CN106406085B - Based on the space manipulator Trajectory Tracking Control method across Scale Model - Google Patents

Abstract

A space manipulator trajectory tracking control method based on a cross-scale model, in the case of parametric and non-parametric cross-scale features in the analysis of the modeling process of the floating-based space manipulator system, the real-time online tracking control of the manipulator joint space is performed. The control method introduces the radial basis neural network to approximate the variation term with cross-scale features in the dynamic model of the space manipulator, and uses the learning ability of the neural network to effectively suppress the influence of the variation term on the system, and design an adaptive law in real time. The weights of the neural network are adjusted, and the plane 2-link space manipulator is taken as an example for simulation verification, which realizes the fast and accurate tracking of the desired trajectory in the joint space of the space manipulator.

Description

Trajectory tracking control method of space manipulator based on cross-scale model

technical field

The invention belongs to the technical field of intelligent control and system simulation, and in particular relates to a trajectory tracking control method of a space manipulator based on a cross-scale model.

Background technique

With the continuous development of space technology, space exploration activities are further extended. However, the space environment has the characteristics of microgravity, high vacuum, strong radiation, and large temperature difference. In such a dangerous environment, the use of space robotic arms to assist or replace astronauts to complete a large number of arduous and dangerous tasks has become the unanimous goal of the world's space powers.

A significant difference from the ground manipulator is that the base of the space manipulator is moving, which is a very complex multi-input-multiple-output strongly coupled nonlinear time-varying system, which makes the control problem of the space manipulator different from that of the ground manipulator. Compared with many new features. The cross-scale features in the mathematical model of the space manipulator system are mainly manifested in the cross-scale of parametric and non-parametric changes. The cross-scale characteristics of parameters are mainly manifested in the dynamic and kinematic parameters that are difficult to obtain accurately, such as the position of the center of mass of each part, the moment of inertia, the load mass, etc. At the same time, there are many low-order time-varying parameters, such as fuel consumption base changes in quality, etc. Nonparametric cross-scale features cannot be described by steady parameters, such as nonlinear friction, structural resonance, and some higher-order unmodeled errors when the manipulator moves at low speeds. Some control methods that can achieve better results for ground manipulators may not be suitable for space manipulators. For the trajectory tracking control problem, the commonly used control methods at present mainly include PID control, adaptive control, robust control and intelligent control.

Parlaktuna and Ozkan transformed the control problem of the floating-based space manipulator from inertial space into joint space. After obtaining the dynamic equations of the linearization of the parameters of the space manipulator, a trajectory tracking of the floating-based space manipulator in joint space was designed. PD control method. However, PID control is a linear control method, ignoring the nonlinear factors and external disturbances in the space manipulator system. At the same time, PID control often requires large control energy, which is not suitable for situations with high tracking accuracy requirements. Therefore, when the space manipulator system has parametric or non-parametric cross-scale features, the control effect is not ideal.

Wang H and Xie Y designed a recursive adaptive control method for a floating-based space manipulator, using parameter adaptive law to estimate control parameters in real time; Liang Jie and Chen Li designed a nominal computational torque control with additional adaptive fuzzy The composite control method of compensation control can effectively overcome the influence of the unknown parameters of the space manipulator system; Zhang Fuhai et al. designed an adaptive trajectory tracking control method in Cartesian space, which can ensure the reversibility of the inertia matrix while maintaining the Real-time estimation of control parameters. However, the above adaptive control methods can only effectively overcome the influence of parameter changes on the space manipulator system. When the floating-based space manipulator system has non-parametric cross-scale characteristics such as external disturbances, it is difficult to ensure the space by simply using the adaptive control method. The stability of the manipulator system needs to be combined with other advanced control strategies to improve the robustness of the space manipulator system.

Xie Limin et al. designed a robust adaptive hybrid control method for the complex situation of limited input torque amplitude of space manipulator joint control and uncertain parameters in the space manipulator system, and robustly adaptively adjusted parameters; Pazelli et al. For the floating-based space manipulator system with the influence of parameter changes and external disturbances, various nonlinear H _∞ control methods are studied and analyzed. However, the above robust control method is designed based on the upper bound of prior knowledge, which is a relatively conservative control strategy, so it is not an optimal control.

Guo Yishen and Chen Li used radial basis neural network to propose an adaptive neural network control method that does not require a dynamic model of the manipulator, but did not discuss the solution when the model has cross-scale features; Xie Jian et al. For the neural network adaptive control method of floating base space manipulator, the nonlinear function and uncertainty upper bound of the model are approximated by radial basis neural network, and the proposed adaptive control law ensures the boundedness of the weights, but the The designed adaptive law is relatively complex, which affects the calculation speed; Zhang Wenhui et al. designed a robust adaptive control method of radial basis neural network, which is applied to the floating-based space manipulator system. Arm system, a neural network adaptive control method is designed. However, the compensation laws designed by these two methods for parameter changes contain all the information of the dynamic model, in which the nominal part of the model is known information. is the redundant part.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a neural network adaptive control method, which can achieve fast and accurate tracking of the desired trajectory in joint space for a space manipulator system with parametric and non-parametric cross-scales in the dynamic model.

In order to achieve the above object, the present invention provides a space manipulator trajectory tracking control method based on a cross-scale model. item is represented as The change term f is approximated by the neural network, so as to realize the compensation of the change term f. The control law of the neural network is: v is a robust term for overcoming the approximation error of the neural network, and its value is v=K _v sgn(r); the error function is The form of the neural network is a radial basis neural network, and the input of the radial basis neural network is taken as The ideal approximation algorithm is Then the output of the network is The weight adjustment adaptive law of radial basis neural network is D ₀ , C ₀ are the nominal model of the object, D ₀ =D-ΔD, C ₀ =C-ΔC, ΔD, ΔC are modeling error matrices, d is the total disturbance, e=q _d -q sum are the joint angle tracking error and angular velocity tracking error, respectively, q _d and q are the expected and actual joint vectors, respectively, K _P and K _I are the positive definite proportional and integral gain matrices, respectively, K _v is the robust term coefficient, is the weight vector of the neural network, is the output vector of the Gaussian basis function, c _i is the center vector of the ith node of the network, and b _i is the basis width parameter of node i.

Compared with the prior art, the beneficial effects of the present invention are:

Considering the modeling errors and external disturbances in the space manipulator system, the radial basis neural network is used to approximate the parameters and non-parametric terms f with cross-scale features in the dynamic model of the space manipulator system online. Error ΔD(q), and unknown interference Known nominal models do not need to be considered. Using the learning ability of the neural network, the influence of the cross-scale changes of parameters and non-parameters on the space manipulator system is effectively suppressed. The adaptive law can adjust the weights of the neural network online, which ensures the boundedness of the weights and solves the unknown upper bound. Bounded problem.

The simulation results of the present invention show that within 2s, the angular displacement and angular velocity of joint 1 and joint 2 quickly track the desired trajectory. The joint angle tracking error is stable within ±5×10 ^-3 rad, and the joint angular velocity error is stable within ±5×10 ^-3 rad/s, enabling fast and accurate tracking of the desired trajectory in the joint space of the space manipulator.

Description of drawings

Figure 1 is a model diagram of a plane 2-link space manipulator;

Fig. 2 is the structural block diagram of the neural network adaptive control method;

Fig. 3 is the curve of joint 1 angle tracking changing with time;

Fig. 4 is the curve of joint 2 angle tracking changing with time;

Fig. 5 is the curve of joint 1 angular velocity tracking changing with time;

Fig. 6 is the curve of joint 2 angular velocity tracking changing with time;

Fig. 7 is the curve of joint angle tracking error of joint 1 changing with time;

Fig. 8 is the curve of joint angle tracking error of joint 2 changing with time;

Fig. 9 is the curve that joint 1 joint angular velocity tracking error changes with time;

Fig. 10 is the curve of joint 2 joint angular velocity tracking error changing with time;

Fig. 11 is the curve of the control torque of joint 1 changing with time;

FIG. 12 is a graph showing the change of the control torque of the joint 2 with time.

Among them: ∑I, inertial coordinate system; ∑0, motion base coordinate system; O, origin of inertial coordinate system; CM, total center of mass of space manipulator system; B _i , rigid body i, ith link of manipulator; B ₀ , moving base, link 0; C _i , the center of mass of link i; C ₀ , the center of mass of the base; ri ∈ R ² , the position vector of the center of mass of link _i ; r ₀ , the position vector of the center of mass of the base ; _rc ∈ R ² , the position vector of the centroid CM of the space manipulator system; p _i ∈ R ² , the position vector of the link i; a _i , the vector from the joint J _i to the centroid of the link i; b _i , from the link The vector from the bar i centroid to the joint J _i+1 ; b ₀ , the vector from the base centroid to the joint J ₁ .

Detailed ways

The plane 2-link space manipulator model is shown in Figure 1, which consists of a freely floating motion base B ₀ and two arms B ₁ and B ₂ .

The dynamic parameters of the space manipulator system are described in Table 1. The vector composed of the initial position and attitude angle of the base and the initial attitude angles of link 1 and link 2 is [q _b , q _s ] ^T = [ x, y, q ₀ , q ₁ , q ₂ ] ^T , the initial velocity vectors of the base and link 1 and link 2 are The initial values of various parameters and expected trajectories are shown in Table 2.

Table 1 Plane 2-link space manipulator system parameter table

Table 2. Initial value of neural network adaptive control simulation for space manipulator

Set the control parameters as K _P =diag{100,100,100,100,100}, K _I =diag{250,250,250,250,250}, _Kv =0.2, F _W =diag{0.0005,0.0005,0.0005,0.0005,0.0005}, according to the control method structure block diagram of Figure 2 Simulation verification shows that the present invention takes the plane 2-link floating base space manipulator system as the research object, and the dynamic equation is

Among them, q=[q ₁ q ₂ ] ^T is the joint angular displacement, D(q) _5×5 is the inertia matrix of the space manipulator, represents a matrix including nonlinear centrifugal force and Coriolis force, and τ is the control torque.

The dynamic equation of the space manipulator satisfies the following properties:

Property 1 The inertia matrix D(q) is a symmetric, positive definite, bounded matrix.

Property 2 Choose the appropriate can make D(q) and Satisfy

Property 3 exists k _c > 0 and positive definite function make

Property 4 The given error matrix satisfies ΔD _l ≤||ΔD||≤ΔD _h , ΔC _l ≤||ΔC||≤ΔC _h , where h and l are the upper and lower bounds respectively.

In order to achieve fast and accurate tracking of the desired trajectory in the joint space, the parametric and non-parametric cross-scale characteristics of the space manipulator system should also be considered during modeling. Introducing external disturbances, the dynamic equation can be rewritten into the following form

in, is the sum of disturbances, including friction torque disturbances and other external disturbances.

In practical engineering, the actual model of the object is difficult to obtain, that is, it is impossible to obtain accurate D(q), Only ideal nominal models can be built. The dynamic equation is written in the form of the sum of the ideal model and the variation term with cross-scale characteristics, then it can be expressed as

Among them, D ₀ and C ₀ are nominal models of the object, D ₀ (q)=D(q)-ΔD(q), ΔD(q), is the error matrix, is the parametric and non-parametric terms with cross-scale features including modeling error and external disturbance torque, is an unknown nonlinear time-varying function, and the specific form is

Since D(q) is reversible, we can get

The design error function is

where e=q _d −q and are the joint angle tracking error and acceleration tracking error, respectively, q _d and q are the expected and actual joint vectors, respectively, and K _P and K _I are the positive definite proportional and integral gain matrices, respectively.

derivation available

make Derive Equivalent Control Law

Therefore, the stable closed-loop system is obtained as

For the nominal model, the control law is designed as

Taking into account the unknown interference, it can be concluded that

have to

It can be seen that the variation term of cross-scale features in the model is

The radial basis neural network is used to approximate f, and the network input takes Then the network output is

but

The design control law is

Among them, v=K _v sgn(r) is a robust term, which is used to overcome the influence caused by the approximation error of the neural network.

Define the Lyapunov function as

Among them, D and F _W are positive definite matrices, namely Then V is positive definite.

Take the derivative, and combine with property 2 to get

tidy up

According to conditions Considering v=K _v sgn(r), we can get

Pick Then the following adaptive law can be designed to adjust the weights of the radial basis neural network

So get

For the convenience of description, define

then

From properties 3 and 4, K _v I _n >|Q|, where I _n =[1,1,...,1] ^T ∈R ⁿ , then

The input of the control structure is the expected trajectory of the joint angle, and the actual value of the output joint angle is compared with the actual value of the joint angle as negative feedback, and the neural network adaptive control system is designed according to the tracking error, error function and robust term of the joint angle. The simulation results are shown in Figure 3-Figure 12.

The time-varying curves of the angle of joint 1 and joint 2 are shown in Figures 3 and 4, and the time-varying curves of the angular velocity are shown in Figures 5 and 6. The red dashed line represents the expected value of trajectory tracking, and the blue solid line represents the actual joint vector. It can be seen that the angular displacement and angular velocity of joint 1 and joint 2 quickly track the desired trajectory within 2s.

The time-dependent curves of the angle tracking errors of joint 1 and joint 2 are shown in Figure 7 and Figure 8. It can be seen that the joint angle tracking error remains within the range of ±5×10 ^-3 rad.

The angular velocity tracking error curves of joint 1 and joint 2 are shown in Figure 9 and Figure 10. It can be seen that the joint angular velocity tracking error remains within the range of ±5×10 ^-3 rad/s.

The curves of the control torque of joint 1 and joint 2 with time are shown in Figure 11 and Figure 12. It can be seen that the control torque of each joint is kept within the achievable range.

The curve of the position and attitude angle of the moving base with time, it can be seen that the movement of link 1 and link 2 causes the change of the position and attitude of the base to be relatively gentle, which is suitable for the trajectory tracking control of the floating-based space manipulator.

The experimental results verify the effectiveness of the neural network adaptive control algorithm. When there are parametric and non-parametric cross-scale features in the dynamic model, the desired trajectory can be quickly tracked online, with certain robustness and anti-interference.

Claims (1)

1. A space manipulator trajectory tracking control method based on a cross-scale model, characterized in that: a neural network adaptive control law is designed, and the variation term that exists in the space manipulator system dynamics model with cross-scale features is expressed as: The change term f is approximated by the neural network, so as to realize the compensation of the change term f. The control law of the neural network is: v is a robust term used to overcome the approximation error of the neural network, and its value is v=K _v sgn(r); the error function is The form of the neural network is the radial basis neural network, and the input of the radial basis neural network is taken as The ideal approximation algorithm is Then the output of the network is The weight adjustment adaptive law of radial basis neural network is D ₀ , C ₀ are the nominal model of the object, D ₀ =D-ΔD, C ₀ =C-ΔC, ΔD, ΔC are modeling error matrices, d is the total disturbance, e=q _d -q sum are the joint angle tracking error and angular velocity tracking error, respectively, q _d and q are the expected and actual joint vectors, respectively, K _P and K _I are the positive definite proportional and integral gain matrices, respectively, K _v is the robust term coefficient, is the weight vector of the neural network, is the output vector of the Gaussian basis function, c _i is the center vector of the ith node of the network, b _i is the basis width parameter of node i, D is the inertia matrix of the space manipulator, and C represents the nonlinear centrifugal force and Coriolis force. matrix, F _W is a positive definite matrix.