CN113359432B - Control law design method for distributed self-adaptive state estimator of multi-rigid-body target system - Google Patents
Control law design method for distributed self-adaptive state estimator of multi-rigid-body target system Download PDFInfo
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Abstract
The invention discloses a control law design method of a distributed self-adaptive state estimator of a multi-rigid-body target system, which comprises the following steps: s1, determining the global state error of each rigid body, including leader dynamics, angular velocity and attitude error; s2, designing a distributed adaptive leader state estimator for each following rigid body; s3, giving sufficient conditions containing topology information and communication link faults to ensure the existence of the distributed state estimator; and S4, designing a fully distributed single rigid body control law by using a deterministic equivalence principle. The invention provides a distributed state estimator and a control law design of a multi-rigid system under the condition of communication link faults, eliminates the influence of the communication link faults on the consistency control law design of the multi-rigid system through a self-adaptive strategy, simultaneously reduces the requirements on communication topology connectivity, and has better universality and flexibility.
Description
Technical Field
The invention belongs to the field of multi-agent distributed consistency control, and particularly relates to a control law design method of a distributed self-adaptive state estimator of a multi-rigid-body target system.
Background
Cooperative control is an important research content in multi-agent system (MAS) control, which is used in a wide range of applications in various fields, such as attitude alignment of satellites and spacecraft; coordinated control of the aircraft; unmanned aerial vehicle formation flight, etc. The problem of consistency of distributed cooperative control is to design a communication exchange rule and a control law and to specify information exchange between two parties, so that all individuals can converge to a uniform state.
Conventional consistency control algorithms typically require that the communication topology of the entire system have a directed spanning tree with the leader as the root node, that the topology does not change throughout the communication, and that the communication weights are typically assumed to be constant. In practical applications, the existence of the above-mentioned problems increases the difficulty of specifying the communication interaction algorithm due to the existence of communication link failures (packet loss, time delay, quantization errors, communication noise, etc.). In order to realize the consistency of a multi-rigid-body system under the condition of communication link failure, the communication link failure is subjected to mathematical modeling, and an adaptive strategy is introduced to enable each rigid body to realize the estimation of a leader state under the condition of communication uncertainty, so that the problem of consistency of multiple rigid bodies is converted into the problem of single rigid body tracking.
The invention provides a design method of a completely distributed self-adaptive estimator and a control law, avoids dependence on communication topology and has better flexibility.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a control law design method for a distributed self-adaptive state estimator of a multi-rigid-body target system, which relaxes the requirement of the attitude consistency of the multi-rigid-body system on communication weight, eliminates the dependence of a communication network on global information, and has stronger robustness and better flexibility.
The invention content is as follows: the invention provides a control law design method of a distributed self-adaptive state estimator of a multi-rigid-body target system, which comprises the following steps:
s1, determining the global state error of each rigid body, including leader dynamics, angular velocity and attitude error;
s2, designing a distributed adaptive leader state estimator for each following rigid body;
s3, giving sufficient conditions containing topology information and communication link faults to ensure the existence of the distributed state estimator;
and S4, designing a fully distributed single rigid body control law by using a deterministic equivalence principle.
Specifically, the step S1 includes the following steps:
s11, carrying out global error modeling on each rigid body to obtain the error sum of each rigid body relative to the neighbor of the rigid body;
first, an angular velocity and attitude estimator is defined for each rigid body
Wherein the attitude estimator belongs to a unit quaternion space, the angular velocity estimator belongs to a three-dimensional Euclidean space, and a distributed estimation error of each rigid body is obtained:
wherein H i Is the distributed attitude error, Γ, of each rigid body with its neighbor rigid bodies i Is the distributed angular velocity error of each rigid body and its neighboring rigid bodies;
s12, establishing the dynamics of the leader;
the leader dynamics of the rigid body system include attitude dynamics and angular velocity dynamics based on quaternion representations:
wherein
The angular velocity of the leader is represented,
representing the pose of the leader.
Specifically, the step S2 includes the following steps:
s21, designing the dynamics of the estimator according to the single rigid body distributed estimation error established in the step S1, wherein the specific form is as follows:
wherein alpha and beta are more than 0 and are constants, and the initial value of the adaptive parameter of each rigid body is more than 1, a ξi (0)，a ηi (0)≥1。
Specifically, the step S3 is implemented as follows:
s31, determining sufficient conditions including communication topology and communication link faults, wherein the specific conditions are as follows:
(1) the communication topology initial state of the whole multi-rigid body system comprises a cluster of directed spanning trees taking a leader as a root node;
(2) the leader's angular velocity system matrix is critically stable;
(3) communication link failure is reflected in the effect on the communication weights, which effect and its derivatives are bounded;
(4) a communication link failure may cause the communication weight between any two rigid bodies to be 0, i.e., no communication.
(5) The communication topology changes caused by communication link faults, and a union set of subgraphs in limited time has a cluster of directed spanning trees taking a leader as a root node;
s32, establishing the following Lyapunov function according to the 5-point condition and the Lyapunov stability theory:
specifically, the step S4 includes the following steps:
s41, establishing the self dynamics of each rigid body, wherein the concrete form is as follows:
wherein
Is a unit quaternion representing the reference frame of each rigid body per se relative to the inertial reference frame,
representing the inertia tensor of each rigid body relative to its own frame of reference,
representing the control torque of each rigid body;
s42, establishing an error system of each rigid body, wherein the specific form is as follows:
wherein
Their kinetics are as follows:
s43, according to the state estimator containing communication topology and communication link failure established in step S3, converging sufficient conditions, and the state estimator based on self-adaption established in step S2, applying the principle of determinism equivalence, reestablishing the following error system:
their kinetics have the following form:
wherein
Has the following form:
wherein:
s44, designing temporary variables, and reestablishing the error system in the step S43:
wherein
S45, after the system modeling is completed, designing the following control law:
wherein k is i2 Is a constant greater than 0.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a distributed state estimator and a control law design of a multi-rigid system under the condition of communication link faults, eliminates the influence of the communication link faults on the consistency control law design of the multi-rigid system through a self-adaptive strategy, simultaneously reduces the requirements on communication topology connectivity, and has better universality and flexibility.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In order to explain the technical means of the present invention, the following description will be given by way of specific examples.
Examples
As shown in fig. 1, the present embodiment provides a method for designing a control law of a distributed adaptive state estimator of a multi-rigid-body target system, including the following steps:
step S1, determining a global state error of each rigid body, including leader dynamics, angular velocity, and attitude error, specifically including the following steps:
s11, carrying out global error modeling on each rigid body to obtain the error sum of each rigid body relative to the neighbor (including the leader) of each rigid body;
first, an angular velocity and attitude estimator is defined for each rigid body
Wherein the attitude estimator belongs to a unit quaternion space, the angular velocity estimator belongs to a three-dimensional Euclidean space, and a distributed estimation error of each rigid body is obtained:
wherein H i Is the distributed attitude error, Γ, of each rigid body with its neighbor rigid bodies (including the leader) i Is the distributed angular velocity error of each rigid body with its neighbors (including the leader), after which its global form is defined:
further, the global leader state estimation error is defined as:
deriving the global leader error from the distributed attitude estimation error and the global leader state estimation error for each rigid body may be expressed as
L when a cluster of directed spanning trees with the leader as a root node exists in the communication topology G (t) must be a reversible matrix, then the following inequality is derived:
with the same definition, the following inequality can also be obtained:
wherein
The above two inequalities provide proof antecedents for establishing the existence of the sufficient condition assurance estimator containing topology information and communication link failure at step S3;
s12, establishing the dynamics of the leader (the follower is unknown);
the leader dynamics of the rigid body system include attitude dynamics and angular velocity dynamics based on quaternion representations:
wherein
The angular velocity of the leader is represented,
the pose of the leader is represented as a gesture,
is a constant matrix and the angular velocity dynamical system represented by the constant matrix needs to meet the condition of critical stability;
step S2, designing a distributed adaptive state estimator for each rigid body, specifically including the following steps:
s21, designing the dynamics of the estimator according to the single rigid body distributed estimation error established in the step S1, wherein the specific form is as follows:
wherein alpha and beta are more than 0 and are constants, and the initial value of the adaptive parameter of each rigid body is more than 1, a ξi (0)，a ηi (0) Not less than 1; the leader system matrix estimator adopts a first-order synovium estimator to ensure that the leader system matrix estimator converges in a limited time;
step S3, providing sufficient conditions including topology information and communication link failure to ensure existence of the distributed adaptive estimator, and the specific implementation process is as follows:
s31, determining sufficient conditions including communication topology and communication link faults, wherein the specific conditions are as follows:
(1) the communication topology initial state of the whole multi-rigid body system comprises a cluster of directed spanning trees taking a leader as a root node;
(2) the leader's angular velocity system matrix is critically stable;
(3) communication link failure is reflected in the effect on the communication weights, which effect and its derivatives are bounded;
(4) a communication link failure may cause the communication weight between any two rigid bodies to be 0, i.e., no communication.
(5) The communication topology changes caused by communication link failure, and a union of subgraphs has a cluster of directed spanning trees with a leader as a root node in a limited time.
S32, establishing the following Lyapunov function according to the 5-point condition and the Lyapunov stability theory:
the Lyapunov is established based on the condition 1, and the existence of an adaptive state estimator designed by S2 under the condition of global existence communication is ensured;
in the case of condition 5, the following lyapunov function is established:
the Lyapunov function ensures that when the communication link fault divides the whole system into a plurality of sub-graphs, the leader of the self-adaptive state estimator of each sub-graph estimates the property of invariable error;
step S4, designing a fully distributed control law by using a deterministic equivalence principle on the basis of step S3, specifically including the steps of:
s41, establishing the self-dynamics of each rigid body, wherein the specific form is as follows:
wherein
Is a unit quaternion representing the reference frame of each rigid body per se relative to the inertial reference frame,
representing the inertia tensor of each rigid body relative to its own frame of reference,
representing the control torque of each rigid body;
s42, establishing an error system of each rigid body, wherein the specific form is as follows:
wherein
Their kinetics are as follows:
s43, according to the state estimator containing communication topology and communication link failure established in step S3, converging sufficient conditions, and the state estimator based on self-adaption established in step S2, applying the principle of determinism equivalence, reestablishing the following error system:
their kinetics have the following form:
wherein
Has the following form:
wherein:
s44, designing temporary variables, and reestablishing the error system in S43.
Wherein
S45, after the system modeling is completed, designing the following control law:
wherein k is i2 Is a constant greater than 0.
The present invention is not limited to the above preferred embodiments, and any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A control law design method for a distributed self-adaptive state estimator of a multi-rigid-body target system is characterized by comprising the following steps:
s1, determining the global state error of each rigid body, including leader dynamics, angular velocity and attitude error;
s2, designing a distributed adaptive leader state estimator for each following rigid body;
s3, giving sufficient conditions containing topology information and communication link faults to ensure the existence of the distributed state estimator;
step S3 is implemented as follows:
s31, determining sufficient conditions including communication topology and communication link faults, wherein the specific conditions are as follows:
(1) the communication topology initial state of the whole multi-rigid body system comprises a cluster of directed spanning trees taking a leader as a root node;
(2) the leader's angular velocity system matrix is critically stable;
(3) communication link failure is reflected in the effect on the communication weights, which effect and its derivatives are bounded;
(4) communication link failure can make the communication weight between any two rigid bodies be 0, i.e. no communication;
(5) the communication topology changes caused by communication link faults, and a union of subgraphs in limited time has a cluster of directed spanning trees with a leader as a root node;
s32, establishing the following Lyapunov function according to the 5-point condition and the Lyapunov stability theory:
and S4, designing a fully distributed single rigid body control law by using a deterministic equivalence principle.
2. The distributed adaptive state estimator control law design method for multi-rigid body target system according to claim 1, wherein said step S1 comprises the steps of:
s11, carrying out global error modeling on each rigid body to obtain the error sum of each rigid body relative to the neighbor of the rigid body;
first, an angular velocity and attitude estimator is defined for each rigid body
Wherein the attitude estimator belongs to a unit quaternion space, the angular velocity estimator belongs to a three-dimensional Euclidean space, and a distributed estimation error of each rigid body is obtained:
wherein H i Is the distributed attitude error, Γ, of each rigid body with its neighbor rigid bodies i Is the distributed angular velocity error of each rigid body with its neighbor rigid bodies；
S12, establishing the dynamics of the leader;
the leader dynamics of the rigid body system include attitude dynamics and angular velocity dynamics based on quaternion representations:
wherein
The angular velocity of the leader is represented,
representing the pose of the leader.
3. The distributed adaptive state estimator control law design method for multi-rigid body target system according to claim 1, wherein said step S2 comprises the steps of:
s21, designing the dynamics of the estimator according to the single rigid body distributed estimation error established in the step S1, wherein the specific form is as follows:
wherein alpha and beta are more than 0 and are constants, and the initial value of the adaptive parameter of each rigid body is more than 1, a ξi (0)，a ηi (0)≥1。
4. The distributed adaptive state estimator control law design method for multi-rigid body target system according to claim 1, wherein said step S4 comprises the steps of:
s41, establishing the self-dynamics of each rigid body, wherein the specific form is as follows:
wherein
Is a unit quaternion representing the reference frame of each rigid body per se relative to the inertial reference frame,
representing the inertia tensor of each rigid body relative to its own frame of reference,
representing the control torque of each rigid body;
s42, establishing an error system of each rigid body, wherein the specific form is as follows:
wherein
Their kinetics are as follows:
s43, according to the state estimator containing communication topology and communication link failure established in step S3, converging sufficient conditions, and the state estimator based on self-adaption established in step S2, applying the principle of determinism equivalence, reestablishing the following error system:
their kinetics have the following form:
wherein
Has the following form:
wherein:
s44, designing temporary variables, and reestablishing the error system in the step S43:
wherein
S45, after the system modeling is completed, designing the following control law:
wherein k is i2 Is a constant greater than 0.
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