive design methods, most of the research results can only solve the manipulator control problem with constant output constraints, and usually set the upper and lower bounds of the restricted output relatively loosely, which increases the conservativeness of the algorithm. At the same time, it also limits the practicability of the algorithm.

As a time-varying, coupled multi-input and multi-output complex nonlinear system, the motion control of the multi-joint manipulator is extremely complex, and in the actual control design process, the parameters of the manipulator are often unknown, or the parameters are measured. There is a large error, so there is a need for a controller design tool for the unknown parameter model. The artificial neural network uses the approximation of the neural network to approximate the unknown dynamic model of the manipulator system by using the neural network, so as to achieve the purpose of precise control even when the system has unknown parameters. There have been strict theoretical analysis methods for the selection of neural network topology and the adjustment of neural network weights, so neural networks have been widely used in manipulator control.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art and provide a multi-joint mechanical arm control method with time-varying output constraints. The invention can realize the high-precision tracking control of the multi-joint mechanical arm with time-varying output constraints under the condition that the parameters are completely unknown. The invention converts a system with time-varying output constraints into a new system without constraints by establishing a system conversion method, solves the problem of unknown parameters of the manipulator by using a neural network, and combines the backstepping method to establish an automatic system for the converted nonlinear system. A neural network controller is adapted to realize trajectory tracking control. The invention realizes fast and stable tracking control while ensuring the time-varying output constraint of the mechanical arm.

The object of the present invention can be realized through the following technical solutions:

A multi-joint manipulator control method with time-varying output constraints, the specific steps include:

(1) Establish the dynamic model of the multi-joint manipulator under the time-varying output constraint and the desired tracking trajectory;

(2) Establish a transfer function that converts a system with time-varying output constraints into a new system without constraints;

(3) According to the conversion function obtained in step (2), the original manipulator system is converted into a new manipulator system;

(4) Define the tracking error signal of the robotic arm system after conversion;

(5) Design a stable adaptive neural network controller for the converted manipulator system.

Specifically, in step (1), the dynamic model of the multi-joint manipulator under the time-varying output constraint is a dynamic model of the manipulator with strong nonlinear coupling, which is expressed as:

where X ₁ =q, τ represents the control torque, M(X ₁ ) represents the inertia matrix, C _m (X ₁ , X ₂ ) represents the centripetal force matrix, G(X ₁ ) represents the universal gravitational vector, and J ^T (X ₁ ) represents the Jacobian matrix of the manipulator, F(X ₂ ) represents the friction vector, f(t) represents the disturbance term from people and the outside world; M(X ₁ ), C _m (X ₁ , X ₂ ), G(X ₁ ), F(X ₂ ) , J ^T (X ₁ ), f(t) are unknown; the time-varying output constraint of the manipulator is expressed as:

Further, the established dynamic model of the manipulator takes the joint angular displacement and the joint angular displacement of the manipulator as state variables, which are expressed as:

Among them, q=[q ₁ q ₂ ... q _n ] ^T represents the angular displacement, q _d =[q _d1 q _d2 ... q _dn ] ^T represents the given output tracking trajectory, e=[e ₁ e ₂ ... e _n ] ^T represents the output tracking error, and q = [ q ₁ q ₂ ... q _n ] represent the upper and lower bounds of the time-varying output constraints of the manipulator, respectively, n represents the number of joints of the rigid manipulator with time-varying output constraints, and η _i (t) are intermediate variables.

Specifically, in the step (2), the constraint of the time-varying output is first converted into a constraint on the tracking error of the output angle of the manipulator, and then a conversion function is designed to convert the originally constrained manipulator system into an unconstrained manipulator system. New robotic arm system.

Design a new state variable s _i and a strictly monotonically increasing smooth function Q _i (s _i ,η _i ) about s _i and η _i , expressed as:

It only needs to be _bounded to make the output satisfy the time-varying output constraint.

Further, the strictly monotonically increasing smooth function and transition state variables are specifically expressed as:

in, represents the derivative of the transformation variable _si with respect to time.

Specifically, in the step (3), the converted new system obtained according to the specific conversion function is expressed as:

in, Represents the derivative of the transformed intermediate variable, H and R are expressed as:

Specifically, in the step (4), the tracking error of the robotic arm system after conversion is expressed as:

z ₁ =[z ₁₁ ,z ₁₂ ,...,z _1n ] ^T =[s ₁ ,s ₂ ,...,s _n ] ^T

z ₂ =[z ₂₁ ,z ₂₂ ,...,z _2n ] ^T =X ₂ -α

Among them, z ₁ , z ₂ represent the error variables used in the backstepping design process in the new system. α is a virtual control variable, which is expressed as:

Wherein, k ₁ =diag{k ₁₁ ,k ₁₂ ,...,k _1n } represents a parameter matrix that needs to be set.

Specifically, in the step (5), the designed multi-joint manipulator adaptive neural network controller with time-varying output constraints is expressed as:

Among them, k ₂ =diag{k ₂₁ ,k ₂₂ ,...,k _2n } represents a set parameter matrix, represents a local RBF neural network for approximating unknown dynamics in closed-loop systems, Represents the Gaussian base function, N is the number of nodes in the neural network, ξ _j , j=1,...N represents different nodes in the space, called the center point of the Gaussian function, η _j ,j=1,... N represents the center width, represents the input of the neural network, An estimated vector representing the weights of the RBF neural network used.

Further, the weight update rate of the neural network is:

in, It represents a constant representing the learning rate that can be set artificially, and σ _i > 0 represents a small constant that can be set artificially.

Compared with the prior art, the present invention has the following beneficial effects:

1. The control method provided by the present invention does not require system parameters of the manipulator, and can perform high-performance tracking control on the manipulator when the system has unknown external disturbances without destroying the time-varying output constraints.

2. The present invention converts the multi-joint mechanical arm with time-varying output constraints into a new system without constraints by establishing a system conversion method, thereby reducing the conservative design of the control scheme.

3. The controller in the present invention can ensure that the manipulator satisfies the time-varying output constraint under any given known time-varying output constraint, and solves the possibility of existing conventional adaptive neural network controllers facing the time-varying output constraint. Existing out-of-bounds issues.

Description of drawings

FIG. 1 is a schematic diagram of a connecting rod plane manipulator in an embodiment of the present invention.

FIG. 2 is a control method of a multi-joint robotic arm with time-varying output constraints provided by an embodiment of the present invention.

FIG. 3 is a simulation diagram of the tracking situation of the angular displacement of the joint of the manipulator in the embodiment of the present invention.

FIG. 4 is a simulation diagram of the tracking situation of the angular displacement of the joint of the manipulator in the embodiment of the present invention.

FIG. 5 is an error diagram between a joint angular displacement and a given tracking angular displacement trajectory in an embodiment of the present invention.

FIG. 6 is a change curve diagram of a conversion variable in an embodiment of the present invention.

FIG. 7 is a simulation diagram of a control input of a robotic arm in an embodiment of the present invention.

FIG. 8 is a simulation diagram of the control input of the manipulator in the embodiment of the present invention.

Detailed ways

The present invention will be described in further detail below with reference to the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

Example

In this embodiment, the manipulator is a two-link plane manipulator, and the specific structure is shown in FIG. 1 .

Figure 2 shows a specific flow chart of a multi-joint manipulator control method with time-varying output constraints. The specific steps include:

(1) Establish the dynamic model of the multi-joint manipulator under the time-varying output constraint and the desired tracking trajectory;

The two-link mechanical arm is composed of two connecting rods, and angular displacement sensors and speed sensors are installed at each joint point of the connecting rods to measure the joint angular position and angular velocity. The dynamic model of the two-link planar manipulator is expressed as:

where X ₁ =q, The joint angular displacement vector is q=[q ₁ ,q ₂ ] ^T , and the joint angular velocity vector is represents the friction term, τ represents the control torque, M(q) represents the inertia matrix, represents the centripetal force matrix, G(q) represents the universal gravitational vector; J(q) represents the Jacobian matrix of the manipulator, f(t) represents the unknown disturbance, M(q), G(q), J(q), are unknown.

In this embodiment, the given reference trajectory is expressed as:

X _d1 = [sin(t), cos(t)] ^T

Further set the time-varying output constraint, which is expressed as:

q (t)=[-0.1× ^2-0.8-0.04 +sin(t)-0.495× ^2-1.2t- 0.03+cos(t)] ^T

In this embodiment, it is necessary to ensure the time-varying output constraint Next, the trajectory tracking control of the two-link planar manipulator is realized.

M(q), G(q), J(q), It is represented as:

Among them, q ₁ , q ₂ represent the angular displacement of joint 1 and joint 2 respectively; m ₁ , m ₂ represent the mass of link 1 and link 2 respectively; l ₁ , l ₂ represent the mass of link 1 and link 2 respectively length; I ₁ , I ₂ represent the inertia of connecting rod 1 and connecting rod 2 respectively; g represents the acceleration of gravity;

In this embodiment, the relevant parameters of the system are specifically:

l ₁ =0.36m,l ₂ =0.32m,m ₁ =2.2Kg,m ₂ =0.86Kg,g=9.8m/s ²

I ₁ =64.25×10 ^-3 kgm ² , I ₂ =22.42×10 ^-3 kgm ²

The friction term is expressed as:

The disturbance term from the environment is expressed as:

f(t)=[sin(t)+1 cos(t)+0.5] ^T

(2) Establish a transfer function that converts a system with time-varying output constraints into a new system without constraints;

Design a new state variable s _i and a strictly monotonically increasing smooth function Q _i (s _i ,η _i ) about s _i and η _i . The strictly monotonically increasing smooth function and transition state variables are specifically expressed as:

in, represents the derivative of the transformation variable s _i with respect to time, e _i , η _i , The specific expression is:

(3) According to the conversion function obtained in step (2), the original manipulator system is converted into a new manipulator system; the converted new system obtained according to the specific conversion function is expressed as:

in, Represents the derivative of the transformed intermediate variable, H and R are expressed as:

(4) Define the tracking error signal of the robotic arm system after conversion;

In this embodiment, since the dynamic model of the robotic arm is completely unknown, a neural network is used. Approximate the unknown dynamics of a closed-loop system.

input to the neural network and have:

Wherein, k ₁ =diag{k ₁₁ ,k ₁₂ } represents the designed feedback gain parameter.

(5) Design a stable adaptive neural network controller for the converted manipulator system.

The designed multi-joint manipulator adaptive neural network controller with time-varying output constraints is expressed as:

where k ₂ =diag{k ₂₁ ,k ₂₂ } represents the control gain matrix, represents a local RBF neural network for approximating unknown dynamics in a closed-loop system, S _i (Z)=[s _i1 (||Z-ξ ₁ ||),…,s _iN (||Z-ξ _N ||) ] ^T , represents the Gaussian base function, N represents the number of Gaussian base functions in the neural network, ξ _j , j=1,...N represents different nodes in the space, called the center point of the Gaussian function, η _j , j=1, ...N is the center width, represents the input of the neural network, represents the estimated vector of the weights of the RBF neural network used, and N represents the number of nodes in the neural network.

Further, the weight update rate of the neural network is:

in, It represents a constant representing the learning rate that can be set artificially, and σ _i > 0 represents a small constant that can be set artificially.

In this embodiment, the initial conditions of the system are:

X(0)=[0,1;0,0]

Controller parameters: initial value of neural network weights The number of neural network nodes is N=4096, Γ=diag{70}, η=0.7, δ=0.01, k ₁ =diag{80 40}, k ₂ =diag{88 86}.

Figure 3 is a simulation diagram of the tracking situation of the joint angular displacement _q1 of the manipulator. FIG. 4 is a simulation diagram of the tracking situation of the joint angular displacement q ₂ of the manipulator. Fig. 5 is an error diagram between the joint angular displacements q ₁ , q ₂ and the given tracking angular displacement trajectories q _d1 , q _d2 . It can be seen from Figure 3, Figure 4 and Figure 5 that under the designed controller, the manipulator can achieve a good output trajectory tracking effect, and its output can meet the given time-varying output constraints. Figure 6 is the change diagram of the designed joint angular displacement tracking error transformation variables s ₁ , s ₂ . The boundedness of the error transformation variables s ₁ , s ₂ also ensures that the time-varying output constraints are satisfied. Fig. 7 is the simulation diagram of the control input u1 _of the manipulator. Fig. 8 is a simulation diagram of the control input u ₂ of the manipulator.

The above-mentioned embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above-mentioned embodiments, and any other changes, modifications, substitutions, combinations, The simplification should be equivalent replacement manners, which are all included in the protection scope of the present invention.

Claims (9)

1. a multi-joint mechanical arm control method with time-varying output constraint, is characterized in that, concrete steps comprise: (1) Establish the dynamic model of the multi-joint manipulator under the time-varying output constraint and the desired tracking trajectory; (2) Establish a transfer function that converts a system with time-varying output constraints into a new system without constraints; (3) According to the conversion function obtained in step (2), the original manipulator system is converted into a new manipulator system; (4) Define the tracking error signal of the robotic arm system after conversion; (5) Design a stable adaptive neural network controller for the converted manipulator system. 2. a kind of multi-joint manipulator control method with time-varying output constraint according to claim 1, is characterized in that, in step (1), the multi-joint manipulator dynamic model under described time-varying output constraint is: The dynamic model of the manipulator with strong nonlinear coupling is expressed as: where X ₁ =q, q=[q ₁ q ₂ ... q _n ] ^T represents the angular displacement, τ represents the control torque, M(X ₁ ) represents the inertia matrix, C _m (X ₁ , X ₂ ) represents the centripetal force matrix, G(X ₁ ) represents the universal gravitational vector, J ^T (X ₁ ) represents the Jacobian matrix of the manipulator, F(X ₂ ) represents the friction force vector, and f(t) represents the disturbance term from people and the outside world; M(X ₁ ), C _m ( X ₁ , X ₂ ), G(X ₁ ), F(X ₂ ), J ^T (X ₁ ), f(t) are all unknown; the time-varying output constraints of the manipulator are expressed as: 3. a kind of multi-joint mechanical arm control method with time-varying output constraint according to claim 2 is characterized in that, the established dynamic model of the mechanical arm takes the joint angular displacement of the mechanical arm and the joint angular displacement as state variables, representing for: Among them, q=[q ₁ q ₂ ... q _n ] ^T represents the angular displacement, q _d =[q _d1 q _d2 ... q _dn ] ^T represents the given output tracking trajectory, e=[e ₁ e ₂ ... e _n ] ^T represents the output tracking error, and q = [ q ₁ q ₂ ... q _n ] represent the upper and lower bounds of the time-varying output constraints of the manipulator, respectively, n represents the number of joints of the rigid manipulator with time-varying output constraints, and η _i (t) are intermediate variables. 4. a kind of multi-joint manipulator control method with time-varying output constraint according to claim 1, is characterized in that, in described step (2), design a new state variable _si and one about _si Strictly monotonically increasing smooth function Q _i (s _i ,η _i ) with η _i , expressed as: Among them, e=[e ₁ e ₂ ... e _n ] ^T represents the output tracking error, and q = [ q ₁ q ₂ ... q _n ] represent the upper and lower bounds of the time-varying output constraints of the manipulator, respectively, n represents the number of joints of the rigid manipulator with time-varying output constraints, and η _i (t) are intermediate variables; It only needs to be _bounded to make the output satisfy the time-varying output constraint. 5. a kind of multi-joint manipulator control method with time-varying output constraint according to claim 4, is characterized in that, strictly monotonically increasing smooth function and transition state variable are specifically expressed as: in, represents the derivative of the transformation variable _si with respect to time. 6. A multi-joint manipulator control method with time-varying output constraints according to claim 1, wherein in the step (3), the converted new system obtained according to the specific conversion function is expressed as : in, Represents the derivative of the transformed intermediate variable, H and R are expressed as: in, q=[q ₁ q ₂ ... q _n ] ^T represents the angular displacement, M(q) represents the inertia matrix, represents the centripetal force matrix, G(q) represents the universal gravitational vector, J ^T (q) represents the Jacobian matrix of the manipulator, f(t) represents the disturbance term from people and the outside world, e=[e ₁ e ₂ ... e _n ] ^T represents the output tracking error, and η _i (t) are intermediate variables. 7. a kind of multi-joint manipulator control method with time-varying output constraint according to claim 1, is characterized in that, in described step (4), the tracking error of manipulator system after conversion is expressed as: z ₁ =[z ₁₁ ,z ₁₂ ,...,z _1n ] ^T =[s ₁ ,s ₂ ,...,s _n ] ^T z ₂ =[z ₂₁ ,z ₂₂ ,...,z _2n ] ^T =X ₂ -α where z ₁ , z ₂ represent the error variables used in the backstepping design process in the new system, α is a virtual control variable, which is expressed as: Among them, k ₁ =diag{k ₁₁ ,k ₁₂ ,...,k _1n } represents a parameter matrix to be set, and q _d =[q _d1 q _d2 ... q _dn ] ^T represents a given output tracking trajectory . 8. The method for controlling a multi-joint manipulator with time-varying output constraints according to claim 1, wherein in the step (5), the designed multi-joint manipulator with time-varying output constraints automatically The adaptive neural network controller is expressed as: Among them, k ₂ =diag{k ₂₁ ,k ₂₂ ,...,k _2n } represents a set parameter matrix, represents a local RBF neural network, S _i (Z)=[s _i1 (||Z-ξ ₁ ||),…,s _iN (||Z-ξ _N ||)] ^T , represents the Gaussian base function, N represents the number of Gaussian base functions in the neural network, ξ _j , j=1,...N represents different nodes in the space, called the center point of the Gaussian function, η _j , j=1, ...N is the center width, represents the input of the neural network, Represents the estimated vector of the weights of the RBF neural network used, z ₁ , z ₂ represent the error variables in the new system, and α is the virtual control quantity. 9. A multi-joint robotic arm control method with time-varying output constraints according to claim 8, wherein the weight update rate of the neural network is: in, It represents a constant representing the learning rate that can be set artificially, and σ _i > 0 represents a small constant that can be set artificially.