CN111736593A - Stage mobile robot formation asynchronous control method for preventing uncertain DoS attack - Google Patents
Stage mobile robot formation asynchronous control method for preventing uncertain DoS attack Download PDFInfo
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Abstract
The invention discloses an asynchronous control method for stage mobile robot formation for preventing uncertain DoS attack, which comprises the steps of firstly establishing a state space model corresponding to a leader and a follower by adopting a formation method of pilot following, then simulating the phenomenon by adopting a Markov system method in consideration of model jump and controller asynchronous problems caused by attack and interference, designing a universal controller form for ensuring the tracking consistency of a heterogeneous mobile stage robot under directed connection, then obtaining two types of LMIs for solving the gain of a controller by adopting a Lyapunov stability theory and a correlation matrix analysis method for an error system model established by control theory analysis, and obtaining the gain F of the asynchronous controller by applying an LMI-Toolbox tool in Matlabσ(k)And Kiσ(k)The controller designed according to the method can ensure the formation consistency of the mobile stage robot system.
Description
Technical Field
The invention relates to the field of stage mobile robot formation control, in particular to an uncertain DoS attack prevention stage mobile robot formation asynchronous control method.
Background
In the formation control problem, the traditional theory can be generally classified into three research methods, namely a pilot following method, a behavior-based method and a virtual structure method, wherein the group behaviors cannot be clearly defined on the basis of the behavior method, the mathematical analysis on the group behaviors is difficult, and the stability of the formation cannot be ensured; the virtual structure method requires the formation to move to a virtual structure, and limits the application range of the method; the most common method is following piloting, that is, one robot is taken as a leader, and the rest other robots are taken as followers to follow the leader to realize certain formation or make corresponding actions.
In the application of an actual stage mobile robot system, a piloting following method is generally adopted to realize the cooperative control of multiple robots, and certain formation motion or formation form change is kept to finish a specific situation effect. In practical application, the traditional single isomorphic system control is often unable to meet the performance requirements, and the isomorphic system control means that each individual in the system has completely the same system information, the corresponding requirement in the actual program performance is that each robot on the stage is of the same series and the same model, in large-scale cultural performance, mobile robots with various functions are often required to be coordinated and matched with each other in order to produce gorgeous and rich program effects and bring wonderful and shocking visual experience to audiences, therefore, we need to meet this requirement by adopting a method of heterogeneous system control, i.e. each individual in the system has a different model (isomorphism can be regarded as a special case of heterogeneity), the control method can bring better program effect in actual scene application and has smaller application limitation. On the other hand, due to the manufacturing process problem, the actual parameters of the same type of robot may be different, so that a control error may be caused by constructing the system by using a simple isomorphic model, and the control error may come in and go out with an ideal control effect to a certain extent.
In order to realize information exchange among specific formation depending on each other, the multi-mobile-stage robots mainly adopt undirected graphs to describe the information exchange in the system in the traditional method, so that full-duplex communication is required among the mobile robots of all followers, and bandwidth waste is caused to a certain extent. In addition, the information may be attacked and interfered by the network in the interaction process, so that the robot cannot acquire the real-time information of the neighboring robot. For example, when a Denial of service (DoS) network attack occurs, state information collected by a robot cannot be sent to a neighboring robot through a network, which results in a formation failure. Due to the complex attack behaviors, the acquisition of the attack modes is very difficult, so that an asynchronous (lagging or leading) phenomenon is generated between the mode designed by the controller and a system model, and the system is out of control, which can cause the formation of the stage mobile robot system to generate non-preset abnormal changes, and can cause program performance failure, and serious personal injury to actors or audiences can be caused, so that performance accidents can be caused.
Disclosure of Invention
The method aims to overcome the asynchronous problem between a controller and a system model, which can be caused by the influence of attack or interference in transmission, so that the form of the stage mobile robot formation in the process of performance is changed in a non-preset mode. The invention provides an asynchronous control method for stage mobile robot formation for preventing uncertain DoS attacks. When the stage robot formation system is attacked by a network, the consistency of the formation of the mobile stage robot can be well ensured no matter whether the attack occurs between the (stage) robot and the robot or between the robot and the controller.
The technical problem of the invention is mainly solved by the following technical scheme:
a stage mobile robot formation asynchronous control method for preventing uncertain DoS attacks comprises the following steps: s01: establishing a discrete time kinematic model of a leader and a follower of the heterogeneous mobile stage robot system under DoS attack; s02: designing an asynchronous controller form for ensuring the consistency of the heterogeneous mobile stage robot system according to the model; s03: the linear matrix inequality toolkit is applied to solve for asynchronous controller gains.
Specifically, S01: establishing a discrete time kinematic model of the mobile stage robot system under DoS attack, and referring to the formulas (1) and (2):
the leader:
following the person:
wherein k represents the current time, k +1 represents the next time, n represents that n mobile stage robots in the system are used as followers, the subscript i represents the ith robot, and the subscript 0 corresponds to the leader robot. x is the number ofi(k)＝[xi1(k) xi2(k) xi3(k)]TReferred to as state vector, of which xi1(k)、xi2(k)、xi3(k) Respectively corresponding to the position, speed and acceleration of the mobile robot. y isi(k) Is the system output, uiσ(k)(k) For the desired controller, omegai(k) For external interference signals, lower footmarks
Indicating the length of DoS attacks the system has been subjected to,
representing an asynchronous phenomenon generated by the controller under interference.
And
Aiρ(k)and CiState matrix and output matrix, B, of leader and follower, respectivelyiρ(k)And Diρ(k)Respectively the input matrix and the interference matrix of the follower.
S02: the asynchronous controller for ensuring the consistency of the heterogeneous mobile stage robot system is designed in the following form:
wherein Fσ(k)And Kiσ(k)Referred to as the controller gain, ζi(k) Indicating the internal state of the controller at time k, the lower subscript i, j representing the ith and jth followers, aij> 0 means that there is at least one unidirectional information path between the ith and jth followers, gi> 0 means that the ith follower can obtain the information of the leader,
is the concept of a neighbor set in graph theory, representing the set of all other followers that can provide information to the ith follower. II typeiAndiρ(k)are two parameter matrices related to the system model, and must satisfy the following relationship:
s03: solving asynchronous controller gain F by applying matlab linear matrix inequality toolkit (LMI-Toolbox)σ(k)And Kiσ(k)Specific LMIs are as follows:
solving for Fσ(k)：
Specifically, solving LMI (5) to obtain corresponding matrix variables H,
Solving for Kiσ(k)：
In particular by adjusting parameters
γ so that LMI (6) can obtain corresponding matrix variable Liφ、Viφ。
Wherein P iss、G、
H、Q、RsφAnd
are all dimension-appropriate positive definite symmetric matrix variables,
is a general matrix variable, Liφ、ViφIs the controller gain Kiσ(k)The decomposed matrix variable, gamma, represents the system robustness (anti-interference performance index),
y is a system parameter matrix,
is the eigenvalue of the system topology matrix (the eigenvalue of the directed graph is an imaginary number). Therein about
Comprises the following steps:
wherein
Representing a partial set of known information derived by employing large data statistical analysis for DoS attacks,
in order to not determine the set of information,
for a set of unknown information, pistPr (ρ (k +1) ═ t | ρ (k) ═ s) represents the probability value of the system mode at the next moment of hopping from the current system mode s to the system mode at t,
representing the uncertain but bounded (boundary measurable by sliding mode control) transition probability distributed on a convex hull, where r is the number of convex hull surfaces, musφPr (σ (k) ═ Φ | ρ (k) ═ s) represents the probability that the asynchronous controller mode corresponding to the system mode s is Φ at the current time.
Preferably, the leader is one and the followers are three.
The technical conception of the invention is as follows: aiming at the problems that in the process of the formation performance of the mobile stage robots, because of the fact that uncertain DoS network attacks, fixed periodic sampling instructions sent by a controller are lost, the model generates uncertain jumping and an asynchronous phenomenon occurs between the controller and a system model, and therefore the consistency of the system cannot be guaranteed, the formation performance of the formation stage robots in the performance is affected by the fact that the formation performance of the formation stage robots is subjected to non-preset unpredictable changes, and even personal injuries are caused to actors or field audiences. Aiming at the problem, firstly, a state space model corresponding to a leader and a follower is established by adopting a pilot following formation method, then, model jump and controller asynchronous problems caused by attack and interference are considered, a Markov system method is adopted to simulate the phenomenon, a universal controller form for ensuring the heterogeneous mobile stage robot to track and be consistent under directed connection is designed, then, a Lyapunov stability theory and a correlation matrix analysis method are adopted for an error system model established by control theory analysis to obtain two types of LMIs for solving the gain of the controller, and an asynchronous controller gain F can be obtained by applying an LMI-Toolbox tool in Matlabσ(k)And Kiσ(k)The controller designed according to the method can ensure the formation consistency of the mobile stage robot system.
The beneficial effects of the invention are mainly expressed as follows:
1. establishing a model of the heterogeneous mobile stage robot, expanding the range of control objects, and particularly showing that the robots in the stage formation can have different styles, greatly enriching the formation types and reducing the limitation in the practical application process;
2. the communication connection between the stage robots is directed connection, and the traditional undirected connection is a special case of directed connection, so that the method is more universal and universal, and has smaller limitation in practical application;
3. the attack information suffered by the method can be determined, uncertain or even unknown, so that the data volume requirement and the limitation of computer storage and CPU operation performance in the process of big data statistical analysis are reduced;
4. the designed asynchronous controller comprises a common model independent controller
And a synchronous controller (
And musφ1), has universality and has smaller limitation in practical application.
Drawings
FIG. 1 is a diagram of system mode and asynchronous controller mode changes under attack and disturbance;
FIG. 2 is a position tracking curve of the mobile stage robotic system;
fig. 3 is an output error curve of the mobile stage robot system.
Detailed Description
The technical solution of the present application will be described with reference to the following examples. In addition, numerous specific details are set forth below in order to provide a better understanding of the present invention. It will be understood by those skilled in the art that the present invention may be practiced without some of these specific details. In some instances, methods, means, elements and circuits that are well known to those skilled in the art have not been described in detail so as not to obscure the present invention.
Example (b):
a stage mobile robot formation asynchronous control method for preventing uncertain DoS attacks comprises the following steps: s01: establishing a discrete time kinematic model of a leader and a follower of the heterogeneous mobile stage robot system under DoS attack; s02: designing an asynchronous controller form for ensuring the consistency of the heterogeneous mobile stage robot system according to the model; s03: the linear matrix inequality toolkit is applied to solve for asynchronous controller gains.
Specifically, S01: establishing a discrete time kinematic model of the mobile stage robot system under DoS attack, and referring to the formulas (1) and (2):
the leader:
following the person:
wherein k represents the current time, k +1 represents the next time, n represents that n mobile stage robots in the system are used as followers, the subscript i represents the ith robot, and the subscript 0 corresponds to the leader robot. x is the number ofi(k)＝[xi1(k) xi2(k) xi3(k)]TReferred to as state vector, of which xi1(k)、xi2(k)、xi3(k) Respectively corresponding to the position, speed and acceleration of the mobile robot. y isi(k) Is the system output, uiσ(k)(k) For the desired controller, omegai(k) For external interference signals, lower footmarks
Indicating the length of DoS attacks the system has been subjected to,
representing an asynchronous phenomenon generated by the controller under interference.
And
Aiρ(k)and CiState matrix and output matrix, B, of leader and follower, respectivelyiρ(k)And Diρ(k)Respectively the input matrix and the interference matrix of the follower.
S02: the asynchronous controller for ensuring the consistency of the heterogeneous mobile stage robot system is designed in the following form:
wherein Fσ(k)And Kiσ(k)Referred to as the controller gain, ζi(k) Indicating the internal state of the controller at time k, the lower subscript i, j representing the ith and jth followers, aij> 0 means that there is at least one unidirectional information path between the ith and jth followers, gi> 0 means that the ith follower can obtain the information of the leader,
is the concept of a neighbor set in graph theory, representing the set of all other followers that can provide information to the ith follower. II typeiAndiρ(k)are two parameter matrices related to the system model, and must satisfy the following relationship:
s03: solving asynchronous controller gain F by applying matlab linear matrix inequality toolkit (LMI-Toolbox)σ(k)And Kiσ(k)Specific LMIs are as follows:
solving for Fσ(k)：
Specifically, solving LMI (5) to obtain corresponding matrix variables H,
Solving for Kiσ(k)：
In particular by adjusting parameters
γ so that LMI (6) can obtain corresponding matrix variable Liφ、Viφ。
Wherein P iss、G、
H、Q、RsφAnd
are all dimension-appropriate positive definite symmetric matrix variables,
is a general matrix variable, Liφ、ViφIs the controller gain Kiσ(k)The decomposed matrix variable, gamma, represents the system robustness (anti-interference performance index),
y is a system parameter matrix,
is the eigenvalue of the system topology matrix (the eigenvalue of the directed graph is an imaginary number). Therein about
Comprises the following steps:
wherein
Representing a partial set of known information derived by employing large data statistical analysis for DoS attacks,
in order to not determine the set of information,
for a set of unknown information, pistPr (ρ (k +1) ═ t | ρ (k) ═ s) represents the probability value of the system mode at the next moment of hopping from the current system mode s to the system mode at t,
representing the uncertain but bounded (boundary measurable by sliding mode control) transition probability distributed on a convex hull, where r is the number of convex hull surfaces, musφPr (σ (k) ═ Φ | ρ (k) ═ s) represents the probability that the asynchronous controller mode corresponding to the system mode s is Φ at the current time.
As shown in fig. 1 to 3, the present embodiment uses a mobile stage robot system of one leader and three followers, so that specific values are taken into the following:
the leader continuation model is:
y0＝(1 0)x0
the follower continuous model is:
yi＝(1 0 0)xii＝1,2,3
wherein { ai,bi,ci,di,eiThe values of 1,2 and 3 are {2,1,1,10 and 1}, {2,1,1,3 and 1}, and {2,2,1,10 and 1}, respectively. Fixed sampling period T00.01 corresponds to
Are respectively { T0,2T0,3T0}. The initial values of the system state variables are x respectively0(0)＝[6 1]T，x1(0)＝[7.8 1 1]T，x2(0)＝[3.8 1 1]T，x3(0)＝[4.6 1 1]TThe input interference functions are 0.5sin (k), and-sin (k), respectively.
The probability of system modal jump under DoS attack obtained by big data statistical analysis is as follows:
the controller model is in the form of:
wherein the controller state variable ζi(0) The initial value may be arbitrarily selected, and preferably, ζ is taken in this example1(0)＝[-10 -20]T，ζ2(0)＝[10 20]T，ζ3(0)＝[-8 -10]TFrom (4), can be found
The asynchronous jump probability of the controller is as follows:
solving the linear matrix inequality by using the LMI-Toolbox toolkit in matlab (5) And (6) obtaining the designed gain of the asynchronous controller, wherein adjustable parameters are taken
Υ＝[1 0 0]Based on this, obtain
And
the obtained controller uiσ(k)(k) The position of the leader robot can be tracked in real time by the position of each follower moving stage robot, the cooperative control of the heterogeneous moving stage robot system is realized, and the whole stage robot formation keeps the preset formation to perform according to the preset track.
The above illustrates the synergistic control effect of the mobile stage robot system with excellent performance exhibited by one embodiment of the present invention.
Through the above description of the embodiments, those skilled in the art can understand that the embodiments of the present application, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a readable storage medium. Based on such understanding, the technical solutions of the embodiments of the present application may be essentially or partially contributed to by the prior art, or all or part of the technical solutions may be embodied in the form of a software product, where the software product is stored in a storage medium and includes several instructions to enable a device (which may be a single chip, a chip, or the like) or a processor (processor) to execute all or part of the steps of the methods of the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (6)
1. A stage mobile robot formation asynchronous control method for preventing uncertain DoS attacks is characterized by comprising the following steps:
s01: establishing a discrete time kinematic model of a leader and a follower of the heterogeneous mobile stage robot system under DoS attack;
s02: designing an asynchronous controller form for ensuring the consistency of the heterogeneous mobile stage robot system according to the model;
s03: the linear matrix inequality toolkit is applied to solve for asynchronous controller gains.
2. The stage mobile robot formation asynchronous control method for preventing uncertain DoS attacks according to claim 1, wherein the kinematic model of step S01 comprises:
the leader:
following the person:
wherein k represents the current time, k +1 represents the next time, n represents that n mobile stage robots in the system are used as followers, the subscript i represents the ith robot, the subscript 0 corresponds to the leader robot, and x represents the current time, k +1 represents the next time, n represents that n mobile stage robots in the system are used as followers, and x represents the current time, andi(k)＝[xi1(k) xi2(k) xi3(k)]Treferred to as state vector, of which xi1(k)、xi2(k)、xi3(k) Respectively corresponding to the position, speed, acceleration, y of the mobile roboti(k) Is the system output, uiσ(k)(k) For the desired controller, omegai(k) For external interference signals, lower footmarks
Indicating the length of DoS attacks the system has been subjected to,
representing an asynchronous phenomenon generated by the controller under interference,
and
Aiρ(k)and CiState matrix and output matrix, B, of leader and follower, respectivelyiρ(k)And Diρ(k)Respectively the input matrix and the interference matrix of the follower.
3. The stage mobile robot formation asynchronous control method for preventing uncertain DoS attacks according to claim 2, wherein the asynchronous controller form in step S02 comprises:
wherein Fσ(k)And Kiσ(k)Referred to as the controller gain, ζi(k) Indicating the internal state of the controller at time k, the lower subscript i, j representing the ith and jth followers, aij> 0 means that there is at least one unidirectional information path between the ith and jth followers, gi> 0 means that the ith follower can obtain the information of the leader,
is the concept of a neighbor set in graph theory, representing the set of all other followers, Π, that are able to provide information to the ith followeriAndiρ(k)are two parameter matrices associated with the system model,the following relationship must be satisfied:
4. the stage mobile robot formation asynchronous control method for preventing uncertain DoS attacks according to claim 3, wherein the linear matrix inequality toolkit in step S03 is: matlab linear matrix inequality toolkit LMI-Toolbox.
5. The stage mobile robot formation asynchronous control method for preventing uncertain DoS attack as claimed in claim 4, wherein the step S03 of solving gain F of asynchronous controllerσ(k)And Kiσ(k)Specific LMIs are as follows:
solving for Fσ(k)：
Specifically, the corresponding matrix variables H, H are obtained by solving the following formula,
Solving for Kiσ(k)：
Particularly by adjusting the parameters xiiφY, so that the following formula can be used to obtain the corresponding matrix variable Liφ、Viφ：
Wherein P iss、G、
H、Q、RsφAnd
are all dimension-appropriate positive definite symmetric matrix variables,
is a general matrix variable, Liφ、ViφIs the controller gain Kiσ(k)Decomposed matrix variable, gamma denotes system robustness (anti-interference performance index), xiiφY is a system parameter matrix,
is an eigenvalue (the directed graph eigenvalue is an imaginary number) of the system topology matrix, with respect to
Comprises the following steps:
wherein
Representing a partial set of known information derived by employing large data statistical analysis for DoS attacks,
in order to not determine the set of information,
for a set of unknown information, pistPr (ρ (k +1) ═ t | ρ (k) ═ s) represents the probability value of the system mode at the next moment of hopping from the current system mode s to the system mode at t,
representing the uncertain but bounded (boundary measurable by sliding mode control) transition probability distributed on a convex hull, where r is the number of convex hull surfaces, musφPr (σ (k) ═ Φ | ρ (k) ═ s) represents the probability that the asynchronous controller mode corresponding to the system mode s is Φ at the current time.
6. The stage mobile robot formation asynchronous control method for preventing uncertain DoS attacks according to claim 1, wherein the number of the leaders is one and the number of the followers is three.
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