CN111923037A - Space manipulator shutdown optimization method for joint locking fault - Google Patents

Abstract

The embodiment of the present invention provides a method for optimizing the shutdown of a joint-locking fault space manipulator, including: according to each movement capability index of the joint-locking fault space manipulator after standardized processing, and solving each movement capability based on an improved analytic hierarchy process and an entropy value method The weight of the index can realize the comprehensive characterization of the movement ability of the manipulator, and construct the optimal model of the manipulator in the joint locking fault space. Then, based on the Monte Carlo numerical method, the optimal stopping model of the manipulator can be solved, and the optimal stopping mode of the manipulator with the joint locking failure is obtained. Mechanism type, and then considering the characteristics of the stop motion, the motion planning of the manipulator is based on the six-degree polynomial, and then the safety and stability of the manipulator during the stop process are considered, and the optimization model of the stop motion of the space manipulator is constructed and solved, and the joint locking fault space machine is completed. Stop optimization of the arm. According to the technical solutions provided by the embodiments of the present invention, the safe and stable shutdown of the joint-locking fault space manipulator can be realized.

Description

A shutdown optimization method of a joint-locking fault space manipulator

【Technical field】

The invention relates to a stop optimization method of a mechanical arm in a joint locking fault space, and belongs to the field of stop motion optimization of a mechanical arm.

【Background technique】

The military, political, people's livelihood, economic and other strategic positions of space have prompted countries around the world to pay more and more attention to space exploration. With the continuous deepening of human exploration of space, space manipulators with the characteristics of large span, flexible operation and strong load capacity are increasingly used. However, the harsh space environment, the heavy operation tasks and the complex joint structure make the joint locking failure of the space manipulator very likely to occur during the long-term service process, and usually cannot be repaired in time. At this time, if the manipulator is controlled to continue to move according to the original task requirements, that is, to continue to perform the task without stopping, the operating parameters of the manipulator (joint speed, acceleration, torque, etc.) will inevitably change due to the influence of locking the faulty joint. The sudden change of the operating parameters of the space manipulator may cause joint speed/torque exceeding the limit, deformation of the manipulator arm or even damage to the manipulator, which will not only lead to the failure of space manipulation tasks, but also seriously affect the stability of the manipulator operation, threatening the space manipulator and spacecraft safety. Therefore, there is an urgent need to carry out research on the optimization method of stopping the joint-locking fault space manipulator.

The shutdown optimization of the joint-locked fault space manipulator is realized through the optimization of the stop model and the optimization of the stop motion of the joint-locked fault space manipulator. The existing research on the shutdown optimization of the manipulator in the joint locking fault space does not consider whether the motion capability of the manipulator in the configuration after the shutdown can meet the requirements of the subsequent tasks. The situation required by the task; the existing research on the optimization of the stop motion of the manipulator with joint locking failure does not consider the characteristics of the floating base of the space manipulator. During the shutdown process, the disturbance torque of the base will cause the manipulator to lose control, which seriously threatens the safety of the space manipulator. Reliable operation.

[Content of the invention]

In view of this, the present invention provides a shutdown optimization method for a joint-locking failure space manipulator, so as to realize the shutdown optimization of the joint-locking failure space manipulator.

An embodiment of the present invention provides a method for optimizing the shutdown of a joint-locking fault space manipulator, including:

According to each kinematic capability index of the manipulator in the joint locking fault space after standardized processing, the weight of each kinematic capability index is calculated based on the improved analytic hierarchy process and entropy method, so as to realize the comprehensive characterization of the kinematic capability of the manipulator;

According to the comprehensive characterization of the motion capability of the space manipulator, the optimal model of the joint-locking fault space manipulator was constructed, and then the optimal stopping model was solved based on the Monte Carlo numerical method to obtain the optimal stopping type of the joint-locking faulty manipulator;

According to the optimal stopping model of the joint-locking fault space manipulator, the motion planning of the manipulator is based on the six-order polynomial considering the characteristics of the stopping motion, and then the safety and stability of the manipulator during the stopping process are considered, and the optimization coefficient is introduced to construct the space manipulator. The shutdown motion optimization model, solve the shutdown motion optimization model, and complete the shutdown optimization of the joint locking fault space manipulator.

In the above method, the weight of each exercise ability index is calculated based on the improved analytic hierarchy process and the entropy value method according to the standardized processing of each exercise ability index of the joint-locking fault space manipulator, so as to realize the comprehensive characterization of the exercise ability of the manipulator, include:

Analyze and analyze the kinematic performance indicators of the joint locking fault space manipulator, including the minimum singular value s, the condition number k, and the operability w;

For the minimum singular value and operability, the standard minimum singular value and standard operability are obtained after normalization:

表示标准最小奇异值，

表示标准可操作度，s_min表示最小奇异值的最小值，s_max表示最小奇异值的最大值，w_min表示可操作度的最小值，w_max表示可操作度的最小值；In the above formula,

represents the standard minimum singular value,

Represents the standard operability, s _min represents the minimum value of the minimum singular value, s _max represents the maximum value of the minimum singular value, w _min represents the minimum value of the operability, and w _max represents the minimum value of the operability;

For condition numbers, standard condition numbers are obtained after normalization:

表示标准条件数；In the above formula,

represents the standard condition number;

Considering the requirements of the task for each movement capability of the manipulator, the subjective weights of the standard minimum singular value, standard condition number, and standard operability are solved based on the improved AHP:

STEP1 constructs a hierarchical structure model: Considering that different tasks have different requirements for the unilateral movement ability indicators of the manipulator, build a top-to-bottom hierarchical structure: target layer (comprehensive representation of movement ability), criterion layer (task requirements), sub-layers Criterion layer (each unilateral exercise ability index), in which the target layer is the highest layer in the hierarchical structure, that is, the final target to be obtained, and the criterion layer and sub-criteria layers are used to evaluate the target results;

STEP2 constructs a judgment matrix: In order to be able to judge the influence of each factor of the same level on the factors of the upper level, the importance of each element is defined based on the 1-7 scaling method, and then the judgment matrix is constructed;

STEP3 Consistency test: Use the maximum eigenvalue method to solve the judgment matrix, get the maximum eigenvalue of the judgment matrix, and then check the consistency of the results to judge whether the matrix is reasonable:

STEP4 subjective weight solution: calculate the eigenvector corresponding to the maximum eigenvalue of the judgment matrix, and the elements in the eigenvector correspond to the subjective weights ω _{CR_1} , ω _{CR_2} , ω _{CR_3} of each athletic ability index;

Based on the entropy method, the objective weights ω _{CP_1} , ω _{CP_2} , ω _{CP_3} of the standard minimum singular value, standard condition number and standard operability are obtained, and denoted as ω _CP =[ω _{CP_1} ,ω _{CP_2} ,ω _{CP_3} ];

Based on the obtained subjective weights and objective weights, the final weights of each athletic ability index are obtained as ω=[ω _{CR_1} +ω _{CP_1} ,ω _{R_2} +ω _{CP_2} ,ω _{CR_3} +ω _{CP_3} ]=[ω _{C_1} ,ω _{C_2} ,ω _{C_3} ] , and the comprehensive characterization of the motion capability of the space manipulator can be expressed as:

In the above formula, q _λ indicates that the manipulator is in the λth configuration.

In the above method, according to the comprehensive characterization of the motion capability of the space manipulator, the optimal model of the stop type of the space manipulator with joint lock failure is constructed, and then the optimal model of the stop type is solved based on the Monte Carlo numerical method, and the optimal model of the stop type of the joint lock fault manipulator is obtained. Optimal shutdown patterns, including:

According to the comprehensive characterization of the motion capability of the space manipulator, the optimal model of the stop type of the space manipulator with joint locking failure is constructed:

find q _best

max CP(q _best )

In the above formula, q _best represents the optimal stopping type of the joint-locking fault space manipulator;

Based on Monte Carlo numerical method, the optimal model of stop configuration is solved:

内利用随机数法在0到1之间产生K个随机数，记为

进而可以得到故障机械臂各关节的关节角伪随机数：STEP1 is aimed at each joint of the faulty manipulator, in the range of the respective joint angle

The random number method is used to generate K random numbers between 0 and 1, which are recorded as

Then, the pseudo-random number of the joint angle of each joint of the faulty manipulator can be obtained:

In the above formula,

STEP2 expresses the pseudo-random number of the joint angle of each joint as the following form:

In the above formula, each column of CS corresponds to a configuration of the faulty manipulator, then CS can be written as

According to the comprehensive characterization of the motion capability of the space manipulator, solve the CP(q _λ ) of the manipulator under each configuration, and select the corresponding q _best = [θ _1best θ _2best ... θ _nbest ] that satisfies max CP(q _best ), That is the optimal stop type of the faulty manipulator.

In the above method, according to the optimal stopping model of the joint-locking fault space manipulator, the motion planning of the manipulator is based on the six-order polynomial in consideration of the characteristics of the stopping motion, and then the safety and stability of the manipulator during the stopping process are considered, and the introduction is made. The optimization coefficients are used to construct the optimization model of the stop motion of the space manipulator, solve the optimization model of the stop motion, and complete the stop optimization of the space manipulator with joint locking failure, including:

According to the optimal stopping model of the joint-locked fault space manipulator, the motion planning of the manipulator is based on the six-order polynomial considering the characteristics of the stopping motion:

θ(t)=a ₀ +a ₁ t+a ₂ t ² +a ₃ t ³ +a ₄ t ⁴ +a ₅ t ⁵ +a ₆ t ⁶

In the above formula, a ₀ ~ a ₆ are undetermined coefficients;

Since the configuration of the manipulator at the end of the stop motion is the optimal stop configuration, and the speed and acceleration of each joint are 0, it can be obtained:

表示停机初始时刻下机械臂各关节的关节角速度，

表示停机终止时刻下机械臂各关节的关节角速度，

表示停机初始时刻下机械臂各关节的关节角加速度，

表示停机终止时刻下机械臂各关节的关节角加速度；In the above formula, t ₀ represents the initial time of shutdown, t _f represents the termination time of shutdown, θ ₀ represents the joint angle of each joint of the manipulator at the initial moment of shutdown, θ _f represents the joint angle of each joint of the manipulator at the end of shutdown,

represents the joint angular velocity of each joint of the manipulator at the initial moment of shutdown,

represents the joint angular velocity of each joint of the manipulator at the time of stopping the stop,

represents the joint angular acceleration of each joint of the manipulator at the initial moment of shutdown,

Indicates the joint angular acceleration of each joint of the manipulator at the time of stopping the stop;

By setting the optimization coefficient k, set a ₆ =k to obtain:

为优化目标，以停机过程中机械臂关节运行参数lim(k)为约束，构建关节锁定故障空间机械臂停机运动优化模型：Considering the safety and stability of the faulty manipulator during the shutdown process, the global base disturbance torque of the manipulator during the shutdown process

In order to optimize the objective, with the joint operating parameter lim(k) of the manipulator as the constraint during the shutdown process, an optimization model of the stop motion of the manipulator in the joint-locking fault space is constructed:

find k

min

s.t.lim(k)

According to the genetic algorithm, the optimization model of the stopping motion of the joint-locking fault space manipulator can be solved, and the stopping motion optimization of the joint-locking fault space manipulator can be completed.

The technical scheme of the embodiment of the present invention has the following beneficial effects:

(1) The present invention solves the weight of each movement ability index based on the standardization processing of each movement ability index, based on the improved AHP and entropy value method, and realizes the joint realization from the two aspects of the robot arm's own movement ability characteristics and on-orbit operation task requirements. A comprehensive characterization of the motion capability of the robotic arm.

(2) The present invention obtains the optimal stopping model of the joint-locking faulty manipulator by constructing the optimal model of the joint-locking fault space manipulator, and then solving the optimal stopping model based on the Monte Carlo numerical method. The movement ability of the manipulator under the optimal stop configuration is the best.

(3) The present invention performs motion planning for the manipulator based on the six-order polynomial considering the characteristics of the stopping motion, and then considers the safety and stability of the manipulator during the stopping process, and introduces optimization coefficients to construct an optimization model of the stopping motion of the spatial manipulator, and solve the optimization of the stopping motion. The model realizes the safe and stable shutdown of the joint-locking fault space manipulator.

【Description of drawings】

In order to illustrate the technical solutions of the embodiments of the present invention more clearly, the following will briefly introduce the accompanying drawings used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention, which are common in the art. As far as technical personnel are concerned, other drawings can also be obtained based on these drawings without the premise of creativity and labor.

1 is a schematic flowchart of a method for optimizing the shutdown of a manipulator in a joint locking fault space provided by an embodiment of the present invention;

2 is a schematic diagram of an initial configuration of a seven-degree-of-freedom space manipulator in an embodiment of the present invention;

FIG. 3 is a schematic diagram of changes in the corresponding movement capabilities of each joint of the joint locking fault space manipulator in the embodiment of the present invention;

FIG. 4 is a schematic diagram of the variation of the global base disturbance torque of the joint locking fault space manipulator under different k values in an embodiment of the present invention

[specific embodiment]

In order to better understand the technical solutions of the present invention, the embodiments of the present invention are described in detail below with reference to the accompanying drawings.

It should be understood that the described embodiments are only some, but not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

An embodiment of the present invention provides a method for optimizing the shutdown of a manipulator in a joint-locked fault space. Please refer to FIG. 1 , which is a schematic flowchart of the method for optimizing the shutdown of a manipulator in a joint-locked fault space provided by an embodiment of the present invention, as shown in FIG. 1 . , the method includes the following steps:

Step 101 , standardize each motion capability index of the joint-locking fault space manipulator, and then calculate the weight of each motion capability index based on the improved AHP and entropy method to realize a comprehensive representation of the manipulator's motion capability.

Specifically, singular value decomposition is performed on the Jacobian matrix J(q) of the space manipulator, as shown in the following formula:

J(q)=UΣV

In the above formula, U represents an m×m-dimensional orthogonal matrix, V represents an n×n-dimensional orthogonal matrix, Σ represents an m×n-dimensional diagonal matrix whose diagonal is a non-negative real number, and Σ has the following form:

In the above formula, σ ₁ ,σ ₂ ,…,σ _m are singular values of the Jacobian matrix J(q), and σ ₁ ≥σ ₂ ≥…≥σ _m ≥0.

When the manipulator is in a non-singular configuration, Rank(Σ)=Rank(J(q))=m; when the manipulator is in a singular configuration, Rank(Σ)=Rank(J(q))=r<m , at this time, the diagonal matrix Σ has the following form:

In the above formula, σ ₁ represents the largest singular value of J(q), and σ _r represents the non-zero smallest singular value of J(q).

Based on the singular values of the Jacobian matrix and the definitions of the indicators of the space manipulator, the correlation analysis of indicators such as the minimum singular value, condition number, and operability can be obtained, as shown in Table 1.

Table 1 The kinematics indexes of the joint-locking fault space manipulator

For the minimum singular value, operability, and condition number, standard minimum singular value, standard operability, and standard condition number are obtained after normalization:

表示标准最小奇异值，

表示标准可操作度，

表示标准条件数，s_min表示最小奇异值的最小值，s_max表示最小奇异值的最大值，w_min表示可操作度的最小值，w_max表示可操作度的最小值。In the above formula,

represents the standard minimum singular value,

represents the standard operability,

Represents the standard condition number, s _min represents the minimum value of the smallest singular value, s _max represents the maximum value of the smallest singular value, w _min represents the minimum value of the operability, and w _max represents the minimum value of the operability.

Considering the requirements of the task for each movement capability of the manipulator, the subjective weights of the standard minimum singular value, standard condition number, and standard operability are solved based on the improved AHP:

STEP1 constructs a hierarchical structure model: Considering that different tasks have different requirements for the unilateral movement ability indicators of the manipulator, build a top-to-bottom hierarchical structure: target layer (comprehensive representation of movement ability), criterion layer (task requirements), sub-layers Criterion layer (each unilateral exercise ability index), in which the target layer is the highest layer in the hierarchical structure, that is, the final target to be obtained, and the criterion layer and sub-criteria layers are used to evaluate the target results;

STEP2 constructs a judgment matrix: In order to be able to judge the influence of each factor of the same level on the factors of the upper level, the importance of each element is defined based on the 1-7 scaling method, and then the judgment matrix is constructed;

STEP3 Consistency test: use the maximum eigenvalue method to solve the judgment matrix, and then check the consistency of the results after obtaining the maximum eigenvalue of the judgment matrix to judge whether the matrix is reasonable;

STEP4 subjective weight solution: calculate the eigenvector corresponding to the maximum eigenvalue of the judgment matrix, and the elements in the eigenvector correspond to the subjective weights ω _{CR_1} , ω _{CR_2} , ω _{CR_3} of each athletic ability index.

Based on the entropy method, the objective weights ω _{CP_1} , ω _{CP_2} , ω _{CP_3} of the standard minimum singular value, standard condition number and standard operability are obtained, and denoted as ω _CP =[ω _{CP_1} ,ω _{CP_2} ,ω _{CP_3} ], and then based on the obtained The subjective weight and objective weight of , obtain the final weight of each athletic ability index as ω=[ω _{CR_1} +ω _{CP_1} ,ω _{R_2} +ω _{CP_2} ,ω _{CR_3} +ω _{CP_3} ]=[ω _{C_1} ,ω _{C_2} ,ω _{C_3} ], and then The comprehensive characterization of the motion capability of the space manipulator can be expressed as:

In the above formula, q _λ indicates that the manipulator is in the λth configuration.

Step 102 , constructing an optimal model of the joint-locking fault space manipulator stop type, and then solving the optimal stop type model based on the Monte Carlo numerical method to obtain the optimal stop type of the joint-locking faulty manipulator.

Specifically, construct the optimal model of the stop type of the manipulator in the joint locking fault space:

find q _best

max CP(q _best )

In the above formula, q _best represents the optimal stop configuration of the joint-locking fault space manipulator.

Based on Monte Carlo numerical method, the optimal model of stop configuration is solved:

内利用随机数法在0到1之间产生K个随机数，记为

进而可以得到故障机械臂各关节的关节角伪随机数：STEP1 is aimed at each joint of the faulty manipulator, in the range of the respective joint angle

The random number method is used to generate K random numbers between 0 and 1, which are recorded as

Then, the pseudo-random number of the joint angle of each joint of the faulty manipulator can be obtained:

In the above formula,

STEP2 expresses the pseudo-random number of the joint angle of each joint as the following form:

In the above formula, each column of CS corresponds to a configuration of the faulty manipulator, then CS can be written as

According to the comprehensive characterization of the motion capability of the space manipulator, solve the CP(q _λ ) of the manipulator under each configuration, and select the corresponding q _best = [θ _1best θ _2best ... θ _nbest ] that satisfies max CP(q _best ), That is the optimal stop type of the faulty manipulator.

Step 103 , planning the motion of the manipulator based on the six-order polynomial considering the characteristics of the stopping motion, and then considering the safety and stability of the manipulator during the stopping process, introducing optimization coefficients to construct a stopping motion optimization model of the spatial manipulator, and solving the stopping motion optimization model, Complete the shutdown optimization of the joint-locked fault space manipulator.

Specifically, the motion planning of the manipulator is based on the sixth-order polynomial considering the characteristics of the stop motion:

θ(t)=a ₀ +a ₁ t+a ₂ t ² +a ₃ t ³ +a ₄ t ⁴ +a ₅ t ⁵ +a ₆ t ⁶

In the above formula, a ₀ to a ₆ are undetermined coefficients.

Since the configuration of the manipulator at the end of the stop motion is the optimal stop configuration, and the speed and acceleration of each joint are 0, it can be obtained:

表示停机初始时刻下机械臂各关节的关节角速度，

表示停机终止时刻下机械臂各关节的关节角速度，

表示停机初始时刻下机械臂各关节的关节角加速度，

表示停机终止时刻下机械臂各关节的关节角加速度。In the above formula, t ₀ represents the initial time of shutdown, t _f represents the termination time of shutdown, θ ₀ represents the joint angle of each joint of the manipulator at the initial moment of shutdown, θ _f represents the joint angle of each joint of the manipulator at the end of shutdown,

represents the joint angular velocity of each joint of the manipulator at the initial moment of shutdown,

represents the joint angular velocity of each joint of the manipulator at the time of stopping the stop,

represents the joint angular acceleration of each joint of the manipulator at the initial moment of shutdown,

Indicates the joint angular acceleration of each joint of the robotic arm at the time of stopping the stop.

By setting the optimization coefficient k, set a ₆ =k to obtain:

为优化目标，以停机过程中机械臂关节运行参数lim(k)为约束，构建关节锁定故障空间机械臂停机运动优化模型：Considering the safety and stability of the faulty manipulator during the shutdown process, the global base disturbance torque of the manipulator during the shutdown process

In order to optimize the objective, with the joint operating parameter lim(k) of the manipulator as the constraint during the shutdown process, an optimization model of the stop motion of the manipulator in the joint-locking fault space is constructed:

find k

min

s.t.lim(k)

According to the genetic algorithm, the optimal model of the stop motion of the manipulator in the joint locking fault space is solved:

STEP1 initialization: According to the accuracy of the solution result and the solution space of the optimization coefficient, select the binary encoding method, encode the population, and obtain the initial population in the encoding space of the optimization coefficient. At the same time, set the current evolutionary algebra G=0, and set the maximum evolutionary algebra G _max ;

STEP2 Individual evaluation: Set the fitness function to calculate the fitness of the coefficient k in the population. For the optimization problem of the stop motion of the faulty manipulator, the reciprocal of the global base disturbance torque of the faulty manipulator can be selected as the fitness function, which is

According to the fitness function, the coefficient k that satisfies max f in the current population is obtained.

STEP3 genetic operator: including selection, crossover and mutation.

(1) Select the operation. The superior coefficients in STEP2 are directly passed on to the next generation or new individuals are generated by paired crossover and then passed on to the next generation. In this paper, the elite mechanism is used for selection, that is, the coefficient corresponding to the highest fitness must be selected, and the probability of each coefficient being selected is proportional to the fitness value corresponding to the coefficient. Calculate the probability that each coefficient is chosen:

where ξ is the number of individuals in the initial population.

(2) Crossover operation. Calculate the crossover probability p _c , and perform the crossover operation between two individuals according to the crossover probability:

In the formula, f _max is the maximum fitness value in the population; f _avg is the average fitness value of the population; f is the larger fitness value of the two individuals performing the crossover operation; g ₁ , g ₂ are set constants.

(3) Mutation operation. Calculate the mutation probability, and perform mutation operation on the individuals in the population according to the mutation probability:

Termination condition of STEP4: when the evolutionary algebra G= _Gmax , the coefficient k corresponding to the obtained maximum fitness value is taken as the optimal solution; otherwise, the steps from STEP2 to STEP4 are repeated.

According to the above-mentioned method provided by the embodiment of the present invention, a simulation is carried out on the shutdown optimization method of the seven-degree-of-freedom space manipulator.

Table 2 is the DH parameters of the simulation object 7R robot arm, and Table 3 is the dynamic parameters of the simulation object 7R robot arm

Table 2 Initial DH parameters of the seven-degree-of-freedom space manipulator

Table 3 Dynamic parameters of the seven-degree-of-freedom space manipulator

Assuming that joint 4 of the space manipulator is locked due to a joint failure, the initial shutdown configuration of the faulty manipulator is q ₀ =[-180° -180° -100° -10° 20° 20°], the operating range of each joint of the manipulator is is [-180°, 180°], and the number of random numbers generated is K=36000. It can be seen from the previous analysis that the configuration of the faulty manipulator—the comprehensive motion capability is a set of 7-dimensional arrays, that is, 6 joint angles correspond to a comprehensive motion capability value. Therefore, the simulation obtained by using the Monte Carlo method should be a seven-dimensional space graph. , in order to draw conclusions more conveniently and intuitively, the 7-dimensional coordinate diagram is transformed into 6 two-dimensional plane diagrams by using the form of cross-sectional diagram, that is, the angle of each joint - the comprehensive exercise capacity value, as shown in Figure 3, in which Figure 3 Figures (a) to (f) correspond to the joint angle-comprehensive exercise capacity value of each joint of the joint locking failure space manipulator, respectively. According to Fig. 3, it can be obtained that the configuration corresponding to the best motion capability of the faulty manipulator is q _best = [-167° -90° 40° -158° 90° -62°], which is the optimal stop of the faulty manipulator. Institutional type. At the same time, it can be found that the sub-optimal stop configuration of the faulty manipulator is q _sub = [-52° 90° 84° 148° -90° 157°], and the movement capacity of the corresponding faulty manipulator under this configuration is 0.2969, It can be seen from the comparison that the movement capacity of the faulty manipulator under the optimal stop configuration is higher than that of the suboptimal configuration (1-0.2969)/0.2969=236.8%, that is, the movement capacity of the faulty manipulator under the optimal configuration is far greater than that of the suboptimal configuration. Much better athletic ability than other configurations.

关节加速度为

每个关节速度约束为

每个关节加速度约束为

整个停机过程用时为T＝10s。故障机械停机运动过程中的全局基座扰动力矩

随系数k的变化如图4所示，其中图(a)为当k∈[0,0.1]时的全局基座扰动力矩，图(b)为当k∈[0,0.01]时的全局基座扰动力矩，图(c)为不同k值所对应的基座扰动力矩变化。根据图4可以得到，当k＝0.0018时，故障机械臂的全局基座扰动力矩最小，为15.55N·m；当k＝0时，机械臂的全局基座扰动力矩为22.25N·m，则优化后较优化前机械臂的全局基座扰动力矩降低了(22.25-15.55)/22.25＝30.1％，由此可以证明本发明所提关节锁定故障空间机械臂停机优化方法的正确性与有效性。Assume that the joint speed at the initial moment of stop of the manipulator is

The joint acceleration is

Each joint velocity is constrained to be

The acceleration of each joint is constrained to be

The entire shutdown process takes T=10s. Global pedestal disturbance torque during shutdown motion of faulty machinery

The variation with the coefficient k is shown in Fig. 4, where Fig. (a) is the global base perturbation moment when k ∈ [0, 0.1], and Fig. (b) is the global basis when k ∈ [0, 0.01] pedestal disturbance moment, Figure (c) shows the variation of the pedestal disturbance moment corresponding to different k values. According to Figure 4, when k=0.0018, the global base disturbance torque of the faulty manipulator is the smallest, which is 15.55N m; when k=0, the global base disturbance torque of the manipulator is 22.25N m, then After optimization, the global base disturbance torque of the manipulator is reduced by (22.25-15.55)/22.25=30.1%, which can prove the correctness and effectiveness of the optimization method for stopping the manipulator in the joint locking fault space.

The technical scheme of the embodiment of the present invention has the following beneficial effects:

(1) The present invention solves the weight of each movement ability index based on the standardization processing of each movement ability index, based on the improved AHP and entropy value method, and realizes the joint realization from the two aspects of the robot arm's own movement ability characteristics and on-orbit operation task requirements. A comprehensive characterization of the movement capability of the robotic arm;

(2) The present invention obtains the optimal stopping model of the joint-locking faulty manipulator by constructing the optimal model of the joint-locking fault space manipulator, and then solving the optimal stopping model based on the Monte Carlo numerical method. The movement ability of the manipulator under the optimal stop configuration is the best;

(3) The present invention performs motion planning for the manipulator based on the six-order polynomial considering the characteristics of the stopping motion, and then considers the safety and stability of the manipulator during the stopping process, and introduces optimization coefficients to construct an optimization model of the stopping motion of the spatial manipulator, and solve the optimization of the stopping motion. The model realizes the safe and stable shutdown of the joint-locking fault space manipulator.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the present invention. within the scope of protection.

The content not described in detail in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims (4)

1. A joint locking fault space manipulator shutdown optimization method is characterized by comprising the following steps:

(1) according to each motion capability index after standardized processing of the space manipulator with the joint locking fault, solving the weight of each motion capability index based on an improved analytic hierarchy process and an entropy method, and further realizing comprehensive representation of the motion capability of the manipulator;

(2) according to the comprehensive representation of the motion capability of the space manipulator, a joint locking fault space manipulator stop mechanism type optimal model is constructed, and then the stop mechanism type optimal model is solved based on a Monte Carlo numerical method, so that the optimal stop mechanism of the joint locking fault manipulator is obtained;

(3) according to the optimal shutdown configuration of the joint locking fault space manipulator, the motion planning is carried out on the manipulator based on the sextic polynomial in consideration of the shutdown motion characteristics, the safety and the stability of the manipulator in the shutdown process are further considered, an optimization coefficient is introduced to construct a space manipulator shutdown motion optimization model, the shutdown motion optimization model is solved, and the shutdown optimization of the joint locking fault space manipulator is completed.

2. The method according to claim 1, wherein the step of solving the weight of each motion capability index based on an improved analytic hierarchy process and an entropy method according to each motion capability index after the mechanical arm standardization processing of the joint locking fault space, so as to realize the comprehensive characterization of the motion capability of the mechanical arm comprises the following steps:

(1) analyzing each motion capability index of the joint locking fault space mechanical arm, wherein the motion capability index comprises a minimum singular value s, a condition number k and an operability degree w;

aiming at the minimum singular value and the operability, obtaining a standard minimum singular value and a standard operability after standardization treatment:

in the above formula, the first and second carbon atoms are,

the standard minimum singular value is represented as,

indicates the standard operability, s_minMinimum value, s, representing the minimum singular value_maxRepresenting the maximum value of the minimum singular value, w_minMinimum value of the degree of operability, w_maxRepresents the minimum value of the operability;

for condition numbers, standard condition numbers were obtained after normalization treatment:

in the above formula, the first and second carbon atoms are,

represents a standard condition number;

(2) considering the requirements of tasks on the motion capability of the mechanical arm, and solving the subjective weight of a standard minimum singular value, a standard condition number and a standard operability based on an improved analytic hierarchy process:

STEP1 constructs a hierarchical model: considering that different tasks have different requirements on each unilateral movement capability index of the mechanical arm, a hierarchical structure from top to bottom is constructed: a target layer (comprehensive representation of motion ability), a criterion layer (task requirement) and a sub-criterion layer (each unilateral motion ability index), wherein the target layer is the highest layer in the hierarchical structure, namely a target to be finally obtained, and the criterion layer and the sub-criterion layer are used for evaluating a target result;

STEP2 constructs a decision matrix: in order to judge the influence of each factor of the same layer on the factor of the upper layer, defining the importance among the elements based on a 1-7 scale method, and further constructing a judgment matrix;

STEP3 consistency check: solving the judgment matrix by using a maximum eigenvalue method, and carrying out consistency check on the result after obtaining the maximum eigenvalue of the judgment matrix so as to judge whether the matrix is reasonable or not;

STEP4 subjective weight solution: calculating the eigenvector corresponding to the maximum eigenvalue of the judgment matrix, wherein the elements in the eigenvector correspond to the subjective weight omega of each motion capability index_{CR_1},ω_{CR_2},ω_{CR_3}；

Objective weight omega for solving standard minimum singular value, standard condition number and standard operability based on entropy method_{CP_1},ω_{CP_2},ω_{CP_3}And is denoted by ω_CP＝[ω_{CP_1},ω_{CP_2},ω_{CP_3}]；

(3) Based on the obtained subjective weight and objective weight, the final weight of each athletic performance index is obtained as omega ═ omega_{CR_1}+ω_{CP_1},ω_{R_2}+ω_{CP_2},ω_{CR_3}+ω_{CP_3}]＝[ω_{C_1},ω_{C_2},ω_{C_3}]Further, the comprehensive characterization of the motion capability of the space manipulator can be expressed as:

in the above formula, q_λIndicating that the robotic arm is in the lambda configuration.

3. The method according to claim 1, wherein the step of constructing a preferred model of the spatial manipulator stop mechanism type with the joint locking fault according to the comprehensive characterization of the motion capability of the spatial manipulator, and then solving the preferred model of the stop mechanism type based on a Monte Carlo numerical method to obtain the optimal stop mechanism type of the spatial manipulator with the joint locking fault comprises the following steps:

(1) according to the comprehensive representation of the motion capability of the space manipulator, constructing a joint locking fault space manipulator stop mechanism type optimal model:

find q_best

max CP(q_best)

in the above formula, q_bestRepresenting the optimal shutdown configuration of the mechanical arm in the joint locking fault space;

(2) solving a shutdown configuration optimal model based on a Monte Carlo numerical method:

STEP1 is for each joint of a failed robotic arm, within each joint angle range

Generating K random numbers between 0 and 1 by using random number method

And then joint angle pseudo-random numbers of each joint of the fault mechanical arm can be obtained:

in the above formula, the first and second carbon atoms are,

STEP2 represents the joint angle pseudo-random numbers for each joint in the form:

in the above equation, each column of CS corresponds to a configuration of the malfunctioning arm, and CS can be written as

According to the comprehensive representation of the motion capability of the space manipulator, the CP (q) of the manipulator under each configuration is solved_λ) And selects to satisfy max CP (q)_best) Corresponding q_best＝[θ_1best θ_2best…θ_nbest]And the optimal shutdown configuration of the fault mechanical arm is obtained.

4. The method according to claim 1, wherein the motion planning is performed on the mechanical arm based on a sextic polynomial in consideration of the stop motion characteristics according to the optimal stop configuration of the joint locking fault space mechanical arm, and further in consideration of the safety and stability of the mechanical arm in the stop process, an optimization coefficient is introduced to construct a space mechanical arm stop motion optimization model, the stop motion optimization model is solved, and the stop optimization of the joint locking fault space mechanical arm is completed, and the method comprises the following steps:

(1) according to the optimal shutdown configuration of the joint locking fault space mechanical arm, the mechanical arm is subjected to motion planning based on a sextic polynomial in consideration of the shutdown motion characteristics:

θ(t)＝a₀+a₁t+a₂t²+a₃t³+a₄t⁴+a₅t⁵+a₆t⁶

in the above formula, a₀～a₆Is the undetermined coefficient;

because the configuration of the mechanical arm is the optimal shutdown configuration at the moment of stopping the shutdown motion, and the speed and the acceleration of each joint are both 0, the following can be obtained:

in the above formula, t₀Indicating the initial moment of shutdown, t_fIndicating the stop ending time, theta₀Indicates the joint angle theta of each joint of the mechanical arm at the initial stopping time_fThe joint angle of each joint of the mechanical arm is shown at the moment of stopping the machine,

the joint angular velocity of each joint of the mechanical arm at the initial stopping moment is shown,

the joint angular velocity of each joint of the mechanical arm at the moment of stopping is shown,

the joint angular acceleration of each joint of the mechanical arm at the initial stopping moment is shown,

representing the joint angular acceleration of each joint of the mechanical arm at the moment of stopping;

by setting an optimization coefficient k, let a₆K can be obtained:

(2) considering the safety and stability of a fault mechanical arm in the shutdown process so as to obtain the global base disturbance torque of the mechanical arm in the shutdown process

For optimization purposes, the mechanical arm joint is operated during the shutdown processAnd (k) constructing a joint locking fault space mechanical arm shutdown motion optimization model by taking the parameter lim (k) as constraint:

find k

s.t.lim(k)

and solving the shutdown motion optimization model of the space manipulator with the joint locking fault according to a genetic algorithm, so that the shutdown motion optimization of the space manipulator with the joint locking fault can be completed.

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