CN117331317A - Under-actuated underwater helicopter surrounding control method based on width learning - Google Patents
Under-actuated underwater helicopter surrounding control method based on width learning Download PDFInfo
- Publication number
- CN117331317A CN117331317A CN202311631122.6A CN202311631122A CN117331317A CN 117331317 A CN117331317 A CN 117331317A CN 202311631122 A CN202311631122 A CN 202311631122A CN 117331317 A CN117331317 A CN 117331317A
- Authority
- CN
- China
- Prior art keywords
- representing
- control
- surrounding
- basis function
- underwater
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 28
- 230000006870 function Effects 0.000 claims abstract description 81
- 238000013528 artificial neural network Methods 0.000 claims abstract description 51
- 230000015572 biosynthetic process Effects 0.000 claims abstract description 33
- 230000003044 adaptive effect Effects 0.000 claims abstract description 16
- 239000013598 vector Substances 0.000 claims description 26
- 238000004422 calculation algorithm Methods 0.000 claims description 21
- 239000011159 matrix material Substances 0.000 claims description 15
- 238000005070 sampling Methods 0.000 claims description 3
- 238000013016 damping Methods 0.000 claims description 2
- 238000013461 design Methods 0.000 claims description 2
- 238000006073 displacement reaction Methods 0.000 claims description 2
- 230000009466 transformation Effects 0.000 claims description 2
- 238000004519 manufacturing process Methods 0.000 claims 1
- 238000004364 calculation method Methods 0.000 abstract description 9
- 238000005755 formation reaction Methods 0.000 description 28
- 238000004891 communication Methods 0.000 description 7
- 230000001537 neural effect Effects 0.000 description 6
- 238000011217 control strategy Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 230000001133 acceleration Effects 0.000 description 3
- 230000009471 action Effects 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 3
- 230000007613 environmental effect Effects 0.000 description 3
- 238000005259 measurement Methods 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 230000006399 behavior Effects 0.000 description 2
- 230000008859 change Effects 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000003993 interaction Effects 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 230000004044 response Effects 0.000 description 2
- 238000012549 training Methods 0.000 description 2
- 230000006978 adaptation Effects 0.000 description 1
- 239000003795 chemical substances by application Substances 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 239000012530 fluid Substances 0.000 description 1
- 238000010801 machine learning Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 230000010355 oscillation Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 208000011580 syndromic disease Diseases 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
- Feedback Control In General (AREA)
Abstract
The invention discloses an underactuated underwater helicopter surrounding control method based on width learning, which belongs to the technical field of mechanical control and comprises the following steps: establishing a dynamics model; determining constraint conditions of the dynamic model; the method comprises the steps of introducing auxiliary variables to redefine surrounding control errors of an underwater helicopter in a dynamics model, selecting virtual control variables, and determining virtual control rate under the surrounding control errors; determining a lumped uncertainty of the surrounding formation based on the dynamics model; designing an improved radial basis function neural network based on width learning; defining error variables with respect to the virtual control variables and the virtual control rate, and determining a control rate with respect to the error variables; determining an adaptive update rate of the improved radial basis function neural network; the lumped uncertainty is approximated at a control rate by modifying the radial basis function neural network such that the follower is located in a geometric convexity composed of pilots. And the calculation consumption and the hardware requirement are reduced, and the control precision and the cruising ability of the formation are improved.
Description
Technical Field
The invention belongs to the technical field of mechanical control, and particularly relates to an underactuated underwater helicopter surrounding control method based on width learning.
Background
The submarine mobile observation, submarine resource exploration, sensitive submarine area cruising and detecting, submarine pipeline monitoring and maintaining, submarine rescue and salvaging, submarine archaeology and other works have high requirements on the maneuvering performance and working mode of the submersible, and the submersible similar to the characteristics of a land helicopter is often needed. The underwater helicopter (Autonomous underwater helicopter, AUH) is beneficial to improving the maneuvering performance of the submersible, increasing the working mode from the seabed to the seabed, developing the seabed operation application more efficiently and with higher quality, and in addition, carrying out cooperative control on a plurality of AUH to form a system based on network space organic connection, so that more complex operation tasks can be completed. In some cases, the follower-AUH is required to enter a geometric area composed of a plurality of pilot-AUHs, and this control mode is called surrounding control, and becomes a research hotspot in the current underwater robot control field.
Due to the limitations of the number of propellers and the propeller layout of the underwater helicopter, the degree of freedom of the control input in the underwater helicopter control system is smaller than the degree of freedom of the motion thereof, which is defined as the problem of underactuated control of the underwater helicopter, in addition, the underwater helicopter has complex fluid dynamics characteristics, and is difficult to accurately establish a dynamics model, so that the uncertainty of the model is necessary to be considered in underactuated surrounding control, the uncertainty of the dynamics is approximated by using a radial basis function neural network (Radial Basis Function Neural Network, RBFNN) in the prior art, however, the neural nodes in the radial basis function neural network are preset, a certain priori knowledge is needed, and at the same time, a large number of nodes are needed to be arranged to improve the approximation precision, which increases the calculation burden of the controller and improves the requirement on hardware.
In summary, the degree of freedom of control input in the current underwater helicopter control system is smaller than the degree of freedom of motion, the underactuated control problem exists, the neural nodes in the radial basis function neural network for approximating the dynamics uncertainty are preset, a certain priori knowledge is needed, a large number of nodes are needed to be arranged to improve the approximation accuracy, the calculation burden is increased, and the hardware requirement is high.
Disclosure of Invention
In order to solve the technical problems that the degree of freedom of control input in an underwater helicopter control system is smaller than the degree of freedom of motion, the underactuated control problem exists, the neural nodes in a radial basis function neural network for approximating dynamic uncertainty are preset, a certain priori knowledge is needed, a large number of nodes are needed to be arranged to improve approximation accuracy, calculation load is increased, and hardware requirements are high in the prior art, the invention provides an underactuated underwater helicopter surrounding control method based on width learning.
The invention provides an underactuated underwater helicopter surrounding control method based on width learning, which comprises the following steps:
s101: establishing a dynamics model of an encircling formation consisting of a plurality of followers and a plurality of pilots;
s102: determining constraint conditions of the dynamic model;
s103: the method comprises the steps of introducing auxiliary variables to redefine surrounding control errors of an underwater helicopter in a dynamics model, selecting virtual control variables, and determining virtual control rate under the surrounding control errors;
s104: determining a lumped uncertainty of the surrounding formation based on the dynamics model;
s105: designing an improved radial basis function neural network based on width learning by combining a width learning algorithm;
s106: defining error variables with respect to the virtual control variables and the virtual control rate, and determining a control rate with respect to the error variables;
s107: determining an adaptive update rate of the improved radial basis function neural network;
s108: the lumped uncertainty is approximated at a control rate by modifying the radial basis function neural network in conjunction with an adaptive update rate such that the follower is located in a geometric convexity comprised of a pilot.
Compared with the prior art, the invention has at least the following beneficial technical effects:
according to the invention, the underactuation problem caused by the fact that the degree of freedom of control input in the underwater helicopter control system is smaller than the degree of freedom of motion is solved by introducing the auxiliary variable, the surrounding control error of the underwater helicopter in the dynamics model is redefined, a new virtual control rate is designed based on the newly determined surrounding control error, the control rate comprising the auxiliary variable is redetermined to control the underwater helicopter, and the feasibility and the control accuracy of a control algorithm are improved. By designing the radial basis function neural network under the framework of the width learning algorithm, the self-adaptive update rate of the improved radial basis function neural network is determined, the nodes of the neural network can be dynamically updated to match new input vectors, the requirement on priori knowledge of the neural nodes is relaxed, the number of the nodes is reduced, better approximation capability can be realized, the control capability is improved, the calculation consumption and the hardware requirement are reduced, and the control precision and the cruising capability of the surrounding formation are further improved.
Drawings
The above features, technical features, advantages and implementation of the present invention will be further described in the following description of preferred embodiments with reference to the accompanying drawings in a clear and easily understood manner.
FIG. 1 is a schematic flow chart of an underactuated underwater helicopter surrounding control method based on width learning;
fig. 2 is a communication topology description diagram of a 4×4 underwater helicopter formation provided by the present invention;
fig. 3 is a schematic diagram of a structure of a surrounding control moving path according to the present invention.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description will explain the specific embodiments of the present invention with reference to the accompanying drawings. It is evident that the drawings in the following description are only examples of the invention, from which other drawings and other embodiments can be obtained by a person skilled in the art without inventive effort.
For simplicity of the drawing, only the parts relevant to the invention are schematically shown in each drawing, and they do not represent the actual structure thereof as a product. Additionally, in order to simplify the drawing for ease of understanding, components having the same structure or function in some of the drawings are shown schematically with only one of them, or only one of them is labeled. Herein, "a" means not only "only this one" but also "more than one" case.
It should be further understood that the term "and/or" as used in the present specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
In this context, it should be noted that the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected, unless explicitly stated or limited otherwise; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In addition, in the description of the present invention, the terms "first," "second," and the like are used merely to distinguish between descriptions and are not to be construed as indicating or implying relative importance.
Examples
In one embodiment, referring to fig. 1 of the specification, a schematic flow chart of the method for controlling the periphery of an under-actuated underwater helicopter based on width learning provided by the invention is shown.
The invention provides an underactuated underwater helicopter surrounding control method based on width learning, which comprises the following steps:
s101: a dynamics model of an integrated team consisting of a plurality of followers and a plurality of pilots is established.
In one possible embodiment, the kinetic model is specifically:
wherein,represent the firsti=1，2，···，mDisplacement and course deflection angle of underwater helicopter in world coordinate system>Representing the position of an underwater helicopter in world coordinate system,/->Indicating the yaw angle of the underwater helicopter, +.>Wherein->Wherein->Representing the linear speed of the underwater helicopter in the x-axis and y-axis, respectively, < >>Respectively representing the linear speed and the angular speed of the underwater helicopter in a body coordinate system, +.>Representing an inertial matrix comprising additional masses, +.>Representing a coordinate transformation matrix between the world coordinate system and the body coordinate system,/for>Representing the coriolis force and centripetal force matrix with uncertainty,>representing a hydrodynamic damping matrix with uncertainty,representing a control input.
It should be noted that, the goal of establishing a dynamics model of an encircling formation composed of a plurality of followers and a plurality of pilots is to establish a dynamics model for underwater helicopters in the encircling formation, so as to describe the movement behavior and interaction mode of each aircraft, and the dynamics model is helpful for understanding and controlling the behavior of the encircling formation. Number of underwater helicopters: the surrounding formation consists of a plurality of followers and a plurality of pilots, each underwater helicopter needs to be considered in the model. State variables for each underwater helicopter: this includes state variables for the position, speed, acceleration, etc. of each underwater helicopter that describe the state of motion of each aircraft in three dimensions. Control input: representing the control inputs, such as thrust, heading angle, etc., experienced by each of the underwater helicopters that will affect the motion of each of the underwater helicopters. The dynamics model relates state variables to control inputs to simulate the dynamics of an underwater helicopter. The model needs to take into account uncertainties such as measurement errors, environmental changes, sensor errors, etc., to more accurately reflect the actual situation.
The establishment of this kinetic model is the basis for the surrounding control, since it helps to understand the interactions and the law of motion between the aircraft, providing important information for the subsequent control algorithm, and this model will be used to implement the surrounding control, ensuring that the surrounding aircraft move according to the predetermined target.
S102: and determining constraint conditions of the dynamic model.
In one possible implementation, the constraints include the presence of a directed spanning tree in the surrounding formation with the pilot as the root node, the pilot trace, and the first derivative of the pilot trace with respect to time.
The directed spanning tree is a concept in graph theory, and the communication topological structure of the underwater helicopter surrounding formation in the application is constructed by the graph theory. A directed tree is a directed graph in which each node has only one parent node, only one node called the root node has no parent node, and othersThe nodes are reachable to the root node, and the directed graph is defined to include a directed spanning tree if and only if at least one node in the directed graph can reach every other node. Definition mapWherein->Representing vertex set, ++>Representing the set of adjacent edges, vertex->Is defined as +.>Representing a weighted adjacency matrix if->Then->On the contrary->. Laplacian matrix->. Furthermore, if->Define +.>Is undirected graph, otherwise->Is a directed graph. In the directed graph, if there is +.>Edge sequences of the form, which are then called by vertex +.>To the vertex->Is directed to the path of (1), at the same time, the vertexFor vertex->Is reachable. In the undirected graph, let>The edge sequence of the form is represented by vertex +>To the vertex->In addition, if there is one undirected path between each vertex pair, the undirected graph is connected. In the directed graph, one directed edge is denoted +.>Wherein->Called parent vertex>Called child vertices. The communication topology between AUH formations is depicted graphically, wherein,mperson follower-AUH->The representation is made of a combination of a first and a second color,nthe pilots are marked as。
It should be noted that in the task of the coaming, the underwater helicopter is subjected to various constraints, which may include that there is typically a directed spanning tree structure with the pilot as the root node in the coaming, representing the communication and navigation relationships between each follower and the pilot, and this spanning tree may be used to determine the relationships and communication paths between the aircraft. The track derivatives (e.g., speed, acceleration) over time of the encircling underwater helicopter may need to be kept within a bounded range to ensure smooth motion, avoiding excessive accelerations or speed variations, i.e., track derivatives are bounded.
The definition and consideration of these constraints are critical to the control of the surrounding formation, and when designing the control algorithm, it is necessary to ensure that the underwater helicopters in the surrounding formation can still effectively complete the surrounding task while taking these constraints into account, where the constraints are pre-conditions that are feasible by the kinetic model, so as to comply with physical and operational constraints while meeting the requirements of the surrounding task.
S103: and (3) leading in auxiliary variables to redefine the surrounding control error of the underwater helicopter in the dynamics model, selecting the surrounding control error as a virtual control variable, and determining the virtual control rate under the surrounding control error.
It should be noted that under-actuated control problems mean that the degree of freedom (control capability) of the control inputs (typically the power output of the propeller or engine) available in the control system of the underwater helicopter is less than the degree of freedom of its movements (movements or actions that can be performed), in short, the control inputs of the underwater helicopter are limited and all possible movements cannot be controlled independently, in under-actuated control problems, the degree of freedom of the underwater helicopter (movements or actions that can be performed) is limited, thus introducing a set of auxiliary variables for redefining the surrounding control errors, which can help to extend the degree of freedom of the control system, making it easier to handle the movement control problems. In the surrounding control, which is usually required to follow the pilot or the surrounding target to complete the task, the surrounding control error is a position error between the underwater helicopter and the pilot, and is redefined by introducing auxiliary variables to take the action of the auxiliary variables into account so as to better control the motion of the underwater helicopter. The virtual control variable is selected as an intermediate variable for expanding the degree of freedom of the control system, and the control problem is easier to solve by introducing the virtual control variable. Based on the virtual control variable and redefined surrounding control error, calculating and determining a virtual control rate, wherein the virtual control rate is a control input for guiding the movement of the underwater helicopter so as to realize the goal of surrounding control. This control rate is based on the calculation of virtual control variables to ensure that the aircraft can effectively complete the surrounding mission under-actuated control.
By introducing auxiliary variables, redefining the surrounding control error and selecting virtual control variables and virtual control rates, control of the surrounding formation is made more flexible and feasible, and these control strategies help ensure that the underwater helicopter can effectively follow the trajectory of the pilot or surrounding target during the surrounding mission even if limited by control inputs.
In one possible implementation, S103 specifically includes:
s1031: surrounding control error of underwater helicopter in redefined dynamics model by introducing auxiliary variable：
Wherein,representing auxiliary variables +.>，Representation matrix->Transpose of->Indicating that the underwater helicopter is inAngular velocity in the body coordinate system, +.>Indicate->The individual underwater jack can obtain +.>Status information of the individual underwater helicopter, otherwise, < >>Likewise, the->Represent the firstiThe underwater helicopter can obtain the firstkStatus information of the individual virtual pilots, otherwise, < >>Wherein->Representing the number of virtual pilots that are to be performed,wherein->And->All represent intermediate variables;
s1032: calculating a first derivative of the surrounding control error with respect to time:
wherein,；
s1033: selecting intermediate variablesAs a virtual control variable, a virtual control rate +_under the surrounding control error is determined>：
Wherein,representing a diagonal gain matrix.
S104: based on the dynamics model, a lumped uncertainty of the surrounding formation is determined.
Where lumped uncertainty is a concept describing the sum of multiple sources of uncertainty or factors that coexist in a system or process, these sources of uncertainty may come from various aspects including measurement errors, environmental changes, randomness, parameter estimation uncertainty, and so forth.
In one possible implementation, S104 specifically includes:
s1041: calculated according to the dynamics model：
Wherein,representing the lumped uncertainty;
s1042: the aggregate uncertainty is specifically:
wherein,respectively represent uncertaintySex is atu、v、rComponents in the degrees of freedom of motion.
S105: and designing an improved radial basis function neural network based on width learning by combining a width learning algorithm.
The width learning algorithm is a machine learning technology, and is used for determining the width or shape parameter of each basis function in the radial basis function neural network, the width of each basis function influences the response degree of the radial basis function neural network to input data, through the width learning, the system can adaptively determine the width of each basis function so as to better fit the distribution of the input data, which means that the width learning algorithm can determine the influence range of each basis function so as to adapt to different data distribution and problem requirements. The radial basis function neural network is a type of neural network, and consists of an input layer, an implicit layer and an output layer. The hidden layer contains a set of radial basis functions centered on the input data, and the output values are calculated from the distance from the center, the radial basis function neural network is typically used to approximate complex functions, classification problems, regression problems, etc., which approximate the input data in the form of radial basis functions in the data space. The width learning system shows excellent approximation and generalization capability due to the increment characteristics, on the basis, the novel RBFNN with the width learning framework can realize better approximation capability, specifically, the nodes of the neural network can be dynamically updated to match new input vectors, and the requirement on prior knowledge of the neural nodes is relaxed.
In one possible implementation, S105 specifically includes:
s1051: defining an objective function of a radial basis function neural network：
Wherein,representing the optimal weight coefficient,/->Representing an inherent approximation error, +.>The input vector is represented as such,representing a basis function vector, wherein,krepresenting the total node number of the radial basis function neural network, < ->，Represent the firstiA Gaussian function corresponding to each node, wherein +.>And->Respectively represent +.>Center vectors and base widths of the individual nodes;
s1052: calculating incremental nodes of the radial basis function neural network:
wherein,representing +.>Recently->Personal node->Representation->Individual node distance input vector->Average distance of>Representing the adjustment parameters;
s1053: setting an updating threshold value, and updating the center vector:
wherein,Drepresenting an update threshold value,the sampling interval is represented by the number of samples,trepresenting the current time;
s1054: calculating the current timetEnhancement layer vector for width learning algorithm：
Wherein the symbol "col" represents a column vector function,krepresentation oftThe number of moment center vectors;
s1055: determining hidden layers of a width learning algorithm based on enhancement layer vectors：
S1056: determining update timeNumber of new nodes generatednImproved radial basis function neural network at update time is determined +.>：
Wherein,representing the transpose of the weight coefficients.
Specifically, an objective function is first definedThis function is usually used to estimate or approximate a certain characteristic of the system, the objective function +.>In relation to the control performance of the surrounding formation, there may be a performance metric that needs to be minimized or optimized. For a designed radial basis function neural network incremental nodes are calculated and determined, which are key parts in the network, which are used to estimate or approximate the objective function +.>These nodes are based on the input vector +.>To better fit the objective function. An update threshold is then set for determining when an update to the central vector of the network is required, the central vector being a key element in the radial basis function neural network, which are used to calculate the output of the network, by setting the appropriate update threshold it is ensured that the approximation performance of the network is improved. Calculating the current time using the selected width learning algorithmtIs part of a radial basis function neural network for improving the approximation capability of the network to betterAdapting to the characteristics of the system. Based on the result of the calculation of the enhancement layer vector, a hidden layer of the breadth-learning algorithm is determined, which is part of a neural network that is used to process the input data and produce the appropriate output. Determining the number of new nodes generated at the update time according to the calculation resultnAnd how to update the improved radial basis function neural network. Finally, the radial basis function neural network is improved by utilizing a width learning algorithm to better approximate or estimate the characteristics or performance metrics of the system, which helps to improve the control performance of the surrounding formation, so that the underwater helicopter can better perform the surrounding task.
The radial basis function is improved through a width learning algorithm, the width defect of the basis function is usually required to be manually set in the traditional radial basis function neural network, the performance is poor under different problems and data distribution, and the width learning algorithm can adaptively adjust the width of the basis function to adapt to different data distribution and problems, so that the approximation performance of a model is improved. Through width learning, the radial basis function neural network can be better generalized to new data, not just adapt to training data, so that the model can handle the condition which is not seen, and the overfitting of the training data is avoided. By improving the basis function width of the radial basis function neural network, it can better fit nonlinear and complex functional relationships. Along with the change of data and the evolution of problems, the width learning algorithm enables the radial basis function neural network to have adaptability, and the width of the basis function can be adjusted in real time so as to maintain the performance of the model. The method has the main advantages that the method provides a modeling method which is more flexible, adaptive and strong in adaptability, can better cope with various data distribution and problem requirements, and improves the performance and generalization capability of the model.
S106: error variables are defined for the virtual control variables and the virtual control rate, and the control rate for the error variables is determined.
In one possible implementation, S106 specifically includes:
s1061: defining error variables for virtual control variables and virtual control rates：
；
S1062: calculating the first derivative of the error variable with respect to time：
Wherein,wherein (1)>Representation matrix->Is->The number of elements to be added to the composition,，to lumped the dynamics uncertainty term, the improved radial basis function neural network is used to approximate it, wherein,
wherein,and->Respectively represent approximation +.>And->Is used for the optimization of the weight coefficient of (c),and->The representation comprises->A basis function vector of each node;
s1063: calculating the first derivative of the virtual control rate with respect to time by a nonlinear differentiator：
Wherein,and->Estimated values representing the first derivative of the nonlinear differentiator with respect to the virtual control rate and the virtual control rate with respect to time, respectively,/->Representing design parameters;
s1064: determining control rate for error variable：
Wherein,representation->Estimated value of ∈10->Wherein the symbol "blockdiag" represents a block diagonal matrix, ++>。
Specifically, first, in this step, an error variable is defined for measuring the difference between the virtual control variable and the desired control target, which may be expressed as the difference between the virtual control variable and the desired trajectory or surrounding target. Second, to better understand the dynamic performance of the error variable, a first derivative of the error variable with respect to time is calculated, which represents the rate of change of the error variable, i.e., how the error evolves over time during control, and this first derivative provides information about the dynamic performance of the error variable. The first derivative of the virtual control rate with respect to time is then calculated using a nonlinear differentiator, which is typically used to estimate the control rate and the first derivative of the control rate with respect to time, which provides dynamic performance information of the control rate to help adjust the control strategy. Finally, a control rate for the error variable is determined, which is designed to ensure that the error variable can converge to zero rapidly, i.e. to ensure that the underwater helicopter can adapt to the error effectively and correct its trajectory to meet the control objectives of the surrounding formation. A control strategy is established to ensure that the underwater helicopter is able to stably track the desired trajectory or bounding target during the control of the bounding formation, and remain stable even in the presence of uncertainties and external disturbances.
S107: an adaptive update rate of the improved radial basis function neural network is determined.
In one possible implementation, the adaptive update rate is specifically:
wherein,representing a positive fixed gain matrix.
Wherein the adaptive update rate is a control parameter that determines the update rate of the central node and parameters of the improved radial basis function, which function ensures that the improved radial basis function can adapt quickly to the dynamic performance of the system without causing instability or oscillations, and the adaptive update rate is adjusted to balance the convergence rate and stability. Positive gain matrices are typically used in control systems to adjust the convergence speed and stability of the control strategy, which can be adjusted according to the characteristics and performance requirements of the system.
The purpose of the adaptive update rate is to enable the improved radial basis function to adapt to changing control inputs and system responses to achieve control goals for the surrounding formation, since the surrounding task may involve complex system dynamics and control scenarios, by determining the adaptive update rate based on the control inputs, control performance and stability may be balanced, ensuring that the underwater helicopter is able to effectively adapt to changing conditions in the surrounding task, which helps to maintain the shape and performance of the surrounding formation.
S108: the lumped uncertainty is approximated at a control rate by modifying the radial basis function neural network in conjunction with an adaptive update rate such that the follower is located in a geometric convexity comprised of a pilot.
In one possible implementation, the description of S108 is specifically:
wherein,represent the firstkPosition of individual navigator, +.>Representation oftTime of day (time)iPosition of AUH,>representing a positive constant.
It will be appreciated that the adaptation helps ensure that the network is able to adapt to the dynamic performance of the system under different control conditions, the improved radial basis function neural network is used to approximate the lumped uncertainty of the system, which means that the network is designed to estimate or approximate the sum of uncertainty sources present in the system, which may include measurement errors, environmental changes, parameter uncertainties, etc., which are modeled and estimated in an adaptive manner. The final objective is to ensure that the follower underwater helicopter is located in a geometric convexity made up of pilots, which means that the control objective of the surrounding formation is to keep the follower within a certain spatial geometry to ensure the effectiveness and stability of the surrounding.
The estimation and approximation of the aggregate uncertainty is achieved using an improved radial basis function neural network and adaptive control strategy to ensure that the underwater helicopter can remain stably within the geometric convexity formed with the pilot, which helps to efficiently perform the task of encircling the formation and to ensure that the relative position between the follower and pilot is controlled and adjusted.
In order to prove the effectiveness of the control method, a Lyapunov function is designed to prove the method, and the Lyapunov function is specifically:
wherein,；
substituting the virtual control rate into the first derivative of the surrounding control error with respect to time to obtain:
substituting the control rate for the error variable into the first derivative of the error variable with respect to time yields:
wherein,is a nonlinear differentiator pair->Is a bounded approximation error of (2);
the Lyapunov function is calculated by combining the self-adaptive update rate and the two formulas, and is obtained by:
from the young's inequality it follows that:
；
and then obtain:
wherein,；
and then can obtain:
wherein,is a tunable tight set;
from this, it can be seen that:
i.e. errorsConverging to a tunable tight set, controlling error +.f by the surrounding of the underwater helicopter in the redefined dynamics model>It is known that by selecting the auxiliary variable +.>Can make the surrounding control error +>Convergence to a tight set, and complete the syndrome.
Referring to the specification and the attached figure 2, a communication topological structure description diagram of a 4×4 underwater helicopter formation is shown.
5, 6, 7 and 8 in fig. 2 are pilots of the underwater helicopter formation, and 1, 2, 3 and 4 are followers of the underwater helicopter formation.
The effectiveness of the invention is further proved by carrying out simulation experiments, and a multi-agent system consisting of 4 follower AUH and 4 navigator is selected for carrying out the simulation experiments so as to verify the effectiveness of the proposed formation control rate.
The navigator movement paths are described as:
。
the initial state of the follower of the underwater helicopter is set as follows，。
The parameter value of the controller is designed asThe adaptive update rate parameter is designed as +.>The parameters of the nonlinear differentiator are designed as +.>. The initial nodes of RBFNN are set to be 100, and are uniformly distributed in the interval +.>The base width b is set to 1, the adjustment parameter in the width learning system +.>Sampling time->Threshold->。
Referring to fig. 3 of the drawings, a schematic diagram of a structure of a surrounding control moving path according to the present invention is shown.
In fig. 3, the broken line portions represent the trajectories of pilots 5, 6, 7, and 8, and the middle solid line portions represent the tracking trajectories of followers 1, 2, 3, and 4. Fig. 3 shows simulation results, showing the tracking path of the underwater helicopter, with the follower-AUH entering and operating stably within the geometric region constituted by the pilot.
Compared with the prior art, the invention has at least the following beneficial technical effects:
according to the invention, the underactuation problem caused by the fact that the degree of freedom of control input in the underwater helicopter control system is smaller than the degree of freedom of motion is solved by introducing the auxiliary variable, the surrounding control error of the underwater helicopter in the dynamics model is redefined, a new virtual control rate is designed based on the newly determined surrounding control error, the control rate comprising the auxiliary variable is redetermined to control the underwater helicopter, and the feasibility and the control accuracy of a control algorithm are improved. By designing the radial basis function neural network under the framework of the width learning algorithm, the self-adaptive update rate of the improved radial basis function neural network is determined, the nodes of the neural network can be dynamically updated to match new input vectors, the requirement on priori knowledge of the neural nodes is relaxed, the number of the nodes is reduced, better approximation capability can be realized, the control capability is improved, the calculation consumption and the hardware requirement are reduced, and the control precision and the cruising capability of the surrounding formation are further improved.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The foregoing examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (9)
1. The method for controlling the surrounding of the under-actuated underwater helicopter based on the width learning is characterized by comprising the following steps of:
s101: establishing a dynamics model of an encircling formation consisting of a plurality of followers and a plurality of pilots;
s102: determining constraint conditions of the dynamic model;
s103: redefining an encircling control error of the underwater helicopter in the dynamics model by introducing an auxiliary variable, selecting a virtual control variable, and determining a virtual control rate under the encircling control error;
s104: determining a lumped uncertainty of the surrounding formation based on the dynamics model;
s105: designing an improved radial basis function neural network based on width learning by combining a width learning algorithm;
s106: defining an error variable with respect to the virtual control variable and the virtual control rate, determining a control rate with respect to the error variable;
s107: determining an adaptive update rate of the improved radial basis function neural network;
s108: the lumped uncertainty is approximated at the control rate by the modified radial basis function neural network in conjunction with the adaptive update rate such that the follower is located in a geometric convexity comprised of the navigator.
2. The width learning-based under-actuated underwater helicopter surrounding control method as claimed in claim 1, wherein the dynamics model is specifically:，
wherein,represent the firsti=1，2，···，mDisplacement and course deflection angle of underwater helicopter in world coordinate system>Representing the position of an underwater helicopter in world coordinate system,/->Indicating the yaw angle of the underwater helicopter, +.>Wherein->Wherein->Respectively represent the underwater helicopter inxShaft and method for producing the sameyLinear speed of shaft>Respectively representing the linear speed and the angular speed of the underwater helicopter in a body coordinate system, +.>Representing an inertial matrix comprising additional masses, +.>Representing a coordinate transformation matrix between the world coordinate system and the body coordinate system,/for>Representing the coriolis force and centripetal force matrix with uncertainty,>represents a hydrodynamic damping matrix with uncertainty, < +.>Representing a control input.
3. The width learning based under-actuated underwater helicopter surrounding control method of claim 1 wherein the constraint condition comprises the presence in the surrounding formation of a pilot-rooted directed spanning tree, a pilot trajectory and a first derivative of the pilot trajectory with respect to time.
4. The width learning-based underwater helicopter surrounding control method according to claim 1, wherein S103 specifically comprises:
s1031: redefining surrounding control errors of underwater helicopters in the dynamics model by introducing the auxiliary variables：Wherein (1)>The auxiliary variable is represented by a value of the auxiliary variable,，representation matrix->Transpose of->Representing the angular velocity of an underwater helicopter in a body coordinate system,/->Indicate->The individual underwater jack can obtain +.>Status information of the individual underwater helicopter, otherwise, < >>Likewise, the->Represent the firstiThe underwater helicopter can obtain the firstkStatus information of the individual virtual pilots, otherwise, < >>Wherein->Representing the number of virtual pilots, < >>Wherein->And->All represent intermediate variables;
s1032: calculating a first derivative of the surrounding control error with respect to time:wherein,；
s1033: selecting intermediate variablesAs a virtual control variable, determining a virtual control rate under the surrounding control error：
Wherein (1)>Representing a diagonal gain matrix.
5. The width learning-based underwater helicopter surrounding control method of claim 1, wherein S104 specifically comprises:
s1041: calculated according to the dynamics model：
Wherein,
representing the lumped uncertainty;
s1042: the lumped uncertainty is specifically:wherein (1)>Respectively represent uncertainty inu、v、rComponents in the degrees of freedom of motion.
6. The width learning-based underwater helicopter surrounding control method of claim 1, wherein S105 specifically comprises:
s1051: defining an objective function of a radial basis function neural network：
Wherein (1)>Representing the optimal weight coefficient,/->Representing an inherent approximation error, +.>Representing the input vector +.>Representing a basis function vector, wherein,krepresenting the total node number of the radial basis function neural network, < >>，Represent the firstiA Gaussian function corresponding to each node, wherein +.>And->Respectively represent +.>Center vectors and base widths of the individual nodes;
s1052: calculating incremental nodes of the radial basis function neural network:wherein,representing +.>Recently->Personal node->Watch (watch)
Showing theThe individual nodes are located at a distance from the input vector>Average distance of>Representing the adjustment parameters;
s1053: setting an updating threshold value, and updating the center vector:wherein,Drepresenting the update threshold,/->The sampling interval is represented by the number of samples,trepresenting the current time;
s1054: calculating the current timetEnhancement layer vector of the width learning algorithm：Wherein the symbol "col" represents a column vector function,krepresentation oftThe number of moment center vectors;
s1055: determining a hidden layer of the width learning algorithm based on the enhancement layer vector：The method comprises the steps of carrying out a first treatment on the surface of the S1056: determining update time +.>Number of new nodes generatednDetermining an improved radial basis function neural network at said update time instant>：Wherein (1)>Representing the transpose of the weight coefficients.
7. The width learning-based underwater helicopter surrounding control method of claim 1, wherein S106 specifically comprises:
s1061: defining error variables for the virtual control variables and the virtual control rate：S1062: calculating the first derivative of said error variable with respect to time +.>：Wherein,wherein->Representation matrix->A kind of electronic device
Element(s)>，Approximation of the modified radial basis function neural network for lumped dynamics uncertainty term, wherein +_>Wherein (1)>And->Respectively represent approximation +.>And->Is>And->Representing a basis function vector comprising nodes; s1063: calculating the first derivative of the virtual control rate with respect to time by means of a nonlinear differentiator>：Wherein (1)>And->Estimated values representing the first derivative of the nonlinear differentiator with respect to the virtual control rate and the virtual control rate with respect to time, respectively,/->Representing design parameters;
s1064: determining a control rate for the error variable：Wherein (1)>Representation->Estimated value of ∈10->Wherein the symbol "blockdiag" represents a block diagonal matrix, ++>。
8. The width learning-based under-actuated underwater helicopter surrounding control method as claimed in claim 1, wherein the self-adaptive update rate is specifically:wherein (1)>Representing a positive fixed gain matrix.
9. The width learning-based underwater helicopter surrounding control method according to claim 1, wherein the description of S108 is specifically:wherein (1)>Represent the firstkPosition of individual navigator, +.>Representation oftTime of day (time)iPosition of AUH,>representing a positive constant.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311631122.6A CN117331317B (en) | 2023-12-01 | 2023-12-01 | Under-actuated underwater helicopter surrounding control method based on width learning |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311631122.6A CN117331317B (en) | 2023-12-01 | 2023-12-01 | Under-actuated underwater helicopter surrounding control method based on width learning |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN117331317A true CN117331317A (en) | 2024-01-02 |
| CN117331317B CN117331317B (en) | 2024-02-20 |
Family
ID=89279761
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202311631122.6A Active CN117331317B (en) | 2023-12-01 | 2023-12-01 | Under-actuated underwater helicopter surrounding control method based on width learning |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117331317B (en) |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101706367B1 (en) * | 2015-11-27 | 2017-02-14 | 공주대학교 산학협력단 | Neural network-based fault-tolerant control method of underactuated autonomous vehicle |
| CN108983612A (en) * | 2018-08-08 | 2018-12-11 | 华南理工大学 | A kind of underwater robot formation control method kept with default capabilities and connection |
| CN111766783A (en) * | 2020-06-29 | 2020-10-13 | 北京航空航天大学 | Cluster system-oriented formation enclosure tracking method capable of converging in limited time |
| CN113821028A (en) * | 2021-08-30 | 2021-12-21 | 浙江大学 | Under-actuated AUV formation trajectory tracking control method based on distributed model predictive control |
| US20220004191A1 (en) * | 2020-07-01 | 2022-01-06 | Wuhan University Of Technology | Usv formation path-following method based on deep reinforcement learning |
| CN114020042A (en) * | 2021-12-14 | 2022-02-08 | 北京航空航天大学 | Heterogeneous unmanned cluster formation enclosure tracking control method and system |
| CN116149351A (en) * | 2022-11-22 | 2023-05-23 | 南京航空航天大学 | Unmanned aerial vehicle cluster interference surrounding control method in non-ideal communication environment |
| CN116360470A (en) * | 2023-04-23 | 2023-06-30 | 浙江大学 | Multi-underwater helicopter cooperative formation control method |
| CN116578106A (en) * | 2023-05-12 | 2023-08-11 | 浙江大学 | Underwater helicopter formation control method for coastal acoustic tomography observation |
-
2023
- 2023-12-01 CN CN202311631122.6A patent/CN117331317B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101706367B1 (en) * | 2015-11-27 | 2017-02-14 | 공주대학교 산학협력단 | Neural network-based fault-tolerant control method of underactuated autonomous vehicle |
| CN108983612A (en) * | 2018-08-08 | 2018-12-11 | 华南理工大学 | A kind of underwater robot formation control method kept with default capabilities and connection |
| CN111766783A (en) * | 2020-06-29 | 2020-10-13 | 北京航空航天大学 | Cluster system-oriented formation enclosure tracking method capable of converging in limited time |
| US20220004191A1 (en) * | 2020-07-01 | 2022-01-06 | Wuhan University Of Technology | Usv formation path-following method based on deep reinforcement learning |
| CN113821028A (en) * | 2021-08-30 | 2021-12-21 | 浙江大学 | Under-actuated AUV formation trajectory tracking control method based on distributed model predictive control |
| CN114020042A (en) * | 2021-12-14 | 2022-02-08 | 北京航空航天大学 | Heterogeneous unmanned cluster formation enclosure tracking control method and system |
| CN116149351A (en) * | 2022-11-22 | 2023-05-23 | 南京航空航天大学 | Unmanned aerial vehicle cluster interference surrounding control method in non-ideal communication environment |
| CN116360470A (en) * | 2023-04-23 | 2023-06-30 | 浙江大学 | Multi-underwater helicopter cooperative formation control method |
| CN116578106A (en) * | 2023-05-12 | 2023-08-11 | 浙江大学 | Underwater helicopter formation control method for coastal acoustic tomography observation |
Also Published As
| Publication number | Publication date |
|---|---|
| CN117331317B (en) | 2024-02-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Yan et al. | Consensus formation tracking for multiple AUV systems using distributed bioinspired sliding mode control | |
| CN112904728B (en) | Mechanical arm sliding mode control track tracking method based on improved approach law | |
| CN104865829B (en) | Multi-robot system distributed self-adaption neutral net continuous tracking control method of electro | |
| CN113342037B (en) | Multi-rotor unmanned aerial vehicle time-varying formation control method and system with input saturation | |
| CN105912009B (en) | Four-rotor aircraft control method based on pole allocation and fuzzy active disturbance rejection control technology | |
| CN110658821A (en) | Multi-robot anti-interference grouping time-varying formation control method and system | |
| CN113589689A (en) | Sliding mode controller design method based on multi-parameter adaptive neural network | |
| Li et al. | Trajectory tracking and obstacle avoidance for wheeled mobile robots based on EMPC with an adaptive prediction horizon | |
| Kolaric et al. | Consensus controller for multi-UAV navigation | |
| Fu et al. | A cross‐coupling control approach for coordinated formation of surface vessels with uncertain disturbances | |
| Elhaki et al. | Robust amplitude-limited interval type-3 neuro-fuzzy controller for robot manipulators with prescribed performance by output feedback | |
| CN110362103B (en) | Distributed autonomous underwater vehicle attitude collaborative optimization control method | |
| CN115826594A (en) | Unmanned underwater vehicle switching topology formation control method independent of dynamic model parameters | |
| CN116360470A (en) | Multi-underwater helicopter cooperative formation control method | |
| CN117226849B (en) | Multi-mechanical arm self-adaptive sliding mode control method and system | |
| Scola et al. | Limbic system-inspired performance-guaranteed control for nonlinear multi-agent systems with uncertainties | |
| CN109079779B (en) | Multi-mobile mechanical arm optimal cooperation method based on terminal estimation and operation degree adjustment | |
| CN117331317B (en) | Under-actuated underwater helicopter surrounding control method based on width learning | |
| CN116954258A (en) | Hierarchical control method and device for multi-four-rotor unmanned aerial vehicle formation under unknown disturbance | |
| CN116449703A (en) | AUH formation cooperative control method under finite time frame | |
| CN114637301B (en) | Multi-robot dynamic obstacle avoidance device and method based on optimal affine formation transformation | |
| Son et al. | Model predictive control of a multi-rotor with a slung load for avoiding obstacles | |
| Arab et al. | Distributed adaptive containment control for a group of aerial robots with external disturbances | |
| CN115576335A (en) | Self-adaptive neural network trajectory tracking method for autonomous underwater helicopter | |
| CN110703792B (en) | Underwater robot attitude control method based on reinforcement learning |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CB03 | Change of inventor or designer information |
Inventor after: Song Zilong Inventor after: Huang Haocai Inventor after: Wu Zheyuan Inventor after: Wang Qing Inventor after: Lu Xiaolu Inventor before: Song Zilong Inventor before: Huang Haocai Inventor before: Wu Zheyuan Inventor before: Wang Qing Inventor before: Lu Xiaolu |
|
| CB03 | Change of inventor or designer information |