CN111761585B - Soft and smooth stabilization control method in process of capturing irregular moving target in space - Google Patents

Abstract

The invention discloses a compliant and calm control method in a process of catching a spatial irregular moving target, which designs a track simultaneously considering the angular movement size of a joint, the terminal distance movement size, the angular velocity size of the joint, the damping time and the control moment size of a mechanical arm by using a corrected genetic algorithm, thereby achieving mechanical arm calm rapidly and safely, being capable of despin the damping generated by the relative movement of the target and a body, and providing a new thought for the mechanical arm after the catching of the damping calm.

Description

Soft and smooth stabilization control method in process of capturing irregular moving target in space

Technical Field

The invention relates to the field of space robots, in particular to a smooth and steady control method in a process of capturing a space irregular moving target.

Background

The space operation is an important trend of future spacecraft development, in the process of completing the task of space operation, the tail end of a mechanical arm is contacted with a captured target, the transient collision generated will generate disturbance on a spacecraft-mechanical arm system, and the system can be overturned and unstable in severe cases. Since the impact force in the target capturing process has a significant effect, a control strategy in the capturing process needs to be researched.

The common method for capturing the spacecraft in the existing orbit is as follows: aiming at a known or stable moving target, a joint is locked and then despun is carried out during capturing, the method requires that a mechanical arm joint can bear the torsion moment when the target and a body move relatively, but the implementation mode is simple, only the time for capturing the target needs to be judged, and then the joint is locked. The patent with the application number of CN201611009932.8 and the name of 'a linear feedback global stabilization method for controlling a restricted spacecraft rendezvous control system' is retrieved, the patent relates to a controller design method of a spacecraft rendezvous control system, provides a global stabilization control law based on linear state feedback, provides an optimal selection scheme of control law parameters, ensures that a closed-loop system has the fastest convergence speed, solves the problem of fast convergence of the spacecraft control system, and solves the problem of despinning a combined body by adopting a mechanical arm, and the method and the purpose are different. The related prior art at home and abroad is also different from the technical scheme, and the scheme despin the relative motion state between the target and the body through the joint compliance control of the mechanical arm, so that the stable control of the combination is realized by utilizing the joint damping of the mechanical arm.

Disclosure of Invention

The invention aims to provide a method for controlling compliance and stabilization in the process of capturing an irregular motion target in a space, which optimizes damping time, joint and tail end angular velocity and angular acceleration to plan joint tracks in an equivalent manner and carries out compliance damping and stabilization control on the capturing motion of a mechanical arm.

In order to achieve the purpose, the invention is realized by the following technical scheme:

a smooth and steady control method in the process of catching a spatial irregular moving target is characterized by comprising the following steps:

s1, determining optimization variables when the mechanical arm catches the target, wherein the optimization variables comprise: damping time, tip velocity, joint angular velocity, and joint angular acceleration;

s2, aiming at the captured n-degree-of-freedom mechanical arm, designing a fourth-order polynomial damping track:

wherein theta is_iI-1 … n is an n-degree-of-freedom joint angle, since the polynomial has 5 unknown variables a_0i,a_1i,a_2i,a_3i,a_4iThus, five conditions are required to determine the polynomial;

s3, establishing joint angular velocity and angular acceleration constraint conditions of initial contact and ending contact;

knowing the initial joint angle theta after impact_0iInitial joint angular velocity

Ending joint angular velocity

And ending the joint angular acceleration

Determining coefficients of polynomials

Where T, θ_TiRespectively representing the track planning time and the size of the terminal joint angle;

s4, establishing a joint track target optimization equation;

by optimizing the damping time and the joint angle at the end point state, the target function for enabling the track to meet the requirement is as follows:

wherein, K₁、K₂、K₃、K₄Respectively is a damping time coefficient, a terminal velocity coefficient, a joint angular velocity coefficient and a joint angular acceleration coefficient, T is damping time, v is_eTo end speed, θ ═ θ₁ θ₂ θ₃ … θ₇]^TThe angle of each joint is, for example,

for the angular velocity of each joint,

the angular acceleration of each joint.

Let Delta theta be [ Delta theta ]₁,…Δθ₇]^TIs a modified variable of the genetic algorithm, where Δ θ_i＝θ_i0-θ_iTRepresenting the difference between the joint angle of the ith joint terminal state and the joint angle of the initial state;

s5, utilizing

Initializing population, j ═ 1, …, D; i-1, …, NP wherein

Represents the ith population of the jth individual in the 0 th generation;

s6, generating individual variation by variation operation, and setting variation operation variable

The operation formula of variation is

Wherein

Respectively representing the r1, r2 and r3 populations of the jth individual in the g generation, r1, r2, r3 epsilon {1,2, … and NP } and r1, r2 and r3 are different from each other, F is a scaling factor and has the value range of [0, 1]；

Setting cross-operating variables

Order to

Where CR is the crossover probability, j_randIs [1, …, D ]]A random integer of (a);

in order to satisfy the boundary condition constraint, setting a boundary constraint condition:

s7, selecting next generation population individuals, and updating the next generation population:

s8, solving the terminal joint angle, the optimization time and the optimal value of the objective function through iteration of the objective function;

s9, obtaining the desired trajectory with damping effect.

The step S9 specifically includes:

substituting the parameters solved in step S8 into equations (1) and (2) to obtain a desired trajectory having a damping effect.

Compared with the prior art, the invention has the following advantages:

the corrected genetic algorithm is used for designing a track which simultaneously considers the angular movement size of the joint of the mechanical arm, the terminal distance movement size, the angular velocity size of the joint, the damping time and the control torque size, so that the stabilization of the mechanical arm is realized quickly and safely, the damping generated by the relative movement of the target and the body can be despuned, and a new thought is provided for the mechanical arm after the damping stabilization is caught.

Drawings

FIG. 1 is a flow chart of a compliance and stabilization control method in a process of capturing a spatial irregular moving target according to the present invention;

fig. 2 is a curve of an objective function curve with an iterative algebraic variation.

Detailed Description

The present invention will now be further described by way of the following detailed description of a preferred embodiment thereof, taken in conjunction with the accompanying drawings.

As shown in fig. 1, a method for controlling compliance and stability in the process of capturing a spatially irregular moving target includes the following steps:

s1, determining optimization variables when the mechanical arm catches the target, wherein the optimization variables comprise: damping time, tip velocity, joint angular velocity, and joint angular acceleration;

in order to make damping fast, optimization of time is one of the factors to be considered; secondly, preventing the joint angular velocity from being too high in the damping process is also a problem to be considered in the trajectory planning; finally, the magnitude of the control moment is also the content in which optimization is required in order to match the actual engineering. And (4) designing and optimizing the track by using a modified genetic algorithm.

S2, aiming at the captured n-degree-of-freedom mechanical arm, designing a fourth-order polynomial damping track:

wherein theta is_iI-1 … n is an n-degree-of-freedom joint angle, since the polynomial has 5 unknown variables a_0i,a_1i,a_2i,a_3i,a_4iFive conditions are required to determine the polynomial;

s3, establishing joint angular velocity and angular acceleration constraint conditions of initial contact and ending contact;

knowing the initial joint angle theta after impact_0iInitial joint angular velocity

Ending joint angular velocity

And ending the joint angular acceleration

Determining coefficients of polynomials

Where T, θ_TiRespectively representing the track planning time and the size of the terminal joint angle;

s4, establishing a joint track target optimization equation;

as can be seen from equation (2), four timesInterpolating polynomial locus by T, theta_TiDetermining that the target function for enabling the track to meet the requirement is as follows through optimizing the damping time and the joint angle in the end point state:

wherein, K₁、K₂、K₃、K₄Respectively is a damping time coefficient, a terminal velocity coefficient, a joint angular velocity coefficient and a joint angular acceleration coefficient, T is damping time, v is_eTo end speed, θ ═ θ₁ θ₂ θ₃ … θ₇]^TThe angle of each joint is, for example,

for the angular velocity of each joint,

the angular acceleration of each joint.

Let Delta theta be [ Delta theta ]₁,…Δθ₇]^TIs a modified variable of the genetic algorithm, where Δ θ_i＝θ_i0-θ_iTRepresenting the difference between the joint angle of the ith joint terminal state and the joint angle of the initial state;

s5, initializing the population;

by using

Initializing population, j ═ 1, …, D; i-1, …, NP wherein

Represents the ith population of the jth individual in the 0 th generation;

s6, generating individual variation by variation operation, and setting variation operation variable

The operation formula of variation is

Wherein

Respectively representing the r1, r2 and r3 populations of the jth individual in the g generation, r1, r2, r3 epsilon {1,2, … and NP } and r1, r2 and r3 are different from each other, F is a scaling factor and has the value range of [0, 1]；

Setting cross-operating variables

Order to

Where CR is the crossover probability, j_randIs [1, …, D ]]Is a random integer of (a).

In order to satisfy the boundary condition constraint, setting a boundary constraint condition:

s7, selecting next generation population individuals, and updating the next generation population:

s8, solving the terminal joint angle, the optimization time and the optimal value, and iteratively solving the terminal joint angle, the optimization time and the optimal value of the objective function through an objective function (formula 3);

and S9, substituting the solved parameters into a fourth-order polynomial to obtain the expected track with the damping effect.

And substituting the optimized terminal joint angle and the optimized damping time as parameters of the trajectory planning into equations (1) and (2) to obtain the designed expected trajectory.

The present example is illustrated in detail by the following examples:

setting upper and lower bounds Δ θ in a modified genetic algorithm_min＝[-10,-10,-10,-14,-14,-20,-20]°，Δθ_max＝[10,10,10,14,14,20,20]Degree, population number NP equal to 40, variable dimension D equal to 8, evolution generation g equal to 50, and mutation factor F_i0.85, and 0.8. Initial size of joint angle θ₀＝[75,70,110,10,110,-96,94]Angular velocity of joints

After the constraint condition is converted into the objective function in the form of a penalty function, a curve of the objective function along with the iterative algebraic change is shown in fig. 2.

The distal joint angle Δ θ [ -1.2,2.2,4.2, -8.12,20, -20,20] ° can be obtained, the optimization time T is 27.65s, and the optimal value V is 54.11. And substituting the optimized terminal joint angle and the optimized damping time as parameters of the trajectory planning into equations (1) and (2) to obtain the designed expected trajectory.

While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (1)

1. A method for controlling compliance and stabilization in the process of capturing a spatial irregular moving target is characterized by comprising the following steps:

s1, determining optimization variables when the mechanical arm catches the target, wherein the optimization variables comprise: damping time, tip velocity, joint angular velocity, and joint angular acceleration;

s2, aiming at the captured n-degree-of-freedom mechanical arm, designing a fourth-order polynomial damping track:

wherein theta is_iI-1 … n is an n-degree-of-freedom joint angle, since the polynomial has 5 unknown variables a_0i,a_1i,a_2i,a_3i,a_4iThus, five conditions are required to determine the polynomial;

s3, establishing joint angular velocity and angular acceleration constraint conditions of initial contact and ending contact;

knowing the initial joint angle theta after impact_0iInitial joint angular velocity

Ending joint angular velocity

And ending the joint angular acceleration

Determining coefficients of polynomials

Where T, θ_TiRespectively representing the track planning time and the size of the terminal joint angle;

s4, establishing a joint track target optimization equation;

by optimizing the damping time and the joint angle at the end point state, the target function for enabling the track to meet the requirement is as follows:

wherein, K₁、K₂、K₃、K₄Respectively is a damping time coefficient, a terminal velocity coefficient, a joint angular velocity coefficient and a joint angular acceleration coefficient, T is damping time, v is_eTo end speed, θ ═ θ₁ θ₂ θ₃ … θ₇]^TThe angle of each joint is, for example,

for the angular velocity of each joint,

angular acceleration of each joint;

let Delta theta be [ Delta theta ]₁,…Δθ₇]^TIs a modified variable of the genetic algorithm, where Δ θ_i＝θ_i0-θ_iTRepresenting the difference between the joint angle of the ith joint terminal state and the joint angle of the initial state;

s5, utilizing

Initializing population, j ═ 1, …, D; i-1, …, NP wherein

Represents the ith population of the jth individual in the 0 th generation;

s6, generating individual variation by variation operation, and setting variation operation variable

The operation formula of variation is

Wherein

Respectively representing the r1, r2 and r3 populations of the jth individual in the g generation, r1, r2, r3 epsilon {1,2, … and NP } and r1, r2 and r3 are different from each other, F is a scaling factor and has the value range of [0, 1]；

Setting cross-operating variables

Order to

Where CR is the crossover probability, j_randIs [1, …, D ]]A random integer of (a);

in order to satisfy the boundary condition constraint, setting a boundary constraint condition:

s7, selecting next generation population individuals, and updating the next generation population:

s8, solving the terminal joint angle, the optimization time and the optimal value of the objective function through iteration of the objective function;

and S9, substituting the parameters solved in the step S8 into the formula (1) and the formula (2) to obtain the expected track with the damping effect.

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