An aeronautical vehicle control method based on an optimized bayesian network

Abstract

The application relates to the technical field of water-land cross-domain robot control, solves the technical problem that water-land cross-domain robot motion control is difficult to realize in the prior art, and particularly relates to a water-land cross-domain robot motion control method based on an optimized Bayesian network, which comprises the following steps: constructing a three-layer Bayesian network structure, performing structure learning of the three-layer Bayesian network structure through an MMPC-K2 algorithm, performing parameter learning of the Bayesian network model by adopting an IF-THEN inference rule with improved confidence, feeding a decision scheme with the maximum probability into a designed CPG output network to control the leg part of the water-land cross-domain robot to perform gait switching, and the like. The application can comprehensively consider all sensor information, output an optimal scheme by using the network structure with the highest score, the input node prior probability and the improved IF-THEN rule, realize autonomous decision of the water-land cross-domain robot, and realize switching of corresponding gaits of the leg part of the robot according to different terrains.

Description

Technical Field

[0001] This invention relates to the field of water and land cross-domain robot control technology, and in particular to a motion control method for water and land cross-domain robots based on optimized Bayesian networks. Background Technology

[0002] With the development of technology and the expansion of human exploration, the demand for robots capable of performing tasks in complex environments is increasing. Aquatic-land-transition robots possess advantages such as efficient obstacle crossing, high maneuverability, and rapid transition between land and water, enabling them to freely switch and operate in both terrestrial and underwater environments. Therefore, they have broad application prospects in fields such as military reconnaissance, marine exploration, underwater archaeology, environmental monitoring, and disaster relief. However, aquatic-land-transition robots need to possess the ability to operate stably in various environments, requiring their design to fully consider the characteristics of hydrodynamics and terrestrial mechanics, as well as how to smoothly transition between land and water. However, the motion control of aquatic-land-transition robots faces the following challenges:

[0003] 1. Relying solely on the GPS, depth gauge, and altimeter information carried by the amphibious robot makes it difficult to accurately predict potential dangers in complex amphibious transition environments, which poses challenges to the robot's perception, especially as complex terrain and medium transitions increase the instability of its movement.

[0004] 2. Reinforcement learning typically abandons existing strategies and starts learning from the initial state. This approach has low tracking efficiency and does not fully utilize existing experience, which is inconsistent with actual needs.

[0005] 3. Bayesian networks with unoptimized structure and parameters are susceptible to direct influence from observed signals. Faced with sudden changes in sensor signals, the amphibious robot is unable to make correct decisions during training, its safety cannot be guaranteed, and it is therefore difficult to complete the task.

[0006] Therefore, based on the above three challenges, it is necessary to design more effective motion control methods to enable the amphibious robot to make better decision-making choices, achieve better stability, and meet the needs of practical engineering. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a motion control method for cross-domain robots between water and land based on optimized Bayesian networks, which solves the technical problem that existing technologies struggle to achieve motion control for cross-domain robots between water and land.

[0008] To address the aforementioned technical problems, this invention provides the following technical solution: a motion control method for a cross-domain robot between land and water based on an optimized Bayesian network, the method comprising the following steps:

[0009] S1. Analyze the decision-making state, associated state, and autonomous decision-making scheme of the amphibious robot under different environmental working modes, and determine the input nodes, intermediate nodes, and decision nodes used to initially construct a three-layer Bayesian network structure.

[0010] S2. The structure of the three-layer Bayesian network is learned through the MMPC-K2 algorithm, and the network structure with the highest score is obtained as the final Bayesian network model.

[0011] S3. Analyze the expert evaluations given by multiple experts for each node, and fuse the multiple expert evaluations to determine the prior probability distribution of each node in the Bayesian network model.

[0012] S4. The parameters of the Bayesian network model are learned by adopting the IF-THEN inference rule with improved confidence, and the qualitative evaluation is transformed into quantitative probability to determine the posterior probability of the decision node.

[0013] S5. Using real-time environmental information acquired by multiple sensors as input to a Bayesian network model after structure learning and parameter learning, a decision-making scheme for controlling an amphibious robot in an uncertain environment is generated.

[0014] S6. Feed back the decision scheme with the highest probability to the CPG output network used to control the gait switching of the amphibious robot, so as to enable the amphibious robot's legs to switch the corresponding gait according to different terrains.

[0015] Furthermore, in step S1, based on the dependencies between input nodes, intermediate nodes, and decision nodes, a three-layer Bayesian network structure is initially constructed; wherein,

[0016] The decision-making state is determined by analyzing the working process of the amphibious robot, which is the input node of the three-layer Bayesian network structure. The input data of the input node includes the battery voltage, GPS signal, depth gauge, altimeter, terrain, obstacle distance, and rain sensor information during the working process of the amphibious robot.

[0017] The correlation status, i.e., intermediate nodes, is determined by analyzing the correlation between node variables, including environmental perception and task detection.

[0018] Formulate corresponding autonomous decision-making plans, i.e. decision nodes, including thruster start / stop and gait switching.

[0019] Furthermore, in step S2, the specific process includes the following steps:

[0020] S21. Use the MMPC algorithm to learn each node and the dataset, and select the node with any variable X using the max-min heuristic strategy. iWhen the association rule with the lowest correlation is found, the association rule with the highest correlation is denoted as assocF, and the corresponding variable is F. If the association rule assocF ≠ 0, then the variable F is added to the candidate parent-child node set CPC. i In Chinese, it is denoted as CPC. i =CPC i ∪F, otherwise the candidate parent-child node set CPC i constant;

[0021] S22, Let Where (i1,i2,…,i) m ) is any subset of (1,2,…,n), for any variable If a subset S exists i and So that in subset S i Under the conditions, With X i The correlation function value is 0;

[0022] S23, the candidate parent-child node set of the root decision node variable, i.e.

[0023] S24. Input variable set V = {x1, x2, x3, ..., x n} and its observation dataset D, determine variable X i The family K2 scoring function g(i,pa(i)) is expressed as:

[0024]

[0025] Where i represents each node variable; pa(i) represents the set of parent nodes for that node variable; q i Represents variable X i The total number of state combinations that can be obtained from the parent node variable; r i The total number of states obtained; m ijk X represents a variable X in the observation dataset D. i When the state is k, the total number of samples whose parent node set has state combination j.

[0026] S25. Initialize the network structure, let the network structure dag = zeros(n,n), and calculate each variable X. i Let the family K2 scoring function value be g(i,pa(i)), i = 1, 2, ..., n, and let bestg(i,pa(i)) = g(i,pa(i)), i = 1, 2, ..., n, and let i = 1;

[0027] S26. Call the MMPC algorithm to return variable X. iCPC (Choice of Parent-Child Nodes) i ;

[0028] S27, Regarding variable X i and its candidate parent-child node set CPC i For each Add directed edges respectively or We obtain a series of information about variable X i For each candidate local structure, calculate the family K2 score function value of each candidate local structure, and retain the maximum function value g(i,pa(i))=maxg(i,pa(i));

[0029] If g(i,pa(i))>bestg(i,pa(i)), then bestg(i,pa(i))=g(i,pa(i)), and the corresponding network structure is the optimal structure;

[0030] Otherwise, output bestg(i,pa(i)) and its corresponding optimal structure remain unchanged, and i = i + 1, then execute step S26;

[0031] S28. Regarding variable X i The optimal local structure for each Add directed edges respectively or A series of candidate structures were obtained;

[0032] For any Reverse directed edges A series of candidate structures were obtained;

[0033] For any Reverse directed edges A series of candidate structures were obtained;

[0034] For each Delete directed edges or A series of candidate structures were obtained;

[0035] S29. Calculate the structure of all candidate structures with respect to variable X. i The K2 scoring function value, and g(i,pa(i))=maxg(i,pa(i));

[0036] If g(i,pa(i))>bestg(i,pa(i)), then bestg(i,pa(i))=g(i,pa(i)), and the corresponding structure is the optimal structure;

[0037] Otherwise, return bestg(i,pa(i)) and its corresponding optimal structure unchanged, and let i = i + 1;

[0038] S210. If i ≤ n, return to step S27; if i > n, the algorithm stops and returns the optimal network structure dag.

[0039] Furthermore, in step S3, the specific process includes the following steps:

[0040] S31. Perform distortion error analysis on each node. This raises suspicion of evaluation distortion error, where:

[0041]

[0042] u=∣v1v2+v2v3+…+v n-1 v n |

[0043]

[0044] In the formula, w i The values ​​were assigned by experts; ν is the sample mean; n is the number of evaluations; i Represents the residual;

[0045] S32. Perform an empirical error analysis on each node. If |ν i |>Z c If σ is the population standard deviation, then this data is outlier; Z is the population standard deviation. c These are the Schauville criterion coefficients;

[0046] S33. Conduct expert evaluation and integration;

[0047] The expert node scoring data is divided into two batches for processing. Experts 1 and 2, and experts 3 and 4 are in one group, and the rest are in the other group. The arithmetic mean X1 and X2, and the standard deviation σ1 and σ2 are calculated for the data after batch processing. Finally, the fusion value M is calculated, and the evaluation fusion value function is expressed as follows:

[0048]

[0049] S34. Calculate the expert evaluation uncertainty used to indicate the reliability of the rating results. The expert evaluation uncertainty x can be expressed as:

[0050]

[0051] In the formula, U is the mean of the uncertainty; U is the total uncertainty; U a Type A uncertainty; U b Type B uncertainty;

[0052] S35. Based on the above formula and the expert evaluation fusion value, the final qualitative evaluation with uncertainty can be obtained. The initial prior probability distribution is obtained by statistically analyzing the sample data of each node.

[0053] Furthermore, in step S34, the formula for calculating Type A uncertainty is:

[0054] U a =k p b

[0055] In the formula, k p is the coverage factor; b is the standard deviation of the arithmetic mean, calculated using the following formula:

[0056]

[0057] In the formula, The average value assigned to the experts;

[0058] The formula for calculating Type B uncertainty is:

[0059]

[0060] In the formula, a is the confidence interval; k is the corresponding coverage factor.

[0061] Furthermore, in step S4, the specific process includes the following steps:

[0062] S41. Transform all input information from the input nodes into a unified confidence framework to obtain the matching degree corresponding to the confidence distribution. The conversion formula is:

[0063]

[0064] Where, x i It is the input value of the i-th index; A i,j This represents the attribute reference value; j represents the number of reference levels. f(·) represents the matching degree of the i-th input index relative to the j-th reference level; f(·) represents the transformation function;

[0065] S42. Based on matching degree Calculate the activation weight w for the corresponding rule k Activation weights are used to represent the degree to which the input information activates the rule;

[0066] S43. Use the Evidence-Based Reasoning (ER) algorithm to determine conditions 0. <w k Rules with a value ≤1 are fused to obtain the confidence score. The expression is:

[0067]

[0068] Where, β n,k This indicates that the k-th rule applies to the n-th reference level D. n Confidence level; β i,k This indicates that the k-th rule applies to the i-th reference level D. n The confidence level; N represents the number of reference levels; This represents the nth reference level D in the output. n The confidence level, and satisfying μ is the utility value;

[0069] S44. Using confidence levels The IF-THEN rule is improved by establishing inference rules between input nodes, intermediate nodes, and decision nodes, transforming qualitative evaluation into quantitative probability to determine the posterior probability S(x) of the decision node. i ),Right now:

[0070]

[0071] Where S(·) represents the output function.

[0072] S45. Based on several posterior probabilities S(x) i Establish a conditional probability table for input nodes, intermediate nodes, and decision nodes, and select the decision scheme with the highest posterior probability.

[0073] Further, in step S42, the activation weight w k The calculation formula is:

[0074]

[0075] Among them, w k This represents the activation weight of the k-th rule, when 0 <w k If θ ≤ 1, the corresponding rule is considered to have been activated; k θ l represents the rule weights of the k-th and l-th rules, respectively; L represents the total number of rules; M represents the number of input metrics; This indicates the degree of matching between the i-th input and its reference value in the rule; δ represents the degree of matching between the i-th input and its reference value in rule l; i Indicates attribute weight; This represents the normalized relative attribute weights.

[0076] Furthermore, in step S6, the specific process includes the following steps:

[0077] S61. Couple several Hopf oscillator models to form a CPG output network, wherein the Hopf oscillators of each neuron adopt a bidirectional coupling mechanism, then the mathematical model of the Hopf oscillator of the i-th neuron is expressed as:

[0078]

[0079] in, σ is the state variable of the neuron oscillator; x and y are the outputs of the neuron oscillator; σ is the intensity factor; R is the radius of the limit cycle; ω is the oscillation frequency; λ is the coupling coefficient. For coupling terms; Let be the phase difference between the j-th neuron oscillator and the i-th neuron oscillator;

[0080] S62. Mathematical Model Construction Based on Hopf Oscillator: A Hopf oscillator model that generates corresponding asymmetric waveforms based on the occupancy coefficients of different time states is represented as follows:

[0081]

[0082] Where H is the joint rotation speed of the amphibious robot, and ε is the footprint coefficient; y ik Let y be the value of the state variable y of the i-th oscillator at time k;

[0083] S63. Establish a mapping function D(x) that maps the approximate sinusoidal signal output by the CPG output network to the range of joint rotation from 0 to 360°, i.e.:

[0084]

[0085] Where x and y are the outputs of the CPG output network; θ s It is the support angle, that is, the angle through which the joint rotates during the support phase; θ t It is the swing angle, that is, the angle through which the joint rotates during the swing phase.

[0086] S64. During the transition between multiple gait states, a strategy of continuously varying parameters is adopted to smoothly transition the phase difference and gait coefficient from the values ​​of the current gait state to the values ​​of the target gait state within a certain time period. The change process is represented as follows:

[0087]

[0088] in, and ε + These are the phase difference and footprint coefficient of the target gait; and ε -t0 represents the phase difference and gait coefficient of the current gait; t0 represents the moment when the gait switching command is received; t is the cumulative time since t0; w is the convergence factor, used to adjust the rate of change of the phase difference and gait coefficient parameters of the target gait.

[0089] S65. Establish a convergence factor function to adjust the rate of change of the phase difference and footprint coefficient parameters of the target gait, namely:

[0090]

[0091] Where t1 is the predetermined time to achieve the target gait.

[0092] By employing the above technical solution, the present invention provides a motion control method for a cross-domain robot between land and water based on an optimized Bayesian network, which has at least the following beneficial effects:

[0093] 1. This invention can comprehensively consider all sensor information, utilize the network structure with the highest score, the prior probability of input nodes, and the improved IF-THEN rule to output the optimal solution, thereby realizing autonomous decision-making for cross-domain robots.

[0094] 2. This invention solves the parent-child node set using the MMPC-K2 algorithm, and then finds the network skeleton through the scoring function, thus completing the Bayesian network structure learning for the motion control method of the water and land cross-domain robot. This avoids missing relevant dependencies and simplifies the calculation of conditional probabilities. At the same time, it can greatly reduce the computational amount of the parent-child node set and the hill-climbing search algorithm, and calculate the most suitable network structure through K2 scoring.

[0095] 3. This invention utilizes an improved IF-THEN rule to calculate the posterior probability of the control scheme, completing the Bayesian network parameter learning for the cross-domain robot motion control method. It can integrate expert knowledge and experience, transforming this difficult-to-quantify information into operable rules, and is insensitive to small changes in input data, thus exhibiting excellent robustness in the face of noise and interference.

[0096] 4. This invention can help the amphibious robot complete gait switching after receiving the decision scheme of the optimized Bayesian network solution, enabling the amphibious robot to complete tasks such as entering the water, exiting the water, and crawling on land.

[0097] 5. This invention enables a waterborne cross-domain robot to control the rotation of its leg motors according to a decision-making scheme during the transition between land and water, forming triangular gait, quadrupedal gait, and undulating gait to traverse terrain, helping the robot to enter and exit the water. This method allows the robot's legs to switch to the corresponding gait based on different terrains with high switching efficiency. Attached Figure Description

[0098] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0099] Figure 1 This is a block diagram illustrating the principle of motion control for a cross-domain robot based on an optimized Bayesian network in this invention.

[0100] Figure 2 This is a block diagram illustrating the principle of optimizing a three-layer Bayesian network structure using the MMPC-K2 algorithm in this invention.

[0101] Figure 3 This is a schematic diagram illustrating the principle of the IF-THEN rule with improved confidence introduced in this invention.

[0102] Figure 4 This is a block diagram illustrating the principle of single-leg control for the amphibious robot in this invention.

[0103] Figure 5 This is a block diagram illustrating the gait switching principle of the water-land cross-domain robot in this invention. Detailed Implementation

[0104] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0105] To overcome the aforementioned challenges in motion control of the amphibious robot, this embodiment first equips the robot with various sensors, including a vision module, IMU, and rain sensors, enabling it to collect more environmental information in complex water-land transition environments. Secondly, this embodiment abandons the reinforcement learning-based autonomous decision-making scheme. For decision-making problems lacking sufficient sample data, the optimal approach is to build a Bayesian network model. A Bayesian network is a graphical model used to represent conditional dependencies and joint probability distributions. This method reflects the probabilistic relationships between data in the entire database, allowing for the construction of an accurate model even without a specific data variable.

[0106] Please refer to Figures 1-5This embodiment proposes a motion control method for a cross-domain robot based on an optimized Bayesian network. By constructing a Bayesian network model suitable for the motion control of the robot, and using this model to output motion control schemes for the robot in underwater, land, and water-land transition zones, the method comprehensively considers all sensor information. It utilizes the highest-scoring network structure, prior probabilities of input nodes, and an improved IF-THEN rule to output the optimal solution, enabling autonomous decision-making for the cross-domain robot. The method includes the following steps:

[0107] S1. Analyze the decision-making state, correlation state, and autonomous decision-making scheme of the amphibious robot under different environmental working modes to determine the input nodes, intermediate nodes, and decision nodes used to construct the three-layer Bayesian network structure. Specifically, the decision-making state (i.e., the input nodes of the three-layer Bayesian network structure) is determined by analyzing the robot's working process. The input data for these nodes includes battery voltage, GPS signal, depth gauge, altimeter, terrain, obstacle distance, and rain sensor information during the robot's operation. The correlation state (i.e., the intermediate nodes) is determined by analyzing the correlation between node variables, including environmental perception and task detection. The corresponding autonomous decision-making scheme (i.e., the decision nodes) is formulated, including thruster start / stop and gait switching.

[0108] In this embodiment, a three-layer Bayesian network structure is initially constructed based on the dependencies between input nodes, intermediate nodes, and decision nodes. Specifically, when studying how a cross-domain robot works in different environments, its working mode is analyzed, and three key stages are identified: the decision state, the design-related state, and the decision-making process. The decision state is the starting point for the robot to receive input information, the design-related state is the process of processing information internally, and the decision-making process is the endpoint where the robot outputs action instructions based on the processing results. To better understand and simulate this process, this embodiment uses a Bayesian network to construct a three-layer network structure. This network structure can reflect the dependencies between different nodes, namely the interaction between input nodes, intermediate nodes, and decision nodes.

[0109] S2. The structure of the three-layer Bayesian network is learned using the MMPC-K2 algorithm, and the network structure with the highest score is selected as the final Bayesian network model. Since the water-land transition zone involves multiple media and a complex environment, direct input of data from multiple sensors can adversely affect environmental perception, making it difficult to make decisions about potential situations. Therefore, this embodiment uses the MMPC-K2 algorithm to learn the structure of the three-layer Bayesian network. The specific process is as follows:

[0110] S21. Use the MMPC (Max-Min Parents and Children) algorithm to learn each node and the dataset, and select the node with respect to any variable X using a max-min heuristic strategy. i When the association rule with the lowest correlation is found, the association rule with the highest correlation is denoted as assocF, and the corresponding variable is F. If the association rule assocF ≠ 0, then the variable F is added to the candidate parent-child node set CPC. i In Chinese, it is denoted as CPC. i =CPC i ∪F, otherwise the candidate parent-child node set CPC i constant.

[0111] The max-min heuristic strategy mentioned here is a method for selecting association rules. Specifically, this strategy involves selecting association rules with a given variable X. i When choosing an association rule with the lowest correlation, find the one with the highest correlation, denoted as assocF. Then, select a variable, denoted as F, based on association rule assocF. If the correlation of this association rule is not equal to 0, add variable F to the candidate parent-child node set CPC. i If the value is 0, then the candidate parent-child node set CPC remains unchanged. i .

[0112] S22, when the candidate parent-child node set CPC is excluded i The variables in the variable X, and all other variables related to variable X. i Given a candidate set of parent and child nodes (CPC) i When all conditions are independent, test the candidate parent-child node set CPC. i Remove unnecessary variables from the set; that is, assume no loss to freedom. Where (i1,i2,…,i) m ) is any subset of (1,2,…,n), for any variable If a subset S exists i and So that in subset S i Under the conditions, With X i If the correlation function value is 0, then the candidate parent-child node set

[0113] S23. Based on the candidate parent-child node set of the decision node variables from step S22, i.e.

[0114] S24. Input variable set V = {x1, x2, x3, ..., x n} and its observation dataset D, determine variable X iThe family K2 scoring function g(i,pa(i)) is expressed as:

[0115]

[0116] Where i represents each node variable; pa(i) represents the set of parent nodes for that node variable; q i Represents variable X i The total number of state combinations that can be obtained from the parent node variable; r i The total number of states obtained; m ijk X represents a variable X in the observation dataset D. i When the state is k, the total number of samples whose parent node set has state combination j.

[0117] S25. Initialize the network structure, let the network structure dag = zeros(n,n), and calculate each variable X. i Let the family K2 score function value be g(i,pa(i)), i=1,2,…,n, and let bestg(i,pa(i))=g(i,pa(i)), i=1,2,…,n, and let i=1, where bestg(i,pa(i)) is the largest family K2 score function value.

[0118] S26. Call the MMPC algorithm to return variable X. i CPC (Choice of Parent-Child Nodes) i .

[0119] S27, Regarding variable X i and its candidate parent-child node set CPC i For each Add directed edges respectively or We obtain a series of information about variable X i For each candidate local structure, calculate the family K2 score function value of each candidate local structure, and retain the maximum function value g(i,pa(i))=max g(i,pa(i));

[0120] If g(i,pa(i))>bestg(i,pa(i)), then bestg(i,pa(i))=g(i,pa(i)), and the corresponding network structure is the optimal structure;

[0121] Otherwise, output bestg(i,pa(i)) and its corresponding optimal structure remain unchanged, and i = i + 1, then execute step S26.

[0122] S28. Regarding variable X i The optimal local structure for each Add directed edges respectively or A series of candidate structures were obtained;

[0123] For any Reverse directed edges A series of candidate structures were obtained;

[0124] For any Reverse directed edges A series of candidate structures were obtained;

[0125] For each Delete directed edges or A series of candidate structures were obtained.

[0126] S29. Calculate the structure of all candidate structures with respect to variable X. i The K2 scoring function value, and g(i,pa(i))=maxg(i,pa(i));

[0127] If g(i,pa(i))>bestg(i,pa(i)), then bestg(i,pa(i))=g(i,pa(i)), and the corresponding structure is the optimal structure;

[0128] Otherwise, return bestg(i,pa(i)) and its corresponding optimal structure unchanged, and let i = i + 1.

[0129] S210. If i ≤ n, return to step S27; if i > n, the algorithm stops and returns the optimal network structure dag.

[0130] Ordinary Bayesian networks require finding input nodes and dependencies to build the network structure. However, networks without structure learning and parameter learning are easily influenced by a single node, leading to incorrect inferences. The Bayesian network of this invention first uses the Max-Min Parents and Children-K2 (MMPC-K2) algorithm to learn the Bayesian network structure, obtaining the network structure with the highest score. This avoids missing relevant dependencies and simplifies the calculation of conditional probabilities. Compared to the BIC scoring function used in the ordinary MMPC algorithm, the K2 function can select structures with higher posterior probabilities.

[0131] In this embodiment, the method utilizes the MMPC-K2 algorithm to solve for the parent-child node set, and then finds the network skeleton through a scoring function, thus completing the Bayesian network structure learning for the motion control method of the water-land cross-domain robot. Figure 1As shown, the robot acquires information about different environments through various sensors carried by the amphibious robot, uses a structure-optimized Bayesian network to make inference decisions, obtains the decision scheme with the highest probability, and finally controls the robot's movement.

[0132] like Figure 2 As shown, a preliminary Bayesian network is established for the given network nodes using expert experience and node dependencies. The initial skeleton of the network is determined using the Max-Min Parents and Children (MMPC) algorithm. Starting from this skeleton, the algorithm performs a greedy hill-climbing search to refine the local structure and generate candidate structures. This step uses the K2 scoring function to select the addition, deletion, or directional adjustment of edges that maximize the score. During the search process, the algorithm continuously tries new network structure changes and selects those changes that can improve the score, gradually approaching the optimal network structure. Finally, when the score cannot be further improved through any single-step changes, the algorithm stops searching and outputs the network structure with the highest current score as the final Bayesian network model. This method combines the ideas of local learning, constraint-based learning, and search scoring techniques, which can greatly reduce the computational cost of the parent-child node set and hill-climbing search algorithm, and calculate the most suitable network structure through K2 scoring.

[0133] S3. Analyze the expert evaluations given by multiple experts for each node, and fuse these evaluations to determine the prior probability table, i.e., the prior probability distribution, for each node in the Bayesian network model. Each node includes input nodes, intermediate nodes, and decision nodes. It needs further explanation that this example fuses expert evaluations and sample data. Four experts are invited to evaluate each node, and evaluation distortion error analysis, evaluation experience error analysis, and expert evaluation fusion are performed to determine the prior probability table for the Bayesian network nodes. Therefore, after fusion, each node corresponds to a prior probability, and the prior probabilities corresponding to all nodes, after integration, constitute a prior probability table. Specifically, in step S3, the process includes the following steps:

[0134] S31. Analyze the distortion error of each node.

[0135] To determine the error of random errors, the sample standard deviation is first calculated using Bessel's formula, i.e.:

[0136]

[0137] In the formula, w i The values ​​were assigned by experts; is the sample mean; n is the number of evaluations.

[0138]

[0139] In the formula, ν iRepresenting the residuals, the residuals ν are expressed using the Abbe-Hermet criterion. i Perform statistical analysis, that is:

[0140] u=∣v1v2+v2v3+…+v n-1 v n |

[0141] like This raises suspicion of evaluation distortion or error.

[0142] S32. Conduct an empirical error analysis for each node;

[0143] Because the evaluation data sample is small and expert opinions carry high weight, analyzing evaluation experience errors can further improve the accuracy of probabilities. This embodiment employs mathematical statistics principles to perform joint analysis of expert experience errors using the Gershovelli criterion, thereby improving the reliability of the judgment. According to the Gershovelli criterion, multiple experts score the probability of each evidence point, and the residuals are calculated. And the population standard deviation σ, if |ν i |>Z c σ indicates that this data is abnormal, where Z c These are the Schauville criterion coefficients.

[0144] S33. Conduct expert evaluation and integration;

[0145] Based on the theories of arithmetic mean and batch estimation, the expert node scoring data is divided into two batches: experts 1 and 2, and experts 3 and 4 form one group, and the rest form the other. The arithmetic means X1 and X2, and the standard deviations σ1 and σ2 are calculated for the batched data. Finally, the fusion value M is calculated, and the fusion value function is expressed as:

[0146]

[0147] S34. Calculation of uncertainty in expert evaluation;

[0148] The evaluation results from experts contain a certain degree of error. Uncertainty can be used to indicate the reliability of these results. Uncertainty can be expressed as:

[0149]

[0150] In the formula, U represents the total uncertainty; U a Type A uncertainty; U b Let the uncertainty be Type B, where:

[0151] The formula for calculating Type A uncertainty is:

[0152] U a =k p b

[0153] In the formula, k p is the coverage factor; b is the standard deviation of the arithmetic mean, calculated using the following formula:

[0154]

[0155] The formula for calculating Type B uncertainty is:

[0156]

[0157] In the formula, a is the confidence interval; k is the corresponding coverage factor.

[0158] S35. Finally, based on the formula and the fusion value of expert evaluation, the final qualitative evaluation with uncertainty can be obtained. The initial prior probability distribution is obtained by statistical analysis of the sample data of each node.

[0159] S4. The parameters of the Bayesian network model are learned using the IF-THEN inference rule with improved confidence, and the qualitative evaluation is transformed into quantitative probability to determine the posterior probability of the decision node. In step S4, the specific process includes the following steps:

[0160] S41. Transform all input information from the input nodes into a unified confidence framework to obtain the matching degree corresponding to the confidence distribution. Input transformation unifies various forms of input information into a belief framework. In existing research, the quantitative input of a traditional Belief Rule Base (BRB) model can be represented as:

[0161]

[0162] Where, x i It is the input value of the i-th index; A i,j This represents the attribute reference value; j represents the number of reference levels. f(·) represents the matching degree of the i-th input index relative to the j-th reference level; f(·) represents the transformation function;

[0163] S42. Based on matching degree Calculate the activation weight w for the corresponding rule k Activation weights represent the degree to which input information activates a rule. After obtaining the matching degree, the activation weights of the corresponding rules need to be calculated by combining attribute weights and rule weights. The calculation formula is as follows:

[0164]

[0165] Among them, w k This represents the activation weight of the k-th rule, when 0 <w k If θ ≤ 1, the corresponding rule is considered to have been activated;k θ l represents the rule weights of the k-th and l-th rules, respectively; L represents the total number of rules; M represents the number of input metrics; This indicates the degree of matching between the i-th input and its reference value in the rule; δ represents the degree of matching between the i-th input and its reference value in rule l; i Indicates attribute weight; This represents the normalized relative attribute weights;

[0166] S43. Use the Evidential Reasoning (ER) algorithm to determine the conditions that meet the criteria. <w k Rules with a value ≤1 are fused to obtain the confidence score. The expression is:

[0167]

[0168] Where, β n,k This indicates that the k-th rule applies to the n-th reference level D. n Confidence level; β i,k This indicates that the k-th rule applies to the i-th reference level D. n The confidence level; N represents the number of reference levels; This represents the nth reference level D in the output. n The confidence level, and satisfying μ is the utility value.

[0169] S44. Using confidence levels The IF-THEN rule is improved by establishing inference rules between input nodes, intermediate nodes, and decision nodes, transforming qualitative evaluation into quantitative probability to determine the posterior probability S(x) of the decision node. i The evaluation result obtained after reasoning can be represented by the confidence distribution shown below:

[0170]

[0171] Where S(·) represents the output function.

[0172] S45. Based on several posterior probabilities S(x) i Establish a conditional probability table for input nodes, intermediate nodes, and decision nodes, and select the decision scheme with the highest posterior probability.

[0173] In this embodiment, after the input information is converted into a confidence distribution, it needs to undergo rule activation and fusion. The output result serves as the confidence distribution of intermediate nodes and as the input information for decision nodes, until the posterior probability of the final decision scheme is generated. This method utilizes an improved IF-THEN rule to calculate the posterior probability of the control scheme, completing the Bayesian network parameter learning for the cross-domain robot motion control method.

[0174] like Figure 3 As shown, the method first transforms all information into a unified confidence framework. After the input information is converted into a confidence distribution, rule activation and fusion are performed. The evaluation results are used as the confidence distribution of intermediate nodes and as the input information for decision nodes. Rule activation and fusion are repeated until the confidence score of the final decision node is generated. Secondly, the generated confidence scores are used to improve the IF-THEN rule, establishing inference rules between input nodes, intermediate nodes, and decision nodes, transforming qualitative evaluation into quantitative probability. This establishes a conditional probability table for input nodes, intermediate nodes, and decision nodes, ultimately obtaining the decision scheme with the highest probability at a given evidence node. This method can integrate expert knowledge and experience, transforming this difficult-to-quantify information into actionable rules, and is insensitive to small changes in input data, making it robust to noise and interference.

[0175] This embodiment introduces the IF-THEN inference rule with improved confidence to learn Bayesian network parameters, improves the fuzzy rule base, transforms qualitative evaluation into quantitative probability, and obtains the posterior probability of a relatively subjective decision scheme. After optimization through parameter learning and structure learning, a complete Bayesian network model is obtained, which greatly improves the stability and accuracy of decision reasoning.

[0176] S5. Using real-time environmental information acquired by multiple sensors as input to a Bayesian network model after structure learning and parameter learning, a decision-making scheme for controlling the amphibious robot in an uncertain environment is generated. The amphibious robot acquires real-time environmental information on land and underwater using its onboard visual sensors, GPS, rain sensors, depth gauge, and IMU.

[0177] In this embodiment, a fuzzy-to-define approach is used to process the sensor data corresponding to the environmental information, and membership functions for the input layer variables are established. Battery voltage and GPS signals use S-shaped membership functions; depth gauge, altimeter, terrain, obstacle distance, and rain sensor information use triangular membership functions. The shape of the triangular membership function curve is determined by three parameters a, b, and c, and is expressed as:

[0178]

[0179] The sigmoid membership function is determined by parameters a and c, and is expressed as:

[0180]

[0181] Where x represents the input variable of the input node, i.e., the input data in S1; f(·) represents the membership function.

[0182] When the robot operates across land and water, the state variables of each sensor are input into an optimized Bayesian network model for autonomous decision-making and reasoning. The probability of the preset decision scheme is calculated, and the decision scheme with the highest probability is fed back to the controller for execution. This includes land leg motion control, switching between legs and propellers in the land-water transition area, and underwater navigation motion control.

[0183] In this embodiment, the working modes of the cross-domain robot in different environments are first analyzed to determine the decision state (input node), design associated states (intermediate nodes), and formulate decision schemes (decision nodes). A three-layer Bayesian network structure is initially constructed based on node dependencies, and sensor data is preprocessed. The Bayesian network structure is learned using the MMPC-K2 algorithm. Expert evaluation and sample data fusion are performed to analyze expert evaluation errors and determine the prior probability distribution of network nodes. Network parameters are learned by incorporating the improved IF-THEN rule based on confidence, obtaining the posterior probability of output nodes that are more susceptible to subjective influence. Finally, by inputting sensor data from the perceived environment, the constructed Bayesian network model is used to make autonomous decisions, outputting the scheme with the highest probability. This method can comprehensively consider all sensor information, utilize the highest-scoring network structure, the prior probabilities of input nodes, and the improved IF-THEN rule to output the optimal scheme, achieving autonomous decision-making for the robot.

[0184] S6. The decision-making scheme is fed back to the CPG output network used to control the gait switching of the amphibious robot, enabling the robot's legs to switch to corresponding gaits according to different terrains. By feeding back the decision scheme with the highest probability value to the controller, the robot executes the corresponding decision scheme, achieving autonomous decision-making capability for the amphibious robot in uncertain environments. The robot's leg control is mainly based on an amphibious robot gait planning algorithm that optimizes the CPG output network, selecting appropriate gait movements according to different terrains. For water-land transition areas, an optimized Bayesian network model autonomously determines the control scheme for the robot's leg and propeller start / stop.

[0185] When a terrestrial robot traverses land, it needs to make autonomous decisions based on complex information such as its own posture, terrain, and distance to obstacles. With the construction of a Bayesian network model and the determination of the posterior probability of the decision nodes, the terrestrial robot can make autonomous decisions based on real-time sensor data and the Bayesian network model, choosing an appropriate gait to traverse land terrain, including entering shallow water areas, exiting shallow water areas, moving on flat ground, traversing rugged roads, and climbing slopes.

[0186] Traditional legged amphibious robots often lack precise control over leg joint rotation during gait transitions. Discrete signals are prone to abrupt changes, leading to reciprocating or rapid rotation of the leg joints, which negatively impacts robot stability. Directly inputting control parameters for each gait can distort the output signal of the oscillator network, potentially causing severe impacts on the joint drive motors and resulting in unstable support during gait transitions.

[0187] This invention designs a gait planning algorithm for a cross-domain robot based on an optimized Hopf oscillator, optimizing the spatial mapping relationship of leg joints and the relationship of oscillator parameter changes. The specific steps are as follows:

[0188] S61. To enable the six legs of the cross-domain robot to coordinate their movements according to specific phase relationships of triangular gait, quadrupedal gait, and wavering gait, it is necessary to couple six Hopf oscillator models to form a central pattern generator (CPG) network, such as... Figure 5 The CPG output network shown employs a bidirectional coupling mechanism between the Hopf oscillators of each neuron. The mathematical model of the Hopf oscillator of the i-th neuron can be expressed as:

[0189]

[0190] Where, U = [xy] T Let be the state variables of the neuron oscillator; a stable limit cycle exists within the xy plane, where x and y can be used as the outputs of the neuron oscillator; σ is the intensity factor, determining the convergence speed; R is the radius of the limit cycle, determining the amplitude of the oscillator output; ω is the oscillation frequency, determining the robot's speed; λ is the coupling coefficient, which adjusts the coupling strength between neuron oscillators; where Δ is the coupling term, representing the effect of other neurons in the CPG output network on the i-th neuron, which can be expressed as:

[0191]

[0192] in, Let be the phase difference between the j-th neuron oscillator and the i-th neuron oscillator.

[0193] S62. In the Hopf oscillator model, the rising and falling phases of the output waveform have equal durations. This characteristic makes it suitable for triangular gait because the support and oscillation phases within a single cycle are of equal duration, resulting in a footprint factor of 1 / 2. However, for quadrupedal and undulating gait, the asymmetry in the durations of the support and oscillation phases within a single cycle leads to footprint factors of 2 / 3 and 5 / 6, respectively, causing distortion in the Hopf oscillator's output waveform.

[0194] Therefore, this embodiment improves upon the Hopf oscillator model by introducing a footprint factor and joint rotation speed, enabling it to generate corresponding asymmetric waveforms based on the footprint factors of different time states. The improved Hopf oscillator model can be expressed as:

[0195]

[0196] Where H is the joint rotation speed of the amphibious robot; ε is the footprint coefficient; y ik Let y be the value of the state variable y of the i-th oscillator at time k.

[0197] S63. The signal output by the CPG output network is transformed using trigonometric functions. In each control stage, the new mapping function can map the approximately sinusoidal output signal to the range of 0 to 360° of joint rotation, thereby achieving smooth joint control. The new mapping relationship can be expressed as:

[0198]

[0199] Where x and y are the outputs of the CPG oscillator; θ s It is the support angle, that is, the angle through which the joint rotates during the support phase; θ t It is the swing angle, that is, the angle through which the joint rotates during the swing phase. After modifying the oscillation frequency of any leg of the robot, it can output the corresponding gait waveform, which is converted into the joint space through the new mapping relationship to complete the control of the robot's leg.

[0200] S64. After optimizing the mapping relationship and oscillation frequency, the cross-domain robot can accurately switch to the target gait after a period of time. However, it is also very easy for the oscillator output waveform to have spikes and frequency fluctuations after changing the control parameters of the gait. This situation may cause a strong impact on the joint drive motor, resulting in unstable support during gait switching.

[0201] To ensure smooth robot movement and reliable drive system operation, a strategy of continuously varying parameters is adopted. This means that during gait transitions, the phase difference and footprint coefficient smoothly transition from the values ​​of the current gait to those of the target gait within a certain timeframe. This process can be represented as:

[0202]

[0203]

[0204] in, and ε + These are the phase difference and footprint coefficient of the target gait; and ε - t0 represents the phase difference and gait coefficient of the current gait; t0 represents the moment when the gait switching command is received; t represents the cumulative time since time t0.

[0205] S65 and w are convergence factors used to adjust the rate of change of the phase difference and the footprint coefficient parameters of the target gait. Their change process can be expressed as follows:

[0206]

[0207] Where t1 is the predetermined time to achieve the target gait.

[0208] In this embodiment, the method proposed in step S6 is mainly used for leg movement control of the amphibious robot in the transition area between land and water. After receiving the decision scheme calculated by the optimized Bayesian network, it helps the amphibious robot to complete gait switching, enabling the amphibious robot to complete tasks such as entering the water, exiting the water, and crawling on land.

[0209] The gait planning algorithm of this invention is applied to the single leg control of a robot in transitional areas between land and water, such as... Figure 4 As shown, by introducing a footprint coefficient to improve the oscillation frequency of the oscillators, and combining the initial state variables and phase differences of each leg oscillator, the Runge-Kutta function is used to calculate the new state variables of each leg at each time step, forming the output waveform of the Hopf network. A new mapping function maps the output waveform of the Hopf network to the joint space to control the motor rotation. Six Hopf oscillators form the CPG output network, and the six legs work together to form the corresponding gait.

[0210] like Figure 5 As shown, to avoid spikes and frequency fluctuations in the oscillator output waveform during various gait switching processes, a strategy of continuously varying parameters is adopted. This allows the phase difference and footprint coefficient to smoothly transition from the current gait value to the target gait value within a certain time. To optimize switching efficiency, a convergence factor function is designed to adjust the rate of change of the phase difference and footprint coefficient parameters of the target gait. During the transition between land and water, the legs of the aquatic cross-domain robot can control the rotation of the leg motors according to the optimal solution calculated by the optimized Bayesian network, forming triangular gait, quadrupedal gait, and undulating gait to traverse the terrain, helping the robot to enter and exit the water. This method enables the robot's legs to switch to the corresponding gait according to different terrains with high switching efficiency.

[0211] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0212] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Since the above embodiments are substantially similar to the method embodiments, their descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0213] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A motion control method for a cross-domain robot between land and water based on an optimized Bayesian network, characterized in that, The method includes the following steps: S1. Analyze the decision-making state, associated state, and autonomous decision-making scheme of the amphibious robot under different environmental working modes, and determine the input nodes, intermediate nodes, and decision nodes used to initially construct a three-layer Bayesian network structure. Based on the dependencies between input nodes, intermediate nodes, and decision nodes, a preliminary three-layer Bayesian network structure is constructed; among them... The decision-making state is determined by analyzing the working process of the amphibious robot, which is the input node of the three-layer Bayesian network structure. The input data of the input node includes the battery voltage, GPS signal, depth gauge, altimeter, terrain, obstacle distance, and rain sensor information during the working process of the amphibious robot. The correlation status, i.e., intermediate nodes, is determined by analyzing the correlation between node variables, including environmental perception and task detection. Formulate corresponding autonomous decision-making plans, i.e. decision-making nodes, including thruster start / stop and gait switching; S2. The structure of the three-layer Bayesian network is learned through the MMPC-K2 algorithm, and the network structure with the highest score is obtained as the final Bayesian network model. S3. Analyze the expert evaluations given by multiple experts for each node, and fuse the multiple expert evaluations to determine the prior probability distribution of each node in the Bayesian network model. S4. The parameters of the Bayesian network model are learned using the IF-THEN inference rule with improved confidence, and the qualitative evaluation is transformed into quantitative probability to determine the posterior probability of the decision node. The specific process includes the following steps: S41. Transform all input information from the input nodes into a unified confidence framework to obtain the matching degree corresponding to the confidence distribution. The conversion formula is: Where, x i It is the input value of the i-th index; A i,j This represents the attribute reference value; j represents the number of reference levels. f(·) represents the matching degree of the i-th input index relative to the j-th reference level; f(·) represents the transformation function; S42. Based on matching degree Calculate the activation weight w for the corresponding rule k Activation weights are used to represent the degree to which the input information activates the rule; S43. Use the Evidence-Based Reasoning (ER) algorithm to determine conditions 0. <w k Rules with a value ≤1 are fused to obtain the confidence score. The expression is: Where, β n,k This indicates that the k-th rule applies to the n-th reference level D. n Confidence level; β i,k This indicates that the k-th rule applies to the i-th reference level D. n The confidence level; N represents the number of reference levels; This represents the nth reference level D in the output. n The confidence level, and satisfying μ is the utility value; S44. Using confidence levels The IF-THEN rule is improved by establishing inference rules between input nodes, intermediate nodes, and decision nodes, transforming qualitative evaluation into quantitative probability to determine the posterior probability S(x) of the decision node. i ),Right now: Where S(·) represents the output function; S45. Based on several posterior probabilities S(x) i Establish a conditional probability table for input nodes, intermediate nodes, and decision nodes, and select the decision scheme with the highest posterior probability. S5. Using real-time environmental information acquired by multiple sensors as input to a Bayesian network model after structure learning and parameter learning, a decision-making scheme for controlling an amphibious robot in an uncertain environment is generated. S6. Feed back the decision scheme with the highest probability to the CPG output network used to control the gait switching of the amphibious robot, so as to enable the amphibious robot's legs to switch the corresponding gait according to different terrains.

2. The motion control method for a cross-domain robot according to claim 1, characterized in that, In step S2, the specific process includes the following steps: S21. Use the MMPC algorithm to learn each node and the dataset, and select the node with any variable X using the max-min heuristic strategy. i When the association rule with the lowest correlation is found, the association rule with the highest correlation is denoted as assocF, and the corresponding variable is F. If the association rule assocF ≠ 0, then the variable F is added to the candidate parent-child node set CPC. i In Chinese, it is denoted as CPC. i =CPC i ∪F, otherwise the candidate parent-child node set CPC i constant; S22, Let Where (i1,i2,…,i) m ) is any subset of (1,2,…,n), for any variable If a subset S exists i and So that in subset S i Under the conditions, With X i The correlation function value is 0; S23, the candidate parent-child node set of the root decision node variable, i.e. S24. Input variable set V = {x1, x2, x3, ..., x n } and its observation dataset D, determine variable X i The family K2 scoring function g(i,pa(i)) is expressed as: Where i represents each node variable; pa(i) represents the set of parent nodes for that node variable; q i Represents variable X i The total number of state combinations that can be obtained from the parent node variable; r i The total number of states obtained; m ijk X represents a variable X in the observation dataset D. i When the state is k, the total number of samples whose parent node set has state combination j. S25. Initialize the network structure, let the network structure dag = zeros(n,n), and calculate each variable X. i Let the family K2 scoring function value be g(i,pa(i)), i = 1, 2, ..., n, and let bestg(i,pa(i)) = g(i,pa(i)), i = 1, 2, ..., n, and let i = 1; S26. Call the MMPC algorithm to return variable X. i CPC (Choice of Parent-Child Nodes) i ; S27, Regarding variable X i and its candidate parent-child node set CPC i For each Add directed edges respectively or We obtain a series of information about variable X i For each candidate local structure, calculate the family K2 score function value of each candidate local structure, and retain the maximum function value g(i,pa(i))=max g(i,pa(i)); If g(i,pa(i))>bestg(i,pa(i)), then bestg(i,pa(i))=g(i,pa(i)), and the corresponding network structure is the optimal structure; Otherwise, output bestg(i,pa(i)) and its corresponding optimal structure remain unchanged, and i = i + 1, then execute step S26; S28. Regarding variable X i The optimal local structure for each Add directed edges respectively or A series of candidate structures were obtained; For any Reverse directed edges A series of candidate structures were obtained; For any Reverse directed edges A series of candidate structures were obtained; For each Delete directed edges or A series of candidate structures were obtained; S29. Calculate the structure of all candidate structures with respect to variable X. i The K2 scoring function value, and g(i,pa(i))=max g(i,pa(i)); If g(i,pa(i))>bestg(i,pa(i)), then bestg(i,pa(i))=g(i,pa(i)), and the corresponding structure is the optimal structure; Otherwise, return bestg(i,pa(i)) and its corresponding optimal structure unchanged, and let i = i + 1; S210. If i ≤ n, return to step S27; if i > n, the algorithm stops and returns the optimal network structure dag.

3. The motion control method for a cross-domain robot according to claim 1, characterized in that, In step S3, the specific process includes the following steps: S31. Perform distortion error analysis on each node. This raises suspicion of evaluation distortion error, where: u=∣v1v2+v2v3+…+v n-1 v n ∣ In the formula, w i The values ​​were assigned by experts; ν is the sample mean; n is the number of evaluations; i Represents the residual; S32. Perform an empirical error analysis on each node. If |ν i |>Z c If σ is the population standard deviation, then this data is outlier; Z is the population standard deviation. c These are the Schauville criterion coefficients; S33. Conduct expert evaluation and integration; The expert node scoring data is divided into two batches for processing. Experts 1 and 2, and experts 3 and 4 are in one group, and the rest are in the other group. The arithmetic mean X1 and X2, and the standard deviation σ1 and σ2 are calculated for the data after batch processing. Finally, the fusion value M is calculated, and the evaluation fusion value function is expressed as follows: S34. Calculate the expert evaluation uncertainty used to indicate the reliability of the rating results. The expert evaluation uncertainty x can be expressed as: In the formula, U is the mean of the uncertainty; U is the total uncertainty; U a Type A uncertainty; U b Type B uncertainty; S35. Based on the above formula and the expert evaluation fusion value, the final qualitative evaluation with uncertainty can be obtained. The initial prior probability distribution is obtained by statistically analyzing the sample data of each node.

4. The motion control method for a cross-domain robot according to claim 3, characterized in that, In step S34, the formula for calculating Type A uncertainty is: U a =k p b In the formula, k p is the coverage factor; b is the standard deviation of the arithmetic mean, calculated using the following formula: In the formula, The average value assigned to the experts; The formula for calculating Type B uncertainty is: In the formula, a is the confidence interval; k is the corresponding coverage factor.

5. The motion control method for a cross-domain robot according to claim 1, characterized in that, In step S42, the activation weight w k The calculation formula is: Among them, w k This represents the activation weight of the k-th rule, when 0 <w k If θ ≤ 1, the corresponding rule is considered to have been activated; k θ l represents the rule weights of the k-th and l-th rules, respectively; L represents the total number of rules; M represents the number of input metrics; This indicates the degree of matching between the i-th input and its reference value in the rule; δ represents the degree of matching between the i-th input and its reference value in rule l; i Indicates attribute weight; This represents the normalized relative attribute weights.

6. The motion control method for a cross-domain robot according to claim 1, characterized in that, In step S6, the specific process includes the following steps: S61. Couple several Hopf oscillator models to form a CPG output network, wherein the Hopf oscillators of each neuron adopt a bidirectional coupling mechanism, then the mathematical model of the Hopf oscillator of the i-th neuron is expressed as: in, σ is the state variable of the neuron oscillator; x and y are the outputs of the neuron oscillator; σ is the intensity factor; R is the radius of the limit cycle; ω is the oscillation frequency; λ is the coupling coefficient. For coupling terms; Let be the phase difference between the j-th neuron oscillator and the i-th neuron oscillator; S62. Mathematical Model Construction Based on Hopf Oscillator: A Hopf oscillator model that generates corresponding asymmetric waveforms based on the occupancy coefficients of different time states is represented as follows: Where H is the joint rotation speed of the amphibious robot, and ε is the footprint coefficient; y ik Let y be the value of the state variable y of the i-th oscillator at time k; S63. Establish a mapping function D(x) that maps the approximate sinusoidal signal output by the CPG output network to the range of joint rotation from 0 to 360°, i.e.: Where x and y are the outputs of the CPG output network; θ s It is the support angle, that is, the angle through which the joint rotates during the support phase; θ t It is the swing angle, that is, the angle through which the joint rotates during the swing phase. S64. During the transition between multiple gait states, a strategy of continuously varying parameters is adopted to smoothly transition the phase difference and gait coefficient from the values ​​of the current gait state to the values ​​of the target gait state within a certain time period. The change process is represented as follows: in, and ε + These are the phase difference and footprint coefficient of the target gait; and ε - t0 represents the phase difference and gait coefficient of the current gait; t0 represents the moment when the gait switching command is received; t is the cumulative time since t0; w is the convergence factor, used to adjust the rate of change of the phase difference and gait coefficient parameters of the target gait. S65. Establish a convergence factor function to adjust the rate of change of the phase difference and footprint coefficient parameters of the target gait, namely: Where t1 is the predetermined time to achieve the target gait.

Images