CN110103218B - Rapid self-adaptive control method for pipeline climbing of snake-shaped robot - Google Patents

Rapid self-adaptive control method for pipeline climbing of snake-shaped robot Download PDF

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CN110103218B
CN110103218B CN201910394875.7A CN201910394875A CN110103218B CN 110103218 B CN110103218 B CN 110103218B CN 201910394875 A CN201910394875 A CN 201910394875A CN 110103218 B CN110103218 B CN 110103218B
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CN110103218A (en
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黄凯
刘林林
程龙
简智勇
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National Sun Yat Sen University
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00Programme-controlled manipulators
    • B25J9/06Programme-controlled manipulators characterised by multi-articulated arms
    • B25J9/065Snake robots
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00Programme-controlled manipulators
    • B25J9/16Programme controls
    • B25J9/1615Programme controls characterised by special kind of manipulator, e.g. planar, scara, gantry, cantilever, space, closed chain, passive/active joints and tendon driven manipulators
    • B25J9/1625Truss-manipulator for snake-like motion

Abstract

The invention relates to a rapid self-adaptive control method for pipeline climbing of a snake-shaped robot. Firstly, defining a change space of control parameters, enabling the robot to climb a pipeline under different parameter combinations, recording the acceleration and the joint angle of the robot by taking 2 seconds as a period, integrating all collected data into a complete data set, and clustering vectors formed by joint angle attributes in the data by using a K-means + + algorithm. In the real-time control, real-time joint angles, accelerations and current control parameters are collected in a period of 2 seconds, a data set in the same cluster is selected through clustering operation, the influence degree on the robot motion is measured by calculating the acceleration entropy variance of each control parameter, the control parameter with the largest influence degree is selected, and the most sensitive parameter value is updated through weighted regression and then is input into a control system, so that the motion gait of the snake-shaped robot is changed. The climbing robot can climb pipelines with different diameters independently, can climb pipelines formed by combining different diameters, and has strong adaptability.

Description

Rapid self-adaptive control method for pipeline climbing of snake-shaped robot
Technical Field
The invention relates to the technical field of robots, in particular to a rapid self-adaptive control method for pipeline climbing of a snake-shaped robot.
Background
The unsupervised learning is a machine learning method which is used for finding patterns in data, classifying the unlabeled input data into different sets according to the internal structure and rule of the unlabeled input data.
The snake-shaped robot is a bionic robot, and researches are carried out by scholars from the 20 th century and the 70 th century, the motion modes of the current snake-shaped robot comprise plane motion, three-dimensional motion and universal motion, the snake-shaped robot is suitable for moving in narrow areas, rugged mountainous regions, pipelines and other places, and functions of detection, rescue, exploration and the like can be realized.
Most of the existing snake-shaped robots are specially customized for a certain type of pipeline, the hardware device is specially designed for climbing the pipeline, corresponding independent adjusting software is not used for independent regulation and control according to the current state, and the self-adaptability is insufficient. When pipelines with different diameters and different scenes are met, a large amount of manpower and material resources are needed to adjust the equipment.
Disclosure of Invention
The invention provides a rapid self-adaptive control method for snake-shaped robot pipeline climbing, aiming at overcoming at least one defect in the prior art, and the method can realize self-adaptive pipeline climbing of the snake-shaped robot.
In order to solve the technical problems, the invention adopts the technical scheme that: a quick self-adaptive control method for pipeline climbing of a snake-shaped robot comprises the following steps:
s1, defining a variation space of parameters; defining snake-shaped robot gait control parameters: the amplitude A, the frequency omega and the phase are in the same variation space, and all the parameters are subjected to full permutation and combination;
s2, controlling the snake-shaped robot to climb a pipeline under different parameter combinations, and collecting the acceleration and the joint angle of the robot in a certain period;
s3, clustering; clustering the collected data by using a K-means + + algorithm, and classifying the collected data into N clusters;
s4, selecting the most sensitive parameters; during real-time movement, periodically collecting data, performing clustering operation on the data, selecting training data with z-axis acceleration in the same cluster larger than real-time z-axis acceleration, calculating the acceleration entropy variance of control parameters, and selecting the most sensitive parameters;
s5, updating the most sensitive parameter value; first, a fitting estimation function F is calculatedwAnd using the square error as an error function, updating the weight W by using a gradient descent algorithm until the weight is stable, and calculating a new most sensitive parameter value for the gait control of the snake-shaped robot.
In the invention, the off-line working algorithm is as follows: collecting off-line data for unsupervised training, and clustering by using a K-means + + algorithm. The operation algorithm in operation: and collecting data in real time, clustering based on the trained clustering result, calculating the acceleration entropy variance of each control parameter, selecting the most sensitive parameter, and modifying the parameter by using a regression algorithm to enable the robot to climb the pipeline smoothly.
The rapid self-adaptive control algorithm for snake-shaped robot pipeline climbing firstly defines the change space of control parameters, enables the robot to climb the pipeline under different parameter combinations, records the acceleration and the joint angle of the robot in a period of 2 seconds, integrates all collected data into a complete data set, and clusters vectors formed by joint angle attributes in the data by using a K-means + + algorithm. And then, collecting real-time joint angles, accelerations and current control parameters in a real-time control process by taking 2 seconds as a period, selecting a data set in the same cluster through clustering operation, calculating an acceleration entropy variance for each control parameter to measure the influence degree on the motion of the robot, selecting the control parameter with the maximum influence degree, and updating the most sensitive parameter value by weighted regression to enter a control system so as to change the motion gait of the snake-shaped robot. Manpower resources do not need to be consumed to manually control the robot; can independently climb the pipeline of different diameters to can climb the pipeline that different diameters make up and form, strong adaptability.
Further, the step S2 specifically includes performing pipeline climbing in the simulation environment by using each parameter combination, and recording the acceleration of the robot in the z-axis direction, the angle of each joint, and the amplitude a, the frequency ω, and the phase e of the control parameter at the time in a certain period.
Further, in the step S3, when the K-means + + algorithm is used, the elbow method is used to select the number of clusters, randomly select N cluster centers, cluster the data set, and continuously update the positions of the cluster centers and the attributions of the data in the N clusters until the cluster centers do not change within the error range.
Further, the step S4 specifically includes:
s41, collecting data in real-time operation of the snake-shaped robot, calculating the distance from the collected data to each cluster center, and selecting a data cluster where the cluster center with the closest distance is located as a data cluster to which the collected data belongs; forming a set P by data of which the acceleration of the z axis in the cluster is larger than the real-time acceleration of the z axis;
s42, discretizing the acceleration in the set P, and processing according to the following formula:
Figure GDA0002662507820000031
in the formula, LDFor adjustable step length, az,iThe value of z-axis acceleration of the ith data in the set P, anew,iIs the value of the z-axis acceleration after discretization of the z-axis acceleration in the set P;
s43, for a gait parameter, a plurality of possible values are obtained by Si,jTo represent a vector of control parameters, the values of i being 0, 1, 2 representing the amplitude a, the frequency ω, the phase e, S, respectivelyi,jRepresenting the j-th possible value of the control parameter i in the current data set, and calculating the entropy value H (S) when the value of the parameter i is the j-th possible valuei,j):
Figure GDA0002662507820000032
In the formula, p (a)new,k) Is that the discretization velocity of the z-axis acceleration is equal to a in all cases where the value of the control parameter i is equal to its j-th value in this data setnew,kThe ratio of (A) to (B); a isnew,kAnd anew,iThe same meaning is obtained, and the values are the z-axis acceleration values after the discretization of the z-axis acceleration in the set P;
s44, calculating the entropy variance Var of the gait parameter ii
Figure GDA0002662507820000033
In the formula (I), the compound is shown in the specification,
Figure GDA0002662507820000034
is the mean value of the acceleration entropy when all the values of the control parameter i are taken, NiThe number of all possible values for the control parameter i;
s45, normalization is carried out on the entropy variance:
Figure GDA0002662507820000035
s46, randomly selecting the most sensitive parameters by using a roulette selection algorithm.
Further, the step S5 specifically includes:
s51, updating the value of the most sensitive gait parameter by adopting a weighted regression analysis method, and solving a weighted least square problem in a fitting regression function by using a gradient descent algorithm, wherein the fitting estimation function is as follows:
Figure GDA0002662507820000041
wherein W is the coefficient vector of the fitting function, m is the number of coefficients, PtThe joint angle of the snake-shaped robot is acquired in real time;
the error function is:
Figure GDA0002662507820000042
Pa=[Pa,1 Pa,2 … Pa,n]
Q=[Qa,1 Qa,2 … Qa,n]T
wherein n is the data quantity of the set P in which the z-axis acceleration is larger than the real-time z-axis acceleration, and PaThe vector is formed by joint angles corresponding to data of which the z-axis acceleration is larger than the real-time z-axis acceleration in the set P, and the vector is formed by combining most sensitive control parameters corresponding to data of which the z-axis acceleration is larger than the real-time z-axis acceleration in the set P.
S52, according to a gradient descent principle, carrying out derivation on D (W):
Figure GDA0002662507820000043
s53, in order to ensure the vector fitting and accelerated regression of the dominant data, a dominant data vector matrix P is subjectedaAccording to its pairThe corresponding acceleration takes a weighting action:
Figure GDA0002662507820000044
Figure GDA0002662507820000045
in the formula, LsFor variable learning step size, M is a learning rate matrix;
s54, updating the coefficient vector W according to the following formulanew
Figure GDA0002662507820000046
S55, continuously iterating until WnewThe value of (a) tends to a steady state; obtaining the optimal fitting coefficient W when the iteration is terminatedbestW is to bebestSubstituting into formula
Fw(Pt)=WTPt
S56, obtaining a regression result of the most sensitive parameters, using the result in gait control, keeping the original values of other parameters, and only modifying the values of the most sensitive parameters.
Compared with the prior art, the beneficial effects are: according to the rapid self-adaptive control method for pipeline climbing of the snake-shaped robot, manual control of the operation of the robot is not needed to consume human resources, pipelines with different diameters can be automatically climbed, the pipelines formed by combining different diameters can be climbed, and the adaptability is high; the invention realizes the climbing effect from the software level and is not influenced by hardware.
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Fig. 1 is an overall flowchart of the control method of the present invention.
FIG. 2 is a flow chart of the K-means + + clustering process of the present invention.
Fig. 3 is a flow chart of the most sensitive parameter selection of the present invention.
FIG. 4 is a flow chart of the present invention for updating the most sensitive parameter values.
Detailed Description
The drawings are for illustration purposes only and are not to be construed as limiting the invention; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the invention.
As shown in fig. 1, a rapid adaptive control method for pipeline climbing of a snake-shaped robot comprises the following steps:
s1, defining a variation space of parameters; defining snake-shaped robot gait control parameters: the amplitude A, the frequency omega and the phase are in the same variation space, and all the parameters are subjected to full permutation and combination;
s2, controlling the snake-shaped robot to climb a pipeline under different parameter combinations, and collecting the acceleration and the joint angle of the robot in a certain period;
s3, clustering; clustering the collected data by using a K-means + + algorithm, and classifying the collected data into N clusters;
s4, selecting the most sensitive parameters; during real-time movement, periodically collecting data, performing clustering operation on the data, selecting training data with z-axis acceleration in the same cluster larger than real-time z-axis acceleration, calculating the acceleration entropy variance of control parameters, and selecting the most sensitive parameters;
s5, updating the most sensitive parameter value; first, a fitting estimation function F is calculatedwAnd using the square error as an error function, updating the weight W by using a gradient descent algorithm until the weight is stable, and calculating a new most sensitive parameter value for the gait control of the snake-shaped robot.
Specifically, the step S2 specifically includes performing pipeline climbing in the simulation environment by using each parameter combination, and recording the acceleration of the robot in the z-axis direction, the angle of each joint, and the amplitude a, the frequency ω, and the phase e of the control parameter at that time in a certain period.
As shown in fig. 2, in the step S3, when the K-means + + algorithm is used, the elbow method is used to select the number of clusters, randomly select N cluster centers, cluster the data set, and continuously update the locations of the cluster centers and the attributions of the data in the N clusters until the cluster centers are not changed within the error range.
As shown in fig. 3, the step S4 specifically includes:
s41, collecting data in real-time operation of the snake-shaped robot, calculating the distance from the collected data to each cluster center, and selecting a data cluster where the cluster center with the closest distance is located as a data cluster to which the collected data belongs; forming a set P by data of which the acceleration of the z axis in the cluster is larger than the real-time acceleration of the z axis;
s42, discretizing the acceleration in the set P, and processing according to the following formula:
Figure GDA0002662507820000061
in the formula, LDFor adjustable step length, az,iThe value of z-axis acceleration of the ith data in the set P, anew,iIs the value of the z-axis acceleration after discretization of the z-axis acceleration in the set P;
s43, for a gait parameter, a plurality of possible values are obtained by Si,jTo represent a vector of control parameters, the values of i being 0, 1, 2 representing the amplitude a, the frequency ω, the phase e, S, respectivelyi,jRepresenting the j-th possible value of the control parameter i in the current data set, and calculating the entropy value H (S) when the value of the parameter i is the j-th possible valuei,j):
Figure GDA0002662507820000062
In the formula, p (a)new,k) Is that the discretization velocity of the z-axis acceleration is equal to a in all cases where the value of the control parameter i is equal to its j-th value in this data setnew,kThe ratio of (A) to (B); a isnew,kAnd anew,iThe same meaning is obtained, and the values are the z-axis acceleration values after the discretization of the z-axis acceleration in the set P;
s44, calculating the entropy variance Var of the gait parameter ii
Figure GDA0002662507820000063
In the formula (I), the compound is shown in the specification,
Figure GDA0002662507820000064
is the mean value of the acceleration entropy when all the values of the control parameter i are taken, NiThe number of all possible values for the control parameter i;
s45, normalization is carried out on the entropy variance:
Figure GDA0002662507820000071
s46, randomly selecting the most sensitive parameters by using a roulette selection algorithm.
As shown in fig. 4, the step S5 specifically includes:
s51, updating the value of the most sensitive gait parameter by adopting a weighted regression analysis method, and solving a weighted least square problem in a fitting regression function by using a gradient descent algorithm, wherein the fitting estimation function is as follows:
Figure GDA0002662507820000072
wherein W is the coefficient vector of the fitting function, m is the number of coefficients, PtThe joint angle of the snake-shaped robot is acquired in real time;
the error function is:
Figure GDA0002662507820000073
Pa=[Pa,1 Pa,2 … Pa,n]
Q=[Qa,1 Qa,2…Qa,n]T
wherein n is the data quantity of the set P in which the z-axis acceleration is larger than the real-time z-axis acceleration, and PaThe vector is formed by joint angles corresponding to data of which the z-axis acceleration is larger than the real-time z-axis acceleration in the set P, and the vector is formed by combining most sensitive control parameters corresponding to data of which the z-axis acceleration is larger than the real-time z-axis acceleration in the set P.
S52, according to a gradient descent principle, carrying out derivation on D (W):
Figure GDA0002662507820000074
s53, in order to ensure the vector fitting and accelerated regression of the dominant data, a dominant data vector matrix P is subjectedaAnd (3) taking weighting operation according to the corresponding acceleration:
Figure GDA0002662507820000075
Figure GDA0002662507820000076
in the formula, LsFor variable learning step size, M is a learning rate matrix;
s54, updating the coefficient vector W according to the following formulanew
Figure GDA0002662507820000081
S55, continuously iterating until WnewThe value of (a) tends to a steady state; obtaining the optimal fitting coefficient W when the iteration is terminatedbestW is to bebestSubstituting into formula
Fw(Pt)=WTPt
S56, obtaining a regression result of the most sensitive parameters, using the result in gait control, keeping the original values of other parameters, and only modifying the values of the most sensitive parameters.
Example 1
As shown in fig. 1, the method includes:
step 1: and defining a parameter space and carrying out full permutation and combination. The gait control parameters of the snake-shaped robot comprise an amplitude (A), a frequency (omega) and a phase (epsilon), the change interval of the A is [40,80], and the change step length is 5; the variation interval of omega is [1.5,3], and the step length is 0.5; the variation interval of epsilon is [0,5], and the variation step length is 1. And carrying out full permutation and combination on all the parameters.
Step 2: select a set of control parameters and collect data.
And step 3: and clustering.
And 4, step 4: the most sensitive parameters are selected.
And 5: and updating the most sensitive parameter values and applying the most sensitive parameter values to the control of the snake-shaped robot.
As shown in fig. 2, a K-means + + clustering process is performed, and the specific process is as follows:
s31, determining the number N of clusters. Using the elbow method, the number of clusters was selected:
Figure GDA0002662507820000082
Figure GDA0002662507820000083
in the formula, NkIs the number of cluster cores, SiIs the mean value of the distances from the member data to the cluster center in each cluster, NkStarting from 1, an attempt is made to calculate N when cluster variance is minimalkN used in the present invention by trial and errork=25;
S32, selecting a cluster center. Randomly selecting 25 cluster centers, and clustering the data set;
s33, continuously updating the positions of the cluster centers and the attributions of the data in the 25 clusters until the cluster centers are not changed within the error range;
s34, obtaining N cluster center results.
As shown in fig. 3, for the selection of the most sensitive parameters, the specific process is as follows:
s41: and collecting data in the real-time operation of the snake-shaped robot, and clustering.
S42: and forming a dominant data set P by using the data of which the acceleration of the z axis in the cluster is greater than the acceleration of the real-time z axis.
S43: discretizing the acceleration in the set P, LDThe variable step size is set to 0.1.
S44: an entropy value for each value of each parameter is calculated.
S45: the entropy variance is calculated.
S46: and carrying out normalization processing on the entropy variance.
S47: the most sensitive parameters are found by the roulette algorithm.
As shown in fig. 4, the specific flow of the update process for the most sensitive parameters is as follows:
s51: setting a fitting estimation function:
Figure GDA0002662507820000091
s52: initial parameter setting, vector coefficient W is initialized to 0, LsThe variable step size is set to 0.5.
S53: the vector coefficients are updated using a gradient descent algorithm.
S54: and repeatedly updating to obtain a best fit coefficient vector, and substituting the best fit coefficient vector into the formula of S51 to obtain the most sensitive parameter value.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (5)

1. A quick self-adaptive control method for pipeline climbing of a snake-shaped robot is characterized by comprising the following steps:
s1, defining a variation space of parameters; defining snake-shaped robot gait control parameters: the amplitude A, the frequency omega and the phase are in the same variation space, and all the parameters are subjected to full permutation and combination;
s2, controlling the snake-shaped robot to climb a pipeline under different parameter combinations, and collecting the acceleration and the joint angle of the robot in a certain period;
s3, clustering; clustering the collected data by using a K-means + + algorithm, and classifying the collected data into N clusters;
s4, selecting the most sensitive parameters; during real-time movement, periodically collecting data, performing clustering operation on the data, selecting training data with z-axis acceleration in the same cluster larger than real-time z-axis acceleration, calculating the acceleration entropy variance of control parameters, and selecting the most sensitive parameters;
s5, updating the most sensitive parameter value; first, a fitting estimation function F is calculatedwAnd using the square error as an error function, updating the weight W by using a gradient descent algorithm until the weight is stable, and calculating a new most sensitive parameter value for the gait control of the snake-shaped robot.
2. The rapid adaptive control method for pipe climbing of a snake-shaped robot as claimed in claim 1, wherein the step S2 comprises performing pipe climbing using each parameter combination in a simulation environment, and recording the acceleration of the robot in the z-axis direction, the angle of each joint and the amplitude a, the frequency ω and the phase e of the control parameter at that time with a certain period.
3. The method for rapid adaptive control of pipeline climbing of a snake-shaped robot as claimed in claim 2, wherein the step S3 is to select the number of clusters by using the elbow method when using the K-means + + algorithm, randomly select N cluster centers, cluster the data set, and continuously update the positions of the cluster centers and the attribution of the data in the N clusters until the cluster centers are not changed within the error range.
4. The method for rapid adaptive control of pipeline climbing of a serpentine robot as claimed in claim 3, wherein the step S4 comprises:
s41, collecting data in real-time operation of the snake-shaped robot, calculating the distance from the collected data to each cluster center, and selecting a data cluster where the cluster center with the closest distance is located as a data cluster to which the collected data belongs; forming a set P by data of which the acceleration of the z axis in the cluster is larger than the real-time acceleration of the z axis;
s42, discretizing the acceleration in the set P, and processing according to the following formula:
Figure FDA0002662507810000021
in the formula, LDFor adjustable step length, az,iThe value of z-axis acceleration of the ith data in the set P, anew,iIs the value of the z-axis acceleration after discretization of the z-axis acceleration in the set P;
s43, for a gait parameter, a plurality of possible values are obtained by Si,jTo represent a vector of control parameters, the values of i being 0, 1, 2 representing the amplitude a, the frequency ω, the phase e, S, respectivelyi,jRepresenting the j-th possible value of the control parameter i in the current data set, and calculating the entropy value H (S) when the value of the parameter i is the j-th possible valuei,j):
Figure FDA0002662507810000022
In the formula, p (a)new,k) Is that the discretization velocity of the z-axis acceleration is equal to a in all cases where the value of the control parameter i is equal to its j-th value in this data setnew,kThe ratio of (A) to (B); a isnew,kAnd anew,iThe same meaning is obtained, and the values are the z-axis acceleration values after the discretization of the z-axis acceleration in the set P;
s44, calculating the entropy variance Var of the gait parameter ii
Figure FDA0002662507810000023
In the formula (I), the compound is shown in the specification,
Figure FDA0002662507810000024
is the mean value of the acceleration entropy when all the values of the control parameter i are taken, NiThe number of all possible values for the control parameter i;
s45, normalization is carried out on the entropy variance:
Figure FDA0002662507810000025
s46, randomly selecting the most sensitive parameters by using a roulette selection algorithm.
5. The method for rapid adaptive control of pipeline climbing of a serpentine robot as claimed in claim 4, wherein the step S5 comprises:
s51, updating the value of the most sensitive gait parameter by adopting a weighted regression analysis method, and solving a weighted least square problem in a fitting regression function by using a gradient descent algorithm, wherein the fitting estimation function is as follows:
Figure FDA0002662507810000026
wherein W is the coefficient vector of the fitting function, m is the number of coefficients, PtThe joint angle of the snake-shaped robot is acquired in real time;
the error function is:
Figure FDA0002662507810000031
Pa=[Pa,1 Pa,2…Pa,n]
Q=[Qa,1 Qa,2…Qa,n]T
wherein n is the data quantity of the set P in which the z-axis acceleration is larger than the real-time z-axis acceleration, and PaThe vector is formed by joint angles corresponding to data of which the z-axis acceleration is greater than the real-time z-axis acceleration in the set P, and Q is a vector formed by combining most sensitive control parameters corresponding to data of which the z-axis acceleration is greater than the real-time z-axis acceleration in the set P;
s52, according to a gradient descent principle, carrying out derivation on D (W):
Figure FDA0002662507810000032
s53, in order to ensure the vector fitting and accelerated regression of the dominant data, a dominant data vector matrix P is subjectedaAnd (3) taking weighting operation according to the corresponding acceleration:
Figure FDA0002662507810000033
Figure FDA0002662507810000034
in the formula, LsFor variable learning step size, M is a learning rate matrix;
s54, updating the coefficient vector W according to the following formulanew
Figure FDA0002662507810000035
S55, continuously iterating until WnewThe value of (a) tends to a steady state; obtaining the optimal fitting coefficient W when the iteration is terminatedbestW is to bebestSubstituting into formula
Fw(Pt)=WTPt
S56, obtaining a regression result of the most sensitive parameters, using the result in gait control, keeping the original values of other parameters, and only modifying the values of the most sensitive parameters.
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