CN106406085B - Based on the space manipulator Trajectory Tracking Control method across Scale Model - Google Patents
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Abstract
It is a kind of based on the space manipulator Trajectory Tracking Control method across Scale Model, there are in the case where parameter and across scale feature nonparametric in analysis free floating space manipulator systems modeling process, real-time online tracing control is carried out to joint of mechanical arm space.The control method is introduced into radial base neural net and is approached in the presence of the variation item across scale feature in space manipulator kinetic model, utilize the learning ability of neural network, effectively inhibit influence of the variation item to system, and design adaptive law adjusts the weight of neural network in real time, simulating, verifying is carried out by taking 2 connecting rod space manipulator of plane as an example, realizes the quick accurate tracking in space manipulator joint space to desired trajectory.
Description
Technical Field
The invention belongs to the technical field of intelligent control and system simulation, and particularly relates to a space manipulator trajectory tracking control method based on a cross-scale model.
Background
With the continuous development of space technology, the space exploration activity is further extended. However, the space environment has the characteristics of microgravity, high vacuum, strong radiation, large temperature difference and the like, and in the dangerous environment, a space mechanical arm is adopted to assist or replace an astronaut to complete a large number of tasks with severe dangers, so that the space mechanical arm becomes a consistent target of all space countries in the world.
One significant difference from a floor robot is that the base of the space robot is moving, which is a very complex multiple-input-multiple-output, strongly coupled nonlinear time varying system, making the control problem of the space robot have many new features compared to a floor robot. The cross-scale characteristics in the mathematical model of the space manipulator system are mainly represented by the cross-scale of parameter and non-parameter changes. The cross-scale characteristics of the parameters are mainly represented by dynamics and kinematics parameters which are difficult to obtain accurately, such as the positions of the mass centers of all parts, the rotational inertia, the load mass and the like, and meanwhile, a plurality of low-order time-varying parameters are also provided, such as the variation of the base mass along with the fuel consumption. The non-parametric cross-scale characteristics cannot be described by constant parameters, such as non-linear friction force, structural resonance, some high-order unmodeled errors and the like when the mechanical arm moves at a low speed. Some control methods that can achieve better results for a ground robot arm are not necessarily applicable to space robots. Aiming at the problem of trajectory tracking control, the current commonly used control methods mainly comprise PID control, self-adaptive control, robust control and intelligent control.
The Parlaktuna and Ozkan convert the control problem of the floating-base space manipulator into a joint space from an inertial space, and after a dynamic equation of space manipulator system parameter linearization is obtained, a PD control method for tracking the track of the floating-base space manipulator in the joint space is designed. However, the PID control belongs to a linear control method, which ignores the non-linear factors and external interference in the space mechanical arm system, and meanwhile, the PID control usually requires a large control energy, and is not suitable for the situation with a high requirement on tracking accuracy. The control effect is not ideal when the spatial mechanical arm system has a parametric or non-parametric cross-scale feature.
Wang H and Xie Y design a recursive self-adaptive control method aiming at the floating-base space manipulator, and estimate control parameters in real time by using a parameter self-adaptive law; the beam agility and the standing force design a composite control method of nominal calculation torque control and additional adaptive fuzzy compensation control, and the influence of unknown parameters of a space manipulator system can be effectively overcome; zhang Fuhai and the like design a self-adaptive track tracking control method in Cartesian space, and control parameters can be estimated in real time while the inertia matrix is ensured to be reversible. However, the above adaptive control method only effectively overcomes the influence of parameter change on the space manipulator system, and when the floating-base space manipulator system has nonparametric cross-scale characteristics such as external disturbance, the stability of the space manipulator system is difficult to be ensured by simply adopting the adaptive control method, and the robustness of the space manipulator system needs to be improved by combining with other advanced control strategies.
Aiming at the complex conditions that the amplitude of the control input torque of the space manipulator joint is limited and uncertain parameters exist in a space manipulator system, such as Xijimin and the like, a robust adaptive hybrid control method is designed to perform robust adaptive adjustment on the parameters; pazelli et al for various nonlinear H aiming at floating-based space manipulator system with parameter change influence and external interference∞The control method is used for research and analysis. However, the robust control method is designed based on the upper bound of the prior knowledge, is a conservative control strategy, and is not optimal control.
Guo Yishen and Chenli utilize the radial basis function neural network, and provide a self-adaptive neural network control method without a mechanical arm dynamic model, but do not discuss a solution method when the model has cross-scale characteristics; xie arrow etc. has proposed a neural network adaptive control method to float the space manipulator of the base, through the nonlinear function and uncertainty upper bound that the neural network approaches the model of radial basis, the adaptive control law put forward has guaranteed the boundedness of the weight, but the adaptive law designed is comparatively complicated, influence the computational rate; zhang Wenhui designs a radial basis neural network robust self-adaptive control method, which is applied to a floating basis space mechanical arm system, and thunder designs a neural network self-adaptive control method aiming at the floating basis space mechanical arm system with limited control moment, however, compensation laws designed by the two methods aiming at parameter change contain all information of a dynamic model, wherein the nominal part of the model is known information, and the compensation laws belong to redundant parts.
Disclosure of Invention
The invention aims to provide a neural network self-adaptive control method, which aims at a spatial mechanical arm system with parametric and nonparametric cross-scale in a dynamic model to realize the rapid and accurate tracking of a joint space to an expected track.
In order to achieve the above object, the present invention provides a space manipulator trajectory tracking control method based on a cross-scale model, which is characterized in that: designing a neural network self-adaptive control law, and expressing a change item with cross-scale characteristics in a space manipulator system dynamic model asApproximating the variation term f using a neural network, therebyThe compensation of the change term f is realized, and the neural network control law isv is a robust term for overcoming the approximation error of the neural network, and has a value of v ═ Kvsgn (r); an error function ofThe neural network is in the form of a radial basis neural network, the inputs to which are takenThe ideal approximation algorithm isThe output of the network isThe weight adjustment of the radial basis function neural network is self-adaptive toD0、C0Being a nominal model of the object, D0＝D-ΔD，C0C- Δ C, Δ D, Δ C are modeling error matrices, D is sum perturbation, e-qdQ andrespectively joint angle tracking error and angular velocity tracking error, qdAnd q are the desired and actual joint vectors, respectively, KP、KIRespectively, a positive proportional and integral gain matrix, KvIn order to be a robust term coefficient,is the weight vector of the neural network,is the output vector of the Gaussian basis function, ciAs the central vector of the ith node of the network, biIs the base width parameter of node i.
Compared with the prior art, the invention has the beneficial effects that:
considering modeling errors and external interference in a space mechanical arm system, performing online approximation on parameters and nonparametric terms f with cross-scale characteristics in a space mechanical arm system dynamic model by using a radial basis function neural network, wherein f only comprises modeling errors delta D (q),And unknown interferenceNo consideration is required for the known nominal model. The learning ability of the neural network is utilized, the influence of parameter and non-parameter cross-scale change on a space mechanical arm system is effectively inhibited, the weight of the neural network can be adjusted on line by a self-adaptive law, the boundedness of the weight is guaranteed, and the problem of unknown bounded upper bound is solved.
The simulation result of the invention shows that the angular displacement and the angular speed of the joint 1 and the joint 2 can track the expected track quickly within 2 s. The tracking error of the joint angle is stabilized within +/-5 multiplied by 10-3Within rad, the angular velocity error of the joint is stabilized at +/-5 multiplied by 10-3Within rad/s, the quick and accurate tracking of the expected track in the space of the space manipulator joint is realized.
Drawings
FIG. 1 is a diagram of a planar 2-link space robot arm model;
FIG. 2 is a block diagram of a neural network adaptive control method;
FIG. 3 is a graph of joint 1 angle tracking over time;
FIG. 4 is a plot of joint 2 angle tracking over time;
FIG. 5 is a graph of the angular velocity tracking of the joint 1 over time;
FIG. 6 is a plot of joint 2 angular velocity tracking over time;
FIG. 7 is a graph of joint angle tracking error of the joint 1 over time;
FIG. 8 is a graph of joint angle tracking error for joint 2 over time;
FIG. 9 is a graph of angular velocity tracking error of the joint 1 over time;
FIG. 10 is a graph of joint 2 joint angular velocity tracking error over time;
fig. 11 is a graph of the control moment of the joint 1 as a function of time;
fig. 12 is a graph of the control torque of the joint 2 as a function of time.
Wherein: Σ I, inertial coordinate system; Σ 0, motion base coordinate system; o, an origin of an inertial coordinate system; CM, spatial robotic arm system total centroid; b isiRigid body i, i-th link of mechanical arm; b is0A motion base, a connecting rod 0; ciThe centroid of link i; c0The center of mass of the base; r isi∈R2Position vector of connecting rod i centroid; r is0The position vector of the center of mass of the base; r isc∈R2The position vector of the mass center CM of the space manipulator system; p is a radical ofi∈R2Position vector of link i; a isiFrom joint JiVector to the centroid of link i; biFrom the centroid of the connecting rod i to the joint Ji+1A vector of (a); b0From the centre of mass of the base to the joint J1The vector of (2).
Detailed Description
A plane 2-link space manipulator model is shown in figure 1 and is composed of a freely-floating motion base B0And two arm bars B1、B2And (4) forming.
Space machineThe dynamic parameters of the mechanical arm system are described in table 1, and the vector composed of the initial position and attitude angle of the base and the initial attitude angles of the connecting rod 1 and the connecting rod 2 is [ q ]b,qs]T＝[x,y,q0,q1,q2]TThe initial velocity vector of the base and the connecting rods 1 and 2 isThe initial values of the parameters and the desired trajectory are shown in table 2.
TABLE 1 PARALLEL METER OF PLANE 2 CONNECTING ROD SPACE MECHANICAL ARM SYSTEM
TABLE 2 simulation initial values for adaptive control of spatial manipulator neural network
Setting the control parameter to KP＝diag{100,100,100,100,100}，KI＝diag{250,250,250,250,250}，Kv＝0.2，FWSimulation verification is carried out according to the structural block diagram of the control method of fig. 2, namely diag {0.0005,0.0005,0.0005,0.0005,0.0005}, in the invention, a planar 2-link floating-base space manipulator system is taken as a research object, and the kinetic equation is
Wherein q is [ q ]1 q2]TIs the amount of angular displacement of joint, D (q)5×5Is an inertial matrix of the space manipulator,representing a matrix comprising nonlinear centrifugal and coriolis forces, τ being the control moment.
The kinetic equation of the space manipulator satisfies the following properties:
property 1 the inertial matrix d (q) is a symmetric, positive definite, bounded matrix.
Property 2 selection of appropriateCan make D (q) andsatisfy the requirement of
Property 3 Presence of kc> 0 and positive definite functionSo that
Property 4 given the error matrix satisfies Δ Dl≤||ΔD||≤ΔDh，ΔCl≤||ΔC||≤ΔChWherein h and l are upper and lower boundary values, respectively.
In order to realize the rapid and accurate tracking of the expected track in the joint space, the existence parameter and non-parameter cross-scale characteristics of the space manipulator system are also considered during modeling. By introducing external disturbances, the kinetic equation can be rewritten as follows
Wherein,are sum disturbances, including friction torque disturbances and other external disturbances.
In practical engineering, the actual model of the object is difficult to obtain, i.e. the exact D (q),Only an ideal nominal model can be built. Writing a kinetic equation in the form of the sum of an ideal model and a variation term for which there is a cross-scale feature can be expressed as
Wherein D is0、C0Being a nominal model of the object, D0(q)＝D(q)-ΔD(q)，ΔD(q)、In order to be the error matrix,the parameter and non-parameter items with cross-scale characteristics, such as modeling error and external disturbance moment, are an unknown non-linear time-varying function in a specific form
Since D (q) is reversible, one can obtain
Design error function of
Wherein e ═ qdQ andrespectively joint angle tracking error and acceleration tracking error, qdAnd q are the desired and actual joint vectors, respectively, KP、KIRespectively, a positive proportional and integral gain matrix.
Derived by derivation
Order toDeriving equivalent control laws
Thus obtaining a stable closed loop system of
For the nominal model, the control law is designed as
Taking into account unknown interference, it can be derived
To obtain
It can be seen that there is a variation term across the scale features in the model of
Approximating f by a radial basis function neural network, and taking the network inputThe network output is
Then
Design control law as
Wherein v ═ Kvsgn (r) is a robust term used to overcome the influence of neural network approximation errors。
Defining the Lyapunov function as
Wherein D and FWIs positively ordered, i.e.Then V is positive.
Derivation, and combination Property 2 derivation
Can be obtained by finishing
According to the conditionsConsider that v ═ Kvsgn (r), available
GetThe following adaptive law can be designed to adjust the weights of the radial basis function neural network
Thus, it is possible to obtain
For convenience of description, definitions
Thus, the
K is taken from property 3 and property 4vIn> | Q |, where In＝[1,1,…,1]T∈RnThen, then
The input of the control structure is the expected track of the joint angle, the actual value of the joint angle is output to be used as negative feedback to be compared with the actual value of the joint angle, a neural network self-adaptive control system is designed according to the tracking error, the error function and the robust item of the joint angle, and the simulation result is shown in figures 3-12.
The time-dependent change curves of the angle of the joint 1 and the joint 2 are shown in fig. 3 and 4, and the time-dependent change curves of the angular speed are shown in fig. 5 and 6. The red dotted line represents the expected value of the trajectory tracking and the blue solid line represents the actual joint vector. It can be seen that the angular displacement, angular velocity of the joints 1 and 2 quickly tracks the desired trajectory within 2 s.
The time-varying curves of the angle tracking errors of the joint 1 and the joint 2 are shown in fig. 7 and 8, and it can be seen that the joint angle tracking error is maintained at ± 5 × 10-3In the rad range.
The curves of the angular velocity tracking errors of the joint 1 and the joint 2 with time are shown in fig. 9 and 10, and it can be seen that the angular velocity tracking error of the joint is maintained at ± 5 × 10-3In the rad/s range.
The control moment of the joints 1 and 2 is plotted against time as shown in fig. 11 and 12, and it can be seen that the respective joint control moments are kept within the achievable range.
The change of the position and the posture of the base caused by the movement of the connecting rod 1 and the connecting rod 2 is relatively gentle according to the change curve of the position and the posture angle of the moving base along with the time, and the method is suitable for track tracking control of the floating base space mechanical arm.
The experimental result verifies the effectiveness of the neural network adaptive control algorithm, and the expected track can be quickly tracked on line under the condition that the parameter and non-parameter cross-scale characteristics exist in the dynamic model, so that the method has certain robustness and anti-interference performance.
Claims (1)
1. A space manipulator trajectory tracking control method based on a cross-scale model is characterized by comprising the following steps: designing a neural network self-adaptive control law, and expressing a change item with cross-scale characteristics in a space manipulator system dynamic model asThe change term f is approximated by a neural network, so that the compensation of the change term f is realized, and the control law of the neural network isv is a robust term for overcoming the approximation error of the neural network, and has a value of v ═ Kvsgn (r); an error function ofThe neural network is in the form of a radial basis neural network, the inputs to which are takenThe ideal approximation algorithm isThe output of the network isThe weight adjustment of the radial basis function neural network is self-adaptive toD0、C0Being a nominal model of the object, D0＝D-ΔD，C0C- Δ C, Δ D, Δ C are modeling error matrices, D is sum perturbation, e-qdQ andrespectively joint angle tracking error and angular velocity tracking error, qdAnd q are the desired and actual joint vectors, respectively, KP、KIRespectively, a positive proportional and integral gain matrix, KvIn order to be a robust term coefficient,is the weight vector of the neural network,is the output vector of the Gaussian basis function, ciAs the central vector of the ith node of the network, biIs a nodei, D is the inertial matrix of the space manipulator, C represents a matrix comprising nonlinear centrifugal and Cogowski forces, and FWIs a positive array.
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